Datasets:

luna-code

/

numpy

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from __future__ import print_function import numpy as np import matplotlib.pyplot as plt class TwoLayerNet(object): """ A two-layer fully-connected neural network. The net has an input dimension of N, a hidden layer dimension of H, and performs classification over C classes. We train the network with a softmax loss function and L2 regularization on the weight matrices. The network uses a ReLU nonlinearity after the first fully connected layer. In other words, the network has the following architecture: input - fully connected layer - ReLU - fully connected layer - softmax The outputs of the second fully-connected layer are the scores for each class. """ def __init__(self, input_size, hidden_size, output_size, std=1e-4): """ Initialize the model. Weights are initialized to small random values and biases are initialized to zero. Weights and biases are stored in the variable self.params, which is a dictionary with the following keys W1: First layer weights; has shape (D, H) b1: First layer biases; has shape (H,) W2: Second layer weights; has shape (H, C) b2: Second layer biases; has shape (C,) Inputs: - input_size: The dimension D of the input data. - hidden_size: The number of neurons H in the hidden layer. - output_size: The number of classes C. """ self.params = {} self.params['W1'] = std * np.random.randn(input_size, hidden_size) self.params['b1'] = np.zeros(hidden_size) self.params['W2'] = std * np.random.randn(hidden_size, output_size) self.params['b2'] = np.zeros(output_size) def loss(self, X, y=None, reg=0.0): """ Compute the loss and gradients for a two layer fully connected neural network. Inputs: - X: Input data of shape (N, D). Each X[i] is a training sample. - y: Vector of training labels. y[i] is the label for X[i], and each y[i] is an integer in the range 0 <= y[i] < C. This parameter is optional; if it is not passed then we only return scores, and if it is passed then we instead return the loss and gradients. - reg: Regularization strength. Returns: If y is None, return a matrix scores of shape (N, C) where scores[i, c] is the score for class c on input X[i]. If y is not None, instead return a tuple of: - loss: Loss (data loss and regularization loss) for this batch of training samples. - grads: Dictionary mapping parameter names to gradients of those parameters with respect to the loss function; has the same keys as self.params. """ # Unpack variables from the params dictionary W1, b1 = self.params['W1'], self.params['b1'] W2, b2 = self.params['W2'], self.params['b2'] N, D = X.shape # Compute the forward pass scores = None ####################################################################### # TODO: Perform the forward pass, computing the class scores for the # # input. Store the result in the scores variable, which should be an # # array of shape (N, C). # ####################################################################### scores1 = X.dot(W1) + b1 # FC1 X2 = np.maximum(0, scores1) # ReLU FC1 scores = X2.dot(W2) + b2 # FC2 ####################################################################### # END OF YOUR CODE # ####################################################################### # If the targets are not given then jump out, we're done if y is None: return scores scores -= np.max(scores) # Fix Number instability scores_exp =

np.exp(scores)

numpy.exp

"""Test the search module""" from collections.abc import Iterable, Sized from io import StringIO from itertools import chain, product from functools import partial import pickle import sys from types import GeneratorType import re import numpy as np import scipy.sparse as sp import pytest from sklearn.utils.fixes import sp_version from sklearn.utils._testing import assert_raises from sklearn.utils._testing import assert_warns from sklearn.utils._testing import assert_warns_message from sklearn.utils._testing import assert_raise_message from sklearn.utils._testing import assert_array_equal from sklearn.utils._testing import assert_array_almost_equal from sklearn.utils._testing import assert_allclose from sklearn.utils._testing import assert_almost_equal from sklearn.utils._testing import ignore_warnings from sklearn.utils._mocking import CheckingClassifier, MockDataFrame from scipy.stats import bernoulli, expon, uniform from sklearn.base import BaseEstimator, ClassifierMixin from sklearn.base import clone from sklearn.exceptions import NotFittedError from sklearn.datasets import make_classification from sklearn.datasets import make_blobs from sklearn.datasets import make_multilabel_classification from sklearn.model_selection import fit_grid_point from sklearn.model_selection import train_test_split from sklearn.model_selection import KFold from sklearn.model_selection import StratifiedKFold from sklearn.model_selection import StratifiedShuffleSplit from sklearn.model_selection import LeaveOneGroupOut from sklearn.model_selection import LeavePGroupsOut from sklearn.model_selection import GroupKFold from sklearn.model_selection import GroupShuffleSplit from sklearn.model_selection import GridSearchCV from sklearn.model_selection import RandomizedSearchCV from sklearn.model_selection import ParameterGrid from sklearn.model_selection import ParameterSampler from sklearn.model_selection._search import BaseSearchCV from sklearn.model_selection._validation import FitFailedWarning from sklearn.svm import LinearSVC, SVC from sklearn.tree import DecisionTreeRegressor from sklearn.tree import DecisionTreeClassifier from sklearn.cluster import KMeans from sklearn.neighbors import KernelDensity from sklearn.neighbors import KNeighborsClassifier from sklearn.metrics import f1_score from sklearn.metrics import recall_score from sklearn.metrics import accuracy_score from sklearn.metrics import make_scorer from sklearn.metrics import roc_auc_score from sklearn.metrics.pairwise import euclidean_distances from sklearn.impute import SimpleImputer from sklearn.pipeline import Pipeline from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression from sklearn.experimental import enable_hist_gradient_boosting # noqa from sklearn.ensemble import HistGradientBoostingClassifier from sklearn.model_selection.tests.common import OneTimeSplitter # Neither of the following two estimators inherit from BaseEstimator, # to test hyperparameter search on user-defined classifiers. class MockClassifier: """Dummy classifier to test the parameter search algorithms""" def __init__(self, foo_param=0): self.foo_param = foo_param def fit(self, X, Y): assert len(X) == len(Y) self.classes_ = np.unique(Y) return self def predict(self, T): return T.shape[0] def transform(self, X): return X + self.foo_param def inverse_transform(self, X): return X - self.foo_param predict_proba = predict predict_log_proba = predict decision_function = predict def score(self, X=None, Y=None): if self.foo_param > 1: score = 1. else: score = 0. return score def get_params(self, deep=False): return {'foo_param': self.foo_param} def set_params(self, **params): self.foo_param = params['foo_param'] return self class LinearSVCNoScore(LinearSVC): """An LinearSVC classifier that has no score method.""" @property def score(self): raise AttributeError X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) y = np.array([1, 1, 2, 2]) def assert_grid_iter_equals_getitem(grid): assert list(grid) == [grid[i] for i in range(len(grid))] @pytest.mark.parametrize("klass", [ParameterGrid, partial(ParameterSampler, n_iter=10)]) @pytest.mark.parametrize( "input, error_type, error_message", [(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'), ([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'), ({'foo': 0}, TypeError, "Parameter.* value is not iterable .*" r"\(key='foo', value=0\)")] ) def test_validate_parameter_input(klass, input, error_type, error_message): with pytest.raises(error_type, match=error_message): klass(input) def test_parameter_grid(): # Test basic properties of ParameterGrid. params1 = {"foo": [1, 2, 3]} grid1 = ParameterGrid(params1) assert isinstance(grid1, Iterable) assert isinstance(grid1, Sized) assert len(grid1) == 3 assert_grid_iter_equals_getitem(grid1) params2 = {"foo": [4, 2], "bar": ["ham", "spam", "eggs"]} grid2 = ParameterGrid(params2) assert len(grid2) == 6 # loop to assert we can iterate over the grid multiple times for i in range(2): # tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2) points = set(tuple(chain(*(sorted(p.items())))) for p in grid2) assert (points == set(("bar", x, "foo", y) for x, y in product(params2["bar"], params2["foo"]))) assert_grid_iter_equals_getitem(grid2) # Special case: empty grid (useful to get default estimator settings) empty = ParameterGrid({}) assert len(empty) == 1 assert list(empty) == [{}] assert_grid_iter_equals_getitem(empty) assert_raises(IndexError, lambda: empty[1]) has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}]) assert len(has_empty) == 4 assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}] assert_grid_iter_equals_getitem(has_empty) def test_grid_search(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3) # make sure it selects the smallest parameter in case of ties old_stdout = sys.stdout sys.stdout = StringIO() grid_search.fit(X, y) sys.stdout = old_stdout assert grid_search.best_estimator_.foo_param == 2 assert_array_equal(grid_search.cv_results_["param_foo_param"].data, [1, 2, 3]) # Smoke test the score etc: grid_search.score(X, y) grid_search.predict_proba(X) grid_search.decision_function(X) grid_search.transform(X) # Test exception handling on scoring grid_search.scoring = 'sklearn' assert_raises(ValueError, grid_search.fit, X, y) def test_grid_search_pipeline_steps(): # check that parameters that are estimators are cloned before fitting pipe = Pipeline([('regressor', LinearRegression())]) param_grid = {'regressor': [LinearRegression(), Ridge()]} grid_search = GridSearchCV(pipe, param_grid, cv=2) grid_search.fit(X, y) regressor_results = grid_search.cv_results_['param_regressor'] assert isinstance(regressor_results[0], LinearRegression) assert isinstance(regressor_results[1], Ridge) assert not hasattr(regressor_results[0], 'coef_') assert not hasattr(regressor_results[1], 'coef_') assert regressor_results[0] is not grid_search.best_estimator_ assert regressor_results[1] is not grid_search.best_estimator_ # check that we didn't modify the parameter grid that was passed assert not hasattr(param_grid['regressor'][0], 'coef_') assert not hasattr(param_grid['regressor'][1], 'coef_') @pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV]) def test_SearchCV_with_fit_params(SearchCV): X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier(expected_fit_params=['spam', 'eggs']) searcher = SearchCV( clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise" ) # The CheckingClassifier generates an assertion error if # a parameter is missing or has length != len(X). err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen." with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(10)) err_msg = "Fit parameter spam has length 1; expected" with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10)) searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10)) @ignore_warnings def test_grid_search_no_score(): # Test grid-search on classifier that has no score function. clf = LinearSVC(random_state=0) X, y = make_blobs(random_state=0, centers=2) Cs = [.1, 1, 10] clf_no_score = LinearSVCNoScore(random_state=0) grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy') grid_search.fit(X, y) grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}, scoring='accuracy') # smoketest grid search grid_search_no_score.fit(X, y) # check that best params are equal assert grid_search_no_score.best_params_ == grid_search.best_params_ # check that we can call score and that it gives the correct result assert grid_search.score(X, y) == grid_search_no_score.score(X, y) # giving no scoring function raises an error grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}) assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit, [[1]]) def test_grid_search_score_method(): X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2, random_state=0) clf = LinearSVC(random_state=0) grid = {'C': [.1]} search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y) search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y) search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid, scoring='roc_auc' ).fit(X, y) search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y) # Check warning only occurs in situation where behavior changed: # estimator requires score method to compete with scoring parameter score_no_scoring = search_no_scoring.score(X, y) score_accuracy = search_accuracy.score(X, y) score_no_score_auc = search_no_score_method_auc.score(X, y) score_auc = search_auc.score(X, y) # ensure the test is sane assert score_auc < 1.0 assert score_accuracy < 1.0 assert score_auc != score_accuracy assert_almost_equal(score_accuracy, score_no_scoring) assert_almost_equal(score_auc, score_no_score_auc) def test_grid_search_groups(): # Check if ValueError (when groups is None) propagates to GridSearchCV # And also check if groups is correctly passed to the cv object rng = np.random.RandomState(0) X, y = make_classification(n_samples=15, n_classes=2, random_state=0) groups = rng.randint(0, 3, 15) clf = LinearSVC(random_state=0) grid = {'C': [1]} group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2), GroupKFold(n_splits=3), GroupShuffleSplit()] for cv in group_cvs: gs = GridSearchCV(clf, grid, cv=cv) assert_raise_message(ValueError, "The 'groups' parameter should not be None.", gs.fit, X, y) gs.fit(X, y, groups=groups) non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()] for cv in non_group_cvs: gs = GridSearchCV(clf, grid, cv=cv) # Should not raise an error gs.fit(X, y) def test_classes__property(): # Test that classes_ property matches best_estimator_.classes_ X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) Cs = [.1, 1, 10] grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) grid_search.fit(X, y) assert_array_equal(grid_search.best_estimator_.classes_, grid_search.classes_) # Test that regressors do not have a classes_ attribute grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]}) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute before it's fit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute without a refit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}, refit=False) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') def test_trivial_cv_results_attr(): # Test search over a "grid" with only one point. clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3) grid_search.fit(X, y) assert hasattr(grid_search, "cv_results_") random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3) random_search.fit(X, y) assert hasattr(grid_search, "cv_results_") def test_no_refit(): # Test that GSCV can be used for model selection alone without refitting clf = MockClassifier() for scoring in [None, ['accuracy', 'precision']]: grid_search = GridSearchCV( clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3 ) grid_search.fit(X, y) assert not hasattr(grid_search, "best_estimator_") and \ hasattr(grid_search, "best_index_") and \ hasattr(grid_search, "best_params_") # Make sure the functions predict/transform etc raise meaningful # error messages for fn_name in ('predict', 'predict_proba', 'predict_log_proba', 'transform', 'inverse_transform'): assert_raise_message(NotFittedError, ('refit=False. %s is available only after ' 'refitting on the best parameters' % fn_name), getattr(grid_search, fn_name), X) # Test that an invalid refit param raises appropriate error messages for refit in ["", 5, True, 'recall', 'accuracy']: assert_raise_message(ValueError, "For multi-metric scoring, the " "parameter refit must be set to a scorer key", GridSearchCV(clf, {}, refit=refit, scoring={'acc': 'accuracy', 'prec': 'precision'} ).fit, X, y) def test_grid_search_error(): # Test that grid search will capture errors on data with different length X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, X_[:180], y_) def test_grid_search_one_grid_point(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]} clf = SVC(gamma='auto') cv = GridSearchCV(clf, param_dict) cv.fit(X_, y_) clf = SVC(C=1.0, kernel="rbf", gamma=0.1) clf.fit(X_, y_) assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_) def test_grid_search_when_param_grid_includes_range(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = None grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3) grid_search.fit(X, y) assert grid_search.best_estimator_.foo_param == 2 def test_grid_search_bad_param_grid(): param_dict = {"C": 1} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'int'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": []} clf = SVC() assert_raise_message( ValueError, "Parameter values for parameter (C) need to be a non-empty sequence.", GridSearchCV, clf, param_dict) param_dict = {"C": "1,2,3"} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'str'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": np.ones((3, 2))} clf = SVC() assert_raises(ValueError, GridSearchCV, clf, param_dict) def test_grid_search_sparse(): # Test that grid search works with both dense and sparse matrices X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180].tocoo(), y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert np.mean(y_pred == y_pred2) >= .9 assert C == C2 def test_grid_search_sparse_scoring(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1") cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1") cv.fit(X_[:180], y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert_array_equal(y_pred, y_pred2) assert C == C2 # Smoke test the score # np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]), # cv.score(X_[:180], y[:180])) # test loss where greater is worse def f1_loss(y_true_, y_pred_): return -f1_score(y_true_, y_pred_) F1Loss = make_scorer(f1_loss, greater_is_better=False) cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss) cv.fit(X_[:180], y_[:180]) y_pred3 = cv.predict(X_[180:]) C3 = cv.best_estimator_.C assert C == C3 assert_array_equal(y_pred, y_pred3) def test_grid_search_precomputed_kernel(): # Test that grid search works when the input features are given in the # form of a precomputed kernel matrix X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) # compute the training kernel matrix corresponding to the linear kernel K_train = np.dot(X_[:180], X_[:180].T) y_train = y_[:180] clf = SVC(kernel='precomputed') cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(K_train, y_train) assert cv.best_score_ >= 0 # compute the test kernel matrix K_test = np.dot(X_[180:], X_[:180].T) y_test = y_[180:] y_pred = cv.predict(K_test) assert np.mean(y_pred == y_test) >= 0 # test error is raised when the precomputed kernel is not array-like # or sparse assert_raises(ValueError, cv.fit, K_train.tolist(), y_train) def test_grid_search_precomputed_kernel_error_nonsquare(): # Test that grid search returns an error with a non-square precomputed # training kernel matrix K_train = np.zeros((10, 20)) y_train = np.ones((10, )) clf = SVC(kernel='precomputed') cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, K_train, y_train) class BrokenClassifier(BaseEstimator): """Broken classifier that cannot be fit twice""" def __init__(self, parameter=None): self.parameter = parameter def fit(self, X, y): assert not hasattr(self, 'has_been_fit_') self.has_been_fit_ = True def predict(self, X): return np.zeros(X.shape[0]) @ignore_warnings def test_refit(): # Regression test for bug in refitting # Simulates re-fitting a broken estimator; this used to break with # sparse SVMs. X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = GridSearchCV(BrokenClassifier(), [{'parameter': [0, 1]}], scoring="precision", refit=True) clf.fit(X, y) def test_refit_callable(): """ Test refit=callable, which adds flexibility in identifying the "best" estimator. """ def refit_callable(cv_results): """ A dummy function tests `refit=callable` interface. Return the index of a model that has the least `mean_test_score`. """ # Fit a dummy clf with `refit=True` to get a list of keys in # clf.cv_results_. X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring='precision', refit=True) clf.fit(X, y) # Ensure that `best_index_ != 0` for this dummy clf assert clf.best_index_ != 0 # Assert every key matches those in `cv_results` for key in clf.cv_results_.keys(): assert key in cv_results return cv_results['mean_test_score'].argmin() X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring='precision', refit=refit_callable) clf.fit(X, y) assert clf.best_index_ == 0 # Ensure `best_score_` is disabled when using `refit=callable` assert not hasattr(clf, 'best_score_') def test_refit_callable_invalid_type(): """ Test implementation catches the errors when 'best_index_' returns an invalid result. """ def refit_callable_invalid_type(cv_results): """ A dummy function tests when returned 'best_index_' is not integer. """ return None X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.1, 1]}, scoring='precision', refit=refit_callable_invalid_type) with pytest.raises(TypeError, match='best_index_ returned is not an integer'): clf.fit(X, y) @pytest.mark.parametrize('out_bound_value', [-1, 2]) @pytest.mark.parametrize('search_cv', [RandomizedSearchCV, GridSearchCV]) def test_refit_callable_out_bound(out_bound_value, search_cv): """ Test implementation catches the errors when 'best_index_' returns an out of bound result. """ def refit_callable_out_bound(cv_results): """ A dummy function tests when returned 'best_index_' is out of bounds. """ return out_bound_value X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = search_cv(LinearSVC(random_state=42), {'C': [0.1, 1]}, scoring='precision', refit=refit_callable_out_bound) with pytest.raises(IndexError, match='best_index_ index out of range'): clf.fit(X, y) def test_refit_callable_multi_metric(): """ Test refit=callable in multiple metric evaluation setting """ def refit_callable(cv_results): """ A dummy function tests `refit=callable` interface. Return the index of a model that has the least `mean_test_prec`. """ assert 'mean_test_prec' in cv_results return cv_results['mean_test_prec'].argmin() X, y = make_classification(n_samples=100, n_features=4, random_state=42) scoring = {'Accuracy': make_scorer(accuracy_score), 'prec': 'precision'} clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring=scoring, refit=refit_callable) clf.fit(X, y) assert clf.best_index_ == 0 # Ensure `best_score_` is disabled when using `refit=callable` assert not hasattr(clf, 'best_score_') def test_gridsearch_nd(): # Pass X as list in GridSearchCV X_4d = np.arange(10 * 5 * 3 * 2).reshape(10, 5, 3, 2) y_3d = np.arange(10 * 7 * 11).reshape(10, 7, 11) check_X = lambda x: x.shape[1:] == (5, 3, 2) check_y = lambda x: x.shape[1:] == (7, 11) clf = CheckingClassifier( check_X=check_X, check_y=check_y, methods_to_check=["fit"], ) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}) grid_search.fit(X_4d, y_3d).score(X, y) assert hasattr(grid_search, "cv_results_") def test_X_as_list(): # Pass X as list in GridSearchCV X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier( check_X=lambda x: isinstance(x, list), methods_to_check=["fit"], ) cv = KFold(n_splits=3) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv) grid_search.fit(X.tolist(), y).score(X, y) assert hasattr(grid_search, "cv_results_") def test_y_as_list(): # Pass y as list in GridSearchCV X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier( check_y=lambda x: isinstance(x, list), methods_to_check=["fit"], ) cv = KFold(n_splits=3) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv) grid_search.fit(X, y.tolist()).score(X, y) assert hasattr(grid_search, "cv_results_") @ignore_warnings def test_pandas_input(): # check cross_val_score doesn't destroy pandas dataframe types = [(MockDataFrame, MockDataFrame)] try: from pandas import Series, DataFrame types.append((DataFrame, Series)) except ImportError: pass X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) for InputFeatureType, TargetType in types: # X dataframe, y series X_df, y_ser = InputFeatureType(X), TargetType(y) def check_df(x): return isinstance(x, InputFeatureType) def check_series(x): return isinstance(x, TargetType) clf = CheckingClassifier(check_X=check_df, check_y=check_series) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}) grid_search.fit(X_df, y_ser).score(X_df, y_ser) grid_search.predict(X_df) assert hasattr(grid_search, "cv_results_") def test_unsupervised_grid_search(): # test grid-search with unsupervised estimator X, y = make_blobs(n_samples=50, random_state=0) km = KMeans(random_state=0, init="random", n_init=1) # Multi-metric evaluation unsupervised scoring = ['adjusted_rand_score', 'fowlkes_mallows_score'] for refit in ['adjusted_rand_score', 'fowlkes_mallows_score']: grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]), scoring=scoring, refit=refit) grid_search.fit(X, y) # Both ARI and FMS can find the right number :) assert grid_search.best_params_["n_clusters"] == 3 # Single metric evaluation unsupervised grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]), scoring='fowlkes_mallows_score') grid_search.fit(X, y) assert grid_search.best_params_["n_clusters"] == 3 # Now without a score, and without y grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4])) grid_search.fit(X) assert grid_search.best_params_["n_clusters"] == 4 def test_gridsearch_no_predict(): # test grid-search with an estimator without predict. # slight duplication of a test from KDE def custom_scoring(estimator, X): return 42 if estimator.bandwidth == .1 else 0 X, _ = make_blobs(cluster_std=.1, random_state=1, centers=[[0, 1], [1, 0], [0, 0]]) search = GridSearchCV(KernelDensity(), param_grid=dict(bandwidth=[.01, .1, 1]), scoring=custom_scoring) search.fit(X) assert search.best_params_['bandwidth'] == .1 assert search.best_score_ == 42 def test_param_sampler(): # test basic properties of param sampler param_distributions = {"kernel": ["rbf", "linear"], "C": uniform(0, 1)} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=10, random_state=0) samples = [x for x in sampler] assert len(samples) == 10 for sample in samples: assert sample["kernel"] in ["rbf", "linear"] assert 0 <= sample["C"] <= 1 # test that repeated calls yield identical parameters param_distributions = {"C": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=3, random_state=0) assert [x for x in sampler] == [x for x in sampler] if sp_version >= (0, 16): param_distributions = {"C": uniform(0, 1)} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=10, random_state=0) assert [x for x in sampler] == [x for x in sampler] def check_cv_results_array_types(search, param_keys, score_keys): # Check if the search `cv_results`'s array are of correct types cv_results = search.cv_results_ assert all(isinstance(cv_results[param], np.ma.MaskedArray) for param in param_keys) assert all(cv_results[key].dtype == object for key in param_keys) assert not any(isinstance(cv_results[key], np.ma.MaskedArray) for key in score_keys) assert all(cv_results[key].dtype == np.float64 for key in score_keys if not key.startswith('rank')) scorer_keys = search.scorer_.keys() if search.multimetric_ else ['score'] for key in scorer_keys: assert cv_results['rank_test_%s' % key].dtype == np.int32 def check_cv_results_keys(cv_results, param_keys, score_keys, n_cand): # Test the search.cv_results_ contains all the required results assert_array_equal(sorted(cv_results.keys()), sorted(param_keys + score_keys + ('params',))) assert all(cv_results[key].shape == (n_cand,) for key in param_keys + score_keys) def test_grid_search_cv_results(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_grid_points = 6 params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]), dict(kernel=['poly', ], degree=[1, 2])] param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel') score_keys = ('mean_test_score', 'mean_train_score', 'rank_test_score', 'split0_test_score', 'split1_test_score', 'split2_test_score', 'split0_train_score', 'split1_train_score', 'split2_train_score', 'std_test_score', 'std_train_score', 'mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time') n_candidates = n_grid_points search = GridSearchCV(SVC(), cv=n_splits, param_grid=params, return_train_score=True) search.fit(X, y) cv_results = search.cv_results_ # Check if score and timing are reasonable assert all(cv_results['rank_test_score'] >= 1) assert (all(cv_results[k] >= 0) for k in score_keys if k != 'rank_test_score') assert (all(cv_results[k] <= 1) for k in score_keys if 'time' not in k and k != 'rank_test_score') # Check cv_results structure check_cv_results_array_types(search, param_keys, score_keys) check_cv_results_keys(cv_results, param_keys, score_keys, n_candidates) # Check masking cv_results = search.cv_results_ n_candidates = len(search.cv_results_['params']) assert all((cv_results['param_C'].mask[i] and cv_results['param_gamma'].mask[i] and not cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'linear') assert all((not cv_results['param_C'].mask[i] and not cv_results['param_gamma'].mask[i] and cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'rbf') def test_random_search_cv_results(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_search_iter = 30 params = [{'kernel': ['rbf'], 'C': expon(scale=10), 'gamma': expon(scale=0.1)}, {'kernel': ['poly'], 'degree': [2, 3]}] param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel') score_keys = ('mean_test_score', 'mean_train_score', 'rank_test_score', 'split0_test_score', 'split1_test_score', 'split2_test_score', 'split0_train_score', 'split1_train_score', 'split2_train_score', 'std_test_score', 'std_train_score', 'mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time') n_cand = n_search_iter search = RandomizedSearchCV(SVC(), n_iter=n_search_iter, cv=n_splits, param_distributions=params, return_train_score=True) search.fit(X, y) cv_results = search.cv_results_ # Check results structure check_cv_results_array_types(search, param_keys, score_keys) check_cv_results_keys(cv_results, param_keys, score_keys, n_cand) n_candidates = len(search.cv_results_['params']) assert all((cv_results['param_C'].mask[i] and cv_results['param_gamma'].mask[i] and not cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'linear') assert all((not cv_results['param_C'].mask[i] and not cv_results['param_gamma'].mask[i] and cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'rbf') @pytest.mark.parametrize( "SearchCV, specialized_params", [(GridSearchCV, {'param_grid': {'C': [1, 10]}}), (RandomizedSearchCV, {'param_distributions': {'C': [1, 10]}, 'n_iter': 2})] ) def test_search_default_iid(SearchCV, specialized_params): # Test the IID parameter TODO: Clearly this test does something else??? # noise-free simple 2d-data X, y = make_blobs(centers=[[0, 0], [1, 0], [0, 1], [1, 1]], random_state=0, cluster_std=0.1, shuffle=False, n_samples=80) # split dataset into two folds that are not iid # first one contains data of all 4 blobs, second only from two. mask = np.ones(X.shape[0], dtype=np.bool) mask[np.where(y == 1)[0][::2]] = 0 mask[np.where(y == 2)[0][::2]] = 0 # this leads to perfect classification on one fold and a score of 1/3 on # the other # create "cv" for splits cv = [[mask, ~mask], [~mask, mask]] common_params = {'estimator': SVC(), 'cv': cv, 'return_train_score': True} search = SearchCV(**common_params, **specialized_params) search.fit(X, y) test_cv_scores = np.array( [search.cv_results_['split%d_test_score' % s][0] for s in range(search.n_splits_)] ) test_mean = search.cv_results_['mean_test_score'][0] test_std = search.cv_results_['std_test_score'][0] train_cv_scores = np.array( [search.cv_results_['split%d_train_score' % s][0] for s in range(search.n_splits_)] ) train_mean = search.cv_results_['mean_train_score'][0] train_std = search.cv_results_['std_train_score'][0] assert search.cv_results_['param_C'][0] == 1 # scores are the same as above assert_allclose(test_cv_scores, [1, 1. / 3.]) assert_allclose(train_cv_scores, [1, 1]) # Unweighted mean/std is used assert test_mean == pytest.approx(np.mean(test_cv_scores)) assert test_std == pytest.approx(np.std(test_cv_scores)) # For the train scores, we do not take a weighted mean irrespective of # i.i.d. or not assert train_mean == pytest.approx(1) assert train_std == pytest.approx(0) def test_grid_search_cv_results_multimetric(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]), dict(kernel=['poly', ], degree=[1, 2])] grid_searches = [] for scoring in ({'accuracy': make_scorer(accuracy_score), 'recall': make_scorer(recall_score)}, 'accuracy', 'recall'): grid_search = GridSearchCV(SVC(), cv=n_splits, param_grid=params, scoring=scoring, refit=False) grid_search.fit(X, y) grid_searches.append(grid_search) compare_cv_results_multimetric_with_single(*grid_searches) def test_random_search_cv_results_multimetric(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_search_iter = 30 # Scipy 0.12's stats dists do not accept seed, hence we use param grid params = dict(C=np.logspace(-4, 1, 3), gamma=np.logspace(-5, 0, 3, base=0.1)) for refit in (True, False): random_searches = [] for scoring in (('accuracy', 'recall'), 'accuracy', 'recall'): # If True, for multi-metric pass refit='accuracy' if refit: probability = True refit = 'accuracy' if isinstance(scoring, tuple) else refit else: probability = False clf = SVC(probability=probability, random_state=42) random_search = RandomizedSearchCV(clf, n_iter=n_search_iter, cv=n_splits, param_distributions=params, scoring=scoring, refit=refit, random_state=0) random_search.fit(X, y) random_searches.append(random_search) compare_cv_results_multimetric_with_single(*random_searches) compare_refit_methods_when_refit_with_acc( random_searches[0], random_searches[1], refit) def compare_cv_results_multimetric_with_single( search_multi, search_acc, search_rec): """Compare multi-metric cv_results with the ensemble of multiple single metric cv_results from single metric grid/random search""" assert search_multi.multimetric_ assert_array_equal(sorted(search_multi.scorer_), ('accuracy', 'recall')) cv_results_multi = search_multi.cv_results_ cv_results_acc_rec = {re.sub('_score$', '_accuracy', k): v for k, v in search_acc.cv_results_.items()} cv_results_acc_rec.update({re.sub('_score$', '_recall', k): v for k, v in search_rec.cv_results_.items()}) # Check if score and timing are reasonable, also checks if the keys # are present assert all((np.all(cv_results_multi[k] <= 1) for k in ( 'mean_score_time', 'std_score_time', 'mean_fit_time', 'std_fit_time'))) # Compare the keys, other than time keys, among multi-metric and # single metric grid search results. np.testing.assert_equal performs a # deep nested comparison of the two cv_results dicts np.testing.assert_equal({k: v for k, v in cv_results_multi.items() if not k.endswith('_time')}, {k: v for k, v in cv_results_acc_rec.items() if not k.endswith('_time')}) def compare_refit_methods_when_refit_with_acc(search_multi, search_acc, refit): """Compare refit multi-metric search methods with single metric methods""" assert search_acc.refit == refit if refit: assert search_multi.refit == 'accuracy' else: assert not search_multi.refit return # search cannot predict/score without refit X, y = make_blobs(n_samples=100, n_features=4, random_state=42) for method in ('predict', 'predict_proba', 'predict_log_proba'): assert_almost_equal(getattr(search_multi, method)(X), getattr(search_acc, method)(X)) assert_almost_equal(search_multi.score(X, y), search_acc.score(X, y)) for key in ('best_index_', 'best_score_', 'best_params_'): assert getattr(search_multi, key) == getattr(search_acc, key) def test_search_cv_results_rank_tie_breaking(): X, y = make_blobs(n_samples=50, random_state=42) # The two C values are close enough to give similar models # which would result in a tie of their mean cv-scores param_grid = {'C': [1, 1.001, 0.001]} grid_search = GridSearchCV(SVC(), param_grid=param_grid, return_train_score=True) random_search = RandomizedSearchCV(SVC(), n_iter=3, param_distributions=param_grid, return_train_score=True) for search in (grid_search, random_search): search.fit(X, y) cv_results = search.cv_results_ # Check tie breaking strategy - # Check that there is a tie in the mean scores between # candidates 1 and 2 alone assert_almost_equal(cv_results['mean_test_score'][0], cv_results['mean_test_score'][1]) assert_almost_equal(cv_results['mean_train_score'][0], cv_results['mean_train_score'][1]) assert not np.allclose(cv_results['mean_test_score'][1], cv_results['mean_test_score'][2]) assert not np.allclose(cv_results['mean_train_score'][1], cv_results['mean_train_score'][2]) # 'min' rank should be assigned to the tied candidates assert_almost_equal(search.cv_results_['rank_test_score'], [1, 1, 3]) def test_search_cv_results_none_param(): X, y = [[1], [2], [3], [4], [5]], [0, 0, 0, 0, 1] estimators = (DecisionTreeRegressor(), DecisionTreeClassifier()) est_parameters = {"random_state": [0, None]} cv = KFold() for est in estimators: grid_search = GridSearchCV(est, est_parameters, cv=cv, ).fit(X, y) assert_array_equal(grid_search.cv_results_['param_random_state'], [0, None]) @ignore_warnings() def test_search_cv_timing(): svc = LinearSVC(random_state=0) X = [[1, ], [2, ], [3, ], [4, ]] y = [0, 1, 1, 0] gs = GridSearchCV(svc, {'C': [0, 1]}, cv=2, error_score=0) rs = RandomizedSearchCV(svc, {'C': [0, 1]}, cv=2, error_score=0, n_iter=2) for search in (gs, rs): search.fit(X, y) for key in ['mean_fit_time', 'std_fit_time']: # NOTE The precision of time.time in windows is not high # enough for the fit/score times to be non-zero for trivial X and y assert np.all(search.cv_results_[key] >= 0) assert np.all(search.cv_results_[key] < 1) for key in ['mean_score_time', 'std_score_time']: assert search.cv_results_[key][1] >= 0 assert search.cv_results_[key][0] == 0.0 assert np.all(search.cv_results_[key] < 1) assert hasattr(search, "refit_time_") assert isinstance(search.refit_time_, float) assert search.refit_time_ >= 0 def test_grid_search_correct_score_results(): # test that correct scores are used n_splits = 3 clf = LinearSVC(random_state=0) X, y = make_blobs(random_state=0, centers=2) Cs = [.1, 1, 10] for score in ['f1', 'roc_auc']: grid_search = GridSearchCV(clf, {'C': Cs}, scoring=score, cv=n_splits) cv_results = grid_search.fit(X, y).cv_results_ # Test scorer names result_keys = list(cv_results.keys()) expected_keys = (("mean_test_score", "rank_test_score") + tuple("split%d_test_score" % cv_i for cv_i in range(n_splits))) assert all(np.in1d(expected_keys, result_keys)) cv = StratifiedKFold(n_splits=n_splits) n_splits = grid_search.n_splits_ for candidate_i, C in enumerate(Cs): clf.set_params(C=C) cv_scores = np.array( list(grid_search.cv_results_['split%d_test_score' % s][candidate_i] for s in range(n_splits))) for i, (train, test) in enumerate(cv.split(X, y)): clf.fit(X[train], y[train]) if score == "f1": correct_score = f1_score(y[test], clf.predict(X[test])) elif score == "roc_auc": dec = clf.decision_function(X[test]) correct_score = roc_auc_score(y[test], dec) assert_almost_equal(correct_score, cv_scores[i]) # FIXME remove test_fit_grid_point as the function will be removed on 0.25 @ignore_warnings(category=FutureWarning) def test_fit_grid_point(): X, y = make_classification(random_state=0) cv = StratifiedKFold() svc = LinearSVC(random_state=0) scorer = make_scorer(accuracy_score) for params in ({'C': 0.1}, {'C': 0.01}, {'C': 0.001}): for train, test in cv.split(X, y): this_scores, this_params, n_test_samples = fit_grid_point( X, y, clone(svc), params, train, test, scorer, verbose=False) est = clone(svc).set_params(**params) est.fit(X[train], y[train]) expected_score = scorer(est, X[test], y[test]) # Test the return values of fit_grid_point assert_almost_equal(this_scores, expected_score) assert params == this_params assert n_test_samples == test.size # Should raise an error upon multimetric scorer assert_raise_message(ValueError, "For evaluating multiple scores, use " "sklearn.model_selection.cross_validate instead.", fit_grid_point, X, y, svc, params, train, test, {'score': scorer}, verbose=True) # FIXME remove test_fit_grid_point_deprecated as # fit_grid_point will be removed on 0.25 def test_fit_grid_point_deprecated(): X, y = make_classification(random_state=0) svc = LinearSVC(random_state=0) scorer = make_scorer(accuracy_score) msg = ("fit_grid_point is deprecated in version 0.23 " "and will be removed in version 0.25") params = {'C': 0.1} train, test = next(StratifiedKFold().split(X, y)) with pytest.warns(FutureWarning, match=msg): fit_grid_point(X, y, svc, params, train, test, scorer, verbose=False) def test_pickle(): # Test that a fit search can be pickled clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, refit=True, cv=3) grid_search.fit(X, y) grid_search_pickled = pickle.loads(pickle.dumps(grid_search)) assert_array_almost_equal(grid_search.predict(X), grid_search_pickled.predict(X)) random_search = RandomizedSearchCV(clf, {'foo_param': [1, 2, 3]}, refit=True, n_iter=3, cv=3) random_search.fit(X, y) random_search_pickled = pickle.loads(pickle.dumps(random_search)) assert_array_almost_equal(random_search.predict(X), random_search_pickled.predict(X)) def test_grid_search_with_multioutput_data(): # Test search with multi-output estimator X, y = make_multilabel_classification(return_indicator=True, random_state=0) est_parameters = {"max_depth": [1, 2, 3, 4]} cv = KFold() estimators = [DecisionTreeRegressor(random_state=0), DecisionTreeClassifier(random_state=0)] # Test with grid search cv for est in estimators: grid_search = GridSearchCV(est, est_parameters, cv=cv) grid_search.fit(X, y) res_params = grid_search.cv_results_['params'] for cand_i in range(len(res_params)): est.set_params(**res_params[cand_i]) for i, (train, test) in enumerate(cv.split(X, y)): est.fit(X[train], y[train]) correct_score = est.score(X[test], y[test]) assert_almost_equal( correct_score, grid_search.cv_results_['split%d_test_score' % i][cand_i]) # Test with a randomized search for est in estimators: random_search = RandomizedSearchCV(est, est_parameters, cv=cv, n_iter=3) random_search.fit(X, y) res_params = random_search.cv_results_['params'] for cand_i in range(len(res_params)): est.set_params(**res_params[cand_i]) for i, (train, test) in enumerate(cv.split(X, y)): est.fit(X[train], y[train]) correct_score = est.score(X[test], y[test]) assert_almost_equal( correct_score, random_search.cv_results_['split%d_test_score' % i][cand_i]) def test_predict_proba_disabled(): # Test predict_proba when disabled on estimator. X = np.arange(20).reshape(5, -1) y = [0, 0, 1, 1, 1] clf = SVC(probability=False) gs = GridSearchCV(clf, {}, cv=2).fit(X, y) assert not hasattr(gs, "predict_proba") def test_grid_search_allows_nans(): # Test GridSearchCV with SimpleImputer X = np.arange(20, dtype=np.float64).reshape(5, -1) X[2, :] = np.nan y = [0, 0, 1, 1, 1] p = Pipeline([ ('imputer', SimpleImputer(strategy='mean', missing_values=np.nan)), ('classifier', MockClassifier()), ]) GridSearchCV(p, {'classifier__foo_param': [1, 2, 3]}, cv=2).fit(X, y) class FailingClassifier(BaseEstimator): """Classifier that raises a ValueError on fit()""" FAILING_PARAMETER = 2 def __init__(self, parameter=None): self.parameter = parameter def fit(self, X, y=None): if self.parameter == FailingClassifier.FAILING_PARAMETER: raise ValueError("Failing classifier failed as required") def predict(self, X): return np.zeros(X.shape[0]) def score(self, X=None, Y=None): return 0. def test_grid_search_failing_classifier(): # GridSearchCV with on_error != 'raise' # Ensures that a warning is raised and score reset where appropriate. X, y = make_classification(n_samples=20, n_features=10, random_state=0) clf = FailingClassifier() # refit=False because we only want to check that errors caused by fits # to individual folds will be caught and warnings raised instead. If # refit was done, then an exception would be raised on refit and not # caught by grid_search (expected behavior), and this would cause an # error in this test. gs = GridSearchCV(clf, [{'parameter': [0, 1, 2]}], scoring='accuracy', refit=False, error_score=0.0) assert_warns(FitFailedWarning, gs.fit, X, y) n_candidates = len(gs.cv_results_['params']) # Ensure that grid scores were set to zero as required for those fits # that are expected to fail. def get_cand_scores(i): return np.array(list(gs.cv_results_['split%d_test_score' % s][i] for s in range(gs.n_splits_))) assert all((np.all(get_cand_scores(cand_i) == 0.0) for cand_i in range(n_candidates) if gs.cv_results_['param_parameter'][cand_i] == FailingClassifier.FAILING_PARAMETER)) gs = GridSearchCV(clf, [{'parameter': [0, 1, 2]}], scoring='accuracy', refit=False, error_score=float('nan')) assert_warns(FitFailedWarning, gs.fit, X, y) n_candidates = len(gs.cv_results_['params']) assert all(np.all(np.isnan(get_cand_scores(cand_i))) for cand_i in range(n_candidates) if gs.cv_results_['param_parameter'][cand_i] == FailingClassifier.FAILING_PARAMETER) ranks = gs.cv_results_['rank_test_score'] # Check that succeeded estimators have lower ranks assert ranks[0] <= 2 and ranks[1] <= 2 # Check that failed estimator has the highest rank assert ranks[clf.FAILING_PARAMETER] == 3 assert gs.best_index_ != clf.FAILING_PARAMETER def test_grid_search_failing_classifier_raise(): # GridSearchCV with on_error == 'raise' raises the error X, y = make_classification(n_samples=20, n_features=10, random_state=0) clf = FailingClassifier() # refit=False because we want to test the behaviour of the grid search part gs = GridSearchCV(clf, [{'parameter': [0, 1, 2]}], scoring='accuracy', refit=False, error_score='raise') # FailingClassifier issues a ValueError so this is what we look for. assert_raises(ValueError, gs.fit, X, y) def test_parameters_sampler_replacement(): # raise warning if n_iter is bigger than total parameter space params = [{'first': [0, 1], 'second': ['a', 'b', 'c']}, {'third': ['two', 'values']}] sampler = ParameterSampler(params, n_iter=9) n_iter = 9 grid_size = 8 expected_warning = ('The total space of parameters %d is smaller ' 'than n_iter=%d. Running %d iterations. For ' 'exhaustive searches, use GridSearchCV.' % (grid_size, n_iter, grid_size)) assert_warns_message(UserWarning, expected_warning, list, sampler) # degenerates to GridSearchCV if n_iter the same as grid_size sampler = ParameterSampler(params, n_iter=8) samples = list(sampler) assert len(samples) == 8 for values in ParameterGrid(params): assert values in samples # test sampling without replacement in a large grid params = {'a': range(10), 'b': range(10), 'c': range(10)} sampler = ParameterSampler(params, n_iter=99, random_state=42) samples = list(sampler) assert len(samples) == 99 hashable_samples = ["a%db%dc%d" % (p['a'], p['b'], p['c']) for p in samples] assert len(set(hashable_samples)) == 99 # doesn't go into infinite loops params_distribution = {'first': bernoulli(.5), 'second': ['a', 'b', 'c']} sampler = ParameterSampler(params_distribution, n_iter=7) samples = list(sampler) assert len(samples) == 7 def test_stochastic_gradient_loss_param(): # Make sure the predict_proba works when loss is specified # as one of the parameters in the param_grid. param_grid = { 'loss': ['log'], } X = np.arange(24).reshape(6, -1) y = [0, 0, 0, 1, 1, 1] clf = GridSearchCV(estimator=SGDClassifier(loss='hinge'), param_grid=param_grid, cv=3) # When the estimator is not fitted, `predict_proba` is not available as the # loss is 'hinge'. assert not hasattr(clf, "predict_proba") clf.fit(X, y) clf.predict_proba(X) clf.predict_log_proba(X) # Make sure `predict_proba` is not available when setting loss=['hinge'] # in param_grid param_grid = { 'loss': ['hinge'], } clf = GridSearchCV(estimator=SGDClassifier(loss='hinge'), param_grid=param_grid, cv=3) assert not hasattr(clf, "predict_proba") clf.fit(X, y) assert not hasattr(clf, "predict_proba") def test_search_train_scores_set_to_false(): X = np.arange(6).reshape(6, -1) y = [0, 0, 0, 1, 1, 1] clf = LinearSVC(random_state=0) gs = GridSearchCV(clf, param_grid={'C': [0.1, 0.2]}, cv=3) gs.fit(X, y) def test_grid_search_cv_splits_consistency(): # Check if a one time iterable is accepted as a cv parameter. n_samples = 100 n_splits = 5 X, y = make_classification(n_samples=n_samples, random_state=0) gs = GridSearchCV(LinearSVC(random_state=0), param_grid={'C': [0.1, 0.2, 0.3]}, cv=OneTimeSplitter(n_splits=n_splits, n_samples=n_samples), return_train_score=True) gs.fit(X, y) gs2 = GridSearchCV(LinearSVC(random_state=0), param_grid={'C': [0.1, 0.2, 0.3]}, cv=KFold(n_splits=n_splits), return_train_score=True) gs2.fit(X, y) # Give generator as a cv parameter assert isinstance(KFold(n_splits=n_splits, shuffle=True, random_state=0).split(X, y), GeneratorType) gs3 = GridSearchCV(LinearSVC(random_state=0), param_grid={'C': [0.1, 0.2, 0.3]}, cv=KFold(n_splits=n_splits, shuffle=True, random_state=0).split(X, y), return_train_score=True) gs3.fit(X, y) gs4 = GridSearchCV(LinearSVC(random_state=0), param_grid={'C': [0.1, 0.2, 0.3]}, cv=KFold(n_splits=n_splits, shuffle=True, random_state=0), return_train_score=True) gs4.fit(X, y) def _pop_time_keys(cv_results): for key in ('mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time'): cv_results.pop(key) return cv_results # Check if generators are supported as cv and # that the splits are consistent np.testing.assert_equal(_pop_time_keys(gs3.cv_results_), _pop_time_keys(gs4.cv_results_)) # OneTimeSplitter is a non-re-entrant cv where split can be called only # once if ``cv.split`` is called once per param setting in GridSearchCV.fit # the 2nd and 3rd parameter will not be evaluated as no train/test indices # will be generated for the 2nd and subsequent cv.split calls. # This is a check to make sure cv.split is not called once per param # setting. np.testing.assert_equal({k: v for k, v in gs.cv_results_.items() if not k.endswith('_time')}, {k: v for k, v in gs2.cv_results_.items() if not k.endswith('_time')}) # Check consistency of folds across the parameters gs = GridSearchCV(LinearSVC(random_state=0), param_grid={'C': [0.1, 0.1, 0.2, 0.2]}, cv=KFold(n_splits=n_splits, shuffle=True), return_train_score=True) gs.fit(X, y) # As the first two param settings (C=0.1) and the next two param # settings (C=0.2) are same, the test and train scores must also be # same as long as the same train/test indices are generated for all # the cv splits, for both param setting for score_type in ('train', 'test'): per_param_scores = {} for param_i in range(4): per_param_scores[param_i] = list( gs.cv_results_['split%d_%s_score' % (s, score_type)][param_i] for s in range(5)) assert_array_almost_equal(per_param_scores[0], per_param_scores[1]) assert_array_almost_equal(per_param_scores[2], per_param_scores[3]) def test_transform_inverse_transform_round_trip(): clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3) grid_search.fit(X, y) X_round_trip = grid_search.inverse_transform(grid_search.transform(X)) assert_array_equal(X, X_round_trip) def test_custom_run_search(): def check_results(results, gscv): exp_results = gscv.cv_results_ assert sorted(results.keys()) == sorted(exp_results) for k in results: if not k.endswith('_time'): # XXX: results['params'] is a list :| results[k] =

np.asanyarray(results[k])

numpy.asanyarray

""" YTArray class. """ from __future__ import print_function #----------------------------------------------------------------------------- # Copyright (c) 2013, yt Development Team. # # Distributed under the terms of the Modified BSD License. # # The full license is in the file COPYING.txt, distributed with this software. #----------------------------------------------------------------------------- import copy import numpy as np from distutils.version import LooseVersion from functools import wraps from numpy import \ add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \ floor_divide, negative, power, remainder, mod, absolute, rint, \ sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \ reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \ hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \ bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \ greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \ logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \ isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \ modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing try: # numpy 1.13 or newer from numpy import positive, divmod as divmod_, isnat, heaviside except ImportError: positive, divmod_, isnat, heaviside = (None,)*4 from yt.units.unit_object import Unit, UnitParseError from yt.units.unit_registry import UnitRegistry from yt.units.dimensions import \ angle, \ current_mks, \ dimensionless, \ em_dimensions from yt.utilities.exceptions import \ YTUnitOperationError, YTUnitConversionError, \ YTUfuncUnitError, YTIterableUnitCoercionError, \ YTInvalidUnitEquivalence, YTEquivalentDimsError from yt.utilities.lru_cache import lru_cache from numbers import Number as numeric_type from yt.utilities.on_demand_imports import _astropy from sympy import Rational from yt.units.unit_lookup_table import \ default_unit_symbol_lut from yt.units.equivalencies import equivalence_registry from yt.utilities.logger import ytLogger as mylog from .pint_conversions import convert_pint_units NULL_UNIT = Unit() POWER_SIGN_MAPPING = {multiply: 1, divide: -1} # redefine this here to avoid a circular import from yt.funcs def iterable(obj): try: len(obj) except: return False return True def return_arr(func): @wraps(func) def wrapped(*args, **kwargs): ret, units = func(*args, **kwargs) if ret.shape == (): return YTQuantity(ret, units) else: # This could be a subclass, so don't call YTArray directly. return type(args[0])(ret, units) return wrapped @lru_cache(maxsize=128, typed=False) def sqrt_unit(unit): return unit**0.5 @lru_cache(maxsize=128, typed=False) def multiply_units(unit1, unit2): return unit1 * unit2 def preserve_units(unit1, unit2=None): return unit1 @lru_cache(maxsize=128, typed=False) def power_unit(unit, power): return unit**power @lru_cache(maxsize=128, typed=False) def square_unit(unit): return unit*unit @lru_cache(maxsize=128, typed=False) def divide_units(unit1, unit2): return unit1/unit2 @lru_cache(maxsize=128, typed=False) def reciprocal_unit(unit): return unit**-1 def passthrough_unit(unit, unit2=None): return unit def return_without_unit(unit, unit2=None): return None def arctan2_unit(unit1, unit2): return NULL_UNIT def comparison_unit(unit1, unit2=None): return None def invert_units(unit): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def bitop_units(unit1, unit2): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def get_inp_u_unary(ufunc, inputs, out_arr=None): inp = inputs[0] u = getattr(inp, 'units', None) if u is None: u = NULL_UNIT if u.dimensions is angle and ufunc in trigonometric_operators: inp = inp.in_units('radian').v if out_arr is not None: out_arr = ufunc(inp).view(np.ndarray) return out_arr, inp, u def get_inp_u_binary(ufunc, inputs): inp1 = coerce_iterable_units(inputs[0]) inp2 = coerce_iterable_units(inputs[1]) unit1 = getattr(inp1, 'units', None) unit2 = getattr(inp2, 'units', None) ret_class = get_binary_op_return_class(type(inp1), type(inp2)) if unit1 is None: unit1 = Unit(registry=getattr(unit2, 'registry', None)) if unit2 is None and ufunc is not power: unit2 = Unit(registry=getattr(unit1, 'registry', None)) elif ufunc is power: unit2 = inp2 if isinstance(unit2, np.ndarray): if isinstance(unit2, YTArray): if unit2.units.is_dimensionless: pass else: raise YTUnitOperationError(ufunc, unit1, unit2) unit2 = 1.0 return (inp1, inp2), (unit1, unit2), ret_class def handle_preserve_units(inps, units, ufunc, ret_class): if units[0] != units[1]: any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) else: if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False): if units[0] != units[1]: u1d = units[0].is_dimensionless u2d = units[1].is_dimensionless any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) elif not any([u1d, u2d]): if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) else: if raise_error: raise YTUfuncUnitError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_multiply_divide_units(unit, units, out, out_arr): if unit.is_dimensionless and unit.base_value != 1.0: if not units[0].is_dimensionless: if units[0].dimensions == units[1].dimensions: out_arr = np.multiply(out_arr.view(np.ndarray), unit.base_value, out=out) unit = Unit(registry=unit.registry) return out, out_arr, unit def coerce_iterable_units(input_object): if isinstance(input_object, np.ndarray): return input_object if iterable(input_object): if any([isinstance(o, YTArray) for o in input_object]): ff = getattr(input_object[0], 'units', NULL_UNIT, ) if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]): raise YTIterableUnitCoercionError(input_object) # This will create a copy of the data in the iterable. return YTArray(input_object) return input_object else: return input_object def sanitize_units_mul(this_object, other_object): inp = coerce_iterable_units(this_object) ret = coerce_iterable_units(other_object) # If the other object is a YTArray and has the same dimensions as the object # under consideration, convert so we don't mix units with the same # dimensions. if isinstance(ret, YTArray): if inp.units.same_dimensions_as(ret.units): ret.in_units(inp.units) return ret def sanitize_units_add(this_object, other_object, op_string): inp = coerce_iterable_units(this_object) ret = coerce_iterable_units(other_object) # Make sure the other object is a YTArray before we use the `units` # attribute. if isinstance(ret, YTArray): if not inp.units.same_dimensions_as(ret.units): # handle special case of adding or subtracting with zero or # array filled with zero if not np.any(other_object): return ret.view(np.ndarray) elif not np.any(this_object): return ret raise YTUnitOperationError(op_string, inp.units, ret.units) ret = ret.in_units(inp.units) else: # If the other object is not a YTArray, then one of the arrays must be # dimensionless or filled with zeros if not inp.units.is_dimensionless and np.any(ret): raise YTUnitOperationError(op_string, inp.units, dimensionless) return ret def validate_comparison_units(this, other, op_string): # Check that other is a YTArray. if hasattr(other, 'units'): if this.units.expr is other.units.expr: if this.units.base_value == other.units.base_value: return other if not this.units.same_dimensions_as(other.units): raise YTUnitOperationError(op_string, this.units, other.units) return other.in_units(this.units) return other @lru_cache(maxsize=128, typed=False) def _unit_repr_check_same(my_units, other_units): """ Takes a Unit object, or string of known unit symbol, and check that it is compatible with this quantity. Returns Unit object. """ # let Unit() handle units arg if it's not already a Unit obj. if not isinstance(other_units, Unit): other_units = Unit(other_units, registry=my_units.registry) equiv_dims = em_dimensions.get(my_units.dimensions, None) if equiv_dims == other_units.dimensions: if current_mks in equiv_dims.free_symbols: base = "SI" else: base = "CGS" raise YTEquivalentDimsError(my_units, other_units, base) if not my_units.same_dimensions_as(other_units): raise YTUnitConversionError( my_units, my_units.dimensions, other_units, other_units.dimensions) return other_units unary_operators = ( negative, absolute, rint, sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, reciprocal, sin, cos, tan, arcsin, arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, invert, logical_not, isreal, iscomplex, isfinite, isinf, isnan, signbit, floor, ceil, trunc, modf, frexp, fabs, spacing, positive, isnat, ) binary_operators = ( add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, power, remainder, mod, arctan2, hypot, bitwise_and, bitwise_or, bitwise_xor, left_shift, right_shift, greater, greater_equal, less, less_equal, not_equal, equal, logical_and, logical_or, logical_xor, maximum, minimum, fmax, fmin, copysign, nextafter, ldexp, fmod, divmod_, heaviside ) trigonometric_operators = ( sin, cos, tan, ) class YTArray(np.ndarray): """ An ndarray subclass that attaches a symbolic unit object to the array data. Parameters ---------- input_array : :obj:`!iterable` A tuple, list, or array to attach units to input_units : String unit specification, unit symbol object, or astropy units The units of the array. Powers must be specified using python syntax (cm**3, not cm^3). registry : ~yt.units.unit_registry.UnitRegistry The registry to create units from. If input_units is already associated with a unit registry and this is specified, this will be used instead of the registry associated with the unit object. dtype : data-type The dtype of the array data. Defaults to the dtype of the input data, or, if none is found, uses np.float64 bypass_validation : boolean If True, all input validation is skipped. Using this option may produce corrupted, invalid units or array data, but can lead to significant speedups in the input validation logic adds significant overhead. If set, input_units *must* be a valid unit object. Defaults to False. Examples -------- >>> from yt import YTArray >>> a = YTArray([1, 2, 3], 'cm') >>> b = YTArray([4, 5, 6], 'm') >>> a + b YTArray([ 401., 502., 603.]) cm >>> b + a YTArray([ 4.01, 5.02, 6.03]) m NumPy ufuncs will pass through units where appropriate. >>> import numpy as np >>> a = YTArray(np.arange(8) - 4, 'g/cm**3') >>> np.abs(a) YTArray([4, 3, 2, 1, 0, 1, 2, 3]) g/cm**3 and strip them when it would be annoying to deal with them. >>> np.log10(a) array([ -inf, 0. , 0.30103 , 0.47712125, 0.60205999, 0.69897 , 0.77815125, 0.84509804]) YTArray is tightly integrated with yt datasets: >>> import yt >>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030') >>> a = ds.arr(np.ones(5), 'code_length') >>> a.in_cgs() YTArray([ 3.08600000e+24, 3.08600000e+24, 3.08600000e+24, 3.08600000e+24, 3.08600000e+24]) cm This is equivalent to: >>> b = YTArray(np.ones(5), 'code_length', registry=ds.unit_registry) >>> np.all(a == b) True """ _ufunc_registry = { add: preserve_units, subtract: preserve_units, multiply: multiply_units, divide: divide_units, logaddexp: return_without_unit, logaddexp2: return_without_unit, true_divide: divide_units, floor_divide: divide_units, negative: passthrough_unit, power: power_unit, remainder: preserve_units, mod: preserve_units, fmod: preserve_units, absolute: passthrough_unit, fabs: passthrough_unit, rint: return_without_unit, sign: return_without_unit, conj: passthrough_unit, exp: return_without_unit, exp2: return_without_unit, log: return_without_unit, log2: return_without_unit, log10: return_without_unit, expm1: return_without_unit, log1p: return_without_unit, sqrt: sqrt_unit, square: square_unit, reciprocal: reciprocal_unit, sin: return_without_unit, cos: return_without_unit, tan: return_without_unit, sinh: return_without_unit, cosh: return_without_unit, tanh: return_without_unit, arcsin: return_without_unit, arccos: return_without_unit, arctan: return_without_unit, arctan2: arctan2_unit, arcsinh: return_without_unit, arccosh: return_without_unit, arctanh: return_without_unit, hypot: preserve_units, deg2rad: return_without_unit, rad2deg: return_without_unit, bitwise_and: bitop_units, bitwise_or: bitop_units, bitwise_xor: bitop_units, invert: invert_units, left_shift: bitop_units, right_shift: bitop_units, greater: comparison_unit, greater_equal: comparison_unit, less: comparison_unit, less_equal: comparison_unit, not_equal: comparison_unit, equal: comparison_unit, logical_and: comparison_unit, logical_or: comparison_unit, logical_xor: comparison_unit, logical_not: return_without_unit, maximum: preserve_units, minimum: preserve_units, fmax: preserve_units, fmin: preserve_units, isreal: return_without_unit, iscomplex: return_without_unit, isfinite: return_without_unit, isinf: return_without_unit, isnan: return_without_unit, signbit: return_without_unit, copysign: passthrough_unit, nextafter: preserve_units, modf: passthrough_unit, ldexp: bitop_units, frexp: return_without_unit, floor: passthrough_unit, ceil: passthrough_unit, trunc: passthrough_unit, spacing: passthrough_unit, positive: passthrough_unit, divmod_: passthrough_unit, isnat: return_without_unit, heaviside: preserve_units, } __array_priority__ = 2.0 def __new__(cls, input_array, input_units=None, registry=None, dtype=None, bypass_validation=False): if dtype is None: dtype = getattr(input_array, 'dtype', np.float64) if bypass_validation is True: obj = np.asarray(input_array, dtype=dtype).view(cls) obj.units = input_units if registry is not None: obj.units.registry = registry return obj if input_array is NotImplemented: return input_array.view(cls) if registry is None and isinstance(input_units, (str, bytes)): if input_units.startswith('code_'): raise UnitParseError( "Code units used without referring to a dataset. \n" "Perhaps you meant to do something like this instead: \n" "ds.arr(%s, \"%s\")" % (input_array, input_units) ) if isinstance(input_array, YTArray): ret = input_array.view(cls) if input_units is None: if registry is None: ret.units = input_array.units else: units = Unit(str(input_array.units), registry=registry) ret.units = units elif isinstance(input_units, Unit): ret.units = input_units else: ret.units = Unit(input_units, registry=registry) return ret elif isinstance(input_array, np.ndarray): pass elif iterable(input_array) and input_array: if isinstance(input_array[0], YTArray): return YTArray(np.array(input_array, dtype=dtype), input_array[0].units, registry=registry) # Input array is an already formed ndarray instance # We first cast to be our class type obj = np.asarray(input_array, dtype=dtype).view(cls) # Check units type if input_units is None: # Nothing provided. Make dimensionless... units = Unit() elif isinstance(input_units, Unit): if registry and registry is not input_units.registry: units = Unit(str(input_units), registry=registry) else: units = input_units else: # units kwarg set, but it's not a Unit object. # don't handle all the cases here, let the Unit class handle if # it's a str. units = Unit(input_units, registry=registry) # Attach the units obj.units = units return obj def __repr__(self): """ """ return super(YTArray, self).__repr__()+' '+self.units.__repr__() def __str__(self): """ """ return str(self.view(np.ndarray)) + ' ' + str(self.units) # # Start unit conversion methods # def convert_to_units(self, units): """ Convert the array and units to the given units. Parameters ---------- units : Unit object or str The units you want to convert to. """ new_units = _unit_repr_check_same(self.units, units) (conversion_factor, offset) = self.units.get_conversion_factor(new_units) self.units = new_units values = self.d values *= conversion_factor if offset: np.subtract(self, offset*self.uq, self) return self def convert_to_base(self, unit_system="cgs"): """ Convert the array and units to the equivalent base units in the specified unit system. Parameters ---------- unit_system : string, optional The unit system to be used in the conversion. If not specified, the default base units of cgs are used. Examples -------- >>> E = YTQuantity(2.5, "erg/s") >>> E.convert_to_base(unit_system="galactic") """ return self.convert_to_units(self.units.get_base_equivalent(unit_system)) def convert_to_cgs(self): """ Convert the array and units to the equivalent cgs units. """ return self.convert_to_units(self.units.get_cgs_equivalent()) def convert_to_mks(self): """ Convert the array and units to the equivalent mks units. """ return self.convert_to_units(self.units.get_mks_equivalent()) def in_units(self, units, equivalence=None, **kwargs): """ Creates a copy of this array with the data in the supplied units, and returns it. Optionally, an equivalence can be specified to convert to an equivalent quantity which is not in the same dimensions. .. note:: All additional keyword arguments are passed to the equivalency, which should be used if that particular equivalency requires them. Parameters ---------- units : Unit object or string The units you want to get a new quantity in. equivalence : string, optional The equivalence you wish to use. To see which equivalencies are supported for this unitful quantity, try the :meth:`list_equivalencies` method. Default: None Returns ------- YTArray """ if equivalence is None: new_units = _unit_repr_check_same(self.units, units) (conversion_factor, offset) = self.units.get_conversion_factor(new_units) new_array = type(self)(self.ndview * conversion_factor, new_units) if offset: np.subtract(new_array, offset*new_array.uq, new_array) return new_array else: return self.to_equivalent(units, equivalence, **kwargs) def to(self, units, equivalence=None, **kwargs): """ An alias for YTArray.in_units(). See the docstrings of that function for details. """ return self.in_units(units, equivalence=equivalence, **kwargs) def to_value(self, units=None, equivalence=None, **kwargs): """ Creates a copy of this array with the data in the supplied units, and returns it without units. Output is therefore a bare NumPy array. Optionally, an equivalence can be specified to convert to an equivalent quantity which is not in the same dimensions. .. note:: All additional keyword arguments are passed to the equivalency, which should be used if that particular equivalency requires them. Parameters ---------- units : Unit object or string, optional The units you want to get the bare quantity in. If not specified, the value will be returned in the current units. equivalence : string, optional The equivalence you wish to use. To see which equivalencies are supported for this unitful quantity, try the :meth:`list_equivalencies` method. Default: None Returns ------- NumPy array """ if units is None: v = self.value else: v = self.in_units(units, equivalence=equivalence, **kwargs).value if isinstance(self, YTQuantity): return float(v) else: return v def in_base(self, unit_system="cgs"): """ Creates a copy of this array with the data in the specified unit system, and returns it in that system's base units. Parameters ---------- unit_system : string, optional The unit system to be used in the conversion. If not specified, the default base units of cgs are used. Examples -------- >>> E = YTQuantity(2.5, "erg/s") >>> E_new = E.in_base(unit_system="galactic") """ return self.in_units(self.units.get_base_equivalent(unit_system)) def in_cgs(self): """ Creates a copy of this array with the data in the equivalent cgs units, and returns it. Returns ------- Quantity object with data converted to cgs units. """ return self.in_units(self.units.get_cgs_equivalent()) def in_mks(self): """ Creates a copy of this array with the data in the equivalent mks units, and returns it. Returns ------- Quantity object with data converted to mks units. """ return self.in_units(self.units.get_mks_equivalent()) def to_equivalent(self, unit, equiv, **kwargs): """ Convert a YTArray or YTQuantity to an equivalent, e.g., something that is related by only a constant factor but not in the same units. Parameters ---------- unit : string The unit that you wish to convert to. equiv : string The equivalence you wish to use. To see which equivalencies are supported for this unitful quantity, try the :meth:`list_equivalencies` method. Examples -------- >>> a = yt.YTArray(1.0e7,"K") >>> a.to_equivalent("keV", "thermal") """ conv_unit = Unit(unit, registry=self.units.registry) if self.units.same_dimensions_as(conv_unit): return self.in_units(conv_unit) this_equiv = equivalence_registry[equiv]() oneway_or_equivalent = ( conv_unit.has_equivalent(equiv) or this_equiv._one_way) if self.has_equivalent(equiv) and oneway_or_equivalent: new_arr = this_equiv.convert( self, conv_unit.dimensions, **kwargs) if isinstance(new_arr, tuple): try: return type(self)(new_arr[0], new_arr[1]).in_units(unit) except YTUnitConversionError: raise YTInvalidUnitEquivalence(equiv, self.units, unit) else: return new_arr.in_units(unit) else: raise YTInvalidUnitEquivalence(equiv, self.units, unit) def list_equivalencies(self): """ Lists the possible equivalencies associated with this YTArray or YTQuantity. """ self.units.list_equivalencies() def has_equivalent(self, equiv): """ Check to see if this YTArray or YTQuantity has an equivalent unit in *equiv*. """ return self.units.has_equivalent(equiv) def ndarray_view(self): """ Returns a view into the array, but as an ndarray rather than ytarray. Returns ------- View of this array's data. """ return self.view(np.ndarray) def to_ndarray(self): """ Creates a copy of this array with the unit information stripped """ return np.array(self) @classmethod def from_astropy(cls, arr, unit_registry=None): """ Convert an AstroPy "Quantity" to a YTArray or YTQuantity. Parameters ---------- arr : AstroPy Quantity The Quantity to convert from. unit_registry : yt UnitRegistry, optional A yt unit registry to use in the conversion. If one is not supplied, the default one will be used. """ # Converting from AstroPy Quantity u = arr.unit ap_units = [] for base, exponent in zip(u.bases, u.powers): unit_str = base.to_string() # we have to do this because AstroPy is silly and defines # hour as "h" if unit_str == "h": unit_str = "hr" ap_units.append("%s**(%s)" % (unit_str, Rational(exponent))) ap_units = "*".join(ap_units) if isinstance(arr.value, np.ndarray): return YTArray(arr.value, ap_units, registry=unit_registry) else: return YTQuantity(arr.value, ap_units, registry=unit_registry) def to_astropy(self, **kwargs): """ Creates a new AstroPy quantity with the same unit information. """ if _astropy.units is None: raise ImportError("You don't have AstroPy installed, so you can't convert to " + "an AstroPy quantity.") return self.value*_astropy.units.Unit(str(self.units), **kwargs) @classmethod def from_pint(cls, arr, unit_registry=None): """ Convert a Pint "Quantity" to a YTArray or YTQuantity. Parameters ---------- arr : Pint Quantity The Quantity to convert from. unit_registry : yt UnitRegistry, optional A yt unit registry to use in the conversion. If one is not supplied, the default one will be used. Examples -------- >>> from pint import UnitRegistry >>> import numpy as np >>> ureg = UnitRegistry() >>> a = np.random.random(10) >>> b = ureg.Quantity(a, "erg/cm**3") >>> c = yt.YTArray.from_pint(b) """ p_units = [] for base, exponent in arr._units.items(): bs = convert_pint_units(base) p_units.append("%s**(%s)" % (bs, Rational(exponent))) p_units = "*".join(p_units) if isinstance(arr.magnitude, np.ndarray): return YTArray(arr.magnitude, p_units, registry=unit_registry) else: return YTQuantity(arr.magnitude, p_units, registry=unit_registry) def to_pint(self, unit_registry=None): """ Convert a YTArray or YTQuantity to a Pint Quantity. Parameters ---------- arr : YTArray or YTQuantity The unitful quantity to convert from. unit_registry : Pint UnitRegistry, optional The Pint UnitRegistry to use in the conversion. If one is not supplied, the default one will be used. NOTE: This is not the same as a yt UnitRegistry object. Examples -------- >>> a = YTQuantity(4.0, "cm**2/s") >>> b = a.to_pint() """ from pint import UnitRegistry if unit_registry is None: unit_registry = UnitRegistry() powers_dict = self.units.expr.as_powers_dict() units = [] for unit, pow in powers_dict.items(): # we have to do this because Pint doesn't recognize # "yr" as "year" if str(unit).endswith("yr") and len(str(unit)) in [2,3]: unit = str(unit).replace("yr","year") units.append("%s**(%s)" % (unit, Rational(pow))) units = "*".join(units) return unit_registry.Quantity(self.value, units) # # End unit conversion methods # def write_hdf5(self, filename, dataset_name=None, info=None, group_name=None): r"""Writes a YTArray to hdf5 file. Parameters ---------- filename: string The filename to create and write a dataset to dataset_name: string The name of the dataset to create in the file. info: dictionary A dictionary of supplementary info to write to append as attributes to the dataset. group_name: string An optional group to write the arrays to. If not specified, the arrays are datasets at the top level by default. Examples -------- >>> a = YTArray([1,2,3], 'cm') >>> myinfo = {'field':'dinosaurs', 'type':'field_data'} >>> a.write_hdf5('test_array_data.h5', dataset_name='dinosaurs', ... info=myinfo) """ from yt.utilities.on_demand_imports import _h5py as h5py from yt.extern.six.moves import cPickle as pickle if info is None: info = {} info['units'] = str(self.units) info['unit_registry'] = np.void(pickle.dumps(self.units.registry.lut)) if dataset_name is None: dataset_name = 'array_data' f = h5py.File(filename) if group_name is not None: if group_name in f: g = f[group_name] else: g = f.create_group(group_name) else: g = f if dataset_name in g.keys(): d = g[dataset_name] # Overwrite without deleting if we can get away with it. if d.shape == self.shape and d.dtype == self.dtype: d[...] = self for k in d.attrs.keys(): del d.attrs[k] else: del f[dataset_name] d = g.create_dataset(dataset_name, data=self) else: d = g.create_dataset(dataset_name, data=self) for k, v in info.items(): d.attrs[k] = v f.close() @classmethod def from_hdf5(cls, filename, dataset_name=None, group_name=None): r"""Attempts read in and convert a dataset in an hdf5 file into a YTArray. Parameters ---------- filename: string The filename to of the hdf5 file. dataset_name: string The name of the dataset to read from. If the dataset has a units attribute, attempt to infer units as well. group_name: string An optional group to read the arrays from. If not specified, the arrays are datasets at the top level by default. """ import h5py from yt.extern.six.moves import cPickle as pickle if dataset_name is None: dataset_name = 'array_data' f = h5py.File(filename) if group_name is not None: g = f[group_name] else: g = f dataset = g[dataset_name] data = dataset[:] units = dataset.attrs.get('units', '') if 'unit_registry' in dataset.attrs.keys(): unit_lut = pickle.loads(dataset.attrs['unit_registry'].tostring()) else: unit_lut = None f.close() registry = UnitRegistry(lut=unit_lut, add_default_symbols=False) return cls(data, units, registry=registry) # # Start convenience methods # @property def value(self): """Get a copy of the array data as a numpy ndarray""" return np.array(self) v = value @property def ndview(self): """Get a view of the array data.""" return self.ndarray_view() d = ndview @property def unit_quantity(self): """Get a YTQuantity with the same unit as this array and a value of 1.0""" return YTQuantity(1.0, self.units) uq = unit_quantity @property def unit_array(self): """Get a YTArray filled with ones with the same unit and shape as this array""" return np.ones_like(self) ua = unit_array def __getitem__(self, item): ret = super(YTArray, self).__getitem__(item) if ret.shape == (): return YTQuantity(ret, self.units, bypass_validation=True) else: if hasattr(self, 'units'): ret.units = self.units return ret # # Start operation methods # if LooseVersion(np.__version__) < LooseVersion('1.13.0'): def __add__(self, right_object): """ Add this ytarray to the object on the right of the `+` operator. Must check for the correct (same dimension) units. """ ro = sanitize_units_add(self, right_object, "addition") return super(YTArray, self).__add__(ro) def __radd__(self, left_object): """ See __add__. """ lo = sanitize_units_add(self, left_object, "addition") return super(YTArray, self).__radd__(lo) def __iadd__(self, other): """ See __add__. """ oth = sanitize_units_add(self, other, "addition") np.add(self, oth, out=self) return self def __sub__(self, right_object): """ Subtract the object on the right of the `-` from this ytarray. Must check for the correct (same dimension) units. """ ro = sanitize_units_add(self, right_object, "subtraction") return super(YTArray, self).__sub__(ro) def __rsub__(self, left_object): """ See __sub__. """ lo = sanitize_units_add(self, left_object, "subtraction") return super(YTArray, self).__rsub__(lo) def __isub__(self, other): """ See __sub__. """ oth = sanitize_units_add(self, other, "subtraction") np.subtract(self, oth, out=self) return self def __neg__(self): """ Negate the data. """ return super(YTArray, self).__neg__() def __mul__(self, right_object): """ Multiply this YTArray by the object on the right of the `*` operator. The unit objects handle being multiplied. """ ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__mul__(ro) def __rmul__(self, left_object): """ See __mul__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rmul__(lo) def __imul__(self, other): """ See __mul__. """ oth = sanitize_units_mul(self, other) np.multiply(self, oth, out=self) return self def __div__(self, right_object): """ Divide this YTArray by the object on the right of the `/` operator. """ ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__div__(ro) def __rdiv__(self, left_object): """ See __div__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rdiv__(lo) def __idiv__(self, other): """ See __div__. """ oth = sanitize_units_mul(self, other) np.divide(self, oth, out=self) return self def __truediv__(self, right_object): ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__truediv__(ro) def __rtruediv__(self, left_object): """ See __div__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rtruediv__(lo) def __itruediv__(self, other): """ See __div__. """ oth = sanitize_units_mul(self, other) np.true_divide(self, oth, out=self) return self def __floordiv__(self, right_object): ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__floordiv__(ro) def __rfloordiv__(self, left_object): """ See __div__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rfloordiv__(lo) def __ifloordiv__(self, other): """ See __div__. """ oth = sanitize_units_mul(self, other) np.floor_divide(self, oth, out=self) return self def __or__(self, right_object): return super(YTArray, self).__or__(right_object) def __ror__(self, left_object): return super(YTArray, self).__ror__(left_object) def __ior__(self, other): np.bitwise_or(self, other, out=self) return self def __xor__(self, right_object): return super(YTArray, self).__xor__(right_object) def __rxor__(self, left_object): return super(YTArray, self).__rxor__(left_object) def __ixor__(self, other): np.bitwise_xor(self, other, out=self) return self def __and__(self, right_object): return super(YTArray, self).__and__(right_object) def __rand__(self, left_object): return super(YTArray, self).__rand__(left_object) def __iand__(self, other): np.bitwise_and(self, other, out=self) return self def __pow__(self, power): """ Raise this YTArray to some power. Parameters ---------- power : float or dimensionless YTArray. The pow value. """ if isinstance(power, YTArray): if not power.units.is_dimensionless: raise YTUnitOperationError('power', power.unit) # Work around a sympy issue (I think?) # # If I don't do this, super(YTArray, self).__pow__ returns a YTArray # with a unit attribute set to the sympy expression 1/1 rather than # a dimensionless Unit object. if self.units.is_dimensionless and power == -1: ret = super(YTArray, self).__pow__(power) return type(self)(ret, input_units='') return super(YTArray, self).__pow__(power) def __abs__(self): """ Return a YTArray with the abs of the data. """ return super(YTArray, self).__abs__() # # Start comparison operators. # def __lt__(self, other): """ Test if this is less than the object on the right. """ # converts if possible oth = validate_comparison_units(self, other, 'less_than') return super(YTArray, self).__lt__(oth) def __le__(self, other): """Test if this is less than or equal to the object on the right. """ oth = validate_comparison_units(self, other, 'less_than or equal') return super(YTArray, self).__le__(oth) def __eq__(self, other): """ Test if this is equal to the object on the right. """ # Check that other is a YTArray. if other is None: # self is a YTArray, so it can't be None. return False oth = validate_comparison_units(self, other, 'equal') return super(YTArray, self).__eq__(oth) def __ne__(self, other): """ Test if this is not equal to the object on the right. """ # Check that the other is a YTArray. if other is None: return True oth = validate_comparison_units(self, other, 'not equal') return super(YTArray, self).__ne__(oth) def __ge__(self, other): """ Test if this is greater than or equal to other. """ # Check that the other is a YTArray. oth = validate_comparison_units( self, other, 'greater than or equal') return super(YTArray, self).__ge__(oth) def __gt__(self, other): """ Test if this is greater than the object on the right. """ # Check that the other is a YTArray. oth = validate_comparison_units(self, other, 'greater than') return super(YTArray, self).__gt__(oth) # # End comparison operators # # # Begin reduction operators # @return_arr def prod(self, axis=None, dtype=None, out=None): if axis is not None: units = self.units**self.shape[axis] else: units = self.units**self.size return super(YTArray, self).prod(axis, dtype, out), units @return_arr def mean(self, axis=None, dtype=None, out=None): return super(YTArray, self).mean(axis, dtype, out), self.units @return_arr def sum(self, axis=None, dtype=None, out=None): return super(YTArray, self).sum(axis, dtype, out), self.units @return_arr def std(self, axis=None, dtype=None, out=None, ddof=0): return super(YTArray, self).std(axis, dtype, out, ddof), self.units def __array_wrap__(self, out_arr, context=None): ret = super(YTArray, self).__array_wrap__(out_arr, context) if isinstance(ret, YTQuantity) and ret.shape != (): ret = ret.view(YTArray) if context is None: if ret.shape == (): return ret[()] else: return ret ufunc = context[0] inputs = context[1] if ufunc in unary_operators: out_arr, inp, u = get_inp_u_unary(ufunc, inputs, out_arr) unit = self._ufunc_registry[context[0]](u) ret_class = type(self) elif ufunc in binary_operators: unit_operator = self._ufunc_registry[context[0]] inps, units, ret_class = get_inp_u_binary(ufunc, inputs) if unit_operator in (preserve_units, comparison_unit, arctan2_unit): inps, units = handle_comparison_units( inps, units, ufunc, ret_class, raise_error=True) unit = unit_operator(*units) if unit_operator in (multiply_units, divide_units): out_arr, out_arr, unit = handle_multiply_divide_units( unit, units, out_arr, out_arr) else: raise RuntimeError( "Support for the %s ufunc has not been added " "to YTArray." % str(context[0])) if unit is None: out_arr = np.array(out_arr, copy=False) return out_arr out_arr.units = unit if out_arr.size == 1: return YTQuantity(np.array(out_arr), unit) else: if ret_class is YTQuantity: # This happens if you do ndarray * YTQuantity. Explicitly # casting to YTArray avoids creating a YTQuantity with # size > 1 return YTArray(np.array(out_arr), unit) return ret_class(np.array(out_arr, copy=False), unit) else: # numpy version equal to or newer than 1.13 def __array_ufunc__(self, ufunc, method, *inputs, **kwargs): func = getattr(ufunc, method) if 'out' in kwargs: out_orig = kwargs.pop('out') out = np.asarray(out_orig[0]) else: out = None if len(inputs) == 1: _, inp, u = get_inp_u_unary(ufunc, inputs) out_arr = func(np.asarray(inp), out=out, **kwargs) if ufunc in (multiply, divide) and method == 'reduce': power_sign = POWER_SIGN_MAPPING[ufunc] if 'axis' in kwargs and kwargs['axis'] is not None: unit = u**(power_sign*inp.shape[kwargs['axis']]) else: unit = u**(power_sign*inp.size) else: unit = self._ufunc_registry[ufunc](u) ret_class = type(self) elif len(inputs) == 2: unit_operator = self._ufunc_registry[ufunc] inps, units, ret_class = get_inp_u_binary(ufunc, inputs) if unit_operator in (comparison_unit, arctan2_unit): inps, units = handle_comparison_units( inps, units, ufunc, ret_class) elif unit_operator is preserve_units: inps, units = handle_preserve_units( inps, units, ufunc, ret_class) unit = unit_operator(*units) out_arr = func(np.asarray(inps[0]),

np.asarray(inps[1])

numpy.asarray

from __future__ import print_function import numpy as np import matplotlib.pyplot as plt class TwoLayerNet(object): """ A two-layer fully-connected neural network. The net has an input dimension of N, a hidden layer dimension of H, and performs classification over C classes. We train the network with a softmax loss function and L2 regularization on the weight matrices. The network uses a ReLU nonlinearity after the first fully connected layer. In other words, the network has the following architecture: input - fully connected layer - ReLU - fully connected layer - softmax The outputs of the second fully-connected layer are the scores for each class. """ def __init__(self, input_size, hidden_size, output_size, std=1e-4): """ Initialize the model. Weights are initialized to small random values and biases are initialized to zero. Weights and biases are stored in the variable self.params, which is a dictionary with the following keys W1: First layer weights; has shape (D, H) b1: First layer biases; has shape (H,) W2: Second layer weights; has shape (H, C) b2: Second layer biases; has shape (C,) Inputs: - input_size: The dimension D of the input data. - hidden_size: The number of neurons H in the hidden layer. - output_size: The number of classes C. """ self.params = {} self.params['W1'] = std * np.random.randn(input_size, hidden_size) self.params['b1'] = np.zeros(hidden_size) self.params['W2'] = std * np.random.randn(hidden_size, output_size) self.params['b2'] = np.zeros(output_size) def loss(self, X, y=None, reg=0.0): """ Compute the loss and gradients for a two layer fully connected neural network. Inputs: - X: Input data of shape (N, D). Each X[i] is a training sample. - y: Vector of training labels. y[i] is the label for X[i], and each y[i] is an integer in the range 0 <= y[i] < C. This parameter is optional; if it is not passed then we only return scores, and if it is passed then we instead return the loss and gradients. - reg: Regularization strength. Returns: If y is None, return a matrix scores of shape (N, C) where scores[i, c] is the score for class c on input X[i]. If y is not None, instead return a tuple of: - loss: Loss (data loss and regularization loss) for this batch of training samples. - grads: Dictionary mapping parameter names to gradients of those parameters with respect to the loss function; has the same keys as self.params. """ # Unpack variables from the params dictionary W1, b1 = self.params['W1'], self.params['b1'] W2, b2 = self.params['W2'], self.params['b2'] N, D = X.shape # Compute the forward pass scores = None ####################################################################### # TODO: Perform the forward pass, computing the class scores for the # # input. Store the result in the scores variable, which should be an # # array of shape (N, C). # ####################################################################### scores1 = X.dot(W1) + b1 # FC1 X2 = np.maximum(0, scores1) # ReLU FC1 scores = X2.dot(W2) + b2 # FC2 ####################################################################### # END OF YOUR CODE # ####################################################################### # If the targets are not given then jump out, we're done if y is None: return scores scores -= np.max(scores) # Fix Number instability scores_exp = np.exp(scores) probs = scores_exp / np.sum(scores_exp, axis=1, keepdims=True) # Compute the loss loss = None ####################################################################### # TODO: Finish the forward pass, and compute the loss. This should # # include both the data loss and L2 regularization for W1 and W2. # # Store the result in the variable loss, which should be a scalar. Use# # the Softmax classifier loss. # ####################################################################### correct_probs = -np.log(probs[

np.arange(N)

numpy.arange

# -*- coding: utf-8 -*- """ Created on Thu Nov 28 12:10:11 2019 @author: Omer """ ## File handler ## This file was initially intended purely to generate the matrices for the near earth code found in: https://public.ccsds.org/Pubs/131x1o2e2s.pdf ## The values from the above pdf were copied manually to a txt file, and it is the purpose of this file to parse it. ## The emphasis here is on correctness, I currently do not see a reason to generalise this file, since matrices will be saved in either json or some matrix friendly format. import numpy as np from scipy.linalg import circulant #import matplotlib.pyplot as plt import scipy.io import common import hashlib import os projectDir = os.environ.get('LDPC') if projectDir == None: import pathlib projectDir = pathlib.Path(__file__).parent.absolute() ## <NAME>: added on 01/12/2020, need to make sure this doesn't break anything. import sys sys.path.insert(1, projectDir) FILE_HANDLER_INT_DATA_TYPE = np.int32 GENERAL_CODE_MATRIX_DATA_TYPE = np.int32 NIBBLE_CONVERTER = np.array([8, 4, 2, 1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) def nibbleToHex(inputArray): n = NIBBLE_CONVERTER.dot(inputArray) if n == 10: h = 'A' elif n== 11: h = 'B' elif n== 12: h = 'C' elif n== 13: h = 'D' elif n== 14: h = 'E' elif n== 15: h = 'F' else: h = str(n) return h def binaryArraytoHex(inputArray): d1 = len(inputArray) assert (d1 % 4 == 0) outputArray = np.zeros(d1//4, dtype = str) outputString = '' for j in range(d1//4): nibble = inputArray[4 * j : 4 * j + 4] h = nibbleToHex(nibble) outputArray[j] = h outputString = outputString + h return outputArray, outputString def hexStringToBinaryArray(hexString): outputBinary = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) for i in hexString: if i == '0': nibble = np.array([0,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '1': nibble = np.array([0,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '2': nibble = np.array([0,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '3': nibble = np.array([0,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '4': nibble = np.array([0,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '5': nibble = np.array([0,1,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '6': nibble = np.array([0,1,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '7': nibble = np.array([0,1,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '8': nibble = np.array([1,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '9': nibble = np.array([1,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'A': nibble = np.array([1,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'B': nibble =

np.array([1,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)

numpy.array

""" Functions for loading input data. Author: <NAME> <<EMAIL>> """ import os import numpy as np def load_img(path: str, img_nums: list, shape: tuple) -> np.array: """ Loads a image in the human-readable format. Args: path: The path to the to the folder with mnist images. img_nums: A list with the numbers of the images we want to load. shape: The shape of a single image. Returns: The images as a MxCx28x28 numpy array. """ images = np.zeros((len(img_nums), *shape), dtype=float) for idx, i in enumerate(img_nums): file = os.path.join(path, "image" + str(i)) with open(file, "r") as f: data = [float(pixel) for pixel in f.readlines()[0].split(",")[:-1]] images[idx, :, :] = np.array(data).reshape(*shape) return images def load_mnist_human_readable(path: str, img_nums: list) -> np.array: """ Loads a mnist image from the neurify dataset. Args: path: The path to the to the folder with mnist images. img_nums: A list with the numbers of the images we want to load. Returns: The images as a Mx28x28 numpy array. """ return load_img(path, img_nums, (28, 28)) def load_cifar10_human_readable(path: str, img_nums: list) -> np.array: """ Loads the Cifar10 images in human readable format. Args: path: The path to the to the folder with mnist images. img_nums: A list with the numbers of the images we want to load. Returns: The images as a Mx3x32x32 numpy array. """ return load_img(path, img_nums, (3, 32, 32)) def load_images_eran(img_csv: str = "../../resources/images/cifar10_test.csv", num_images: int = 100, image_shape: tuple = (3, 32, 32)) -> tuple: """ Loads the images from the eran csv. Args: The csv path Returns: images, targets """ num_images = 100 images_array = np.zeros((num_images, np.prod(image_shape)), dtype=np.float32) targets_array =

np.zeros(num_images, dtype=int)

numpy.zeros

import numpy as np from stumpff import C, S from CelestialBody import BODIES from numerical import newton, laguerre from lagrange import calc_f, calc_fd, calc_g, calc_gd def kepler_chi(chi, alpha, r0, vr0, mu, dt): ''' Kepler's Equation of the universal anomaly, modified for use in numerical solvers. ''' z = alpha*chi**2 return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \ (1 - alpha*r0)*chi**3*S(z) + \ r0*chi - np.sqrt(mu)*dt def dkepler_dchi(chi, alpha, r0, vr0, mu, dt): ''' Derivative of Kepler's Equation of the universal anomaly, modified for use in numerical solvers. ''' z = alpha*chi**2 return (r0*vr0/np.sqrt(mu))*chi*(1 - alpha*chi**2*S(z)) + \ (1 - alpha*r0)*chi**2*C(z) + r0 def d2kepler_dchi2(chi, alpha, r0, vr0, mu, dt): ''' Second derivative of Kepler's Equation of the universal anomaly, modified for use in numerical solvers. ''' z = alpha*chi**2 S_ = S(z) return (r0*vr0/np.sqrt(mu))*(1 - 3*z*S_ + z*(C(z) - 3*S_)) + \ chi*(1 - z*S_)*(1 - alpha*r0) def solve_kepler_chi(r_0, v_0, dt, body=BODIES['Earth'], method='laguerre', tol=1e-7, max_iters=100): ''' Solve Kepler's Equation of the universal anomaly chi using the specified numerical method. Applies Algorithm 3.4 from Orbital Mechanics for Engineering Students, 4 ed, Curtis. :param r_0: `iterable` (km) initial position 3-vector :param v_0: `iterable` (km/s) initial velocity 3-vector :param dt: `float` (s) time after initial state to solve for r, v as 3-vectors :param body: `CelestialBody` (--) the celestial body to use for orbital parameters :param method: `str` (--) which numerical method to use to solve Kepler's Equation :param tol: `float` (--) decimal tolerance for numerical method (default 1e-7 is IEEE 745 single precision) :param max_iters: `int` (--) maximum number of iterations in numerical method before breaking :return: (km) final position 3-vector, (km/s) final velocity 3-vector ''' VALID_METHODS = ('laguerre', 'newton') mu = body.mu # (km**3/s**2) gravitational parameter of the specified primary body r0 = np.linalg.norm(r_0) # (km) initial position magnitude v0 = np.linalg.norm(v_0) # (km/s) initial velocity magnitude vr0 = np.dot(v_0, r_0)/r0 # (km/s) initial radial velocity magnitude alpha = 2/r0 - v0**2/mu # (1/km) inverse of semi-major axis chi0 = np.sqrt(mu)*np.abs(alpha)*dt if method not in VALID_METHODS: print(f'Method \'{method}\' is not valid, must be one of {VALID_METHODS}.\nDefaulting to laguerre method.') chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt) elif method == 'newton': chi, _, _ = newton(chi0, kepler_chi, dkepler_dchi, alpha, r0, vr0, mu, dt) else: # method == 'laguerre' chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt) f = calc_f(chi, r0, alpha) g = calc_g(dt, mu, chi, alpha) r_1 = f*r_0 + g*v_0 r1 = np.linalg.norm(r_1) fd = calc_fd(mu, r1, r0, alpha, chi) gd = calc_gd(chi, r1, alpha) v_1 = fd*r_0 + gd*v_0 return r_1, v_1 def solve_kepler_E(e, Me, tol=1e-7, max_iters=100): ''' Solve Kepler's Equation in the form containing Eccentric Anomaly (E), eccentricity (e), and Mean Anomaly of Ellipse (Me). Uses Algorithm 3.1 from Orbital Mechanics for Engineering Students, 4 ed, Curtis. ''' # TODO: have this function make use of one of the numerical methods in numerical.py def f(E, e, Me): return E - e*np.sin(E) - Me def fp(E, e): return 1 - e*np.cos(E) E = Me + e/2 if Me < np.pi else Me - e/2 ratio = f(E, e, Me)/fp(E, e) iters = 0 while abs(ratio) > tol and iters < max_iters: E -= ratio ratio = f(E, e, Me)/fp(E, e) iters += 1 E -= ratio converged = np.abs(ratio) <= tol return E, iters, converged def test(): ''' Test the functionality of solve_kepler_chi and solve_kepler_laguerre using Problem 3.20 from Orbital Mechanics for Engineering Students, 4 ed, Curtis. ''' # given starting information Earth = BODIES['Earth'] # `CelestialBody` (--) Earth and all the Earth things r_0 = np.array([20000, -105000, -19000]) # (km) initial position vector v_0 = np.array([0.9, -3.4, -1.5]) # (km/s) initial velocity vector dt = 2*60*60 # (s) time of interest after initial time # given correct answer from textbook correct_r_1 = np.array([26338, -128750, -29656]) # (km) final position vector correct_v_1 = np.array([0.86280, -3.2116, -1.4613]) # (km/s) final velocity vector # solve using above methods r_n, v_n = solve_kepler_chi(r_0, v_0, dt, Earth, method='newton') r_l, v_l = solve_kepler_chi(r_0, v_0, dt, Earth, method='laguerre') # check correctness # tolerance based on significant figures of given answers newton_valid =

np.allclose(r_n, correct_r_1, atol=1)

numpy.allclose

# # Copyright (c) 2021 The GPflux Contributors. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # import abc import numpy as np import pytest import tensorflow as tf import tensorflow_probability as tfp from gpflow.kullback_leiblers import gauss_kl from gpflux.encoders import DirectlyParameterizedNormalDiag from gpflux.layers import LatentVariableLayer, LayerWithObservations, TrackableLayer tf.keras.backend.set_floatx("float64") ############ # Utilities ############ def _zero_one_normal_prior(w_dim): """ N(0, I) prior """ return tfp.distributions.MultivariateNormalDiag(loc=np.zeros(w_dim), scale_diag=np.ones(w_dim)) def get_distributions_with_w_dim(): distributions = [] for d in [1, 5]: mean = np.zeros(d) scale_tri_l = np.eye(d) mvn = tfp.distributions.MultivariateNormalTriL(mean, scale_tri_l) std = np.ones(d) mvn_diag = tfp.distributions.MultivariateNormalDiag(mean, std) distributions.append((mvn, d)) distributions.append((mvn_diag, d)) return distributions ############ # Tests ############ @pytest.mark.parametrize("distribution, w_dim", get_distributions_with_w_dim()) def test_local_kls(distribution, w_dim): lv = LatentVariableLayer(encoder=None, prior=distribution) # test kl is 0 when posteriors == priors posterior = distribution assert lv._local_kls(posterior) == 0 # test kl > 0 when posteriors != priors batch_size = 10 params = distribution.parameters posterior_params = { k: [v + 0.5 for _ in range(batch_size)] for k, v in params.items() if isinstance(v, np.ndarray) } posterior = lv.distribution_class(**posterior_params) local_kls = lv._local_kls(posterior) assert np.all(local_kls > 0) assert local_kls.shape == (batch_size,) @pytest.mark.parametrize("w_dim", [1, 5]) def test_local_kl_gpflow_consistency(w_dim): num_data = 400 means = np.random.randn(num_data, w_dim) encoder = DirectlyParameterizedNormalDiag(num_data, w_dim, means) lv = LatentVariableLayer(encoder=encoder, prior=_zero_one_normal_prior(w_dim)) posteriors = lv._inference_posteriors( [np.random.randn(num_data, 3), np.random.randn(num_data, 2)] ) q_mu = posteriors.parameters["loc"] q_sqrt = posteriors.parameters["scale_diag"] gpflow_local_kls = gauss_kl(q_mu, q_sqrt) tfp_local_kls = tf.reduce_sum(lv._local_kls(posteriors)) np.testing.assert_allclose(tfp_local_kls, gpflow_local_kls, rtol=1e-10) class ArrayMatcher: def __init__(self, expected): self.expected = expected def __eq__(self, actual): return

np.allclose(actual, self.expected, equal_nan=True)

numpy.allclose

# -*- coding: utf-8 -*- """ Showcases *ICTCP* *colour encoding* computations. """ import numpy as np import colour from colour.utilities import message_box message_box('"ICTCP" Colour Encoding Computations') RGB = np.array([0.45620519, 0.03081071, 0.04091952]) message_box(('Converting from "ITU-R BT.2020" colourspace to "ICTCP" colour ' 'encoding given "RGB" values:\n' '\n\t{0}'.format(RGB))) print(colour.RGB_to_ICTCP(RGB)) print('\n') ICTCP =

np.array([0.07351364, 0.00475253, 0.09351596])

numpy.array

"""Routines for numerical differentiation.""" from __future__ import division import numpy as np from numpy.linalg import norm from scipy.sparse.linalg import LinearOperator from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find from ._group_columns import group_dense, group_sparse EPS = np.finfo(np.float64).eps def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub): """Adjust final difference scheme to the presence of bounds. Parameters ---------- x0 : ndarray, shape (n,) Point at which we wish to estimate derivative. h : ndarray, shape (n,) Desired finite difference steps. num_steps : int Number of `h` steps in one direction required to implement finite difference scheme. For example, 2 means that we need to evaluate f(x0 + 2 * h) or f(x0 - 2 * h) scheme : {'1-sided', '2-sided'} Whether steps in one or both directions are required. In other words '1-sided' applies to forward and backward schemes, '2-sided' applies to center schemes. lb : ndarray, shape (n,) Lower bounds on independent variables. ub : ndarray, shape (n,) Upper bounds on independent variables. Returns ------- h_adjusted : ndarray, shape (n,) Adjusted step sizes. Step size decreases only if a sign flip or switching to one-sided scheme doesn't allow to take a full step. use_one_sided : ndarray of bool, shape (n,) Whether to switch to one-sided scheme. Informative only for ``scheme='2-sided'``. """ if scheme == '1-sided': use_one_sided = np.ones_like(h, dtype=bool) elif scheme == '2-sided': h = np.abs(h) use_one_sided = np.zeros_like(h, dtype=bool) else: raise ValueError("`scheme` must be '1-sided' or '2-sided'.") if np.all((lb == -np.inf) & (ub == np.inf)): return h, use_one_sided h_total = h * num_steps h_adjusted = h.copy() lower_dist = x0 - lb upper_dist = ub - x0 if scheme == '1-sided': x = x0 + h_total violated = (x < lb) | (x > ub) fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist) h_adjusted[violated & fitting] *= -1 forward = (upper_dist >= lower_dist) & ~fitting h_adjusted[forward] = upper_dist[forward] / num_steps backward = (upper_dist < lower_dist) & ~fitting h_adjusted[backward] = -lower_dist[backward] / num_steps elif scheme == '2-sided': central = (lower_dist >= h_total) & (upper_dist >= h_total) forward = (upper_dist >= lower_dist) & ~central h_adjusted[forward] = np.minimum( h[forward], 0.5 * upper_dist[forward] / num_steps) use_one_sided[forward] = True backward = (upper_dist < lower_dist) & ~central h_adjusted[backward] = -np.minimum( h[backward], 0.5 * lower_dist[backward] / num_steps) use_one_sided[backward] = True min_dist = np.minimum(upper_dist, lower_dist) / num_steps adjusted_central = (~central & (np.abs(h_adjusted) <= min_dist)) h_adjusted[adjusted_central] = min_dist[adjusted_central] use_one_sided[adjusted_central] = False return h_adjusted, use_one_sided relative_step = {"2-point": EPS**0.5, "3-point": EPS**(1/3), "cs": EPS**0.5} def _compute_absolute_step(rel_step, x0, method): if rel_step is None: rel_step = relative_step[method] sign_x0 = (x0 >= 0).astype(float) * 2 - 1 return rel_step * sign_x0 * np.maximum(1.0, np.abs(x0)) def _prepare_bounds(bounds, x0): lb, ub = [np.asarray(b, dtype=float) for b in bounds] if lb.ndim == 0: lb = np.resize(lb, x0.shape) if ub.ndim == 0: ub = np.resize(ub, x0.shape) return lb, ub def group_columns(A, order=0): """Group columns of a 2-D matrix for sparse finite differencing [1]_. Two columns are in the same group if in each row at least one of them has zero. A greedy sequential algorithm is used to construct groups. Parameters ---------- A : array_like or sparse matrix, shape (m, n) Matrix of which to group columns. order : int, iterable of int with shape (n,) or None Permutation array which defines the order of columns enumeration. If int or None, a random permutation is used with `order` used as a random seed. Default is 0, that is use a random permutation but guarantee repeatability. Returns ------- groups : ndarray of int, shape (n,) Contains values from 0 to n_groups-1, where n_groups is the number of found groups. Each value ``groups[i]`` is an index of a group to which ith column assigned. The procedure was helpful only if n_groups is significantly less than n. References ---------- .. [1] <NAME>, <NAME>, and <NAME>, "On the estimation of sparse Jacobian matrices", Journal of the Institute of Mathematics and its Applications, 13 (1974), pp. 117-120. """ if issparse(A): A = csc_matrix(A) else: A = np.atleast_2d(A) A = (A != 0).astype(np.int32) if A.ndim != 2: raise ValueError("`A` must be 2-dimensional.") m, n = A.shape if order is None or np.isscalar(order): rng = np.random.RandomState(order) order = rng.permutation(n) else: order =

np.asarray(order)

numpy.asarray

"""Routines for numerical differentiation.""" from __future__ import division import numpy as np from numpy.linalg import norm from scipy.sparse.linalg import LinearOperator from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find from ._group_columns import group_dense, group_sparse EPS = np.finfo(np.float64).eps def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub): """Adjust final difference scheme to the presence of bounds. Parameters ---------- x0 : ndarray, shape (n,) Point at which we wish to estimate derivative. h : ndarray, shape (n,) Desired finite difference steps. num_steps : int Number of `h` steps in one direction required to implement finite difference scheme. For example, 2 means that we need to evaluate f(x0 + 2 * h) or f(x0 - 2 * h) scheme : {'1-sided', '2-sided'} Whether steps in one or both directions are required. In other words '1-sided' applies to forward and backward schemes, '2-sided' applies to center schemes. lb : ndarray, shape (n,) Lower bounds on independent variables. ub : ndarray, shape (n,) Upper bounds on independent variables. Returns ------- h_adjusted : ndarray, shape (n,) Adjusted step sizes. Step size decreases only if a sign flip or switching to one-sided scheme doesn't allow to take a full step. use_one_sided : ndarray of bool, shape (n,) Whether to switch to one-sided scheme. Informative only for ``scheme='2-sided'``. """ if scheme == '1-sided': use_one_sided = np.ones_like(h, dtype=bool) elif scheme == '2-sided': h = np.abs(h) use_one_sided = np.zeros_like(h, dtype=bool) else: raise ValueError("`scheme` must be '1-sided' or '2-sided'.") if np.all((lb == -np.inf) & (ub == np.inf)): return h, use_one_sided h_total = h * num_steps h_adjusted = h.copy() lower_dist = x0 - lb upper_dist = ub - x0 if scheme == '1-sided': x = x0 + h_total violated = (x < lb) | (x > ub) fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist) h_adjusted[violated & fitting] *= -1 forward = (upper_dist >= lower_dist) & ~fitting h_adjusted[forward] = upper_dist[forward] / num_steps backward = (upper_dist < lower_dist) & ~fitting h_adjusted[backward] = -lower_dist[backward] / num_steps elif scheme == '2-sided': central = (lower_dist >= h_total) & (upper_dist >= h_total) forward = (upper_dist >= lower_dist) & ~central h_adjusted[forward] = np.minimum( h[forward], 0.5 * upper_dist[forward] / num_steps) use_one_sided[forward] = True backward = (upper_dist < lower_dist) & ~central h_adjusted[backward] = -np.minimum( h[backward], 0.5 * lower_dist[backward] / num_steps) use_one_sided[backward] = True min_dist = np.minimum(upper_dist, lower_dist) / num_steps adjusted_central = (~central & (np.abs(h_adjusted) <= min_dist)) h_adjusted[adjusted_central] = min_dist[adjusted_central] use_one_sided[adjusted_central] = False return h_adjusted, use_one_sided relative_step = {"2-point": EPS**0.5, "3-point": EPS**(1/3), "cs": EPS**0.5} def _compute_absolute_step(rel_step, x0, method): if rel_step is None: rel_step = relative_step[method] sign_x0 = (x0 >= 0).astype(float) * 2 - 1 return rel_step * sign_x0 * np.maximum(1.0, np.abs(x0)) def _prepare_bounds(bounds, x0): lb, ub = [np.asarray(b, dtype=float) for b in bounds] if lb.ndim == 0: lb = np.resize(lb, x0.shape) if ub.ndim == 0: ub = np.resize(ub, x0.shape) return lb, ub def group_columns(A, order=0): """Group columns of a 2-D matrix for sparse finite differencing [1]_. Two columns are in the same group if in each row at least one of them has zero. A greedy sequential algorithm is used to construct groups. Parameters ---------- A : array_like or sparse matrix, shape (m, n) Matrix of which to group columns. order : int, iterable of int with shape (n,) or None Permutation array which defines the order of columns enumeration. If int or None, a random permutation is used with `order` used as a random seed. Default is 0, that is use a random permutation but guarantee repeatability. Returns ------- groups : ndarray of int, shape (n,) Contains values from 0 to n_groups-1, where n_groups is the number of found groups. Each value ``groups[i]`` is an index of a group to which ith column assigned. The procedure was helpful only if n_groups is significantly less than n. References ---------- .. [1] <NAME>, <NAME>, and <NAME>, "On the estimation of sparse Jacobian matrices", Journal of the Institute of Mathematics and its Applications, 13 (1974), pp. 117-120. """ if issparse(A): A = csc_matrix(A) else: A = np.atleast_2d(A) A = (A != 0).astype(np.int32) if A.ndim != 2: raise ValueError("`A` must be 2-dimensional.") m, n = A.shape if order is None or np.isscalar(order): rng = np.random.RandomState(order) order = rng.permutation(n) else: order = np.asarray(order) if order.shape != (n,): raise ValueError("`order` has incorrect shape.") A = A[:, order] if issparse(A): groups = group_sparse(m, n, A.indices, A.indptr) else: groups = group_dense(m, n, A) groups[order] = groups.copy() return groups def approx_derivative(fun, x0, method='3-point', rel_step=None, f0=None, bounds=(-np.inf, np.inf), sparsity=None, as_linear_operator=False, args=(), kwargs={}): """Compute finite difference approximation of the derivatives of a vector-valued function. If a function maps from R^n to R^m, its derivatives form m-by-n matrix called the Jacobian, where an element (i, j) is a partial derivative of f[i] with respect to x[j]. Parameters ---------- fun : callable Function of which to estimate the derivatives. The argument x passed to this function is ndarray of shape (n,) (never a scalar even if n=1). It must return 1-D array_like of shape (m,) or a scalar. x0 : array_like of shape (n,) or float Point at which to estimate the derivatives. Float will be converted to a 1-D array. method : {'3-point', '2-point', 'cs'}, optional Finite difference method to use: - '2-point' - use the first order accuracy forward or backward difference. - '3-point' - use central difference in interior points and the second order accuracy forward or backward difference near the boundary. - 'cs' - use a complex-step finite difference scheme. This assumes that the user function is real-valued and can be analytically continued to the complex plane. Otherwise, produces bogus results. rel_step : None or array_like, optional Relative step size to use. The absolute step size is computed as ``h = rel_step * sign(x0) * max(1, abs(x0))``, possibly adjusted to fit into the bounds. For ``method='3-point'`` the sign of `h` is ignored. If None (default) then step is selected automatically, see Notes. f0 : None or array_like, optional If not None it is assumed to be equal to ``fun(x0)``, in this case the ``fun(x0)`` is not called. Default is None. bounds : tuple of array_like, optional Lower and upper bounds on independent variables. Defaults to no bounds. Each bound must match the size of `x0` or be a scalar, in the latter case the bound will be the same for all variables. Use it to limit the range of function evaluation. Bounds checking is not implemented when `as_linear_operator` is True. sparsity : {None, array_like, sparse matrix, 2-tuple}, optional Defines a sparsity structure of the Jacobian matrix. If the Jacobian matrix is known to have only few non-zero elements in each row, then it's possible to estimate its several columns by a single function evaluation [3]_. To perform such economic computations two ingredients are required: * structure : array_like or sparse matrix of shape (m, n). A zero element means that a corresponding element of the Jacobian identically equals to zero. * groups : array_like of shape (n,). A column grouping for a given sparsity structure, use `group_columns` to obtain it. A single array or a sparse matrix is interpreted as a sparsity structure, and groups are computed inside the function. A tuple is interpreted as (structure, groups). If None (default), a standard dense differencing will be used. Note, that sparse differencing makes sense only for large Jacobian matrices where each row contains few non-zero elements. as_linear_operator : bool, optional When True the function returns an `scipy.sparse.linalg.LinearOperator`. Otherwise it returns a dense array or a sparse matrix depending on `sparsity`. The linear operator provides an efficient way of computing ``J.dot(p)`` for any vector ``p`` of shape (n,), but does not allow direct access to individual elements of the matrix. By default `as_linear_operator` is False. args, kwargs : tuple and dict, optional Additional arguments passed to `fun`. Both empty by default. The calling signature is ``fun(x, *args, **kwargs)``. Returns ------- J : {ndarray, sparse matrix, LinearOperator} Finite difference approximation of the Jacobian matrix. If `as_linear_operator` is True returns a LinearOperator with shape (m, n). Otherwise it returns a dense array or sparse matrix depending on how `sparsity` is defined. If `sparsity` is None then a ndarray with shape (m, n) is returned. If `sparsity` is not None returns a csr_matrix with shape (m, n). For sparse matrices and linear operators it is always returned as a 2-D structure, for ndarrays, if m=1 it is returned as a 1-D gradient array with shape (n,). See Also -------- check_derivative : Check correctness of a function computing derivatives. Notes ----- If `rel_step` is not provided, it assigned to ``EPS**(1/s)``, where EPS is machine epsilon for float64 numbers, s=2 for '2-point' method and s=3 for '3-point' method. Such relative step approximately minimizes a sum of truncation and round-off errors, see [1]_. A finite difference scheme for '3-point' method is selected automatically. The well-known central difference scheme is used for points sufficiently far from the boundary, and 3-point forward or backward scheme is used for points near the boundary. Both schemes have the second-order accuracy in terms of Taylor expansion. Refer to [2]_ for the formulas of 3-point forward and backward difference schemes. For dense differencing when m=1 Jacobian is returned with a shape (n,), on the other hand when n=1 Jacobian is returned with a shape (m, 1). Our motivation is the following: a) It handles a case of gradient computation (m=1) in a conventional way. b) It clearly separates these two different cases. b) In all cases np.atleast_2d can be called to get 2-D Jacobian with correct dimensions. References ---------- .. [1] W. H. Press et. al. "Numerical Recipes. The Art of Scientific Computing. 3rd edition", sec. 5.7. .. [2] <NAME>, <NAME>, and <NAME>, "On the estimation of sparse Jacobian matrices", Journal of the Institute of Mathematics and its Applications, 13 (1974), pp. 117-120. .. [3] <NAME>, "Generation of Finite Difference Formulas on Arbitrarily Spaced Grids", Mathematics of Computation 51, 1988. Examples -------- >>> import numpy as np >>> from scipy.optimize import approx_derivative >>> >>> def f(x, c1, c2): ... return np.array([x[0] * np.sin(c1 * x[1]), ... x[0] * np.cos(c2 * x[1])]) ... >>> x0 = np.array([1.0, 0.5 * np.pi]) >>> approx_derivative(f, x0, args=(1, 2)) array([[ 1., 0.], [-1., 0.]]) Bounds can be used to limit the region of function evaluation. In the example below we compute left and right derivative at point 1.0. >>> def g(x): ... return x**2 if x >= 1 else x ... >>> x0 = 1.0 >>> approx_derivative(g, x0, bounds=(-np.inf, 1.0)) array([ 1.]) >>> approx_derivative(g, x0, bounds=(1.0, np.inf)) array([ 2.]) """ if method not in ['2-point', '3-point', 'cs']: raise ValueError("Unknown method '%s'. " % method) x0 = np.atleast_1d(x0) if x0.ndim > 1: raise ValueError("`x0` must have at most 1 dimension.") lb, ub = _prepare_bounds(bounds, x0) if lb.shape != x0.shape or ub.shape != x0.shape: raise ValueError("Inconsistent shapes between bounds and `x0`.") if as_linear_operator and not (np.all(np.isinf(lb)) and np.all(np.isinf(ub))): raise ValueError("Bounds not supported when " "`as_linear_operator` is True.") def fun_wrapped(x): f = np.atleast_1d(fun(x, *args, **kwargs)) if f.ndim > 1: raise RuntimeError("`fun` return value has " "more than 1 dimension.") return f if f0 is None: f0 = fun_wrapped(x0) else: f0 = np.atleast_1d(f0) if f0.ndim > 1: raise ValueError("`f0` passed has more than 1 dimension.") if

np.any((x0 < lb) | (x0 > ub))

numpy.any

############################################################################### # @todo add Pilot2-splash-app disclaimer ############################################################################### """ Get's KRAS states """ import MDAnalysis as mda from MDAnalysis.analysis import align from MDAnalysis.lib.mdamath import make_whole import os import numpy as np import math ############## Below section needs to be uncommented ############ import mummi_core import mummi_ras from mummi_core.utils import Naming # # Logger has to be initialized the first thing in the script from logging import getLogger LOGGER = getLogger(__name__) # # Innitilize MuMMI if it has not been done before # MUMMI_ROOT = mummi.init(True) # This is needed so the Naming works below #@TODO fix this so we don't have these on import make them as an init mummi_core.init() dirKRASStates = Naming.dir_res('states') dirKRASStructures = Naming.dir_res('structures') # #RAS_ONLY_macrostate = np.loadtxt(os.path.join(dirKRASStates, "RAS-ONLY.microstates.txt")) RAS_ONLY_macrostate = np.loadtxt(os.path.join(dirKRASStates, "ras-states.txt"),comments='#') # #RAS_RAF_macrostate = np.loadtxt(os.path.join(dirKRASStates, "RAS-RAF.microstates.txt")) RAS_RAF_macrostate = np.loadtxt(os.path.join(dirKRASStates, "ras-raf-states.txt"),comments='#') # Note diffrent number of columns so index change below # TODO: CS, my edits to test # RAS_ONLY_macrostate = np.loadtxt('ras-states.txt') # RAS_RAF_macrostate = np.loadtxt('ras-raf-states.txt') ############## above section needs to be uncommented ############ # TODO: CS, my edits to test # TODO: TSC, The reference structure has to currently be set as the 'RAS-ONLY-reference-structure.gro' # TODO: TSC, path to the reference structure is: mummi_resources/structures/ kras_ref_universe = mda.Universe(os.path.join(dirKRASStructures, "RAS-ONLY-reference-structure.gro")) # kras_ref_universe = mda.Universe("RAS-ONLY-reference-structure.gro") # kras_ref_universe = mda.Universe('AA_pfpatch_000000004641_RAS_RAF2_411.gro') # TODO: CS, not using these for x4 proteins; instead using protein_systems below to set num_res ######### Below hard codes the number of residues within RAS-only and RAS-RAF ########## RAS_only_num_res = 184 RAS_RAF_num_res = 320 ######### Above hard codes the number of residues within RAS-only and RAS-RAF ########## ####### This can be removed # def get_kras(syst, kras_start): # """Gets all atoms for a KRAS protein starting at 'kras_start'.""" # return syst.atoms[kras_start:kras_start+428] ####### This can be removed def get_segids(u): """Identifies the list of segments within the system. Only needs to be called x1 time""" segs = u.segments segs = segs.segids ras_segids = [] rasraf_segids = [] for i in range(len(segs)): # print(segs[i]) if segs[i][-3:] == 'RAS': ras_segids.append(segs[i]) if segs[i][-3:] == 'RAF': rasraf_segids.append(segs[i]) return ras_segids, rasraf_segids def get_protein_info(u,tag): """Uses the segments identified in get_segids to make a list of all proteins in the systems.\ Outputs a list of the first residue number of the protein, and whether it is 'RAS-ONLY', or 'RAS-RAF'.\ The 'tag' input defines what is used to identify the first residue of the protein. i.e. 'resname ACE1 and name BB'.\ Only needs to be called x1 time""" ras_segids, rasraf_segids = get_segids(u) if len(ras_segids) > 0: RAS = u.select_atoms('segid '+ras_segids[0]+' and '+str(tag)) else: RAS = [] if len(rasraf_segids) > 0: RAF = u.select_atoms('segid '+rasraf_segids[0]+' and '+str(tag)) else: RAF = [] protein_info = []#np.empty([len(RAS)+len(RAF),2]) for i in range(len(RAS)): protein_info.append((RAS[i].resid,'RAS-ONLY')) for i in range(len(RAF)): protein_info.append((RAF[i].resid,'RAS-RAF')) ######## sort protein info protein_info = sorted(protein_info) ######## sort protein info return protein_info def get_ref_kras(): """Gets the reference KRAS struct. Only called x1 time when class is loaded""" start_of_g_ref = kras_ref_universe.residues[0].resid ref_selection = 'resid '+str(start_of_g_ref)+':'+str(start_of_g_ref+24)+' ' +\ str(start_of_g_ref+38)+':'+str(start_of_g_ref+54)+' ' +\ str(start_of_g_ref+67)+':'+str(start_of_g_ref+164)+' ' +\ 'and (name CA or name BB)' r2_26r40_56r69_166_ref = kras_ref_universe.select_atoms(str(ref_selection)) return kras_ref_universe.select_atoms(str(ref_selection)).positions - kras_ref_universe.select_atoms(str(ref_selection)).center_of_mass() # Load inital ref frames (only need to do this once) ref0 = get_ref_kras() def getKRASstates(u,kras_indices): """Gets states for all KRAS proteins in path.""" # res_shift = 8 # all_glycine = u.select_atoms("resname GLY") # kras_indices = [] # for i in range(0, len(all_glycine), 26): # kras_indices.append(all_glycine[i].index) ########## Below is taken out of the function so it is only done once ######### # kras_indices = get_protein_info(u,'resname ACE1 and name BB') ########## Above is taken out of the function so it is only done once ######### # CS, for x4 cases: # [{protein_x4: (protein_type, num_res)}] protein_systems = [{'ras4a': ('RAS-ONLY', 185), 'ras4araf': ('RAS-RAF', 321), 'ras': ('RAS-ONLY', 184), 'rasraf': ('RAS-RAF', 320)}] ALLOUT = [] for k in range(len(kras_indices)): start_of_g = kras_indices[k][0] protein_x4 = str(kras_indices[k][1]) try: protein_type = [item[protein_x4] for item in protein_systems][0][0] # 'RAS-ONLY' OR 'RAS-RAF' num_res = [item[protein_x4] for item in protein_systems][0][1] except: LOGGER.error('Check KRas naming between modules') raise Exception('Error: unknown KRas name') # TODO: CS, replacing this comment section with the above, to handle x4 protein types # --------------------------------------- # ALLOUT = [] # for k in range(len(kras_indices)): # start_of_g = kras_indices[k][0] # protein_type = str(kras_indices[k][1]) # ########## BELOW SECTION TO DETERMINE WHICH RESIDUES ARE PART OF THE PROTEIN GROUP - NEEDED FOR PBC REMOVAL ############## # ########## POTENTIALLY REDO WITH A 'HARD-CODED' NUMBER OF RESIDUES PER PROTEIN GROUP (WHETHER RAS-ONLY OR RAS-RAF) ####### # ########## HAS BEEN REDONE WITH A 'HARD-CODED' NUMBER OF RESIDUES PER PROTEIN GROUP (WHETHER RAS-ONLY OR RAS-RAF) ######## # # if len(kras_indices) == 1: # # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(len(u.residues))+' and name BB') ####### HAS TO BE FIXED FOR BACKBONE ATOMS FOR SPECIFIC PROTEIN # # elif len(kras_indices) > 1: # # if k == len(kras_indices)-1: # # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(len(u.residues))+' and name BB') # # else: # # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(kras_indices[k+1][0])+' and name BB') # ########## ABOVE SECTION TO DETERMINE WHICH RESIDUES ARE PART OF THE PROTEIN GROUP - NEEDED FOR PBC REMOVAL ############## # # ########## Below hard codes the number of residues/beads in the RAS-ONLY and RAS-RAF simulations ######################### # if protein_type == 'RAS-ONLY': # num_res = RAS_only_num_res # elif protein_type == 'RAS-RAF': # num_res = RAS_RAF_num_res # ########## Above hard codes the number of residues/beads in the RAS-ONLY and RAS-RAF simulations ######################### # --------------------------------------- # TODO: TSC, I changed the selection below, which can be used for the make_whole... # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+num_res)+' and (name CA or name BB)') krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+num_res)) krases0_BB.guess_bonds() r2_26r40_56r69_166 = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+24)+' ' +\ str(start_of_g+38)+':'+str(start_of_g+54)+' ' +\ str(start_of_g+67)+':'+str(start_of_g+164)+\ ' and (name CA or name BB)') u_selection = \ 'resid '+str(start_of_g)+':'+str(start_of_g+24)+' '+str(start_of_g+38)+':'+str(start_of_g+54)+' ' +\ str(start_of_g+67)+':'+str(start_of_g+164)+' and (name CA or name BB)' mobile0 = u.select_atoms(str(u_selection)).positions - u.select_atoms(str(u_selection)).center_of_mass() # TODO: CS, something wrong with ref0 from get_kras_ref() # just making ref0 = mobile0 to test for now # ref0 = mobile0 # TSC removed this R, RMSD_junk = align.rotation_matrix(mobile0, ref0) ######## TODO: TSC, Adjusted for AA lipid names ######## # lipids = u.select_atoms('resname POPX POPC PAPC POPE DIPE DPSM PAPS PAP6 CHOL') lipids = u.select_atoms('resname POPC PAPC POPE DIPE SSM PAPS SAPI CHL1') coords = ref0 RotMat = [] OS = [] r152_165 = krases0_BB.select_atoms('resid '+str(start_of_g+150)+':'+str(start_of_g+163)+' and (name CA or name BB)') r65_74 = krases0_BB.select_atoms('resid '+str(start_of_g+63)+':'+str(start_of_g+72)+' and (name CA or name BB)') timeframes = [] # TODO: CS, for AA need bonds to run make_whole() # krases0_BB.guess_bonds() # TODO: CS, turn off for now to test beyond this point ''' *** for AA, need to bring that back on once all else runs *** ''' # @Tim and <NAME>. this was commented out - please check. #make_whole(krases0_BB) j, rmsd_junk = mda.analysis.align.rotation_matrix((r2_26r40_56r69_166.positions-r2_26r40_56r69_166.center_of_mass()), coords) RotMat.append(j) OS.append(r65_74.center_of_mass()-r152_165.center_of_mass()) timeframes.append(u.trajectory.time) if protein_type == 'RAS-RAF': z_pos = [] ############### NEED TO CONFIRM THE SELECTION OF THE RAF LOOP RESIDUES BELOW #################### ############### TODO: TSC, zshifting is set to -1 (instead of -2), as there are ACE caps that are separate residues in AA #zshifting=-1 if protein_x4 == 'rasraf': zshifting = -1 elif protein_x4 == 'ras4araf': zshifting = 0 else: zshifting = 0 LOGGER.error('Found unsupported protein_x4 type') raf_loops_selection = u.select_atoms('resid '+str(start_of_g+zshifting+291)+':'+str(start_of_g+zshifting+294)+' ' +\ str(start_of_g+zshifting+278)+':'+str(start_of_g+zshifting+281)+' ' +\ ' and (name CA or name BB)') ############### NEED TO CONFIRM THE SELECTION OF THE RAF LOOP RESIDUES ABOVE #################### diff = (lipids.center_of_mass()[2]-raf_loops_selection.center_of_mass(unwrap=True)[2])/10 if diff < 0: diff = diff+(u.dimensions[2]/10) z_pos.append(diff) z_pos = np.array(z_pos) RotMatNP = np.array(RotMat) OS = np.array(OS) OA = RotMatNP[:, 2, :]/(((RotMatNP[:, 2, 0]**2)+(RotMatNP[:, 2, 1]**2)+(RotMatNP[:, 2, 2]**2))**0.5)[:, None] OWAS = np.arccos(RotMatNP[:, 2, 2])*180/math.pi OC_temp = np.concatenate((OA, OS), axis=1) t = ((OC_temp[:, 0]*OC_temp[:, 3])+(OC_temp[:, 1]*OC_temp[:, 4]) + (OC_temp[:, 2]*OC_temp[:, 5]))/((OC_temp[:, 0]**2)+(OC_temp[:, 1]**2)+(OC_temp[:, 2]**2)) OC = OA*t[:, None] ORS_tp = np.concatenate((OC, OS), axis=1) ORS_norm = (((ORS_tp[:, 3]-ORS_tp[:, 0])**2)+((ORS_tp[:, 4]-ORS_tp[:, 1])**2)+((ORS_tp[:, 5]-ORS_tp[:, 2])**2))**0.5 ORS = (OS - OC)/ORS_norm[:, None] OACRS = np.cross(OA, ORS) OZCA = OA * OA[:, 2][:, None] Z_unit = np.full([len(OZCA), 3], 1) Z_adjust =

np.array([0, 0, 1])

numpy.array

import os import sys import click import pickle import sncosmo import numpy as np from astropy.table import Table DATA_PATH = '/home/samdixon/jla_light_curves/' def modify_error(lc, error_floor=0.): """Add an error floor of `error_floor` times the maximum flux of the band to each observation """ data = sncosmo.photdata.photometric_data(lc).normalized(zp=25., zpsys='ab') new_lc = {'time': data.time, 'band': data.band, 'flux': data.flux, 'fluxerr': data.fluxerr, 'zp': data.zp, 'zpsys': data.zpsys} for band in set(data.band): band_cut = data.band==band max_flux_in_band =

np.max(data.flux[band_cut])

numpy.max

import os import numpy as np import cv2 import albumentations from PIL import Image from torch.utils.data import Dataset from taming.data.sflckr import SegmentationBase # for examples included in repo class Examples(SegmentationBase): def __init__(self, size=256, random_crop=False, interpolation="bicubic"): super().__init__(data_csv="data/ade20k_examples.txt", data_root="data/ade20k_images", segmentation_root="data/ade20k_segmentations", size=size, random_crop=random_crop, interpolation=interpolation, n_labels=151, shift_segmentation=False) # With semantic map and scene label class ADE20kBase(Dataset): def __init__(self, config=None, size=None, random_crop=False, interpolation="bicubic", crop_size=None): self.split = self.get_split() self.n_labels = 151 # unknown + 150 self.data_csv = {"train": "data/ade20k_train.txt", "validation": "data/ade20k_test.txt"}[self.split] self.data_root = "./data/ade20k_root" with open(os.path.join(self.data_root, "sceneCategories.txt"), "r") as f: self.scene_categories = f.read().splitlines() self.scene_categories = dict(line.split() for line in self.scene_categories) with open(self.data_csv, "r") as f: self.image_paths = f.read().splitlines() self._length = len(self.image_paths) ss = self.split if ss=='train': ss='training' self.labels = { "relative_file_path_": [l for l in self.image_paths], "file_path_": [os.path.join(self.data_root, "images",ss, l) for l in self.image_paths], "relative_segmentation_path_": [l.replace(".jpg", ".png") for l in self.image_paths], "segmentation_path_": [os.path.join(self.data_root, "annotations",ss, l.replace(".jpg", ".png")) for l in self.image_paths], "scene_category": [self.scene_categories[l.replace(".jpg", "")] for l in self.image_paths], } size = None if size is not None and size<=0 else size self.size = size if crop_size is None: self.crop_size = size if size is not None else None else: self.crop_size = crop_size if self.size is not None: self.interpolation = interpolation self.interpolation = { "nearest": cv2.INTER_NEAREST, "bilinear": cv2.INTER_LINEAR, "bicubic": cv2.INTER_CUBIC, "area": cv2.INTER_AREA, "lanczos": cv2.INTER_LANCZOS4}[self.interpolation] self.image_rescaler = albumentations.SmallestMaxSize(max_size=self.size, interpolation=self.interpolation) self.segmentation_rescaler = albumentations.SmallestMaxSize(max_size=self.size, interpolation=cv2.INTER_NEAREST) if crop_size is not None: self.center_crop = not random_crop if self.center_crop: self.cropper = albumentations.CenterCrop(height=self.crop_size, width=self.crop_size) else: self.cropper = albumentations.RandomCrop(height=self.crop_size, width=self.crop_size) self.preprocessor = self.cropper def __len__(self): return self._length def __getitem__(self, i): example = dict((k, self.labels[k][i]) for k in self.labels) image = Image.open(example["file_path_"]) if not image.mode == "RGB": image = image.convert("RGB") image = np.array(image).astype(np.uint8) if self.size is not None: image = self.image_rescaler(image=image)["image"] segmentation = Image.open(example["segmentation_path_"]) segmentation =

np.array(segmentation)

numpy.array

"""Bindings for the Barnes Hut TSNE algorithm with fast nearest neighbors Refs: References [1] <NAME>, L.J.P.; Hinton, G.E. Visualizing High-Dimensional Data Using t-SNE. Journal of Machine Learning Research 9:2579-2605, 2008. [2] <NAME>, L.J.P. t-Distributed Stochastic Neighbor Embedding http://homepage.tudelft.nl/19j49/t-SNE.html """ import numpy as N import ctypes import os import pkg_resources def ord_string(s): b = bytearray() arr = b.extend(map(ord, s)) return N.array([x for x in b] + [0]).astype(N.uint8) class TSNE(object): def __init__(self, n_components=2, perplexity=50.0, early_exaggeration=2.0, learning_rate=200.0, num_neighbors=1023, force_magnify_iters=250, pre_momentum=0.5, post_momentum=0.8, theta=0.5, epssq=0.0025, n_iter=1000, n_iter_without_progress=1000, min_grad_norm=1e-7, perplexity_epsilon=1e-3, metric='euclidean', init='random', return_style='once', num_snapshots=5, verbose=0, random_seed=None, use_interactive=False, viz_timeout=10000, viz_server="tcp://localhost:5556", dump_points=False, dump_file="dump.txt", dump_interval=1, print_interval=10, device=0, ): """Initialization method for barnes hut T-SNE class. """ # Initialize the variables self.n_components = int(n_components) if self.n_components != 2: raise ValueError('The current barnes-hut implementation does not support projection into dimensions other than 2 for now.') self.perplexity = float(perplexity) self.early_exaggeration = float(early_exaggeration) self.learning_rate = float(learning_rate) self.n_iter = int(n_iter) self.n_iter_without_progress = int(n_iter_without_progress) self.min_grad_norm = float(min_grad_norm) if metric not in ['euclidean']: raise ValueError('Non-Euclidean metrics are not currently supported. Please use metric=\'euclidean\' for now.') else: self.metric = metric if init not in ['random']: raise ValueError('Non-Random initialization is not currently supported. Please use init=\'random\' for now.') else: self.init = init self.verbose = int(verbose) # Initialize non-sklearn variables self.num_neighbors = int(num_neighbors) self.force_magnify_iters = int(force_magnify_iters) self.perplexity_epsilon = float(perplexity_epsilon) self.pre_momentum = float(pre_momentum) self.post_momentum = float(post_momentum) self.theta = float(theta) self.epssq =float(epssq) self.device = int(device) self.print_interval = int(print_interval) # Point dumpoing self.dump_file = str(dump_file) self.dump_points = bool(dump_points) self.dump_interval = int(dump_interval) # Viz self.use_interactive = bool(use_interactive) self.viz_server = str(viz_server) self.viz_timeout = int(viz_timeout) # Return style if return_style not in ['once','snapshots']: raise ValueError('Invalid return style...') elif return_style == 'once': self.return_style = 0 elif return_style == 'snapshots': self.return_style = 1 self.num_snapshots = int(num_snapshots) # Build the hooks for the BH T-SNE library self._path = pkg_resources.resource_filename('tsnecuda','') # Load from current location # self._faiss_lib = N.ctypeslib.load_library('libfaiss', self._path) # Load the ctypes library # self._gpufaiss_lib = N.ctypeslib.load_library('libgpufaiss', self._path) # Load the ctypes library self._lib = N.ctypeslib.load_library('libtsnecuda', self._path) # Load the ctypes library # Hook the BH T-SNE function self._lib.pymodule_bh_tsne.restype = None self._lib.pymodule_bh_tsne.argtypes = [

N.ctypeslib.ndpointer(N.float32, ndim=2, flags='ALIGNED, F_CONTIGUOUS, WRITEABLE')

numpy.ctypeslib.ndpointer

''' ------------------------------------------------------------------------------------------------- This code accompanies the paper titled "Human injury-based safety decision of automated vehicles" Author: <NAME>, <NAME>, <NAME>, <NAME> Corresponding author: <NAME> (<EMAIL>) ------------------------------------------------------------------------------------------------- ''' import torch import numpy as np from torch import nn from torch.nn.utils import weight_norm __author__ = "<NAME>" def Collision_cond(veh_striking_list, V1_v, V2_v, delta_angle, veh_param): ''' Estimate the collision condition. ''' (veh_l, veh_w, veh_cgf, veh_cgs, veh_k, veh_m) = veh_param delta_angle_2 = np.arccos(np.abs(np.cos(delta_angle))) if -1e-6 < delta_angle_2 < 1e-6: delta_angle_2 = 1e-6 delta_v1_list = [] delta_v2_list = [] # Estimate the collision condition (delat-v) according to the principal impact direction. for veh_striking in veh_striking_list: if veh_striking[0] == 1: veh_ca = np.arctan(veh_cgf[0] / veh_cgs[0]) veh_a2 = np.abs(veh_cgs[1] - veh_striking[3]) veh_RDS = np.abs(V1_v * np.cos(delta_angle) - V2_v) veh_a1 = np.abs(np.sqrt(veh_cgf[0] ** 2 + veh_cgs[0] ** 2) * np.cos(veh_ca + delta_angle_2)) if (veh_striking[1]+1) in [16, 1, 2, 3, 17, 20, 21] and (veh_striking[2]+1) in [16, 1, 2, 3, 17, 20, 21]: veh_e = 2 / veh_RDS else: veh_e = 0.5 / veh_RDS elif veh_striking[0] == 2: veh_ca = np.arctan(veh_cgf[0] / veh_cgs[0]) veh_a2 = np.abs(veh_cgf[1] - veh_striking[3]) veh_a1 = np.abs(np.sqrt(veh_cgf[0] ** 2 + veh_cgs[0] ** 2) * np.cos(delta_angle_2 - veh_ca + np.pi / 2)) veh_RDS = V1_v * np.sin(delta_angle_2) veh_e = 1.5 / veh_RDS elif veh_striking[0] == 3: veh_ca =

np.arctan(veh_cgf[1] / veh_cgs[1])

numpy.arctan

import gym import numpy as np from itertools import product import matplotlib.pyplot as plt def print_policy(Q, env): """ This is a helper function to print a nice policy from the Q function""" moves = [u'←', u'↓',u'→', u'↑'] if not hasattr(env, 'desc'): env = env.env dims = env.desc.shape policy = np.chararray(dims, unicode=True) policy[:] = ' ' for s in range(len(Q)): idx = np.unravel_index(s, dims) policy[idx] = moves[np.argmax(Q[s])] if env.desc[idx] in ['H', 'G']: policy[idx] = u'·' print('\n'.join([''.join([u'{:2}'.format(item) for item in row]) for row in policy])) def plot_V(Q, env): """ This is a helper function to plot the state values from the Q function""" fig = plt.figure() if not hasattr(env, 'desc'): env = env.env dims = env.desc.shape V = np.zeros(dims) for s in range(len(Q)): idx = np.unravel_index(s, dims) V[idx] = np.max(Q[s]) if env.desc[idx] in ['H', 'G']: V[idx] = 0. plt.imshow(V, origin='upper', extent=[0,dims[0],0,dims[1]], vmin=.0, vmax=.6, cmap=plt.cm.RdYlGn, interpolation='none') for x, y in product(range(dims[0]), range(dims[1])): plt.text(y+0.5, dims[0]-x-0.5, '{:.3f}'.format(V[x,y]), horizontalalignment='center', verticalalignment='center') plt.xticks([]) plt.yticks([]) def plot_Q(Q, env): """ This is a helper function to plot the Q function """ from matplotlib import colors, patches fig = plt.figure() ax = fig.gca() if not hasattr(env, 'desc'): env = env.env dims = env.desc.shape up = np.array([[0, 1], [0.5, 0.5], [1,1]]) down =

np.array([[0, 0], [0.5, 0.5], [1,0]])

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') plt.savefig('jss_figures/DFA_different_trends.png') plt.show() # plot 6b fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[0].set_ylim(-5.5, 5.5) axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].set_ylim(-5.5, 5.5) axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([np.pi, (3 / 2) * np.pi]) axs[2].set_xticklabels([r'$\pi$', r'$\frac{3}{2}\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].set_ylim(-5.5, 5.5) axs[2].set_xlim(0.95 * np.pi, 1.55 * np.pi) plt.savefig('jss_figures/DFA_different_trends_zoomed.png') plt.show() hs_ouputs = hilbert_spectrum(time, imfs_51, hts_51, ifs_51, max_frequency=12, plot=False) # plot 6c ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Simple Sinusoidal Time Seres with Added Noise', 50)) x_hs, y, z = hs_ouputs z_min, z_max = 0, np.abs(z).max() ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) ax.plot(x_hs[0, :], 8 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 8$', Linewidth=3) ax.plot(x_hs[0, :], 4 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 4$', Linewidth=3) ax.plot(x_hs[0, :], 2 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 2$', Linewidth=3) ax.set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi]) ax.set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$']) plt.ylabel(r'Frequency (rad.s$^{-1}$)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.85, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/DFA_hilbert_spectrum.png') plt.show() # plot 6c time = np.linspace(0, 5 * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 51) fluc = Fluctuation(time=time, time_series=time_series) max_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=False) max_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=True) min_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=False) min_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=True) util = Utility(time=time, time_series=time_series) maxima = util.max_bool_func_1st_order_fd() minima = util.min_bool_func_1st_order_fd() ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title(textwrap.fill('Plot Demonstrating Unsmoothed Extrema Envelopes if Schoenberg–Whitney Conditions are Not Satisfied', 50)) plt.plot(time, time_series, label='Time series', zorder=2, LineWidth=2) plt.scatter(time[maxima], time_series[maxima], c='r', label='Maxima', zorder=10) plt.scatter(time[minima], time_series[minima], c='b', label='Minima', zorder=10) plt.plot(time, max_unsmoothed[0], label=textwrap.fill('Unsmoothed maxima envelope', 10), c='darkorange') plt.plot(time, max_smoothed[0], label=textwrap.fill('Smoothed maxima envelope', 10), c='red') plt.plot(time, min_unsmoothed[0], label=textwrap.fill('Unsmoothed minima envelope', 10), c='cyan') plt.plot(time, min_smoothed[0], label=textwrap.fill('Smoothed minima envelope', 10), c='blue') for knot in knots[:-1]: plt.plot(knot * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', zorder=1) plt.plot(knots[-1] * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', label='Knots', zorder=1) plt.xticks((0, 1 * np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi), (r'$0$', r'$\pi$', r'2$\pi$', r'3$\pi$', r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) plt.xlim(-0.25 * np.pi, 5.25 * np.pi) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Schoenberg_Whitney_Conditions.png') plt.show() # plot 7 a = 0.25 width = 0.2 time = np.linspace((0 + a) * np.pi, (5 - a) * np.pi, 1001) knots = np.linspace((0 + a) * np.pi, (5 - a) * np.pi, 11) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] inflection_bool = utils.inflection_point() inflection_x = time[inflection_bool] inflection_y = time_series[inflection_bool] fluctuation = emd_mean.Fluctuation(time=time, time_series=time_series) maxima_envelope = fluctuation.envelope_basis_function_approximation(knots, 'maxima', smooth=False, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] maxima_envelope_smooth = fluctuation.envelope_basis_function_approximation(knots, 'maxima', smooth=True, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] minima_envelope = fluctuation.envelope_basis_function_approximation(knots, 'minima', smooth=False, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] minima_envelope_smooth = fluctuation.envelope_basis_function_approximation(knots, 'minima', smooth=True, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] inflection_points_envelope = fluctuation.direct_detrended_fluctuation_estimation(knots, smooth=True, smoothing_penalty=0.2, technique='inflection_points')[0] binomial_points_envelope = fluctuation.direct_detrended_fluctuation_estimation(knots, smooth=True, smoothing_penalty=0.2, technique='binomial_average', order=21, increment=20)[0] derivative_of_lsq = utils.derivative_forward_diff() derivative_time = time[:-1] derivative_knots = np.linspace(knots[0], knots[-1], 31) # change (1) detrended_fluctuation_technique and (2) max_internal_iter and (3) debug (confusing with external debugging) emd = AdvEMDpy.EMD(time=derivative_time, time_series=derivative_of_lsq) imf_1_of_derivative = emd.empirical_mode_decomposition(knots=derivative_knots, knot_time=derivative_time, text=False, verbose=False)[0][1, :] utils = emd_utils.Utility(time=time[:-1], time_series=imf_1_of_derivative) optimal_maxima = np.r_[False, utils.derivative_forward_diff() < 0, False] & \ np.r_[utils.zero_crossing() == 1, False] optimal_minima = np.r_[False, utils.derivative_forward_diff() > 0, False] & \ np.r_[utils.zero_crossing() == 1, False] EEMD_maxima_envelope = fluctuation.envelope_basis_function_approximation_fixed_points(knots, 'maxima', optimal_maxima, optimal_minima, smooth=False, smoothing_penalty=0.2, edge_effect='none')[0] EEMD_minima_envelope = fluctuation.envelope_basis_function_approximation_fixed_points(knots, 'minima', optimal_maxima, optimal_minima, smooth=False, smoothing_penalty=0.2, edge_effect='none')[0] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Detrended Fluctuation Analysis Examples') plt.plot(time, time_series, LineWidth=2, label='Time series') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(time[optimal_maxima], time_series[optimal_maxima], c='darkred', zorder=4, label=textwrap.fill('Optimal maxima', 10)) plt.scatter(time[optimal_minima], time_series[optimal_minima], c='darkblue', zorder=4, label=textwrap.fill('Optimal minima', 10)) plt.scatter(inflection_x, inflection_y, c='magenta', zorder=4, label=textwrap.fill('Inflection points', 10)) plt.plot(time, maxima_envelope, c='darkblue', label=textwrap.fill('EMD envelope', 10)) plt.plot(time, minima_envelope, c='darkblue') plt.plot(time, (maxima_envelope + minima_envelope) / 2, c='darkblue') plt.plot(time, maxima_envelope_smooth, c='darkred', label=textwrap.fill('SEMD envelope', 10)) plt.plot(time, minima_envelope_smooth, c='darkred') plt.plot(time, (maxima_envelope_smooth + minima_envelope_smooth) / 2, c='darkred') plt.plot(time, EEMD_maxima_envelope, c='darkgreen', label=textwrap.fill('EEMD envelope', 10)) plt.plot(time, EEMD_minima_envelope, c='darkgreen') plt.plot(time, (EEMD_maxima_envelope + EEMD_minima_envelope) / 2, c='darkgreen') plt.plot(time, inflection_points_envelope, c='darkorange', label=textwrap.fill('Inflection point envelope', 10)) plt.plot(time, binomial_points_envelope, c='deeppink', label=textwrap.fill('Binomial average envelope', 10)) plt.plot(time, np.cos(time), c='black', label='True mean') plt.xticks((0, 1 * np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi), (r'$0$', r'$\pi$', r'2$\pi$', r'3$\pi$', r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) plt.xlim(-0.25 * np.pi, 5.25 * np.pi) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/detrended_fluctuation_analysis.png') plt.show() # Duffing Equation Example def duffing_equation(xy, ts): gamma = 0.1 epsilon = 1 omega = ((2 * np.pi) / 25) return [xy[1], xy[0] - epsilon * xy[0] ** 3 + gamma * np.cos(omega * ts)] t = np.linspace(0, 150, 1501) XY0 = [1, 1] solution = odeint(duffing_equation, XY0, t) x = solution[:, 0] dxdt = solution[:, 1] x_points = [0, 50, 100, 150] x_names = {0, 50, 100, 150} y_points_1 = [-2, 0, 2] y_points_2 = [-1, 0, 1] fig, axs = plt.subplots(2, 1) plt.subplots_adjust(hspace=0.2) axs[0].plot(t, x) axs[0].set_title('Duffing Equation Displacement') axs[0].set_ylim([-2, 2]) axs[0].set_xlim([0, 150]) axs[1].plot(t, dxdt) axs[1].set_title('Duffing Equation Velocity') axs[1].set_ylim([-1.5, 1.5]) axs[1].set_xlim([0, 150]) axis = 0 for ax in axs.flat: ax.label_outer() if axis == 0: ax.set_ylabel('x(t)') ax.set_yticks(y_points_1) if axis == 1: ax.set_ylabel(r'$ \dfrac{dx(t)}{dt} $') ax.set(xlabel='t') ax.set_yticks(y_points_2) ax.set_xticks(x_points) ax.set_xticklabels(x_names) axis += 1 plt.savefig('jss_figures/Duffing_equation.png') plt.show() # compare other packages Duffing - top pyemd = pyemd0215() py_emd = pyemd(x) IP, IF, IA = emd040.spectra.frequency_transform(py_emd.T, 10, 'hilbert') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 0.2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using PyEMD 0.2.10', 40)) plt.pcolormesh(t, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht_pyemd.png') plt.show() plt.show() emd_sift = emd040.sift.sift(x) IP, IF, IA = emd040.spectra.frequency_transform(emd_sift, 10, 'hilbert') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 0.2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using emd 0.3.3', 40)) plt.pcolormesh(t, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht_emd.png') plt.show() # compare other packages Duffing - bottom emd_duffing = AdvEMDpy.EMD(time=t, time_series=x) emd_duff, emd_ht_duff, emd_if_duff, _, _, _, _ = emd_duffing.empirical_mode_decomposition(verbose=False) fig, axs = plt.subplots(2, 1) plt.subplots_adjust(hspace=0.3) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) axs[0].plot(t, emd_duff[1, :], label='AdvEMDpy') axs[0].plot(t, py_emd[0, :], '--', label='PyEMD 0.2.10') axs[0].plot(t, emd_sift[:, 0], '--', label='emd 0.3.3') axs[0].set_title('IMF 1') axs[0].set_ylim([-2, 2]) axs[0].set_xlim([0, 150]) axs[1].plot(t, emd_duff[2, :], label='AdvEMDpy') print(f'AdvEMDpy driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - emd_duff[2, :])), 3)}') axs[1].plot(t, py_emd[1, :], '--', label='PyEMD 0.2.10') print(f'PyEMD driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - py_emd[1, :])), 3)}') axs[1].plot(t, emd_sift[:, 1], '--', label='emd 0.3.3') print(f'emd driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - emd_sift[:, 1])), 3)}') axs[1].plot(t, 0.1 * np.cos(0.04 * 2 * np.pi * t), '--', label=r'$0.1$cos$(0.08{\pi}t)$') axs[1].set_title('IMF 2') axs[1].set_ylim([-0.2, 0.4]) axs[1].set_xlim([0, 150]) axis = 0 for ax in axs.flat: ax.label_outer() if axis == 0: ax.set_ylabel(r'$\gamma_1(t)$') ax.set_yticks([-2, 0, 2]) if axis == 1: ax.set_ylabel(r'$\gamma_2(t)$') ax.set_yticks([-0.2, 0, 0.2]) box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) ax.set_xticks(x_points) ax.set_xticklabels(x_names) axis += 1 plt.savefig('jss_figures/Duffing_equation_imfs.png') plt.show() hs_ouputs = hilbert_spectrum(t, emd_duff, emd_ht_duff, emd_if_duff, max_frequency=1.3, plot=False) ax = plt.subplot(111) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using AdvEMDpy', 40)) x, y, z = hs_ouputs y = y / (2 * np.pi) z_min, z_max = 0, np.abs(z).max() figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) ax.pcolormesh(x, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht.png') plt.show() # Carbon Dioxide Concentration Example CO2_data = pd.read_csv('Data/co2_mm_mlo.csv', header=51) plt.plot(CO2_data['month'], CO2_data['decimal date']) plt.title(textwrap.fill('Mean Monthly Concentration of Carbon Dioxide in the Atmosphere', 35)) plt.ylabel('Parts per million') plt.xlabel('Time (years)') plt.savefig('jss_figures/CO2_concentration.png') plt.show() signal = CO2_data['decimal date'] signal = np.asarray(signal) time = CO2_data['month'] time = np.asarray(time) # compare other packages Carbon Dioxide - top pyemd = pyemd0215() py_emd = pyemd(signal) IP, IF, IA = emd040.spectra.frequency_transform(py_emd[:2, :].T, 12, 'hilbert') print(f'PyEMD annual frequency error: {np.round(sum(np.abs(IF[:, 0] - np.ones_like(IF[:, 0]))), 3)}') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using PyEMD 0.2.10', 45)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.pcolormesh(time, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(time, np.ones_like(time), 'k--', label=textwrap.fill('Annual cycle', 10)) box_0 = ax.get_position() ax.set_position([box_0.x0 + 0.0125, box_0.y0 + 0.075, box_0.width * 0.8, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/CO2_Hilbert_pyemd.png') plt.show() emd_sift = emd040.sift.sift(signal) IP, IF, IA = emd040.spectra.frequency_transform(emd_sift[:, :1], 12, 'hilbert') print(f'emd annual frequency error: {np.round(sum(np.abs(IF - np.ones_like(IF)))[0], 3)}') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using emd 0.3.3', 45)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.pcolormesh(time, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(time, np.ones_like(time), 'k--', label=textwrap.fill('Annual cycle', 10)) box_0 = ax.get_position() ax.set_position([box_0.x0 + 0.0125, box_0.y0 + 0.075, box_0.width * 0.8, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/CO2_Hilbert_emd.png') plt.show() # compare other packages Carbon Dioxide - bottom knots = np.linspace(time[0], time[-1], 200) emd_example = AdvEMDpy.EMD(time=time, time_series=signal) imfs, hts, ifs, _, _, _, _ = \ emd_example.empirical_mode_decomposition(knots=knots, knot_time=time, verbose=False) print(f'AdvEMDpy annual frequency error: {np.round(sum(np.abs(ifs[1, :] / (2 * np.pi) - np.ones_like(ifs[1, :]))), 3)}') fig, axs = plt.subplots(2, 2) plt.subplots_adjust(hspace=0.5) axs[0, 0].plot(time, signal) axs[0, 1].plot(time, signal) axs[0, 1].plot(time, imfs[0, :], label='Smoothed') axs[0, 1].legend(loc='lower right') axs[1, 0].plot(time, imfs[1, :]) axs[1, 1].plot(time, imfs[2, :]) axis = 0 for ax in axs.flat: if axis == 0: ax.set(ylabel=R'C0$_2$ concentration') if axis == 1: pass if axis == 2: ax.set(ylabel=R'C0$_2$ concentration') ax.set(xlabel='Time (years)') if axis == 3: ax.set(xlabel='Time (years)') axis += 1 plt.gcf().subplots_adjust(bottom=0.15) axs[0, 0].set_title(r'Original CO$_2$ Concentration') axs[0, 1].set_title('Smoothed CO$_2$ Concentration') axs[1, 0].set_title('IMF 1') axs[1, 1].set_title('Residual') plt.gcf().subplots_adjust(bottom=0.15) plt.savefig('jss_figures/CO2_EMD.png') plt.show() hs_ouputs = hilbert_spectrum(time, imfs, hts, ifs, max_frequency=10, which_imfs=[1], plot=False) x_hs, y, z = hs_ouputs y = y / (2 * np.pi) z_min, z_max = 0, np.abs(z).max() fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.7 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) ax.pcolormesh(x_hs, y,

np.abs(z)

numpy.abs

from __future__ import absolute_import from __future__ import division from __future__ import print_function import cntk as C import numpy as np from .common import floatx, epsilon, image_dim_ordering, image_data_format from collections import defaultdict from contextlib import contextmanager import warnings C.set_global_option('align_axis', 1) b_any = any dev = C.device.use_default_device() if dev.type() == 0: warnings.warn( 'CNTK backend warning: GPU is not detected. ' 'CNTK\'s CPU version is not fully optimized,' 'please run with GPU to get better performance.') # A learning phase is a bool tensor used to run Keras models in # either train mode (learning_phase == 1) or test mode (learning_phase == 0). # LEARNING_PHASE_PLACEHOLDER is the placeholder for dynamic learning phase _LEARNING_PHASE_PLACEHOLDER = C.constant(shape=(), dtype=np.float32, value=1.0, name='_keras_learning_phase') # static learning phase flag, if it is not 0 or 1, we will go with dynamic learning phase tensor. _LEARNING_PHASE = -1 _UID_PREFIXES = defaultdict(int) # cntk doesn't support gradient as symbolic op, to hook up with keras model, # we will create gradient as a constant placeholder, here use this global # map to keep the mapping from grad placeholder to parameter grad_parameter_dict = {} NAME_SCOPE_STACK = [] @contextmanager def name_scope(name): global NAME_SCOPE_STACK NAME_SCOPE_STACK.append(name) yield NAME_SCOPE_STACK.pop() def get_uid(prefix=''): _UID_PREFIXES[prefix] += 1 return _UID_PREFIXES[prefix] def learning_phase(): # If _LEARNING_PHASE is not 0 or 1, return dynamic learning phase tensor return _LEARNING_PHASE if _LEARNING_PHASE in {0, 1} else _LEARNING_PHASE_PLACEHOLDER def set_learning_phase(value): global _LEARNING_PHASE if value not in {0, 1}: raise ValueError('CNTK Backend: Set learning phase ' 'with value %s is not supported, ' 'expected 0 or 1.' % value) _LEARNING_PHASE = value def clear_session(): """Reset learning phase flag for cntk backend. """ global _LEARNING_PHASE global _LEARNING_PHASE_PLACEHOLDER _LEARNING_PHASE = -1 _LEARNING_PHASE_PLACEHOLDER.value = np.asarray(1.0) def in_train_phase(x, alt, training=None): global _LEARNING_PHASE if training is None: training = learning_phase() uses_learning_phase = True else: uses_learning_phase = False # CNTK currently don't support cond op, so here we use # element_select approach as workaround. It may have # perf issue, will resolve it later with cntk cond op. if callable(x) and isinstance(x, C.cntk_py.Function) is False: x = x() if callable(alt) and isinstance(alt, C.cntk_py.Function) is False: alt = alt() if training is True: x._uses_learning_phase = uses_learning_phase return x else: # if _LEARNING_PHASE is static if isinstance(training, int) or isinstance(training, bool): result = x if training == 1 or training is True else alt else: result = C.element_select(training, x, alt) result._uses_learning_phase = uses_learning_phase return result def in_test_phase(x, alt, training=None): return in_train_phase(alt, x, training=training) def _convert_string_dtype(dtype): # cntk only support float32 and float64 if dtype == 'float32': return np.float32 elif dtype == 'float64': return np.float64 else: # cntk only running with float, # try to cast to float to run the model return np.float32 def _convert_dtype_string(dtype): if dtype == np.float32: return 'float32' elif dtype == np.float64: return 'float64' else: raise ValueError('CNTK Backend: Unsupported dtype: %s. ' 'CNTK only supports float32 and ' 'float64.' % dtype) def variable(value, dtype=None, name=None, constraint=None): """Instantiates a variable and returns it. # Arguments value: Numpy array, initial value of the tensor. dtype: Tensor type. name: Optional name string for the tensor. constraint: Optional projection function to be applied to the variable after an optimizer update. # Returns A variable instance (with Keras metadata included). """ if dtype is None: dtype = floatx() if name is None: name = '' if isinstance( value, C.variables.Constant) or isinstance( value, C.variables.Parameter): value = value.value # we don't support init parameter with symbolic op, so eval it first as # workaround if isinstance(value, C.cntk_py.Function): value = eval(value) shape = value.shape if hasattr(value, 'shape') else () if hasattr(value, 'dtype') and value.dtype != dtype and len(shape) > 0: value = value.astype(dtype) # TODO: remove the conversion when cntk supports int32, int64 # https://docs.microsoft.com/en-us/python/api/cntk.variables.parameter dtype = 'float32' if 'int' in str(dtype) else dtype v = C.parameter(shape=shape, init=value, dtype=dtype, name=_prepare_name(name, 'variable')) v._keras_shape = v.shape v._uses_learning_phase = False v.constraint = constraint return v def bias_add(x, bias, data_format=None): if data_format is None: data_format = image_data_format() if data_format not in {'channels_first', 'channels_last'}: raise ValueError('Unknown data_format ' + str(data_format)) dims = len(x.shape) if dims > 0 and x.shape[0] == C.InferredDimension: dims -= 1 bias_dims = len(bias.shape) if bias_dims != 1 and bias_dims != dims: raise ValueError('Unexpected bias dimensions %d, ' 'expected 1 or %d dimensions' % (bias_dims, dims)) if dims == 4: if data_format == 'channels_first': if bias_dims == 1: shape = (bias.shape[0], 1, 1, 1) else: shape = (bias.shape[3],) + bias.shape[:3] elif data_format == 'channels_last': if bias_dims == 1: shape = (1, 1, 1, bias.shape[0]) else: shape = bias.shape elif dims == 3: if data_format == 'channels_first': if bias_dims == 1: shape = (bias.shape[0], 1, 1) else: shape = (bias.shape[2],) + bias.shape[:2] elif data_format == 'channels_last': if bias_dims == 1: shape = (1, 1, bias.shape[0]) else: shape = bias.shape elif dims == 2: if data_format == 'channels_first': if bias_dims == 1: shape = (bias.shape[0], 1) else: shape = (bias.shape[1],) + bias.shape[:1] elif data_format == 'channels_last': if bias_dims == 1: shape = (1, bias.shape[0]) else: shape = bias.shape else: shape = bias.shape return x + reshape(bias, shape) def eval(x): if isinstance(x, C.cntk_py.Function): return x.eval() elif isinstance(x, C.variables.Constant) or isinstance(x, C.variables.Parameter): return x.value else: raise ValueError('CNTK Backend: `eval` method on ' '`%s` type is not supported. ' 'CNTK only supports `eval` with ' '`Function`, `Constant` or ' '`Parameter`.' % type(x)) def placeholder( shape=None, ndim=None, dtype=None, sparse=False, name=None, dynamic_axis_num=1): if dtype is None: dtype = floatx() if not shape: if ndim: shape = tuple([None for _ in range(ndim)]) dynamic_dimension = C.FreeDimension if _get_cntk_version() >= 2.2 else C.InferredDimension cntk_shape = [dynamic_dimension if s is None else s for s in shape] cntk_shape = tuple(cntk_shape) if dynamic_axis_num > len(cntk_shape): raise ValueError('CNTK backend: creating placeholder with ' '%d dimension is not supported, at least ' '%d dimensions are needed.' % (len(cntk_shape, dynamic_axis_num))) if name is None: name = '' cntk_shape = cntk_shape[dynamic_axis_num:] x = C.input( shape=cntk_shape, dtype=_convert_string_dtype(dtype), is_sparse=sparse, name=name) x._keras_shape = shape x._uses_learning_phase = False x._cntk_placeholder = True return x def is_placeholder(x): """Returns whether `x` is a placeholder. # Arguments x: A candidate placeholder. # Returns Boolean. """ return hasattr(x, '_cntk_placeholder') and x._cntk_placeholder def is_keras_tensor(x): if not is_tensor(x): raise ValueError('Unexpectedly found an instance of type `' + str(type(x)) + '`. ' 'Expected a symbolic tensor instance.') return hasattr(x, '_keras_history') def is_tensor(x): return isinstance(x, (C.variables.Constant, C.variables.Variable, C.variables.Parameter, C.ops.functions.Function)) def shape(x): shape = list(int_shape(x)) num_dynamic = _get_dynamic_axis_num(x) non_dyn_shape = [] for i in range(len(x.shape)): if shape[i + num_dynamic] is None: non_dyn_shape.append(x.shape[i]) else: non_dyn_shape.append(shape[i + num_dynamic]) return shape[:num_dynamic] + non_dyn_shape def is_sparse(tensor): return tensor.is_sparse def int_shape(x): if hasattr(x, '_keras_shape'): return x._keras_shape shape = x.shape if hasattr(x, 'dynamic_axes'): dynamic_shape = [None for a in x.dynamic_axes] shape = tuple(dynamic_shape) + shape return shape def ndim(x): shape = int_shape(x) return len(shape) def _prepare_name(name, default): prefix = '_'.join(NAME_SCOPE_STACK) if name is None or name == '': return prefix + '/' + default return prefix + '/' + name def constant(value, dtype=None, shape=None, name=None): if dtype is None: dtype = floatx() if shape is None: shape = () np_value = value * np.ones(shape) const = C.constant(np_value, dtype=dtype, name=_prepare_name(name, 'constant')) const._keras_shape = const.shape const._uses_learning_phase = False return const def random_binomial(shape, p=0.0, dtype=None, seed=None): # use numpy workaround now if seed is None: # ensure that randomness is conditioned by the Numpy RNG seed = np.random.randint(10e7) np.random.seed(seed) if dtype is None: dtype = np.float32 else: dtype = _convert_string_dtype(dtype) size = 1 for _ in shape: if _ is None: raise ValueError('CNTK Backend: randomness op with ' 'dynamic shape is not supported now. ' 'Please provide fixed dimension ' 'instead of `None`.') size *= _ binomial =

np.random.binomial(1, p, size)

numpy.random.binomial

""" Random Variables. This module implements random variables. Random variables are the main in- and outputs of probabilistic numerical methods. """ from typing import Any, Callable, Dict, Generic, Optional, Tuple, TypeVar, Union import numpy as np from probnum import utils as _utils from probnum.type import ( ArrayLikeGetitemArgType, DTypeArgType, FloatArgType, RandomStateArgType, RandomStateType, ShapeArgType, ShapeType, ) try: # functools.cached_property is only available in Python >=3.8 from functools import cached_property except ImportError: from cached_property import cached_property _ValueType = TypeVar("ValueType") class RandomVariable(Generic[_ValueType]): """ Random variables are the main objects used by probabilistic numerical methods. Every probabilistic numerical method takes a random variable encoding the prior distribution as input and outputs a random variable whose distribution encodes the uncertainty arising from finite computation. The generic signature of a probabilistic numerical method is: ``output_rv = probnum_method(input_rv, method_params)`` In practice, most random variables used by methods in ProbNum have Dirac or Gaussian measure. Instances of :class:`RandomVariable` can be added, multiplied, etc. with arrays and linear operators. This may change their ``distribution`` and not necessarily all previously available methods are retained. The internals of :class:`RandomVariable` objects are assumed to be constant over their whole lifecycle. This is due to the caches used to make certain computations more efficient. As a consequence, altering the internal state of a :class:`RandomVariable` (e.g. its mean, cov, sampling function, etc.) will result in undefined behavior. In particular, this should be kept in mind when subclassing :class:`RandomVariable` or any of its descendants. Parameters ---------- shape : Shape of realizations of this random variable. dtype : Data type of realizations of this random variable. If ``object`` will be converted to ``numpy.dtype``. as_value_type : Function which can be used to transform user-supplied arguments, interpreted as realizations of this random variable, to an easy-to-process, normalized format. Will be called internally to transform the argument of functions like ``in_support``, ``cdf`` and ``logcdf``, ``pmf`` and ``logpmf`` (in :class:`DiscreteRandomVariable`), ``pdf`` and ``logpdf`` (in :class:`ContinuousRandomVariable`), and potentially by similar functions in subclasses. For instance, this method is useful if (``log``)``cdf`` and (``log``)``pdf`` both only work on :class:`np.float_` arguments, but we still want the user to be able to pass Python :class:`float`. Then ``as_value_type`` should be set to something like ``lambda x: np.float64(x)``. See Also -------- asrandvar : Transform into a :class:`RandomVariable`. Examples -------- """ # pylint: disable=too-many-instance-attributes,too-many-public-methods def __init__( self, shape: ShapeArgType, dtype: DTypeArgType, random_state: RandomStateArgType = None, parameters: Optional[Dict[str, Any]] = None, sample: Optional[Callable[[ShapeType], _ValueType]] = None, in_support: Optional[Callable[[_ValueType], bool]] = None, cdf: Optional[Callable[[_ValueType], np.float_]] = None, logcdf: Optional[Callable[[_ValueType], np.float_]] = None, quantile: Optional[Callable[[FloatArgType], _ValueType]] = None, mode: Optional[Callable[[], _ValueType]] = None, median: Optional[Callable[[], _ValueType]] = None, mean: Optional[Callable[[], _ValueType]] = None, cov: Optional[Callable[[], _ValueType]] = None, var: Optional[Callable[[], _ValueType]] = None, std: Optional[Callable[[], _ValueType]] = None, entropy: Optional[Callable[[], np.float_]] = None, as_value_type: Optional[Callable[[Any], _ValueType]] = None, ): # pylint: disable=too-many-arguments,too-many-locals """Create a new random variable.""" self.__shape = _utils.as_shape(shape) # Data Types self.__dtype = np.dtype(dtype) self.__median_dtype = RandomVariable.infer_median_dtype(self.__dtype) self.__moment_dtype = RandomVariable.infer_moment_dtype(self.__dtype) self._random_state = _utils.as_random_state(random_state) # Probability distribution of the random variable self.__parameters = parameters.copy() if parameters is not None else {} self.__sample = sample self.__in_support = in_support self.__cdf = cdf self.__logcdf = logcdf self.__quantile = quantile # Properties of the random variable self.__mode = mode self.__median = median self.__mean = mean self.__cov = cov self.__var = var self.__std = std self.__entropy = entropy # Utilities self.__as_value_type = as_value_type def __repr__(self) -> str: return f"<{self.shape} {self.__class__.__name__} with dtype={self.dtype}>" @property def shape(self) -> ShapeType: """Shape of realizations of the random variable.""" return self.__shape @cached_property def ndim(self) -> int: return len(self.__shape) @cached_property def size(self) -> int: return int(np.prod(self.__shape)) @property def dtype(self) -> np.dtype: """Data type of (elements of) a realization of this random variable.""" return self.__dtype @property def median_dtype(self) -> np.dtype: """The dtype of the :attr:`median`. It will be set to the dtype arising from the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`. This is motivated by the fact that, even for discrete random variables, e.g. integer-valued random variables, the :attr:`median` might lie in between two values in which case these values are averaged. For example, a uniform random variable on :math:`\\{ 1, 2, 3, 4 \\}` will have a median of :math:`2.5`. """ return self.__median_dtype @property def moment_dtype(self) -> np.dtype: """The dtype of any (function of a) moment of the random variable, e.g. its :attr:`mean`, :attr:`cov`, :attr:`var`, or :attr:`std`. It will be set to the dtype arising from the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`. This is motivated by the mathematical definition of a moment as a sum or an integral over products of probabilities and values of the random variable, which are represented as using the dtypes :class:`np.float_` and :attr:`dtype`, respectively. """ return self.__moment_dtype @property def random_state(self) -> RandomStateType: """Random state of the random variable. This attribute defines the RandomState object to use for drawing realizations from this random variable. If None (or np.random), the global np.random state is used. If integer, it is used to seed the local :class:`~numpy.random.RandomState` instance. """ return self._random_state @random_state.setter def random_state(self, seed: RandomStateArgType): """Get or set the RandomState object of the underlying distribution. This can be either None or an existing RandomState object. If None (or np.random), use the RandomState singleton used by np.random. If already a RandomState instance, use it. If an int, use a new RandomState instance seeded with seed. """ self._random_state = _utils.as_random_state(seed) @property def parameters(self) -> Dict[str, Any]: """ Parameters of the probability distribution. The parameters of the distribution such as mean, variance, et cetera stored in a ``dict``. """ return self.__parameters.copy() @cached_property def mode(self) -> _ValueType: """ Mode of the random variable. Returns ------- mode : float The mode of the random variable. """ if self.__mode is None: raise NotImplementedError mode = self.__mode() RandomVariable._check_property_value( "mode", mode, shape=self.__shape, dtype=self.__dtype, ) # Make immutable if isinstance(mode, np.ndarray): mode.setflags(write=False) return mode @cached_property def median(self) -> _ValueType: """ Median of the random variable. To learn about the dtype of the median, see :attr:`median_dtype`. Returns ------- median : float The median of the distribution. """ if self.__shape != (): raise NotImplementedError( "The median is only defined for scalar random variables." ) median = self.__median() RandomVariable._check_property_value( "median", median, shape=self.__shape, dtype=self.__median_dtype, ) # Make immutable if isinstance(median, np.ndarray): median.setflags(write=False) return median @cached_property def mean(self) -> _ValueType: """ Mean :math:`\\mathbb{E}(X)` of the distribution. To learn about the dtype of the mean, see :attr:`moment_dtype`. Returns ------- mean : array-like The mean of the distribution. """ if self.__mean is None: raise NotImplementedError mean = self.__mean() RandomVariable._check_property_value( "mean", mean, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(mean, np.ndarray): mean.setflags(write=False) return mean @cached_property def cov(self) -> _ValueType: """ Covariance :math:`\\operatorname{Cov}(X) = \\mathbb{E}((X-\\mathbb{E}(X))(X-\\mathbb{E}(X))^\\top)` of the random variable. To learn about the dtype of the covariance, see :attr:`moment_dtype`. Returns ------- cov : array-like The kernels of the random variable. """ # pylint: disable=line-too-long if self.__cov is None: raise NotImplementedError cov = self.__cov() RandomVariable._check_property_value( "covariance", cov, shape=(self.size, self.size) if self.ndim > 0 else (), dtype=self.__moment_dtype, ) # Make immutable if isinstance(cov, np.ndarray): cov.setflags(write=False) return cov @cached_property def var(self) -> _ValueType: """ Variance :math:`\\operatorname{Var}(X) = \\mathbb{E}((X-\\mathbb{E}(X))^2)` of the distribution. To learn about the dtype of the variance, see :attr:`moment_dtype`. Returns ------- var : array-like The variance of the distribution. """ if self.__var is None: try: var = np.diag(self.cov).reshape(self.__shape).copy() except NotImplementedError as exc: raise NotImplementedError from exc else: var = self.__var() RandomVariable._check_property_value( "variance", var, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(var, np.ndarray): var.setflags(write=False) return var @cached_property def std(self) -> _ValueType: """ Standard deviation of the distribution. To learn about the dtype of the standard deviation, see :attr:`moment_dtype`. Returns ------- std : array-like The standard deviation of the distribution. """ if self.__std is None: try: std = np.sqrt(self.var) except NotImplementedError as exc: raise NotImplementedError from exc else: std = self.__std() RandomVariable._check_property_value( "standard deviation", std, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(std, np.ndarray): std.setflags(write=False) return std @cached_property def entropy(self) -> np.float_: if self.__entropy is None: raise NotImplementedError entropy = self.__entropy() entropy = RandomVariable._ensure_numpy_float( "entropy", entropy, force_scalar=True ) return entropy def in_support(self, x: _ValueType) -> bool: if self.__in_support is None: raise NotImplementedError in_support = self.__in_support(self._as_value_type(x)) if not isinstance(in_support, bool): raise ValueError( f"The function `in_support` must return a `bool`, but its return value " f"is of type `{type(x)}`." ) return in_support def sample(self, size: ShapeArgType = ()) -> _ValueType: """ Draw realizations from a random variable. Parameters ---------- size : tuple Size of the drawn sample of realizations. Returns ------- sample : array-like Sample of realizations with the given ``size`` and the inherent ``shape``. """ if self.__sample is None: raise NotImplementedError("No sampling method provided.") return self.__sample(size=_utils.as_shape(size)) def cdf(self, x: _ValueType) -> np.float_: """ Cumulative distribution function. Parameters ---------- x : array-like Evaluation points of the cumulative distribution function. The shape of this argument should be :code:`(..., S1, ..., SN)`, where :code:`(S1, ..., SN)` is the :attr:`shape` of the random variable. The cdf evaluation will be broadcast over all additional dimensions. Returns ------- q : array-like Value of the cumulative density function at the given points. """ if self.__cdf is not None: return RandomVariable._ensure_numpy_float( "cdf", self.__cdf(self._as_value_type(x)) ) elif self.__logcdf is not None: cdf = np.exp(self.logcdf(self._as_value_type(x))) assert isinstance(cdf, np.float_) return cdf else: raise NotImplementedError( f"Neither the `cdf` nor the `logcdf` of the random variable object " f"with type `{type(self).__name__}` is implemented." ) def logcdf(self, x: _ValueType) -> np.float_: """ Log-cumulative distribution function. Parameters ---------- x : array-like Evaluation points of the cumulative distribution function. The shape of this argument should be :code:`(..., S1, ..., SN)`, where :code:`(S1, ..., SN)` is the :attr:`shape` of the random variable. The logcdf evaluation will be broadcast over all additional dimensions. Returns ------- q : array-like Value of the log-cumulative density function at the given points. """ if self.__logcdf is not None: return RandomVariable._ensure_numpy_float( "logcdf", self.__logcdf(self._as_value_type(x)) ) elif self.__cdf is not None: logcdf = np.log(self.__cdf(x)) assert isinstance(logcdf, np.float_) return logcdf else: raise NotImplementedError( f"Neither the `logcdf` nor the `cdf` of the random variable object " f"with type `{type(self).__name__}` is implemented." ) def quantile(self, p: FloatArgType) -> _ValueType: """Quantile function. The quantile function :math:`Q \\colon [0, 1] \\to \\mathbb{R}` of a random variable :math:`X` is defined as :math:`Q(p) = \\inf\\{ x \\in \\mathbb{R} \\colon p \\le F_X(x) \\}`, where :math:`F_X \\colon \\mathbb{R} \\to [0, 1]` is the :meth:`cdf` of the random variable. From the definition it follows that the quantile function always returns values of the same dtype as the random variable. For instance, for a discrete distribution over the integers, the returned quantiles will also be integers. This means that, in general, :math:`Q(0.5)` is not equal to the :attr:`median` as it is defined in this class. See https://en.wikipedia.org/wiki/Quantile_function for more details and examples. """ if self.__shape != (): raise NotImplementedError( "The quantile function is only defined for scalar random variables." ) if self.__quantile is None: raise NotImplementedError try: p = _utils.as_numpy_scalar(p, dtype=np.floating) except TypeError as exc: raise TypeError( "The given argument `p` can not be cast to a `np.floating` object." ) from exc quantile = self.__quantile(p) if quantile.shape != self.__shape: raise ValueError( f"The quantile function should return values of the same shape as the " f"random variable, i.e. {self.__shape}, but it returned a value with " f"{quantile.shape}." ) if quantile.dtype != self.__dtype: raise ValueError( f"The quantile function should return values of the same dtype as the " f"random variable, i.e. `{self.__dtype.name}`, but it returned a value " f"with dtype `{quantile.dtype.name}`." ) return quantile def __getitem__(self, key: ArrayLikeGetitemArgType) -> "RandomVariable": return RandomVariable( shape=np.empty(shape=self.shape)[key].shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: self.sample(size)[key], mode=lambda: self.mode[key], mean=lambda: self.mean[key], var=lambda: self.var[key], std=lambda: self.std[key], entropy=lambda: self.entropy, as_value_type=self.__as_value_type, ) def reshape(self, newshape: ShapeArgType) -> "RandomVariable": """ Give a new shape to a random variable. Parameters ---------- newshape : int or tuple of ints New shape for the random variable. It must be compatible with the original shape. Returns ------- reshaped_rv : ``self`` with the new dimensions of ``shape``. """ newshape = _utils.as_shape(newshape) return RandomVariable( shape=newshape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: self.sample(size).reshape(size + newshape), mode=lambda: self.mode.reshape(newshape), median=lambda: self.median.reshape(newshape), mean=lambda: self.mean.reshape(newshape), cov=lambda: self.cov, var=lambda: self.var.reshape(newshape), std=lambda: self.std.reshape(newshape), entropy=lambda: self.entropy, as_value_type=self.__as_value_type, ) def transpose(self, *axes: int) -> "RandomVariable": """ Transpose the random variable. Parameters ---------- axes : None, tuple of ints, or n ints See documentation of numpy.ndarray.transpose. Returns ------- transposed_rv : The transposed random variable. """ return RandomVariable( shape=np.empty(shape=self.shape).transpose(*axes).shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: self.sample(size).transpose(*axes), mode=lambda: self.mode.transpose(*axes), median=lambda: self.median.transpose(*axes), mean=lambda: self.mean.transpose(*axes), cov=lambda: self.cov, var=lambda: self.var.transpose(*axes), std=lambda: self.std.transpose(*axes), entropy=lambda: self.entropy, as_value_type=self.__as_value_type, ) T = property(transpose) # Unary arithmetic operations def __neg__(self) -> "RandomVariable": return RandomVariable( shape=self.shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: -self.sample(size=size), in_support=lambda x: self.in_support(-x), mode=lambda: -self.mode, median=lambda: -self.median, mean=lambda: -self.mean, cov=lambda: self.cov, var=lambda: self.var, std=lambda: self.std, as_value_type=self.__as_value_type, ) def __pos__(self) -> "RandomVariable": return RandomVariable( shape=self.shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: +self.sample(size=size), in_support=lambda x: self.in_support(+x), mode=lambda: +self.mode, median=lambda: +self.median, mean=lambda: +self.mean, cov=lambda: self.cov, var=lambda: self.var, std=lambda: self.std, as_value_type=self.__as_value_type, ) def __abs__(self) -> "RandomVariable": return RandomVariable( shape=self.shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: abs(self.sample(size=size)), ) # Binary arithmetic operations __array_ufunc__ = None """ This prevents numpy from calling elementwise arithmetic operations allowing expressions like: y = np.array([1, 1]) + RV to call the arithmetic operations defined by RandomVariable instead of elementwise. Thus no array of RandomVariables but a RandomVariable with the correct shape is returned. """ def __add__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import add return add(self, other) def __radd__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import add return add(other, self) def __sub__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import sub return sub(self, other) def __rsub__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import sub return sub(other, self) def __mul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mul return mul(self, other) def __rmul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mul return mul(other, self) def __matmul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import matmul return matmul(self, other) def __rmatmul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import matmul return matmul(other, self) def __truediv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import truediv return truediv(self, other) def __rtruediv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import truediv return truediv(other, self) def __floordiv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import floordiv return floordiv(self, other) def __rfloordiv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import floordiv return floordiv(other, self) def __mod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mod return mod(self, other) def __rmod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mod return mod(other, self) def __divmod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import divmod_ return divmod_(self, other) def __rdivmod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import divmod_ return divmod_(other, self) def __pow__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import pow_ return pow_(self, other) def __rpow__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import pow_ return pow_(other, self) @staticmethod def infer_median_dtype(value_dtype: DTypeArgType) -> np.dtype: return RandomVariable.infer_moment_dtype(value_dtype) @staticmethod def infer_moment_dtype(value_dtype: DTypeArgType) -> np.dtype: return

np.promote_types(value_dtype, np.float_)

numpy.promote_types

# pvtrace is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # pvtrace is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import numpy as np from external.transformations import translation_matrix, rotation_matrix import external.transformations as tf from Trace import Photon from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm from Materials import Spectrum def random_spherecial_vector(): # This method of calculating isotropic vectors is taken from GNU Scientific Library LOOP = True while LOOP: x = -1. + 2. * np.random.uniform() y = -1. + 2. * np.random.uniform() s = x**2 + y**2 if s <= 1.0: LOOP = False z = -1. + 2. * s a = 2 * np.sqrt(1 - s) x = a * x y = a * y return np.array([x,y,z]) class SimpleSource(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False): super(SimpleSource, self).__init__() self.position = position self.direction = direction self.wavelength = wavelength self.use_random_polarisation = use_random_polarisation self.throw = 0 self.source_id = "SimpleSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength # If use_polarisation is set generate a random polarisation vector of the photon if self.use_random_polarisation: # Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon vec = random_spherecial_vector() vec[2] = 0. vec = norm(vec) R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1]) photon.polarisation = transform_direction(vec, R) else: photon.polarisation = None photon.id = self.throw self.throw = self.throw + 1 return photon class Laser(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None): super(Laser, self).__init__() self.position = np.array(position) self.direction = np.array(direction) self.wavelength = wavelength assert polarisation != None, "Polarisation of the Laser is not set." self.polarisation = np.array(polarisation) self.throw = 0 self.source_id = "LaserSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength photon.polarisation = self.polarisation photon.id = self.throw self.throw = self.throw + 1 return photon class PlanarSource(object): """A box that emits photons from the top surface (normal), sampled from the spectrum.""" def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05): super(PlanarSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.plane = FinitePlane(length=length, width=width) self.length = length self.width = width # direction is the direction that photons are fired out of the plane in the GLOBAL FRAME. # i.e. this is passed directly to the photon to set is's direction self.direction = direction self.throw = 0 self.source_id = "PlanarSource_" + str(id(self)) def translate(self, translation): self.plane.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.plane.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Create a point which is on the surface of the finite plane in it's local frame x = np.random.uniform(0., self.length) y = np.random.uniform(0., self.width) local_point = (x, y, 0.) # Transform the direciton photon.position = transform_point(local_point, self.plane.transform) photon.direction = self.direction photon.active = True if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(

np.random.uniform()

numpy.random.uniform

import numpy as np from stumpff import C, S from CelestialBody import BODIES from numerical import newton, laguerre from lagrange import calc_f, calc_fd, calc_g, calc_gd def kepler_chi(chi, alpha, r0, vr0, mu, dt): ''' Kepler's Equation of the universal anomaly, modified for use in numerical solvers. ''' z = alpha*chi**2 return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \ (1 - alpha*r0)*chi**3*S(z) + \ r0*chi - np.sqrt(mu)*dt def dkepler_dchi(chi, alpha, r0, vr0, mu, dt): ''' Derivative of Kepler's Equation of the universal anomaly, modified for use in numerical solvers. ''' z = alpha*chi**2 return (r0*vr0/np.sqrt(mu))*chi*(1 - alpha*chi**2*S(z)) + \ (1 - alpha*r0)*chi**2*C(z) + r0 def d2kepler_dchi2(chi, alpha, r0, vr0, mu, dt): ''' Second derivative of Kepler's Equation of the universal anomaly, modified for use in numerical solvers. ''' z = alpha*chi**2 S_ = S(z) return (r0*vr0/np.sqrt(mu))*(1 - 3*z*S_ + z*(C(z) - 3*S_)) + \ chi*(1 - z*S_)*(1 - alpha*r0) def solve_kepler_chi(r_0, v_0, dt, body=BODIES['Earth'], method='laguerre', tol=1e-7, max_iters=100): ''' Solve Kepler's Equation of the universal anomaly chi using the specified numerical method. Applies Algorithm 3.4 from Orbital Mechanics for Engineering Students, 4 ed, Curtis. :param r_0: `iterable` (km) initial position 3-vector :param v_0: `iterable` (km/s) initial velocity 3-vector :param dt: `float` (s) time after initial state to solve for r, v as 3-vectors :param body: `CelestialBody` (--) the celestial body to use for orbital parameters :param method: `str` (--) which numerical method to use to solve Kepler's Equation :param tol: `float` (--) decimal tolerance for numerical method (default 1e-7 is IEEE 745 single precision) :param max_iters: `int` (--) maximum number of iterations in numerical method before breaking :return: (km) final position 3-vector, (km/s) final velocity 3-vector ''' VALID_METHODS = ('laguerre', 'newton') mu = body.mu # (km**3/s**2) gravitational parameter of the specified primary body r0 = np.linalg.norm(r_0) # (km) initial position magnitude v0 = np.linalg.norm(v_0) # (km/s) initial velocity magnitude vr0 = np.dot(v_0, r_0)/r0 # (km/s) initial radial velocity magnitude alpha = 2/r0 - v0**2/mu # (1/km) inverse of semi-major axis chi0 = np.sqrt(mu)*np.abs(alpha)*dt if method not in VALID_METHODS: print(f'Method \'{method}\' is not valid, must be one of {VALID_METHODS}.\nDefaulting to laguerre method.') chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt) elif method == 'newton': chi, _, _ = newton(chi0, kepler_chi, dkepler_dchi, alpha, r0, vr0, mu, dt) else: # method == 'laguerre' chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt) f = calc_f(chi, r0, alpha) g = calc_g(dt, mu, chi, alpha) r_1 = f*r_0 + g*v_0 r1 = np.linalg.norm(r_1) fd = calc_fd(mu, r1, r0, alpha, chi) gd = calc_gd(chi, r1, alpha) v_1 = fd*r_0 + gd*v_0 return r_1, v_1 def solve_kepler_E(e, Me, tol=1e-7, max_iters=100): ''' Solve Kepler's Equation in the form containing Eccentric Anomaly (E), eccentricity (e), and Mean Anomaly of Ellipse (Me). Uses Algorithm 3.1 from Orbital Mechanics for Engineering Students, 4 ed, Curtis. ''' # TODO: have this function make use of one of the numerical methods in numerical.py def f(E, e, Me): return E - e*np.sin(E) - Me def fp(E, e): return 1 - e*

np.cos(E)

numpy.cos

"""Routines for numerical differentiation.""" from __future__ import division import numpy as np from numpy.linalg import norm from scipy.sparse.linalg import LinearOperator from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find from ._group_columns import group_dense, group_sparse EPS = np.finfo(np.float64).eps def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub): """Adjust final difference scheme to the presence of bounds. Parameters ---------- x0 : ndarray, shape (n,) Point at which we wish to estimate derivative. h : ndarray, shape (n,) Desired finite difference steps. num_steps : int Number of `h` steps in one direction required to implement finite difference scheme. For example, 2 means that we need to evaluate f(x0 + 2 * h) or f(x0 - 2 * h) scheme : {'1-sided', '2-sided'} Whether steps in one or both directions are required. In other words '1-sided' applies to forward and backward schemes, '2-sided' applies to center schemes. lb : ndarray, shape (n,) Lower bounds on independent variables. ub : ndarray, shape (n,) Upper bounds on independent variables. Returns ------- h_adjusted : ndarray, shape (n,) Adjusted step sizes. Step size decreases only if a sign flip or switching to one-sided scheme doesn't allow to take a full step. use_one_sided : ndarray of bool, shape (n,) Whether to switch to one-sided scheme. Informative only for ``scheme='2-sided'``. """ if scheme == '1-sided': use_one_sided = np.ones_like(h, dtype=bool) elif scheme == '2-sided': h = np.abs(h) use_one_sided = np.zeros_like(h, dtype=bool) else: raise ValueError("`scheme` must be '1-sided' or '2-sided'.") if np.all((lb == -np.inf) & (ub == np.inf)): return h, use_one_sided h_total = h * num_steps h_adjusted = h.copy() lower_dist = x0 - lb upper_dist = ub - x0 if scheme == '1-sided': x = x0 + h_total violated = (x < lb) | (x > ub) fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist) h_adjusted[violated & fitting] *= -1 forward = (upper_dist >= lower_dist) & ~fitting h_adjusted[forward] = upper_dist[forward] / num_steps backward = (upper_dist < lower_dist) & ~fitting h_adjusted[backward] = -lower_dist[backward] / num_steps elif scheme == '2-sided': central = (lower_dist >= h_total) & (upper_dist >= h_total) forward = (upper_dist >= lower_dist) & ~central h_adjusted[forward] = np.minimum( h[forward], 0.5 * upper_dist[forward] / num_steps) use_one_sided[forward] = True backward = (upper_dist < lower_dist) & ~central h_adjusted[backward] = -np.minimum( h[backward], 0.5 * lower_dist[backward] / num_steps) use_one_sided[backward] = True min_dist = np.minimum(upper_dist, lower_dist) / num_steps adjusted_central = (~central & (np.abs(h_adjusted) <= min_dist)) h_adjusted[adjusted_central] = min_dist[adjusted_central] use_one_sided[adjusted_central] = False return h_adjusted, use_one_sided relative_step = {"2-point": EPS**0.5, "3-point": EPS**(1/3), "cs": EPS**0.5} def _compute_absolute_step(rel_step, x0, method): if rel_step is None: rel_step = relative_step[method] sign_x0 = (x0 >= 0).astype(float) * 2 - 1 return rel_step * sign_x0 * np.maximum(1.0, np.abs(x0)) def _prepare_bounds(bounds, x0): lb, ub = [

np.asarray(b, dtype=float)

numpy.asarray

from __future__ import absolute_import from __future__ import division from __future__ import print_function import numpy as np import ray from ray.rllib.ddpg2.models import DDPGModel from ray.rllib.models.catalog import ModelCatalog from ray.rllib.optimizers import PolicyEvaluator from ray.rllib.utils.filter import NoFilter from ray.rllib.utils.process_rollout import process_rollout from ray.rllib.utils.sampler import SyncSampler class DDPGEvaluator(PolicyEvaluator): def __init__(self, registry, env_creator, config): self.env = ModelCatalog.get_preprocessor_as_wrapper( registry, env_creator(config["env_config"])) # contains model, target_model self.model = DDPGModel(registry, self.env, config) self.sampler = SyncSampler( self.env, self.model.model, NoFilter(), config["num_local_steps"], horizon=config["horizon"]) def sample(self): """Returns a batch of samples.""" rollout = self.sampler.get_data() rollout.data["weights"] =

np.ones_like(rollout.data["rewards"])

numpy.ones_like

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time =

np.linspace(0, 11, 1101)

numpy.linspace

""" YTArray class. """ from __future__ import print_function #----------------------------------------------------------------------------- # Copyright (c) 2013, yt Development Team. # # Distributed under the terms of the Modified BSD License. # # The full license is in the file COPYING.txt, distributed with this software. #----------------------------------------------------------------------------- import copy import numpy as np from distutils.version import LooseVersion from functools import wraps from numpy import \ add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \ floor_divide, negative, power, remainder, mod, absolute, rint, \ sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \ reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \ hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \ bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \ greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \ logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \ isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \ modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing try: # numpy 1.13 or newer from numpy import positive, divmod as divmod_, isnat, heaviside except ImportError: positive, divmod_, isnat, heaviside = (None,)*4 from yt.units.unit_object import Unit, UnitParseError from yt.units.unit_registry import UnitRegistry from yt.units.dimensions import \ angle, \ current_mks, \ dimensionless, \ em_dimensions from yt.utilities.exceptions import \ YTUnitOperationError, YTUnitConversionError, \ YTUfuncUnitError, YTIterableUnitCoercionError, \ YTInvalidUnitEquivalence, YTEquivalentDimsError from yt.utilities.lru_cache import lru_cache from numbers import Number as numeric_type from yt.utilities.on_demand_imports import _astropy from sympy import Rational from yt.units.unit_lookup_table import \ default_unit_symbol_lut from yt.units.equivalencies import equivalence_registry from yt.utilities.logger import ytLogger as mylog from .pint_conversions import convert_pint_units NULL_UNIT = Unit() POWER_SIGN_MAPPING = {multiply: 1, divide: -1} # redefine this here to avoid a circular import from yt.funcs def iterable(obj): try: len(obj) except: return False return True def return_arr(func): @wraps(func) def wrapped(*args, **kwargs): ret, units = func(*args, **kwargs) if ret.shape == (): return YTQuantity(ret, units) else: # This could be a subclass, so don't call YTArray directly. return type(args[0])(ret, units) return wrapped @lru_cache(maxsize=128, typed=False) def sqrt_unit(unit): return unit**0.5 @lru_cache(maxsize=128, typed=False) def multiply_units(unit1, unit2): return unit1 * unit2 def preserve_units(unit1, unit2=None): return unit1 @lru_cache(maxsize=128, typed=False) def power_unit(unit, power): return unit**power @lru_cache(maxsize=128, typed=False) def square_unit(unit): return unit*unit @lru_cache(maxsize=128, typed=False) def divide_units(unit1, unit2): return unit1/unit2 @lru_cache(maxsize=128, typed=False) def reciprocal_unit(unit): return unit**-1 def passthrough_unit(unit, unit2=None): return unit def return_without_unit(unit, unit2=None): return None def arctan2_unit(unit1, unit2): return NULL_UNIT def comparison_unit(unit1, unit2=None): return None def invert_units(unit): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def bitop_units(unit1, unit2): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def get_inp_u_unary(ufunc, inputs, out_arr=None): inp = inputs[0] u = getattr(inp, 'units', None) if u is None: u = NULL_UNIT if u.dimensions is angle and ufunc in trigonometric_operators: inp = inp.in_units('radian').v if out_arr is not None: out_arr = ufunc(inp).view(np.ndarray) return out_arr, inp, u def get_inp_u_binary(ufunc, inputs): inp1 = coerce_iterable_units(inputs[0]) inp2 = coerce_iterable_units(inputs[1]) unit1 = getattr(inp1, 'units', None) unit2 = getattr(inp2, 'units', None) ret_class = get_binary_op_return_class(type(inp1), type(inp2)) if unit1 is None: unit1 = Unit(registry=getattr(unit2, 'registry', None)) if unit2 is None and ufunc is not power: unit2 = Unit(registry=getattr(unit1, 'registry', None)) elif ufunc is power: unit2 = inp2 if isinstance(unit2, np.ndarray): if isinstance(unit2, YTArray): if unit2.units.is_dimensionless: pass else: raise YTUnitOperationError(ufunc, unit1, unit2) unit2 = 1.0 return (inp1, inp2), (unit1, unit2), ret_class def handle_preserve_units(inps, units, ufunc, ret_class): if units[0] != units[1]: any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) else: if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False): if units[0] != units[1]: u1d = units[0].is_dimensionless u2d = units[1].is_dimensionless any_nonzero = [

np.any(inps[0])

numpy.any

# # Copyright (c) 2021 The GPflux Contributors. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # import abc import numpy as np import pytest import tensorflow as tf import tensorflow_probability as tfp from gpflow.kullback_leiblers import gauss_kl from gpflux.encoders import DirectlyParameterizedNormalDiag from gpflux.layers import LatentVariableLayer, LayerWithObservations, TrackableLayer tf.keras.backend.set_floatx("float64") ############ # Utilities ############ def _zero_one_normal_prior(w_dim): """ N(0, I) prior """ return tfp.distributions.MultivariateNormalDiag(loc=np.zeros(w_dim), scale_diag=np.ones(w_dim)) def get_distributions_with_w_dim(): distributions = [] for d in [1, 5]: mean = np.zeros(d) scale_tri_l = np.eye(d) mvn = tfp.distributions.MultivariateNormalTriL(mean, scale_tri_l) std = np.ones(d) mvn_diag = tfp.distributions.MultivariateNormalDiag(mean, std) distributions.append((mvn, d)) distributions.append((mvn_diag, d)) return distributions ############ # Tests ############ @pytest.mark.parametrize("distribution, w_dim", get_distributions_with_w_dim()) def test_local_kls(distribution, w_dim): lv = LatentVariableLayer(encoder=None, prior=distribution) # test kl is 0 when posteriors == priors posterior = distribution assert lv._local_kls(posterior) == 0 # test kl > 0 when posteriors != priors batch_size = 10 params = distribution.parameters posterior_params = { k: [v + 0.5 for _ in range(batch_size)] for k, v in params.items() if isinstance(v, np.ndarray) } posterior = lv.distribution_class(**posterior_params) local_kls = lv._local_kls(posterior) assert np.all(local_kls > 0) assert local_kls.shape == (batch_size,) @pytest.mark.parametrize("w_dim", [1, 5]) def test_local_kl_gpflow_consistency(w_dim): num_data = 400 means = np.random.randn(num_data, w_dim) encoder = DirectlyParameterizedNormalDiag(num_data, w_dim, means) lv = LatentVariableLayer(encoder=encoder, prior=_zero_one_normal_prior(w_dim)) posteriors = lv._inference_posteriors( [np.random.randn(num_data, 3), np.random.randn(num_data, 2)] ) q_mu = posteriors.parameters["loc"] q_sqrt = posteriors.parameters["scale_diag"] gpflow_local_kls = gauss_kl(q_mu, q_sqrt) tfp_local_kls = tf.reduce_sum(lv._local_kls(posteriors)) np.testing.assert_allclose(tfp_local_kls, gpflow_local_kls, rtol=1e-10) class ArrayMatcher: def __init__(self, expected): self.expected = expected def __eq__(self, actual): return np.allclose(actual, self.expected, equal_nan=True) @pytest.mark.parametrize("w_dim", [1, 5]) def test_latent_variable_layer_losses(mocker, w_dim): num_data, x_dim, y_dim = 43, 3, 1 prior_shape = (w_dim,) posteriors_shape = (num_data, w_dim) prior = tfp.distributions.MultivariateNormalDiag( loc=np.random.randn(*prior_shape), scale_diag=np.random.randn(*prior_shape) ** 2, ) posteriors = tfp.distributions.MultivariateNormalDiag( loc=np.random.randn(*posteriors_shape), scale_diag=np.random.randn(*posteriors_shape) ** 2, ) encoder = mocker.Mock(return_value=(posteriors.loc, posteriors.scale.diag)) lv = LatentVariableLayer(encoder=encoder, prior=prior) inputs = np.full((num_data, x_dim), np.nan) targets = np.full((num_data, y_dim), np.nan) observations = [inputs, targets] encoder_inputs = np.concatenate(observations, axis=-1) _ = lv(inputs) encoder.assert_not_called() assert lv.losses == [0.0] _ = lv(inputs, observations=observations, training=True) # assert_called_once_with uses == for comparison which fails on arrays encoder.assert_called_once_with(ArrayMatcher(encoder_inputs), training=True) expected_loss = [tf.reduce_mean(posteriors.kl_divergence(prior))] np.testing.assert_equal(lv.losses, expected_loss) # also checks shapes match @pytest.mark.parametrize("w_dim", [1, 5]) @pytest.mark.parametrize("seed2", [None, 42]) def test_latent_variable_layer_samples(mocker, test_data, w_dim, seed2): seed = 123 inputs, targets = test_data num_data, x_dim = inputs.shape prior_shape = (w_dim,) posteriors_shape = (num_data, w_dim) prior = tfp.distributions.MultivariateNormalDiag( loc=np.random.randn(*prior_shape), scale_diag=

np.random.randn(*prior_shape)

numpy.random.randn

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') plt.savefig('jss_figures/DFA_different_trends.png') plt.show() # plot 6b fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[0].set_ylim(-5.5, 5.5) axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].set_ylim(-5.5, 5.5) axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([np.pi, (3 / 2) * np.pi]) axs[2].set_xticklabels([r'$\pi$', r'$\frac{3}{2}\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].set_ylim(-5.5, 5.5) axs[2].set_xlim(0.95 * np.pi, 1.55 * np.pi) plt.savefig('jss_figures/DFA_different_trends_zoomed.png') plt.show() hs_ouputs = hilbert_spectrum(time, imfs_51, hts_51, ifs_51, max_frequency=12, plot=False) # plot 6c ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Simple Sinusoidal Time Seres with Added Noise', 50)) x_hs, y, z = hs_ouputs z_min, z_max = 0, np.abs(z).max() ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) ax.plot(x_hs[0, :], 8 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 8$', Linewidth=3) ax.plot(x_hs[0, :], 4 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 4$', Linewidth=3) ax.plot(x_hs[0, :], 2 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 2$', Linewidth=3) ax.set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi]) ax.set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$']) plt.ylabel(r'Frequency (rad.s$^{-1}$)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.85, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/DFA_hilbert_spectrum.png') plt.show() # plot 6c time = np.linspace(0, 5 * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 51) fluc = Fluctuation(time=time, time_series=time_series) max_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=False) max_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=True) min_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=False) min_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=True) util = Utility(time=time, time_series=time_series) maxima = util.max_bool_func_1st_order_fd() minima = util.min_bool_func_1st_order_fd() ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title(textwrap.fill('Plot Demonstrating Unsmoothed Extrema Envelopes if Schoenberg–Whitney Conditions are Not Satisfied', 50)) plt.plot(time, time_series, label='Time series', zorder=2, LineWidth=2) plt.scatter(time[maxima], time_series[maxima], c='r', label='Maxima', zorder=10) plt.scatter(time[minima], time_series[minima], c='b', label='Minima', zorder=10) plt.plot(time, max_unsmoothed[0], label=textwrap.fill('Unsmoothed maxima envelope', 10), c='darkorange') plt.plot(time, max_smoothed[0], label=textwrap.fill('Smoothed maxima envelope', 10), c='red') plt.plot(time, min_unsmoothed[0], label=textwrap.fill('Unsmoothed minima envelope', 10), c='cyan') plt.plot(time, min_smoothed[0], label=textwrap.fill('Smoothed minima envelope', 10), c='blue') for knot in knots[:-1]: plt.plot(knot * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', zorder=1) plt.plot(knots[-1] * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', label='Knots', zorder=1) plt.xticks((0, 1 * np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi), (r'$0$', r'$\pi$', r'2$\pi$', r'3$\pi$', r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) plt.xlim(-0.25 * np.pi, 5.25 * np.pi) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Schoenberg_Whitney_Conditions.png') plt.show() # plot 7 a = 0.25 width = 0.2 time = np.linspace((0 + a) * np.pi, (5 - a) * np.pi, 1001) knots = np.linspace((0 + a) * np.pi, (5 - a) * np.pi, 11) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] inflection_bool = utils.inflection_point() inflection_x = time[inflection_bool] inflection_y = time_series[inflection_bool] fluctuation = emd_mean.Fluctuation(time=time, time_series=time_series) maxima_envelope = fluctuation.envelope_basis_function_approximation(knots, 'maxima', smooth=False, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] maxima_envelope_smooth = fluctuation.envelope_basis_function_approximation(knots, 'maxima', smooth=True, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] minima_envelope = fluctuation.envelope_basis_function_approximation(knots, 'minima', smooth=False, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] minima_envelope_smooth = fluctuation.envelope_basis_function_approximation(knots, 'minima', smooth=True, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] inflection_points_envelope = fluctuation.direct_detrended_fluctuation_estimation(knots, smooth=True, smoothing_penalty=0.2, technique='inflection_points')[0] binomial_points_envelope = fluctuation.direct_detrended_fluctuation_estimation(knots, smooth=True, smoothing_penalty=0.2, technique='binomial_average', order=21, increment=20)[0] derivative_of_lsq = utils.derivative_forward_diff() derivative_time = time[:-1] derivative_knots = np.linspace(knots[0], knots[-1], 31) # change (1) detrended_fluctuation_technique and (2) max_internal_iter and (3) debug (confusing with external debugging) emd = AdvEMDpy.EMD(time=derivative_time, time_series=derivative_of_lsq) imf_1_of_derivative = emd.empirical_mode_decomposition(knots=derivative_knots, knot_time=derivative_time, text=False, verbose=False)[0][1, :] utils = emd_utils.Utility(time=time[:-1], time_series=imf_1_of_derivative) optimal_maxima = np.r_[False, utils.derivative_forward_diff() < 0, False] & \ np.r_[utils.zero_crossing() == 1, False] optimal_minima = np.r_[False, utils.derivative_forward_diff() > 0, False] & \ np.r_[utils.zero_crossing() == 1, False] EEMD_maxima_envelope = fluctuation.envelope_basis_function_approximation_fixed_points(knots, 'maxima', optimal_maxima, optimal_minima, smooth=False, smoothing_penalty=0.2, edge_effect='none')[0] EEMD_minima_envelope = fluctuation.envelope_basis_function_approximation_fixed_points(knots, 'minima', optimal_maxima, optimal_minima, smooth=False, smoothing_penalty=0.2, edge_effect='none')[0] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Detrended Fluctuation Analysis Examples') plt.plot(time, time_series, LineWidth=2, label='Time series') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(time[optimal_maxima], time_series[optimal_maxima], c='darkred', zorder=4, label=textwrap.fill('Optimal maxima', 10)) plt.scatter(time[optimal_minima], time_series[optimal_minima], c='darkblue', zorder=4, label=textwrap.fill('Optimal minima', 10)) plt.scatter(inflection_x, inflection_y, c='magenta', zorder=4, label=textwrap.fill('Inflection points', 10)) plt.plot(time, maxima_envelope, c='darkblue', label=textwrap.fill('EMD envelope', 10)) plt.plot(time, minima_envelope, c='darkblue') plt.plot(time, (maxima_envelope + minima_envelope) / 2, c='darkblue') plt.plot(time, maxima_envelope_smooth, c='darkred', label=textwrap.fill('SEMD envelope', 10)) plt.plot(time, minima_envelope_smooth, c='darkred') plt.plot(time, (maxima_envelope_smooth + minima_envelope_smooth) / 2, c='darkred') plt.plot(time, EEMD_maxima_envelope, c='darkgreen', label=textwrap.fill('EEMD envelope', 10)) plt.plot(time, EEMD_minima_envelope, c='darkgreen') plt.plot(time, (EEMD_maxima_envelope + EEMD_minima_envelope) / 2, c='darkgreen') plt.plot(time, inflection_points_envelope, c='darkorange', label=textwrap.fill('Inflection point envelope', 10)) plt.plot(time, binomial_points_envelope, c='deeppink', label=textwrap.fill('Binomial average envelope', 10)) plt.plot(time, np.cos(time), c='black', label='True mean') plt.xticks((0, 1 * np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi), (r'$0$', r'$\pi$', r'2$\pi$', r'3$\pi$', r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) plt.xlim(-0.25 * np.pi, 5.25 * np.pi) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/detrended_fluctuation_analysis.png') plt.show() # Duffing Equation Example def duffing_equation(xy, ts): gamma = 0.1 epsilon = 1 omega = ((2 * np.pi) / 25) return [xy[1], xy[0] - epsilon * xy[0] ** 3 + gamma * np.cos(omega * ts)] t = np.linspace(0, 150, 1501) XY0 = [1, 1] solution = odeint(duffing_equation, XY0, t) x = solution[:, 0] dxdt = solution[:, 1] x_points = [0, 50, 100, 150] x_names = {0, 50, 100, 150} y_points_1 = [-2, 0, 2] y_points_2 = [-1, 0, 1] fig, axs = plt.subplots(2, 1) plt.subplots_adjust(hspace=0.2) axs[0].plot(t, x) axs[0].set_title('Duffing Equation Displacement') axs[0].set_ylim([-2, 2]) axs[0].set_xlim([0, 150]) axs[1].plot(t, dxdt) axs[1].set_title('Duffing Equation Velocity') axs[1].set_ylim([-1.5, 1.5]) axs[1].set_xlim([0, 150]) axis = 0 for ax in axs.flat: ax.label_outer() if axis == 0: ax.set_ylabel('x(t)') ax.set_yticks(y_points_1) if axis == 1: ax.set_ylabel(r'$ \dfrac{dx(t)}{dt} $') ax.set(xlabel='t') ax.set_yticks(y_points_2) ax.set_xticks(x_points) ax.set_xticklabels(x_names) axis += 1 plt.savefig('jss_figures/Duffing_equation.png') plt.show() # compare other packages Duffing - top pyemd = pyemd0215() py_emd = pyemd(x) IP, IF, IA = emd040.spectra.frequency_transform(py_emd.T, 10, 'hilbert') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 0.2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using PyEMD 0.2.10', 40)) plt.pcolormesh(t, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht_pyemd.png') plt.show() plt.show() emd_sift = emd040.sift.sift(x) IP, IF, IA = emd040.spectra.frequency_transform(emd_sift, 10, 'hilbert') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 0.2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using emd 0.3.3', 40)) plt.pcolormesh(t, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht_emd.png') plt.show() # compare other packages Duffing - bottom emd_duffing = AdvEMDpy.EMD(time=t, time_series=x) emd_duff, emd_ht_duff, emd_if_duff, _, _, _, _ = emd_duffing.empirical_mode_decomposition(verbose=False) fig, axs = plt.subplots(2, 1) plt.subplots_adjust(hspace=0.3) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) axs[0].plot(t, emd_duff[1, :], label='AdvEMDpy') axs[0].plot(t, py_emd[0, :], '--', label='PyEMD 0.2.10') axs[0].plot(t, emd_sift[:, 0], '--', label='emd 0.3.3') axs[0].set_title('IMF 1') axs[0].set_ylim([-2, 2]) axs[0].set_xlim([0, 150]) axs[1].plot(t, emd_duff[2, :], label='AdvEMDpy') print(f'AdvEMDpy driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - emd_duff[2, :])), 3)}') axs[1].plot(t, py_emd[1, :], '--', label='PyEMD 0.2.10') print(f'PyEMD driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - py_emd[1, :])), 3)}') axs[1].plot(t, emd_sift[:, 1], '--', label='emd 0.3.3') print(f'emd driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - emd_sift[:, 1])), 3)}') axs[1].plot(t, 0.1 * np.cos(0.04 * 2 * np.pi * t), '--', label=r'$0.1$cos$(0.08{\pi}t)$') axs[1].set_title('IMF 2') axs[1].set_ylim([-0.2, 0.4]) axs[1].set_xlim([0, 150]) axis = 0 for ax in axs.flat: ax.label_outer() if axis == 0: ax.set_ylabel(r'$\gamma_1(t)$') ax.set_yticks([-2, 0, 2]) if axis == 1: ax.set_ylabel(r'$\gamma_2(t)$') ax.set_yticks([-0.2, 0, 0.2]) box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) ax.set_xticks(x_points) ax.set_xticklabels(x_names) axis += 1 plt.savefig('jss_figures/Duffing_equation_imfs.png') plt.show() hs_ouputs = hilbert_spectrum(t, emd_duff, emd_ht_duff, emd_if_duff, max_frequency=1.3, plot=False) ax = plt.subplot(111) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using AdvEMDpy', 40)) x, y, z = hs_ouputs y = y / (2 * np.pi) z_min, z_max = 0, np.abs(z).max() figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) ax.pcolormesh(x, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht.png') plt.show() # Carbon Dioxide Concentration Example CO2_data = pd.read_csv('Data/co2_mm_mlo.csv', header=51) plt.plot(CO2_data['month'], CO2_data['decimal date']) plt.title(textwrap.fill('Mean Monthly Concentration of Carbon Dioxide in the Atmosphere', 35)) plt.ylabel('Parts per million') plt.xlabel('Time (years)') plt.savefig('jss_figures/CO2_concentration.png') plt.show() signal = CO2_data['decimal date'] signal = np.asarray(signal) time = CO2_data['month'] time = np.asarray(time) # compare other packages Carbon Dioxide - top pyemd = pyemd0215() py_emd = pyemd(signal) IP, IF, IA = emd040.spectra.frequency_transform(py_emd[:2, :].T, 12, 'hilbert') print(f'PyEMD annual frequency error: {np.round(sum(np.abs(IF[:, 0] - np.ones_like(IF[:, 0]))), 3)}') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using PyEMD 0.2.10', 45)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.pcolormesh(time, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(time, np.ones_like(time), 'k--', label=textwrap.fill('Annual cycle', 10)) box_0 = ax.get_position() ax.set_position([box_0.x0 + 0.0125, box_0.y0 + 0.075, box_0.width * 0.8, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/CO2_Hilbert_pyemd.png') plt.show() emd_sift = emd040.sift.sift(signal) IP, IF, IA = emd040.spectra.frequency_transform(emd_sift[:, :1], 12, 'hilbert') print(f'emd annual frequency error: {np.round(sum(np.abs(IF - np.ones_like(IF)))[0], 3)}') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using emd 0.3.3', 45)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.pcolormesh(time, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(time,

np.ones_like(time)

numpy.ones_like

import argparse import json import numpy as np import pandas as pd import os from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split from sklearn.metrics import classification_report,f1_score from keras.models import Sequential from keras.layers import Dense, Dropout from keras import backend as K from keras.utils.vis_utils import plot_model from sklearn.externals import joblib import time def f1(y_true, y_pred): def recall(y_true, y_pred): """Recall metric. Only computes a batch-wise average of recall. Computes the recall, a metric for multi-label classification of how many relevant items are selected. """ true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1))) possible_positives = K.sum(K.round(K.clip(y_true, 0, 1))) recall = true_positives / (possible_positives + K.epsilon()) return recall def precision(y_true, y_pred): """Precision metric. Only computes a batch-wise average of precision. Computes the precision, a metric for multi-label classification of how many selected items are relevant. """ true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1))) predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1))) precision = true_positives / (predicted_positives + K.epsilon()) return precision precision = precision(y_true, y_pred) recall = recall(y_true, y_pred) return 2*((precision*recall)/(precision+recall+K.epsilon())) def get_embeddings(sentences_list,layer_json): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :return: Dictionary with key each sentence of the sentences_list and as value the embedding ''' sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence embeddings = dict()##dict with key the index of each sentence and as value the its embedding sentence_emb = dict()#key:sentence,value:its embedding with open(sentences_list,'r') as file: for index,line in enumerate(file): sentences[index] = line.strip() with open(layer_json, 'r',encoding='utf-8') as f: for line in f: embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features']) for key,value in sentences.items(): sentence_emb[value] = embeddings[key] return sentence_emb def train_classifier(sentences_list,layer_json,dataset_csv,filename): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :param dataset_csv: the path of the dataset :param filename: The path of the pickle file that the model will be stored :return: ''' dataset = pd.read_csv(dataset_csv) bert_dict = get_embeddings(sentences_list,layer_json) length = list() sentence_emb = list() previous_emb = list() next_list = list() section_list = list() label = list() errors = 0 for row in dataset.iterrows(): sentence = row[1][0].strip() previous = row[1][1].strip() nexts = row[1][2].strip() section = row[1][3].strip() if sentence in bert_dict: sentence_emb.append(bert_dict[sentence]) else: sentence_emb.append(np.zeros(768)) print(sentence) errors += 1 if previous in bert_dict: previous_emb.append(bert_dict[previous]) else: previous_emb.append(np.zeros(768)) if nexts in bert_dict: next_list.append(bert_dict[nexts]) else: next_list.append(np.zeros(768)) if section in bert_dict: section_list.append(bert_dict[section]) else: section_list.append(np.zeros(768)) length.append(row[1][4]) label.append(row[1][5]) sentence_emb = np.asarray(sentence_emb) print(sentence_emb.shape) next_emb = np.asarray(next_list) print(next_emb.shape) previous_emb = np.asarray(previous_emb) print(previous_emb.shape) section_emb = np.asarray(section_list) print(sentence_emb.shape) length = np.asarray(length) print(length.shape) label = np.asarray(label) print(errors) features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1) features = np.column_stack([features, length]) # np.append(features,length,axis=1) print(features.shape) X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42) log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1) log.fit(X_train, y_train) #save the model _ = joblib.dump(log, filename, compress=9) predictions = log.predict(X_val) print("###########################################") print("Results using embeddings from the",layer_json,"file") print(classification_report(y_val, predictions)) print("F1 score using Logistic Regression:",f1_score(y_val, predictions)) print("###########################################") #train a DNN f1_results = list() for i in range(3): model = Sequential() model.add(Dense(64, activation='relu', trainable=True)) model.add(Dense(128, activation='relu', trainable=True)) model.add(Dropout(0.30)) model.add(Dense(64, activation='relu', trainable=True)) model.add(Dropout(0.25)) model.add(Dense(64, activation='relu', trainable=True)) model.add(Dropout(0.35)) model.add(Dense(1, activation='sigmoid')) # compile network model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1]) # fit network model.fit(X_train, y_train, epochs=100, batch_size=64) loss, f_1 = model.evaluate(X_val, y_val, verbose=1) print('\nTest F1: %f' % (f_1 * 100)) f1_results.append(f_1) model = None print("###########################################") print("Results using embeddings from the", layer_json, "file") # evaluate print(np.mean(f1_results)) print("###########################################") def parameter_tuning_LR(sentences_list,layer_json,dataset_csv): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :param dataset_csv: the path of the dataset :return: ''' dataset = pd.read_csv(dataset_csv) bert_dict = get_embeddings(sentences_list,layer_json) length = list() sentence_emb = list() previous_emb = list() next_list = list() section_list = list() label = list() errors = 0 for row in dataset.iterrows(): sentence = row[1][0].strip() previous = row[1][1].strip() nexts = row[1][2].strip() section = row[1][3].strip() if sentence in bert_dict: sentence_emb.append(bert_dict[sentence]) else: sentence_emb.append(np.zeros(768)) print(sentence) errors += 1 if previous in bert_dict: previous_emb.append(bert_dict[previous]) else: previous_emb.append(np.zeros(768)) if nexts in bert_dict: next_list.append(bert_dict[nexts]) else: next_list.append(

np.zeros(768)

numpy.zeros

"""Bindings for the Barnes Hut TSNE algorithm with fast nearest neighbors Refs: References [1] <NAME>, L.J.P.; Hinton, G.E. Visualizing High-Dimensional Data Using t-SNE. Journal of Machine Learning Research 9:2579-2605, 2008. [2] <NAME>, L.J.P. t-Distributed Stochastic Neighbor Embedding http://homepage.tudelft.nl/19j49/t-SNE.html """ import numpy as N import ctypes import os import pkg_resources def ord_string(s): b = bytearray() arr = b.extend(map(ord, s)) return

N.array([x for x in b] + [0])

numpy.array

# pylint: disable=protected-access """ Test the wrappers for the C API. """ import os from contextlib import contextmanager import numpy as np import numpy.testing as npt import pandas as pd import pytest import xarray as xr from packaging.version import Version from pygmt import Figure, clib from pygmt.clib.conversion import dataarray_to_matrix from pygmt.clib.session import FAMILIES, VIAS from pygmt.exceptions import ( GMTCLibError, GMTCLibNoSessionError, GMTInvalidInput, GMTVersionError, ) from pygmt.helpers import GMTTempFile TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data") with clib.Session() as _lib: gmt_version = Version(_lib.info["version"]) @contextmanager def mock(session, func, returns=None, mock_func=None): """ Mock a GMT C API function to make it always return a given value. Used to test that exceptions are raised when API functions fail by producing a NULL pointer as output or non-zero status codes. Needed because it's not easy to get some API functions to fail without inducing a Segmentation Fault (which is a good thing because libgmt usually only fails with errors). """ if mock_func is None: def mock_api_function(*args): # pylint: disable=unused-argument """ A mock GMT API function that always returns a given value. """ return returns mock_func = mock_api_function get_libgmt_func = session.get_libgmt_func def mock_get_libgmt_func(name, argtypes=None, restype=None): """ Return our mock function. """ if name == func: return mock_func return get_libgmt_func(name, argtypes, restype) setattr(session, "get_libgmt_func", mock_get_libgmt_func) yield setattr(session, "get_libgmt_func", get_libgmt_func) def test_getitem(): """ Test that I can get correct constants from the C lib. """ ses = clib.Session() assert ses["GMT_SESSION_EXTERNAL"] != -99999 assert ses["GMT_MODULE_CMD"] != -99999 assert ses["GMT_PAD_DEFAULT"] != -99999 assert ses["GMT_DOUBLE"] != -99999 with pytest.raises(GMTCLibError): ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement def test_create_destroy_session(): """ Test that create and destroy session are called without errors. """ # Create two session and make sure they are not pointing to the same memory session1 = clib.Session() session1.create(name="test_session1") assert session1.session_pointer is not None session2 = clib.Session() session2.create(name="test_session2") assert session2.session_pointer is not None assert session2.session_pointer != session1.session_pointer session1.destroy() session2.destroy() # Create and destroy a session twice ses = clib.Session() for __ in range(2): with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement ses.create("session1") assert ses.session_pointer is not None ses.destroy() with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement def test_create_session_fails(): """ Check that an exception is raised when failing to create a session. """ ses = clib.Session() with mock(ses, "GMT_Create_Session", returns=None): with pytest.raises(GMTCLibError): ses.create("test-session-name") # Should fail if trying to create a session before destroying the old one. ses.create("test1") with pytest.raises(GMTCLibError): ses.create("test2") def test_destroy_session_fails(): """ Fail to destroy session when given bad input. """ ses = clib.Session() with pytest.raises(GMTCLibNoSessionError): ses.destroy() ses.create("test-session") with mock(ses, "GMT_Destroy_Session", returns=1): with pytest.raises(GMTCLibError): ses.destroy() ses.destroy() def test_call_module(): """ Run a command to see if call_module works. """ data_fname = os.path.join(TEST_DATA_DIR, "points.txt") out_fname = "test_call_module.txt" with clib.Session() as lib: with GMTTempFile() as out_fname: lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name)) assert os.path.exists(out_fname.name) output = out_fname.read().strip() assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338" def test_call_module_invalid_arguments(): """ Fails for invalid module arguments. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("info", "bogus-data.bla") def test_call_module_invalid_name(): """ Fails when given bad input. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("meh", "") def test_call_module_error_message(): """ Check is the GMT error message was captured. """ with clib.Session() as lib: try: lib.call_module("info", "bogus-data.bla") except GMTCLibError as error: assert "Module 'info' failed with status code" in str(error) assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error) def test_method_no_session(): """ Fails when not in a session. """ # Create an instance of Session without "with" so no session is created. lib = clib.Session() with pytest.raises(GMTCLibNoSessionError): lib.call_module("gmtdefaults", "") with pytest.raises(GMTCLibNoSessionError): lib.session_pointer # pylint: disable=pointless-statement def test_parse_constant_single(): """ Parsing a single family argument correctly. """ lib = clib.Session() for family in FAMILIES: parsed = lib._parse_constant(family, valid=FAMILIES) assert parsed == lib[family] def test_parse_constant_composite(): """ Parsing a composite constant argument (separated by |) correctly. """ lib = clib.Session() test_cases = ((family, via) for family in FAMILIES for via in VIAS) for family, via in test_cases: composite = "|".join([family, via]) expected = lib[family] + lib[via] parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS) assert parsed == expected def test_parse_constant_fails(): """ Check if the function fails when given bad input. """ lib = clib.Session() test_cases = [ "SOME_random_STRING", "GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR", "GMT_IS_DATASET|NOT_A_PROPER_VIA", "NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX", "NOT_A_PROPER_FAMILY|ALSO_INVALID", ] for test_case in test_cases: with pytest.raises(GMTInvalidInput): lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS) # Should also fail if not given valid modifiers but is using them anyway. # This should work... lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS ) # But this shouldn't. with pytest.raises(GMTInvalidInput): lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None ) def test_create_data_dataset(): """ Run the function to make sure it doesn't fail badly. """ with clib.Session() as lib: # Dataset from vectors data_vector = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_VECTOR", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], # columns, rows, layers, dtype ) # Dataset from matrices data_matrix = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_MATRIX", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) assert data_vector != data_matrix def test_create_data_grid_dim(): """ Create a grid ignoring range and inc. """ with clib.Session() as lib: # Grids from matrices using dim lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) def test_create_data_grid_range(): """ Create a grid specifying range and inc instead of dim. """ with clib.Session() as lib: # Grids from matrices using range and int lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) def test_create_data_fails(): """ Check that create_data raises exceptions for invalid input and output. """ # Passing in invalid mode with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="Not_a_valid_mode", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # Passing in invalid geometry with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_GRID", geometry="Not_a_valid_geometry", mode="GMT_CONTAINER_ONLY", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # If the data pointer returned is None (NULL pointer) with pytest.raises(GMTCLibError): with clib.Session() as lib: with mock(lib, "GMT_Create_Data", returns=None): lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[11, 10, 2, 0], ) def test_virtual_file(): """ Test passing in data via a virtual file with a Dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (5, 3) for dtype in dtypes: with clib.Session() as lib: family = "GMT_IS_DATASET|GMT_VIA_MATRIX" geometry = "GMT_IS_POINT" dataset = lib.create_data( family=family, geometry=geometry, mode="GMT_CONTAINER_ONLY", dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype ) data =

np.arange(shape[0] * shape[1], dtype=dtype)

numpy.arange

import cv2, time import numpy as np import Tkinter """ Wraps up some interfaces to opencv user interface methods (displaying image frames, event handling, etc). If desired, an alternative UI could be built and imported into get_pulse.py instead. Opencv is used to perform much of the data analysis, but there is no reason it has to be used to handle the UI as well. It just happens to be very effective for our purposes. """ def resize(*args, **kwargs): return cv2.resize(*args, **kwargs) def moveWindow(*args,**kwargs): return def imshow(root,args,kwargs): image = cv2.cvtColor(output_frame, cv2.COLOR_BGR2RGB) image = Image.fromarray(image) image = ImageTk.PhotoImage(image) return Tkinter.Label(root, image=kwargs).pack() #return cv2.imshow(*args,**kwargs) def destroyWindow(*args,**kwargs): return cv2.destroyWindow(*args,**kwargs) def waitKey(*args,**kwargs): return cv2.waitKey(*args,**kwargs) """ The rest of this file defines some GUI plotting functionality. There are plenty of other ways to do simple x-y data plots in python, but this application uses cv2.imshow to do real-time data plotting and handle user interaction. This is entirely independent of the data calculation functions, so it can be replaced in the get_pulse.py application easily. """ def combine(left, right): """Stack images horizontally. """ h = max(left.shape[0], right.shape[0]) w = left.shape[1] + right.shape[1] hoff = left.shape[0] shape = list(left.shape) shape[0] = h shape[1] = w comb = np.zeros(tuple(shape),left.dtype) # left will be on left, aligned top, with right on right comb[:left.shape[0],:left.shape[1]] = left comb[:right.shape[0],left.shape[1]:] = right return comb def plotXY(data,size = (280,640),margin = 25,name = "data",labels=[], skip = [], showmax = [], bg = None,label_ndigits = [], showmax_digits=[]): for x,y in data: if len(x) < 2 or len(y) < 2: return n_plots = len(data) w = float(size[1]) h = size[0]/float(n_plots) z = np.zeros((size[0],size[1],3)) if isinstance(bg,np.ndarray): wd = int(bg.shape[1]/bg.shape[0]*h ) bg = cv2.resize(bg,(wd,int(h))) if len(bg.shape) == 3: r = combine(bg[:,:,0],z[:,:,0]) g = combine(bg[:,:,1],z[:,:,1]) b = combine(bg[:,:,2],z[:,:,2]) else: r = combine(bg,z[:,:,0]) g = combine(bg,z[:,:,1]) b = combine(bg,z[:,:,2]) z = cv2.merge([r,g,b])[:,:-wd,] i = 0 P = [] for x,y in data: x = np.array(x) y = -

np.array(y)

numpy.array

import numpy as np import pytest import theano import theano.tensor as tt # Don't import test classes otherwise they get tested as part of the file from tests import unittest_tools as utt from tests.gpuarray.config import mode_with_gpu, mode_without_gpu, test_ctx_name from tests.tensor.test_basic import ( TestAlloc, TestComparison, TestJoinAndSplit, TestReshape, ) from tests.tensor.utils import rand, safe_make_node from theano.gpuarray.basic_ops import ( GpuAlloc, GpuAllocEmpty, GpuContiguous, GpuEye, GpuFromHost, GpuJoin, GpuReshape, GpuSplit, GpuToGpu, GpuTri, HostFromGpu, gpu_contiguous, gpu_join, host_from_gpu, ) from theano.gpuarray.elemwise import GpuDimShuffle, GpuElemwise from theano.gpuarray.subtensor import GpuSubtensor from theano.gpuarray.type import GpuArrayType, get_context, gpuarray_shared_constructor from theano.tensor import TensorType from theano.tensor.basic import alloc pygpu = pytest.importorskip("pygpu") gpuarray = pygpu.gpuarray utt.seed_rng() rng = np.random.RandomState(seed=utt.fetch_seed()) def inplace_func( inputs, outputs, mode=None, allow_input_downcast=False, on_unused_input="raise", name=None, ): if mode is None: mode = mode_with_gpu return theano.function( inputs, outputs, mode=mode, allow_input_downcast=allow_input_downcast, accept_inplace=True, on_unused_input=on_unused_input, name=name, ) def fake_shared(value, name=None, strict=False, allow_downcast=None, **kwargs): from theano.tensor.sharedvar import scalar_constructor, tensor_constructor for c in (gpuarray_shared_constructor, tensor_constructor, scalar_constructor): try: return c( value, name=name, strict=strict, allow_downcast=allow_downcast, **kwargs ) except TypeError: continue def rand_gpuarray(*shape, **kwargs): r = rng.rand(*shape) * 2 - 1 dtype = kwargs.pop("dtype", theano.config.floatX) cls = kwargs.pop("cls", None) if len(kwargs) != 0: raise TypeError("Unexpected argument %s", list(kwargs.keys())[0]) return gpuarray.array(r, dtype=dtype, cls=cls, context=get_context(test_ctx_name)) def makeTester( name, op, gpu_op, cases, checks=None, mode_gpu=mode_with_gpu, mode_nogpu=mode_without_gpu, skip=False, eps=1e-10, ): if checks is None: checks = {} _op = op _gpu_op = gpu_op _cases = cases _skip = skip _checks = checks class Checker(utt.OptimizationTestMixin): op = staticmethod(_op) gpu_op = staticmethod(_gpu_op) cases = _cases skip = _skip checks = _checks def setup_method(self): eval(self.__class__.__module__ + "." + self.__class__.__name__) def test_all(self): if skip: pytest.skip(skip) for testname, inputs in cases.items(): for _ in range(len(inputs)): if type(inputs[_]) is float: inputs[_] = np.asarray(inputs[_], dtype=theano.config.floatX) self.run_case(testname, inputs) def run_case(self, testname, inputs): inputs_ref = [theano.shared(inp) for inp in inputs] inputs_tst = [theano.shared(inp) for inp in inputs] try: node_ref = safe_make_node(self.op, *inputs_ref) node_tst = safe_make_node(self.op, *inputs_tst) except Exception as exc: err_msg = ( "Test %s::%s: Error occurred while making " "a node with inputs %s" ) % (self.gpu_op, testname, inputs) exc.args += (err_msg,) raise try: f_ref = inplace_func([], node_ref.outputs, mode=mode_nogpu) f_tst = inplace_func([], node_tst.outputs, mode=mode_gpu) except Exception as exc: err_msg = ( "Test %s::%s: Error occurred while trying to " "make a Function" ) % (self.gpu_op, testname) exc.args += (err_msg,) raise self.assertFunctionContains1(f_tst, self.gpu_op) ref_e = None try: expecteds = f_ref() except Exception as exc: ref_e = exc try: variables = f_tst() except Exception as exc: if ref_e is None: err_msg = ( "Test %s::%s: exception when calling the " "Function" ) % (self.gpu_op, testname) exc.args += (err_msg,) raise else: # if we raised an exception of the same type we're good. if isinstance(exc, type(ref_e)): return else: err_msg = ( "Test %s::%s: exception raised during test " "call was not the same as the reference " "call (got: %s, expected %s)" % (self.gpu_op, testname, type(exc), type(ref_e)) ) exc.args += (err_msg,) raise for i, (variable, expected) in enumerate(zip(variables, expecteds)): condition = ( variable.dtype != expected.dtype or variable.shape != expected.shape or not TensorType.values_eq_approx(variable, expected) ) assert not condition, ( "Test %s::%s: Output %s gave the wrong " "value. With inputs %s, expected %s " "(dtype %s), got %s (dtype %s)." % ( self.op, testname, i, inputs, expected, expected.dtype, variable, variable.dtype, ) ) for description, check in self.checks.items(): assert check(inputs, variables), ( "Test %s::%s: Failed check: %s " "(inputs were %s, ouputs were %s)" ) % (self.op, testname, description, inputs, variables) Checker.__name__ = name if hasattr(Checker, "__qualname__"): Checker.__qualname__ = name return Checker def test_transfer_cpu_gpu(): a = tt.fmatrix("a") g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g") av = np.asarray(rng.rand(5, 4), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) f = theano.function([a], GpuFromHost(test_ctx_name)(a)) fv = f(av) assert GpuArrayType.values_eq(fv, gv) f = theano.function([g], host_from_gpu(g)) fv = f(gv) assert np.all(fv == av) def test_transfer_gpu_gpu(): g = GpuArrayType( dtype="float32", broadcastable=(False, False), context_name=test_ctx_name )() av = np.asarray(rng.rand(5, 4), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) mode = mode_with_gpu.excluding( "cut_gpua_host_transfers", "local_cut_gpua_host_gpua" ) f = theano.function([g], GpuToGpu(test_ctx_name)(g), mode=mode) topo = f.maker.fgraph.toposort() assert len(topo) == 1 assert isinstance(topo[0].op, GpuToGpu) fv = f(gv) assert GpuArrayType.values_eq(fv, gv) def test_transfer_strided(): # This is just to ensure that it works in theano # libgpuarray has a much more comprehensive suit of tests to # ensure correctness a = tt.fmatrix("a") g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g") av = np.asarray(rng.rand(5, 8), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) av = av[:, ::2] gv = gv[:, ::2] f = theano.function([a], GpuFromHost(test_ctx_name)(a)) fv = f(av) assert GpuArrayType.values_eq(fv, gv) f = theano.function([g], host_from_gpu(g)) fv = f(gv) assert np.all(fv == av) def gpu_alloc_expected(x, *shp): g = gpuarray.empty(shp, dtype=x.dtype, context=get_context(test_ctx_name)) g[:] = x return g TestGpuAlloc = makeTester( name="GpuAllocTester", # The +1 is there to allow the lift to the GPU. op=lambda *args: alloc(*args) + 1, gpu_op=GpuAlloc(test_ctx_name), cases=dict( correct01=(rand(), np.int32(7)), # just gives a DeepCopyOp with possibly wrong results on the CPU # correct01_bcast=(rand(1), np.int32(7)), correct02=(rand(), np.int32(4), np.int32(7)), correct12=(rand(7), np.int32(4), np.int32(7)), correct13=(rand(7), np.int32(2),

np.int32(4)

numpy.int32

""" YTArray class. """ from __future__ import print_function #----------------------------------------------------------------------------- # Copyright (c) 2013, yt Development Team. # # Distributed under the terms of the Modified BSD License. # # The full license is in the file COPYING.txt, distributed with this software. #----------------------------------------------------------------------------- import copy import numpy as np from distutils.version import LooseVersion from functools import wraps from numpy import \ add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \ floor_divide, negative, power, remainder, mod, absolute, rint, \ sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \ reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \ hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \ bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \ greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \ logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \ isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \ modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing try: # numpy 1.13 or newer from numpy import positive, divmod as divmod_, isnat, heaviside except ImportError: positive, divmod_, isnat, heaviside = (None,)*4 from yt.units.unit_object import Unit, UnitParseError from yt.units.unit_registry import UnitRegistry from yt.units.dimensions import \ angle, \ current_mks, \ dimensionless, \ em_dimensions from yt.utilities.exceptions import \ YTUnitOperationError, YTUnitConversionError, \ YTUfuncUnitError, YTIterableUnitCoercionError, \ YTInvalidUnitEquivalence, YTEquivalentDimsError from yt.utilities.lru_cache import lru_cache from numbers import Number as numeric_type from yt.utilities.on_demand_imports import _astropy from sympy import Rational from yt.units.unit_lookup_table import \ default_unit_symbol_lut from yt.units.equivalencies import equivalence_registry from yt.utilities.logger import ytLogger as mylog from .pint_conversions import convert_pint_units NULL_UNIT = Unit() POWER_SIGN_MAPPING = {multiply: 1, divide: -1} # redefine this here to avoid a circular import from yt.funcs def iterable(obj): try: len(obj) except: return False return True def return_arr(func): @wraps(func) def wrapped(*args, **kwargs): ret, units = func(*args, **kwargs) if ret.shape == (): return YTQuantity(ret, units) else: # This could be a subclass, so don't call YTArray directly. return type(args[0])(ret, units) return wrapped @lru_cache(maxsize=128, typed=False) def sqrt_unit(unit): return unit**0.5 @lru_cache(maxsize=128, typed=False) def multiply_units(unit1, unit2): return unit1 * unit2 def preserve_units(unit1, unit2=None): return unit1 @lru_cache(maxsize=128, typed=False) def power_unit(unit, power): return unit**power @lru_cache(maxsize=128, typed=False) def square_unit(unit): return unit*unit @lru_cache(maxsize=128, typed=False) def divide_units(unit1, unit2): return unit1/unit2 @lru_cache(maxsize=128, typed=False) def reciprocal_unit(unit): return unit**-1 def passthrough_unit(unit, unit2=None): return unit def return_without_unit(unit, unit2=None): return None def arctan2_unit(unit1, unit2): return NULL_UNIT def comparison_unit(unit1, unit2=None): return None def invert_units(unit): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def bitop_units(unit1, unit2): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def get_inp_u_unary(ufunc, inputs, out_arr=None): inp = inputs[0] u = getattr(inp, 'units', None) if u is None: u = NULL_UNIT if u.dimensions is angle and ufunc in trigonometric_operators: inp = inp.in_units('radian').v if out_arr is not None: out_arr = ufunc(inp).view(np.ndarray) return out_arr, inp, u def get_inp_u_binary(ufunc, inputs): inp1 = coerce_iterable_units(inputs[0]) inp2 = coerce_iterable_units(inputs[1]) unit1 = getattr(inp1, 'units', None) unit2 = getattr(inp2, 'units', None) ret_class = get_binary_op_return_class(type(inp1), type(inp2)) if unit1 is None: unit1 = Unit(registry=getattr(unit2, 'registry', None)) if unit2 is None and ufunc is not power: unit2 = Unit(registry=getattr(unit1, 'registry', None)) elif ufunc is power: unit2 = inp2 if isinstance(unit2, np.ndarray): if isinstance(unit2, YTArray): if unit2.units.is_dimensionless: pass else: raise YTUnitOperationError(ufunc, unit1, unit2) unit2 = 1.0 return (inp1, inp2), (unit1, unit2), ret_class def handle_preserve_units(inps, units, ufunc, ret_class): if units[0] != units[1]: any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) else: if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False): if units[0] != units[1]: u1d = units[0].is_dimensionless u2d = units[1].is_dimensionless any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] ==

np.bool_(False)

numpy.bool_

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time =

np.linspace(max_discard_time - width, max_discard_time + width, 101)

numpy.linspace

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots =

np.arange(12)

numpy.arange

''' <NAME> set up :2020-1-9 intergrate img and label into one file -- fiducial1024_v1 ''' import argparse import sys, os import pickle import random import collections import json import numpy as np import scipy.io as io import scipy.misc as m import matplotlib.pyplot as plt import glob import math import time import threading import multiprocessing as mp from multiprocessing import Pool import re import cv2 # sys.path.append('/lustre/home/gwxie/hope/project/dewarp/datasets/') # /lustre/home/gwxie/program/project/unwarp/perturbed_imgaes/GAN import utils def getDatasets(dir): return os.listdir(dir) class perturbed(utils.BasePerturbed): def __init__(self, path, bg_path, save_path, save_suffix): self.path = path self.bg_path = bg_path self.save_path = save_path self.save_suffix = save_suffix def save_img(self, m, n, fold_curve='fold', repeat_time=4, fiducial_points = 16, relativeShift_position='relativeShift_v2'): origin_img = cv2.imread(self.path, flags=cv2.IMREAD_COLOR) save_img_shape = [512*2, 480*2] # 320 # reduce_value = np.random.choice([2**4, 2**5, 2**6, 2**7, 2**8], p=[0.01, 0.1, 0.4, 0.39, 0.1]) reduce_value = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.02, 0.18, 0.2, 0.3, 0.1, 0.1, 0.08, 0.02]) # reduce_value = np.random.choice([8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.01, 0.02, 0.2, 0.4, 0.19, 0.18]) # reduce_value = np.random.choice([16, 24, 32, 40, 48, 64], p=[0.01, 0.1, 0.2, 0.4, 0.2, 0.09]) base_img_shrink = save_img_shape[0] - reduce_value # enlarge_img_shrink = [1024, 768] # enlarge_img_shrink = [896, 672] # 420 enlarge_img_shrink = [512*4, 480*4] # 420 # enlarge_img_shrink = [896*2, 768*2] # 420 # enlarge_img_shrink = [896, 768] # 420 # enlarge_img_shrink = [768, 576] # 420 # enlarge_img_shrink = [640, 480] # 420 '''''' im_lr = origin_img.shape[0] im_ud = origin_img.shape[1] reduce_value_v2 = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 28*2, 32*2, 48*2], p=[0.02, 0.18, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1]) # reduce_value_v2 = np.random.choice([16, 24, 28, 32, 48, 64], p=[0.01, 0.1, 0.2, 0.3, 0.25, 0.14]) if im_lr > im_ud: im_ud = min(int(im_ud / im_lr * base_img_shrink), save_img_shape[1] - reduce_value_v2) im_lr = save_img_shape[0] - reduce_value else: base_img_shrink = save_img_shape[1] - reduce_value im_lr = min(int(im_lr / im_ud * base_img_shrink), save_img_shape[0] - reduce_value_v2) im_ud = base_img_shrink if round(im_lr / im_ud, 2) < 0.5 or round(im_ud / im_lr, 2) < 0.5: repeat_time = min(repeat_time, 8) edge_padding = 3 im_lr -= im_lr % (fiducial_points-1) - (2*edge_padding) # im_lr % (fiducial_points-1) - 1 im_ud -= im_ud % (fiducial_points-1) - (2*edge_padding) # im_ud % (fiducial_points-1) - 1 im_hight = np.linspace(edge_padding, im_lr - edge_padding, fiducial_points, dtype=np.int64) im_wide = np.linspace(edge_padding, im_ud - edge_padding, fiducial_points, dtype=np.int64) # im_lr -= im_lr % (fiducial_points-1) - (1+2*edge_padding) # im_lr % (fiducial_points-1) - 1 # im_ud -= im_ud % (fiducial_points-1) - (1+2*edge_padding) # im_ud % (fiducial_points-1) - 1 # im_hight = np.linspace(edge_padding, im_lr - (1+edge_padding), fiducial_points, dtype=np.int64) # im_wide = np.linspace(edge_padding, im_ud - (1+edge_padding), fiducial_points, dtype=np.int64) im_x, im_y = np.meshgrid(im_hight, im_wide) segment_x = (im_lr) // (fiducial_points-1) segment_y = (im_ud) // (fiducial_points-1) # plt.plot(im_x, im_y, # color='limegreen', # marker='.', # linestyle='') # plt.grid(True) # plt.show() self.origin_img = cv2.resize(origin_img, (im_ud, im_lr), interpolation=cv2.INTER_CUBIC) perturbed_bg_ = getDatasets(self.bg_path) perturbed_bg_img_ = self.bg_path+random.choice(perturbed_bg_) perturbed_bg_img = cv2.imread(perturbed_bg_img_, flags=cv2.IMREAD_COLOR) mesh_shape = self.origin_img.shape[:2] self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 256, dtype=np.float32)#np.zeros_like(perturbed_bg_img) # self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 0, dtype=np.int16)#np.zeros_like(perturbed_bg_img) self.new_shape = self.synthesis_perturbed_img.shape[:2] perturbed_bg_img = cv2.resize(perturbed_bg_img, (save_img_shape[1], save_img_shape[0]), cv2.INPAINT_TELEA) origin_pixel_position = np.argwhere(np.zeros(mesh_shape, dtype=np.uint32) == 0).reshape(mesh_shape[0], mesh_shape[1], 2) pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2) self.perturbed_xy_ = np.zeros((self.new_shape[0], self.new_shape[1], 2)) # self.perturbed_xy_ = pixel_position.copy().astype(np.float32) # fiducial_points_grid = origin_pixel_position[im_x, im_y] self.synthesis_perturbed_label = np.zeros((self.new_shape[0], self.new_shape[1], 2)) x_min, y_min, x_max, y_max = self.adjust_position_v2(0, 0, mesh_shape[0], mesh_shape[1], save_img_shape) origin_pixel_position += [x_min, y_min] x_min, y_min, x_max, y_max = self.adjust_position(0, 0, mesh_shape[0], mesh_shape[1]) x_shift = random.randint(-enlarge_img_shrink[0]//16, enlarge_img_shrink[0]//16) y_shift = random.randint(-enlarge_img_shrink[1]//16, enlarge_img_shrink[1]//16) x_min += x_shift x_max += x_shift y_min += y_shift y_max += y_shift '''im_x,y''' im_x += x_min im_y += y_min self.synthesis_perturbed_img[x_min:x_max, y_min:y_max] = self.origin_img self.synthesis_perturbed_label[x_min:x_max, y_min:y_max] = origin_pixel_position synthesis_perturbed_img_map = self.synthesis_perturbed_img.copy() synthesis_perturbed_label_map = self.synthesis_perturbed_label.copy() foreORbackground_label = np.full((mesh_shape), 1, dtype=np.int16) foreORbackground_label_map = np.full((self.new_shape), 0, dtype=np.int16) foreORbackground_label_map[x_min:x_max, y_min:y_max] = foreORbackground_label # synthesis_perturbed_img_map = self.pad(self.synthesis_perturbed_img.copy(), x_min, y_min, x_max, y_max) # synthesis_perturbed_label_map = self.pad(synthesis_perturbed_label_map, x_min, y_min, x_max, y_max) '''*****************************************************************''' is_normalizationFun_mixture = self.is_perform(0.2, 0.8) # if not is_normalizationFun_mixture: normalizationFun_0_1 = False # normalizationFun_0_1 = self.is_perform(0.5, 0.5) if fold_curve == 'fold': fold_curve_random = True # is_normalizationFun_mixture = False normalizationFun_0_1 = self.is_perform(0.2, 0.8) if is_normalizationFun_mixture: alpha_perturbed = random.randint(80, 120) / 100 else: if normalizationFun_0_1 and repeat_time < 8: alpha_perturbed = random.randint(50, 70) / 100 else: alpha_perturbed = random.randint(70, 130) / 100 else: fold_curve_random = self.is_perform(0.1, 0.9) # False # self.is_perform(0.01, 0.99) alpha_perturbed = random.randint(80, 160) / 100 # is_normalizationFun_mixture = False # self.is_perform(0.01, 0.99) synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256) # synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 0, dtype=np.int16) synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label) alpha_perturbed_change = self.is_perform(0.5, 0.5) p_pp_choice = self.is_perform(0.8, 0.2) if fold_curve == 'fold' else self.is_perform(0.1, 0.9) for repeat_i in range(repeat_time): if alpha_perturbed_change: if fold_curve == 'fold': if is_normalizationFun_mixture: alpha_perturbed = random.randint(80, 120) / 100 else: if normalizationFun_0_1 and repeat_time < 8: alpha_perturbed = random.randint(50, 70) / 100 else: alpha_perturbed = random.randint(70, 130) / 100 else: alpha_perturbed = random.randint(80, 160) / 100 '''''' linspace_x = [0, (self.new_shape[0] - im_lr) // 2 - 1, self.new_shape[0] - (self.new_shape[0] - im_lr) // 2 - 1, self.new_shape[0] - 1] linspace_y = [0, (self.new_shape[1] - im_ud) // 2 - 1, self.new_shape[1] - (self.new_shape[1] - im_ud) // 2 - 1, self.new_shape[1] - 1] linspace_x_seq = [1, 2, 3] linspace_y_seq = [1, 2, 3] r_x = random.choice(linspace_x_seq) r_y = random.choice(linspace_y_seq) perturbed_p = np.array( [random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10), random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10 if ((r_x == 1 or r_x == 3) and (r_y == 1 or r_y == 3)) and p_pp_choice: linspace_x_seq.remove(r_x) linspace_y_seq.remove(r_y) r_x = random.choice(linspace_x_seq) r_y = random.choice(linspace_y_seq) perturbed_pp = np.array( [random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10), random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10 # perturbed_p, perturbed_pp = np.array( # [random.randint(0, self.new_shape[0] * 10) / 10, # random.randint(0, self.new_shape[1] * 10) / 10]) \ # , np.array([random.randint(0, self.new_shape[0] * 10) / 10, # random.randint(0, self.new_shape[1] * 10) / 10]) # perturbed_p, perturbed_pp = np.array( # [random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10, # random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10]) \ # , np.array([random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10, # random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10]) '''''' perturbed_vp = perturbed_pp - perturbed_p perturbed_vp_norm = np.linalg.norm(perturbed_vp) perturbed_distance_vertex_and_line = np.dot((perturbed_p - pixel_position), perturbed_vp) / perturbed_vp_norm '''''' # perturbed_v = np.array([random.randint(-3000, 3000) / 100, random.randint(-3000, 3000) / 100]) # perturbed_v = np.array([random.randint(-4000, 4000) / 100, random.randint(-4000, 4000) / 100]) if fold_curve == 'fold' and self.is_perform(0.6, 0.4): # self.is_perform(0.3, 0.7): # perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100]) perturbed_v = np.array([random.randint(-10000, 10000) / 100, random.randint(-10000, 10000) / 100]) # perturbed_v = np.array([random.randint(-11000, 11000) / 100, random.randint(-11000, 11000) / 100]) else: # perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100]) # perturbed_v = np.array([random.randint(-16000, 16000) / 100, random.randint(-16000, 16000) / 100]) perturbed_v = np.array([random.randint(-8000, 8000) / 100, random.randint(-8000, 8000) / 100]) # perturbed_v = np.array([random.randint(-3500, 3500) / 100, random.randint(-3500, 3500) / 100]) # perturbed_v = np.array([random.randint(-600, 600) / 10, random.randint(-600, 600) / 10]) '''''' if fold_curve == 'fold': if is_normalizationFun_mixture: if self.is_perform(0.5, 0.5): perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line)) else: perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2)) else: if normalizationFun_0_1: perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2) else: perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line)) else: if is_normalizationFun_mixture: if self.is_perform(0.5, 0.5): perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line)) else: perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2)) else: if normalizationFun_0_1: perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2) else: perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line)) '''''' if fold_curve_random: # omega_perturbed = (alpha_perturbed+0.2) / (perturbed_d + alpha_perturbed) # omega_perturbed = alpha_perturbed**perturbed_d omega_perturbed = alpha_perturbed / (perturbed_d + alpha_perturbed) else: omega_perturbed = 1 - perturbed_d ** alpha_perturbed '''shadow''' if self.is_perform(0.6, 0.4): synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] = np.minimum(np.maximum(synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] - np.int16(np.round(omega_perturbed[x_min:x_max, y_min:y_max].repeat(3).reshape(x_max-x_min, y_max-y_min, 3) * abs(np.linalg.norm(perturbed_v//2))*np.array([0.4-random.random()*0.1, 0.4-random.random()*0.1, 0.4-random.random()*0.1]))), 0), 255) '''''' if relativeShift_position in ['position', 'relativeShift_v2']: self.perturbed_xy_ += np.array([omega_perturbed * perturbed_v[0], omega_perturbed * perturbed_v[1]]).transpose(1, 2, 0) else: print('relativeShift_position error') exit() ''' flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape( self.new_shape[0] * self.new_shape[1], 2) vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position) wts_sum = np.abs(wts).sum(-1) # flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts) wts = wts[wts_sum <= 1, :] vtx = vtx[wts_sum <= 1, :] synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1, :] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts) synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1, :] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts) foreORbackground_label = np.zeros(self.new_shape) foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts) foreORbackground_label[foreORbackground_label < 0.99] = 0 foreORbackground_label[foreORbackground_label >= 0.99] = 1 # synthesis_perturbed_img = np.around(synthesis_perturbed_img).astype(np.uint8) synthesis_perturbed_label[:, :, 0] *= foreORbackground_label synthesis_perturbed_label[:, :, 1] *= foreORbackground_label synthesis_perturbed_img[:, :, 0] *= foreORbackground_label synthesis_perturbed_img[:, :, 1] *= foreORbackground_label synthesis_perturbed_img[:, :, 2] *= foreORbackground_label self.synthesis_perturbed_img = synthesis_perturbed_img self.synthesis_perturbed_label = synthesis_perturbed_label ''' '''perspective''' perspective_shreshold = random.randint(26, 36)*10 # 280 x_min_per, y_min_per, x_max_per, y_max_per = self.adjust_position(perspective_shreshold, perspective_shreshold, self.new_shape[0]-perspective_shreshold, self.new_shape[1]-perspective_shreshold) pts1 = np.float32([[x_min_per, y_min_per], [x_max_per, y_min_per], [x_min_per, y_max_per], [x_max_per, y_max_per]]) e_1_ = x_max_per - x_min_per e_2_ = y_max_per - y_min_per e_3_ = e_2_ e_4_ = e_1_ perspective_shreshold_h = e_1_*0.02 perspective_shreshold_w = e_2_*0.02 a_min_, a_max_ = 70, 110 # if self.is_perform(1, 0): if fold_curve == 'curve' and self.is_perform(0.5, 0.5): if self.is_perform(0.5, 0.5): while True: pts2 = np.around( np.float32([[x_min_per - (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold], [x_max_per - (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold], [x_min_per + (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold], [x_max_per + (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold]])) # right e_1 = np.linalg.norm(pts2[0]-pts2[1]) e_2 = np.linalg.norm(pts2[0]-pts2[2]) e_3 = np.linalg.norm(pts2[1]-pts2[3]) e_4 = np.linalg.norm(pts2[2]-pts2[3]) if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \ e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \ abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w: a0_, a1_, a2_, a3_ = self.get_angle_4(pts2) if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_): break else: while True: pts2 = np.around( np.float32([[x_min_per + (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold], [x_max_per + (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold], [x_min_per - (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold], [x_max_per - (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold]])) e_1 = np.linalg.norm(pts2[0]-pts2[1]) e_2 = np.linalg.norm(pts2[0]-pts2[2]) e_3 = np.linalg.norm(pts2[1]-pts2[3]) e_4 = np.linalg.norm(pts2[2]-pts2[3]) if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \ e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \ abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w: a0_, a1_, a2_, a3_ = self.get_angle_4(pts2) if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_): break else: while True: pts2 = np.around(np.float32([[x_min_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold], [x_max_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold], [x_min_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold], [x_max_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold]])) e_1 = np.linalg.norm(pts2[0]-pts2[1]) e_2 = np.linalg.norm(pts2[0]-pts2[2]) e_3 = np.linalg.norm(pts2[1]-pts2[3]) e_4 = np.linalg.norm(pts2[2]-pts2[3]) if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \ e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \ abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w: a0_, a1_, a2_, a3_ = self.get_angle_4(pts2) if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_): break M = cv2.getPerspectiveTransform(pts1, pts2) one = np.ones((self.new_shape[0], self.new_shape[1], 1), dtype=np.int16) matr = np.dstack((pixel_position, one)) new = np.dot(M, matr.reshape(-1, 3).T).T.reshape(self.new_shape[0], self.new_shape[1], 3) x = new[:, :, 0]/new[:, :, 2] y = new[:, :, 1]/new[:, :, 2] perturbed_xy_ = np.dstack((x, y)) # perturbed_xy_round_int = np.around(cv2.bilateralFilter(perturbed_xy_round_int, 9, 75, 75)) # perturbed_xy_round_int = np.around(cv2.blur(perturbed_xy_, (17, 17))) # perturbed_xy_round_int = cv2.blur(perturbed_xy_round_int, (17, 17)) # perturbed_xy_round_int = cv2.GaussianBlur(perturbed_xy_round_int, (7, 7), 0) perturbed_xy_ = perturbed_xy_-np.min(perturbed_xy_.T.reshape(2, -1), 1) # perturbed_xy_round_int = np.around(perturbed_xy_round_int-np.min(perturbed_xy_round_int.T.reshape(2, -1), 1)).astype(np.int16) self.perturbed_xy_ += perturbed_xy_ '''perspective end''' '''to img''' flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape( self.new_shape[0] * self.new_shape[1], 2) # self.perturbed_xy_ = cv2.blur(self.perturbed_xy_, (7, 7)) self.perturbed_xy_ = cv2.GaussianBlur(self.perturbed_xy_, (7, 7), 0) '''get fiducial points''' fiducial_points_coordinate = self.perturbed_xy_[im_x, im_y] vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position) wts_sum = np.abs(wts).sum(-1) # flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts) wts = wts[wts_sum <= 1, :] vtx = vtx[wts_sum <= 1, :] synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1, :] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts) synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1, :] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts) foreORbackground_label = np.zeros(self.new_shape) foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts) foreORbackground_label[foreORbackground_label < 0.99] = 0 foreORbackground_label[foreORbackground_label >= 0.99] = 1 self.synthesis_perturbed_img = synthesis_perturbed_img self.synthesis_perturbed_label = synthesis_perturbed_label self.foreORbackground_label = foreORbackground_label '''draw fiducial points stepSize = 0 fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_img.copy() for l in fiducial_points_coordinate.astype(np.int64).reshape(-1,2): cv2.circle(fiducial_points_synthesis_perturbed_img, (l[1] + math.ceil(stepSize / 2), l[0] + math.ceil(stepSize / 2)), 5, (0, 0, 255), -1) cv2.imwrite('/lustre/home/gwxie/program/project/unwarp/unwarp_perturbed/TPS/img/cv_TPS_large.jpg', fiducial_points_synthesis_perturbed_img) ''' '''clip''' perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = -1, -1, self.new_shape[0], self.new_shape[1] for x in range(self.new_shape[0] // 2, perturbed_x_max): if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and perturbed_x_max - 1 > x: perturbed_x_max = x break for x in range(self.new_shape[0] // 2, perturbed_x_min, -1): if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and x > 0: perturbed_x_min = x break for y in range(self.new_shape[1] // 2, perturbed_y_max): if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and perturbed_y_max - 1 > y: perturbed_y_max = y break for y in range(self.new_shape[1] // 2, perturbed_y_min, -1): if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and y > 0: perturbed_y_min = y break if perturbed_x_min == 0 or perturbed_x_max == self.new_shape[0] or perturbed_y_min == self.new_shape[1] or perturbed_y_max == self.new_shape[1]: raise Exception('clip error') if perturbed_x_max - perturbed_x_min < im_lr//2 or perturbed_y_max - perturbed_y_min < im_ud//2: raise Exception('clip error') perfix_ = self.save_suffix+'_'+str(m)+'_'+str(n) is_shrink = False if perturbed_x_max - perturbed_x_min > save_img_shape[0] or perturbed_y_max - perturbed_y_min > save_img_shape[1]: is_shrink = True synthesis_perturbed_img = cv2.resize(self.synthesis_perturbed_img[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR) synthesis_perturbed_label = cv2.resize(self.synthesis_perturbed_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR) foreORbackground_label = cv2.resize(self.foreORbackground_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR) foreORbackground_label[foreORbackground_label < 0.99] = 0 foreORbackground_label[foreORbackground_label >= 0.99] = 1 '''shrink fiducial points''' center_x_l, center_y_l = perturbed_x_min + (perturbed_x_max - perturbed_x_min) // 2, perturbed_y_min + (perturbed_y_max - perturbed_y_min) // 2 fiducial_points_coordinate_copy = fiducial_points_coordinate.copy() shrink_x = im_lr/(perturbed_x_max - perturbed_x_min) shrink_y = im_ud/(perturbed_y_max - perturbed_y_min) fiducial_points_coordinate *= [shrink_x, shrink_y] center_x_l *= shrink_x center_y_l *= shrink_y # fiducial_points_coordinate[1:, 1:] *= [shrink_x, shrink_y] # fiducial_points_coordinate[1:, :1, 0] *= shrink_x # fiducial_points_coordinate[:1, 1:, 1] *= shrink_y # perturbed_x_min_copy, perturbed_y_min_copy, perturbed_x_max_copy, perturbed_y_max_copy = perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = self.adjust_position_v2(0, 0, im_lr, im_ud, self.new_shape) self.synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256) self.synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label) self.foreORbackground_label = np.zeros_like(self.foreORbackground_label) self.synthesis_perturbed_img[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_img self.synthesis_perturbed_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_label self.foreORbackground_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max] = foreORbackground_label center_x, center_y = perturbed_x_min + (perturbed_x_max - perturbed_x_min) // 2, perturbed_y_min + (perturbed_y_max - perturbed_y_min) // 2 if is_shrink: fiducial_points_coordinate += [center_x-center_x_l, center_y-center_y_l] '''draw fiducial points stepSize = 0 fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_img.copy() for l in fiducial_points_coordinate.astype(np.int64).reshape(-1, 2): cv2.circle(fiducial_points_synthesis_perturbed_img, (l[1] + math.ceil(stepSize / 2), l[0] + math.ceil(stepSize / 2)), 5, (0, 0, 255), -1) cv2.imwrite('/lustre/home/gwxie/program/project/unwarp/unwarp_perturbed/TPS/img/cv_TPS_small.jpg',fiducial_points_synthesis_perturbed_img) ''' self.new_shape = save_img_shape self.synthesis_perturbed_img = self.synthesis_perturbed_img[ center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2, center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2, :].copy() self.synthesis_perturbed_label = self.synthesis_perturbed_label[ center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2, center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2, :].copy() self.foreORbackground_label = self.foreORbackground_label[ center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2, center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2].copy() perturbed_x_ = max(self.new_shape[0] - (perturbed_x_max - perturbed_x_min), 0) perturbed_x_min = perturbed_x_ // 2 perturbed_x_max = self.new_shape[0] - perturbed_x_ // 2 if perturbed_x_%2 == 0 else self.new_shape[0] - (perturbed_x_ // 2 + 1) perturbed_y_ = max(self.new_shape[1] - (perturbed_y_max - perturbed_y_min), 0) perturbed_y_min = perturbed_y_ // 2 perturbed_y_max = self.new_shape[1] - perturbed_y_ // 2 if perturbed_y_%2 == 0 else self.new_shape[1] - (perturbed_y_ // 2 + 1) '''clip perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = -1, -1, self.new_shape[0], self.new_shape[1] for x in range(self.new_shape[0] // 2, perturbed_x_max): if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and perturbed_x_max - 1 > x: perturbed_x_max = x break for x in range(self.new_shape[0] // 2, perturbed_x_min, -1): if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and x > 0: perturbed_x_min = x break for y in range(self.new_shape[1] // 2, perturbed_y_max): if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and perturbed_y_max - 1 > y: perturbed_y_max = y break for y in range(self.new_shape[1] // 2, perturbed_y_min, -1): if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and y > 0: perturbed_y_min = y break center_x, center_y = perturbed_x_min+(perturbed_x_max - perturbed_x_min)//2, perturbed_y_min+(perturbed_y_max - perturbed_y_min)//2 perfix_ = self.save_suffix+'_'+str(m)+'_'+str(n) self.new_shape = save_img_shape perturbed_x_ = max(self.new_shape[0] - (perturbed_x_max - perturbed_x_min), 0) perturbed_x_min = perturbed_x_ // 2 perturbed_x_max = self.new_shape[0] - perturbed_x_ // 2 if perturbed_x_%2 == 0 else self.new_shape[0] - (perturbed_x_ // 2 + 1) perturbed_y_ = max(self.new_shape[1] - (perturbed_y_max - perturbed_y_min), 0) perturbed_y_min = perturbed_y_ // 2 perturbed_y_max = self.new_shape[1] - perturbed_y_ // 2 if perturbed_y_%2 == 0 else self.new_shape[1] - (perturbed_y_ // 2 + 1) self.synthesis_perturbed_img = self.synthesis_perturbed_img[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2, :].copy() self.synthesis_perturbed_label = self.synthesis_perturbed_label[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2, :].copy() self.foreORbackground_label = self.foreORbackground_label[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2].copy() ''' '''save''' pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2) if relativeShift_position == 'relativeShift_v2': self.synthesis_perturbed_label -= pixel_position fiducial_points_coordinate -= [center_x - self.new_shape[0] // 2, center_y - self.new_shape[1] // 2] self.synthesis_perturbed_label[:, :, 0] *= self.foreORbackground_label self.synthesis_perturbed_label[:, :, 1] *= self.foreORbackground_label self.synthesis_perturbed_img[:, :, 0] *= self.foreORbackground_label self.synthesis_perturbed_img[:, :, 1] *= self.foreORbackground_label self.synthesis_perturbed_img[:, :, 2] *= self.foreORbackground_label ''' synthesis_perturbed_img_filter = self.synthesis_perturbed_img.copy() synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0) # if self.is_perform(0.9, 0.1) or repeat_time > 5: # # if self.is_perform(0.1, 0.9) and repeat_time > 9: # # synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (7, 7), 0) # # else: # synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (5, 5), 0) # else: # synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0) self.synthesis_perturbed_img[self.foreORbackground_label == 1] = synthesis_perturbed_img_filter[self.foreORbackground_label == 1] ''' ''' perturbed_bg_img = perturbed_bg_img.astype(np.float32) perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label self.synthesis_perturbed_img += perturbed_bg_img HSV perturbed_bg_img = perturbed_bg_img.astype(np.float32) if self.is_perform(0.1, 0.9): if self.is_perform(0.2, 0.8): synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy() synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_RGB2HSV) H_, S_, V_ = (random.random()-0.2)*20, (random.random()-0.2)/8, (random.random()-0.2)*20 synthesis_perturbed_img_clip_HSV[:, :, 0], synthesis_perturbed_img_clip_HSV[:, :, 1], synthesis_perturbed_img_clip_HSV[:, :, 2] = synthesis_perturbed_img_clip_HSV[:, :, 0]-H_, synthesis_perturbed_img_clip_HSV[:, :, 1]-S_, synthesis_perturbed_img_clip_HSV[:, :, 2]-V_ synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_HSV2RGB) perturbed_bg_img[:, :, 0] *= 1-self.foreORbackground_label perturbed_bg_img[:, :, 1] *= 1-self.foreORbackground_label perturbed_bg_img[:, :, 2] *= 1-self.foreORbackground_label synthesis_perturbed_img_clip_HSV += perturbed_bg_img self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV else: perturbed_bg_img_HSV = perturbed_bg_img perturbed_bg_img_HSV = cv2.cvtColor(perturbed_bg_img_HSV, cv2.COLOR_RGB2HSV) H_, S_, V_ = (random.random()-0.5)*20, (random.random()-0.5)/8, (random.random()-0.2)*20 perturbed_bg_img_HSV[:, :, 0], perturbed_bg_img_HSV[:, :, 1], perturbed_bg_img_HSV[:, :, 2] = perturbed_bg_img_HSV[:, :, 0]-H_, perturbed_bg_img_HSV[:, :, 1]-S_, perturbed_bg_img_HSV[:, :, 2]-V_ perturbed_bg_img_HSV = cv2.cvtColor(perturbed_bg_img_HSV, cv2.COLOR_HSV2RGB) perturbed_bg_img_HSV[:, :, 0] *= 1-self.foreORbackground_label perturbed_bg_img_HSV[:, :, 1] *= 1-self.foreORbackground_label perturbed_bg_img_HSV[:, :, 2] *= 1-self.foreORbackground_label self.synthesis_perturbed_img += perturbed_bg_img_HSV # self.synthesis_perturbed_img[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771] else: synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy() perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label synthesis_perturbed_img_clip_HSV += perturbed_bg_img # synthesis_perturbed_img_clip_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img[np.sum(self.synthesis_perturbed_img, 2) == 771] synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_RGB2HSV) H_, S_, V_ = (random.random()-0.5)*20, (random.random()-0.5)/10, (random.random()-0.4)*20 synthesis_perturbed_img_clip_HSV[:, :, 0], synthesis_perturbed_img_clip_HSV[:, :, 1], synthesis_perturbed_img_clip_HSV[:, :, 2] = synthesis_perturbed_img_clip_HSV[:, :, 0]-H_, synthesis_perturbed_img_clip_HSV[:, :, 1]-S_, synthesis_perturbed_img_clip_HSV[:, :, 2]-V_ synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_HSV2RGB) self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV ''' '''HSV_v2''' perturbed_bg_img = perturbed_bg_img.astype(np.float32) # if self.is_perform(1, 0): # if self.is_perform(1, 0): if self.is_perform(0.1, 0.9): if self.is_perform(0.2, 0.8): synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy() synthesis_perturbed_img_clip_HSV = self.HSV_v1(synthesis_perturbed_img_clip_HSV) perturbed_bg_img[:, :, 0] *= 1-self.foreORbackground_label perturbed_bg_img[:, :, 1] *= 1-self.foreORbackground_label perturbed_bg_img[:, :, 2] *= 1-self.foreORbackground_label synthesis_perturbed_img_clip_HSV += perturbed_bg_img self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV else: perturbed_bg_img_HSV = perturbed_bg_img perturbed_bg_img_HSV = self.HSV_v1(perturbed_bg_img_HSV) perturbed_bg_img_HSV[:, :, 0] *= 1-self.foreORbackground_label perturbed_bg_img_HSV[:, :, 1] *= 1-self.foreORbackground_label perturbed_bg_img_HSV[:, :, 2] *= 1-self.foreORbackground_label self.synthesis_perturbed_img += perturbed_bg_img_HSV # self.synthesis_perturbed_img[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771] else: synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy() perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label synthesis_perturbed_img_clip_HSV += perturbed_bg_img synthesis_perturbed_img_clip_HSV = self.HSV_v1(synthesis_perturbed_img_clip_HSV) self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV '''''' # cv2.imwrite(self.save_path+'clip/'+perfix_+'_'+fold_curve+str(perturbed_time)+'-'+str(repeat_time)+'.png', synthesis_perturbed_img_clip) self.synthesis_perturbed_img[self.synthesis_perturbed_img < 0] = 0 self.synthesis_perturbed_img[self.synthesis_perturbed_img > 255] = 255 self.synthesis_perturbed_img = np.around(self.synthesis_perturbed_img).astype(np.uint8) label = np.zeros_like(self.synthesis_perturbed_img, dtype=np.float32) label[:, :, :2] = self.synthesis_perturbed_label label[:, :, 2] = self.foreORbackground_label # grey = np.around(self.synthesis_perturbed_img[:, :, 0] * 0.2989 + self.synthesis_perturbed_img[:, :, 1] * 0.5870 + self.synthesis_perturbed_img[:, :, 0] * 0.1140).astype(np.int16) # synthesis_perturbed_grey = np.concatenate((grey.reshape(self.new_shape[0], self.new_shape[1], 1), label), axis=2) synthesis_perturbed_color = np.concatenate((self.synthesis_perturbed_img, label), axis=2) self.synthesis_perturbed_color = np.zeros_like(synthesis_perturbed_color, dtype=np.float32) # self.synthesis_perturbed_grey = np.zeros_like(synthesis_perturbed_grey, dtype=np.float32) reduce_value_x = int(round(min((random.random() / 2) * (self.new_shape[0] - (perturbed_x_max - perturbed_x_min)), min(reduce_value, reduce_value_v2)))) reduce_value_y = int(round(min((random.random() / 2) * (self.new_shape[1] - (perturbed_y_max - perturbed_y_min)), min(reduce_value, reduce_value_v2)))) perturbed_x_min = max(perturbed_x_min - reduce_value_x, 0) perturbed_x_max = min(perturbed_x_max + reduce_value_x, self.new_shape[0]) perturbed_y_min = max(perturbed_y_min - reduce_value_y, 0) perturbed_y_max = min(perturbed_y_max + reduce_value_y, self.new_shape[1]) if im_lr >= im_ud: self.synthesis_perturbed_color[:, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_color[:, perturbed_y_min:perturbed_y_max, :] # self.synthesis_perturbed_grey[:, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_grey[:, perturbed_y_min:perturbed_y_max, :] else: self.synthesis_perturbed_color[perturbed_x_min:perturbed_x_max, :, :] = synthesis_perturbed_color[perturbed_x_min:perturbed_x_max, :, :] # self.synthesis_perturbed_grey[perturbed_x_min:perturbed_x_max, :, :] = synthesis_perturbed_grey[perturbed_x_min:perturbed_x_max, :, :] '''blur''' if self.is_perform(0.1, 0.9): synthesis_perturbed_img_filter = self.synthesis_perturbed_color[:, :, :3].copy() if self.is_perform(0.1, 0.9): synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (5, 5), 0) else: synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0) if self.is_perform(0.5, 0.5): self.synthesis_perturbed_color[:, :, :3][self.synthesis_perturbed_color[:, :, 5] == 1] = synthesis_perturbed_img_filter[self.synthesis_perturbed_color[:, :, 5] == 1] else: self.synthesis_perturbed_color[:, :, :3] = synthesis_perturbed_img_filter fiducial_points_coordinate = fiducial_points_coordinate[:, :, ::-1] '''draw fiducial points''' stepSize = 0 fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_color[:, :, :3].copy() for l in fiducial_points_coordinate.astype(np.int64).reshape(-1, 2): cv2.circle(fiducial_points_synthesis_perturbed_img, (l[0] + math.ceil(stepSize / 2), l[1] + math.ceil(stepSize / 2)), 2, (0, 0, 255), -1) cv2.imwrite(self.save_path + 'fiducial_points/' + perfix_ + '_' + fold_curve + '.png', fiducial_points_synthesis_perturbed_img) cv2.imwrite(self.save_path + 'png/' + perfix_ + '_' + fold_curve + '.png', self.synthesis_perturbed_color[:, :, :3]) '''forward-begin''' self.forward_mapping =

np.full((save_img_shape[0], save_img_shape[1], 2), 0, dtype=np.float32)

numpy.full

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') plt.savefig('jss_figures/DFA_different_trends.png') plt.show() # plot 6b fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[0].set_ylim(-5.5, 5.5) axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].set_ylim(-5.5, 5.5) axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([np.pi, (3 / 2) * np.pi]) axs[2].set_xticklabels([r'$\pi$', r'$\frac{3}{2}\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].set_ylim(-5.5, 5.5) axs[2].set_xlim(0.95 * np.pi, 1.55 * np.pi) plt.savefig('jss_figures/DFA_different_trends_zoomed.png') plt.show() hs_ouputs = hilbert_spectrum(time, imfs_51, hts_51, ifs_51, max_frequency=12, plot=False) # plot 6c ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Simple Sinusoidal Time Seres with Added Noise', 50)) x_hs, y, z = hs_ouputs z_min, z_max = 0, np.abs(z).max() ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) ax.plot(x_hs[0, :], 8 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 8$', Linewidth=3) ax.plot(x_hs[0, :], 4 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 4$', Linewidth=3) ax.plot(x_hs[0, :], 2 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 2$', Linewidth=3) ax.set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi]) ax.set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$']) plt.ylabel(r'Frequency (rad.s$^{-1}$)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.85, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/DFA_hilbert_spectrum.png') plt.show() # plot 6c time = np.linspace(0, 5 * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 51) fluc = Fluctuation(time=time, time_series=time_series) max_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=False) max_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=True) min_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=False) min_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=True) util = Utility(time=time, time_series=time_series) maxima = util.max_bool_func_1st_order_fd() minima = util.min_bool_func_1st_order_fd() ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title(textwrap.fill('Plot Demonstrating Unsmoothed Extrema Envelopes if Schoenberg–Whitney Conditions are Not Satisfied', 50)) plt.plot(time, time_series, label='Time series', zorder=2, LineWidth=2) plt.scatter(time[maxima], time_series[maxima], c='r', label='Maxima', zorder=10) plt.scatter(time[minima], time_series[minima], c='b', label='Minima', zorder=10) plt.plot(time, max_unsmoothed[0], label=textwrap.fill('Unsmoothed maxima envelope', 10), c='darkorange') plt.plot(time, max_smoothed[0], label=textwrap.fill('Smoothed maxima envelope', 10), c='red') plt.plot(time, min_unsmoothed[0], label=textwrap.fill('Unsmoothed minima envelope', 10), c='cyan') plt.plot(time, min_smoothed[0], label=textwrap.fill('Smoothed minima envelope', 10), c='blue') for knot in knots[:-1]: plt.plot(knot * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', zorder=1) plt.plot(knots[-1] * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', label='Knots', zorder=1) plt.xticks((0, 1 * np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi), (r'$0$', r'$\pi$', r'2$\pi$', r'3$\pi$', r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) plt.xlim(-0.25 * np.pi, 5.25 * np.pi) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Schoenberg_Whitney_Conditions.png') plt.show() # plot 7 a = 0.25 width = 0.2 time = np.linspace((0 + a) * np.pi, (5 - a) * np.pi, 1001) knots = np.linspace((0 + a) * np.pi, (5 - a) * np.pi, 11) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] inflection_bool = utils.inflection_point() inflection_x = time[inflection_bool] inflection_y = time_series[inflection_bool] fluctuation = emd_mean.Fluctuation(time=time, time_series=time_series) maxima_envelope = fluctuation.envelope_basis_function_approximation(knots, 'maxima', smooth=False, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] maxima_envelope_smooth = fluctuation.envelope_basis_function_approximation(knots, 'maxima', smooth=True, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] minima_envelope = fluctuation.envelope_basis_function_approximation(knots, 'minima', smooth=False, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] minima_envelope_smooth = fluctuation.envelope_basis_function_approximation(knots, 'minima', smooth=True, smoothing_penalty=0.2, edge_effect='none', spline_method='b_spline')[0] inflection_points_envelope = fluctuation.direct_detrended_fluctuation_estimation(knots, smooth=True, smoothing_penalty=0.2, technique='inflection_points')[0] binomial_points_envelope = fluctuation.direct_detrended_fluctuation_estimation(knots, smooth=True, smoothing_penalty=0.2, technique='binomial_average', order=21, increment=20)[0] derivative_of_lsq = utils.derivative_forward_diff() derivative_time = time[:-1] derivative_knots = np.linspace(knots[0], knots[-1], 31) # change (1) detrended_fluctuation_technique and (2) max_internal_iter and (3) debug (confusing with external debugging) emd = AdvEMDpy.EMD(time=derivative_time, time_series=derivative_of_lsq) imf_1_of_derivative = emd.empirical_mode_decomposition(knots=derivative_knots, knot_time=derivative_time, text=False, verbose=False)[0][1, :] utils = emd_utils.Utility(time=time[:-1], time_series=imf_1_of_derivative) optimal_maxima = np.r_[False, utils.derivative_forward_diff() < 0, False] & \ np.r_[utils.zero_crossing() == 1, False] optimal_minima = np.r_[False, utils.derivative_forward_diff() > 0, False] & \ np.r_[utils.zero_crossing() == 1, False] EEMD_maxima_envelope = fluctuation.envelope_basis_function_approximation_fixed_points(knots, 'maxima', optimal_maxima, optimal_minima, smooth=False, smoothing_penalty=0.2, edge_effect='none')[0] EEMD_minima_envelope = fluctuation.envelope_basis_function_approximation_fixed_points(knots, 'minima', optimal_maxima, optimal_minima, smooth=False, smoothing_penalty=0.2, edge_effect='none')[0] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Detrended Fluctuation Analysis Examples') plt.plot(time, time_series, LineWidth=2, label='Time series') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(time[optimal_maxima], time_series[optimal_maxima], c='darkred', zorder=4, label=textwrap.fill('Optimal maxima', 10)) plt.scatter(time[optimal_minima], time_series[optimal_minima], c='darkblue', zorder=4, label=textwrap.fill('Optimal minima', 10)) plt.scatter(inflection_x, inflection_y, c='magenta', zorder=4, label=textwrap.fill('Inflection points', 10)) plt.plot(time, maxima_envelope, c='darkblue', label=textwrap.fill('EMD envelope', 10)) plt.plot(time, minima_envelope, c='darkblue') plt.plot(time, (maxima_envelope + minima_envelope) / 2, c='darkblue') plt.plot(time, maxima_envelope_smooth, c='darkred', label=textwrap.fill('SEMD envelope', 10)) plt.plot(time, minima_envelope_smooth, c='darkred') plt.plot(time, (maxima_envelope_smooth + minima_envelope_smooth) / 2, c='darkred') plt.plot(time, EEMD_maxima_envelope, c='darkgreen', label=textwrap.fill('EEMD envelope', 10)) plt.plot(time, EEMD_minima_envelope, c='darkgreen') plt.plot(time, (EEMD_maxima_envelope + EEMD_minima_envelope) / 2, c='darkgreen') plt.plot(time, inflection_points_envelope, c='darkorange', label=textwrap.fill('Inflection point envelope', 10)) plt.plot(time, binomial_points_envelope, c='deeppink', label=textwrap.fill('Binomial average envelope', 10)) plt.plot(time, np.cos(time), c='black', label='True mean') plt.xticks((0, 1 * np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi), (r'$0$', r'$\pi$', r'2$\pi$', r'3$\pi$', r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) plt.xlim(-0.25 * np.pi, 5.25 * np.pi) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/detrended_fluctuation_analysis.png') plt.show() # Duffing Equation Example def duffing_equation(xy, ts): gamma = 0.1 epsilon = 1 omega = ((2 * np.pi) / 25) return [xy[1], xy[0] - epsilon * xy[0] ** 3 + gamma * np.cos(omega * ts)] t = np.linspace(0, 150, 1501) XY0 = [1, 1] solution = odeint(duffing_equation, XY0, t) x = solution[:, 0] dxdt = solution[:, 1] x_points = [0, 50, 100, 150] x_names = {0, 50, 100, 150} y_points_1 = [-2, 0, 2] y_points_2 = [-1, 0, 1] fig, axs = plt.subplots(2, 1) plt.subplots_adjust(hspace=0.2) axs[0].plot(t, x) axs[0].set_title('Duffing Equation Displacement') axs[0].set_ylim([-2, 2]) axs[0].set_xlim([0, 150]) axs[1].plot(t, dxdt) axs[1].set_title('Duffing Equation Velocity') axs[1].set_ylim([-1.5, 1.5]) axs[1].set_xlim([0, 150]) axis = 0 for ax in axs.flat: ax.label_outer() if axis == 0: ax.set_ylabel('x(t)') ax.set_yticks(y_points_1) if axis == 1: ax.set_ylabel(r'$ \dfrac{dx(t)}{dt} $') ax.set(xlabel='t') ax.set_yticks(y_points_2) ax.set_xticks(x_points) ax.set_xticklabels(x_names) axis += 1 plt.savefig('jss_figures/Duffing_equation.png') plt.show() # compare other packages Duffing - top pyemd = pyemd0215() py_emd = pyemd(x) IP, IF, IA = emd040.spectra.frequency_transform(py_emd.T, 10, 'hilbert') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 0.2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using PyEMD 0.2.10', 40)) plt.pcolormesh(t, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht_pyemd.png') plt.show() plt.show() emd_sift = emd040.sift.sift(x) IP, IF, IA = emd040.spectra.frequency_transform(emd_sift, 10, 'hilbert') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 0.2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using emd 0.3.3', 40)) plt.pcolormesh(t, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht_emd.png') plt.show() # compare other packages Duffing - bottom emd_duffing = AdvEMDpy.EMD(time=t, time_series=x) emd_duff, emd_ht_duff, emd_if_duff, _, _, _, _ = emd_duffing.empirical_mode_decomposition(verbose=False) fig, axs = plt.subplots(2, 1) plt.subplots_adjust(hspace=0.3) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) axs[0].plot(t, emd_duff[1, :], label='AdvEMDpy') axs[0].plot(t, py_emd[0, :], '--', label='PyEMD 0.2.10') axs[0].plot(t, emd_sift[:, 0], '--', label='emd 0.3.3') axs[0].set_title('IMF 1') axs[0].set_ylim([-2, 2]) axs[0].set_xlim([0, 150]) axs[1].plot(t, emd_duff[2, :], label='AdvEMDpy') print(f'AdvEMDpy driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - emd_duff[2, :])), 3)}') axs[1].plot(t, py_emd[1, :], '--', label='PyEMD 0.2.10') print(f'PyEMD driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - py_emd[1, :])), 3)}') axs[1].plot(t, emd_sift[:, 1], '--', label='emd 0.3.3') print(f'emd driving function error: {np.round(sum(abs(0.1 * np.cos(0.04 * 2 * np.pi * t) - emd_sift[:, 1])), 3)}') axs[1].plot(t, 0.1 * np.cos(0.04 * 2 * np.pi * t), '--', label=r'$0.1$cos$(0.08{\pi}t)$') axs[1].set_title('IMF 2') axs[1].set_ylim([-0.2, 0.4]) axs[1].set_xlim([0, 150]) axis = 0 for ax in axs.flat: ax.label_outer() if axis == 0: ax.set_ylabel(r'$\gamma_1(t)$') ax.set_yticks([-2, 0, 2]) if axis == 1: ax.set_ylabel(r'$\gamma_2(t)$') ax.set_yticks([-0.2, 0, 0.2]) box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) ax.set_xticks(x_points) ax.set_xticklabels(x_names) axis += 1 plt.savefig('jss_figures/Duffing_equation_imfs.png') plt.show() hs_ouputs = hilbert_spectrum(t, emd_duff, emd_ht_duff, emd_if_duff, max_frequency=1.3, plot=False) ax = plt.subplot(111) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Duffing Equation using AdvEMDpy', 40)) x, y, z = hs_ouputs y = y / (2 * np.pi) z_min, z_max = 0, np.abs(z).max() figure_size = plt.gcf().get_size_inches() factor = 1.0 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) ax.pcolormesh(x, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) plt.plot(t[:-1], 0.124 * np.ones_like(t[:-1]), '--', label=textwrap.fill('Hamiltonian frequency approximation', 15)) plt.plot(t[:-1], 0.04 * np.ones_like(t[:-1]), 'g--', label=textwrap.fill('Driving function frequency', 15)) plt.xticks([0, 50, 100, 150]) plt.yticks([0, 0.1, 0.2]) plt.ylabel('Frequency (Hz)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.75, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/Duffing_equation_ht.png') plt.show() # Carbon Dioxide Concentration Example CO2_data = pd.read_csv('Data/co2_mm_mlo.csv', header=51) plt.plot(CO2_data['month'], CO2_data['decimal date']) plt.title(textwrap.fill('Mean Monthly Concentration of Carbon Dioxide in the Atmosphere', 35)) plt.ylabel('Parts per million') plt.xlabel('Time (years)') plt.savefig('jss_figures/CO2_concentration.png') plt.show() signal = CO2_data['decimal date'] signal = np.asarray(signal) time = CO2_data['month'] time = np.asarray(time) # compare other packages Carbon Dioxide - top pyemd = pyemd0215() py_emd = pyemd(signal) IP, IF, IA = emd040.spectra.frequency_transform(py_emd[:2, :].T, 12, 'hilbert') print(f'PyEMD annual frequency error: {np.round(sum(np.abs(IF[:, 0] - np.ones_like(IF[:, 0]))), 3)}') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using PyEMD 0.2.10', 45)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.pcolormesh(time, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(time, np.ones_like(time), 'k--', label=textwrap.fill('Annual cycle', 10)) box_0 = ax.get_position() ax.set_position([box_0.x0 + 0.0125, box_0.y0 + 0.075, box_0.width * 0.8, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/CO2_Hilbert_pyemd.png') plt.show() emd_sift = emd040.sift.sift(signal) IP, IF, IA = emd040.spectra.frequency_transform(emd_sift[:, :1], 12, 'hilbert') print(f'emd annual frequency error: {np.round(sum(np.abs(IF - np.ones_like(IF)))[0], 3)}') freq_edges, freq_bins = emd040.spectra.define_hist_bins(0, 2, 100) hht = emd040.spectra.hilberthuang(IF, IA, freq_edges) hht = gaussian_filter(hht, sigma=1) fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using emd 0.3.3', 45)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.pcolormesh(time, freq_bins, hht, cmap='gist_rainbow', vmin=0, vmax=np.max(np.max(np.abs(hht)))) plt.plot(time, np.ones_like(time), 'k--', label=textwrap.fill('Annual cycle', 10)) box_0 = ax.get_position() ax.set_position([box_0.x0 + 0.0125, box_0.y0 + 0.075, box_0.width * 0.8, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/CO2_Hilbert_emd.png') plt.show() # compare other packages Carbon Dioxide - bottom knots = np.linspace(time[0], time[-1], 200) emd_example = AdvEMDpy.EMD(time=time, time_series=signal) imfs, hts, ifs, _, _, _, _ = \ emd_example.empirical_mode_decomposition(knots=knots, knot_time=time, verbose=False) print(f'AdvEMDpy annual frequency error: {np.round(sum(np.abs(ifs[1, :] / (2 * np.pi) - np.ones_like(ifs[1, :]))), 3)}') fig, axs = plt.subplots(2, 2) plt.subplots_adjust(hspace=0.5) axs[0, 0].plot(time, signal) axs[0, 1].plot(time, signal) axs[0, 1].plot(time, imfs[0, :], label='Smoothed') axs[0, 1].legend(loc='lower right') axs[1, 0].plot(time, imfs[1, :]) axs[1, 1].plot(time, imfs[2, :]) axis = 0 for ax in axs.flat: if axis == 0: ax.set(ylabel=R'C0$_2$ concentration') if axis == 1: pass if axis == 2: ax.set(ylabel=R'C0$_2$ concentration') ax.set(xlabel='Time (years)') if axis == 3: ax.set(xlabel='Time (years)') axis += 1 plt.gcf().subplots_adjust(bottom=0.15) axs[0, 0].set_title(r'Original CO$_2$ Concentration') axs[0, 1].set_title('Smoothed CO$_2$ Concentration') axs[1, 0].set_title('IMF 1') axs[1, 1].set_title('Residual') plt.gcf().subplots_adjust(bottom=0.15) plt.savefig('jss_figures/CO2_EMD.png') plt.show() hs_ouputs = hilbert_spectrum(time, imfs, hts, ifs, max_frequency=10, which_imfs=[1], plot=False) x_hs, y, z = hs_ouputs y = y / (2 * np.pi) z_min, z_max = 0, np.abs(z).max() fig, ax = plt.subplots() figure_size = plt.gcf().get_size_inches() factor = 0.7 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) ax.set_title(textwrap.fill(r'Gaussian Filtered Hilbert Spectrum of CO$_{2}$ Concentration using AdvEMDpy', 40)) plt.ylabel('Frequency (year$^{-1}$)') plt.xlabel('Time (years)') plt.plot(x_hs[0, :],

np.ones_like(x_hs[0, :])

numpy.ones_like

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi *

np.ones(101)

numpy.ones

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') plt.savefig('jss_figures/DFA_different_trends.png') plt.show() # plot 6b fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[0].set_ylim(-5.5, 5.5) axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].set_ylim(-5.5, 5.5) axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([np.pi, (3 / 2) * np.pi]) axs[2].set_xticklabels([r'$\pi$', r'$\frac{3}{2}\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].set_ylim(-5.5, 5.5) axs[2].set_xlim(0.95 * np.pi, 1.55 * np.pi) plt.savefig('jss_figures/DFA_different_trends_zoomed.png') plt.show() hs_ouputs = hilbert_spectrum(time, imfs_51, hts_51, ifs_51, max_frequency=12, plot=False) # plot 6c ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.title(textwrap.fill('Gaussian Filtered Hilbert Spectrum of Simple Sinusoidal Time Seres with Added Noise', 50)) x_hs, y, z = hs_ouputs z_min, z_max = 0, np.abs(z).max() ax.pcolormesh(x_hs, y, np.abs(z), cmap='gist_rainbow', vmin=z_min, vmax=z_max) ax.plot(x_hs[0, :], 8 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 8$', Linewidth=3) ax.plot(x_hs[0, :], 4 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 4$', Linewidth=3) ax.plot(x_hs[0, :], 2 * np.ones_like(x_hs[0, :]), '--', label=r'$\omega = 2$', Linewidth=3) ax.set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi]) ax.set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$']) plt.ylabel(r'Frequency (rad.s$^{-1}$)') plt.xlabel('Time (s)') box_0 = ax.get_position() ax.set_position([box_0.x0, box_0.y0 + 0.05, box_0.width * 0.85, box_0.height * 0.9]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/DFA_hilbert_spectrum.png') plt.show() # plot 6c time = np.linspace(0, 5 * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 51) fluc = Fluctuation(time=time, time_series=time_series) max_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=False) max_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='maxima', smooth=True) min_unsmoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=False) min_smoothed = fluc.envelope_basis_function_approximation(knots_for_envelope=knots, extrema_type='minima', smooth=True) util = Utility(time=time, time_series=time_series) maxima = util.max_bool_func_1st_order_fd() minima = util.min_bool_func_1st_order_fd() ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title(textwrap.fill('Plot Demonstrating Unsmoothed Extrema Envelopes if Schoenberg–Whitney Conditions are Not Satisfied', 50)) plt.plot(time, time_series, label='Time series', zorder=2, LineWidth=2) plt.scatter(time[maxima], time_series[maxima], c='r', label='Maxima', zorder=10) plt.scatter(time[minima], time_series[minima], c='b', label='Minima', zorder=10) plt.plot(time, max_unsmoothed[0], label=textwrap.fill('Unsmoothed maxima envelope', 10), c='darkorange') plt.plot(time, max_smoothed[0], label=textwrap.fill('Smoothed maxima envelope', 10), c='red') plt.plot(time, min_unsmoothed[0], label=textwrap.fill('Unsmoothed minima envelope', 10), c='cyan') plt.plot(time, min_smoothed[0], label=textwrap.fill('Smoothed minima envelope', 10), c='blue') for knot in knots[:-1]: plt.plot(knot * np.ones(101), np.linspace(-3.0, -2.0, 101), '--', c='grey', zorder=1) plt.plot(knots[-1] * np.ones(101),

np.linspace(-3.0, -2.0, 101)

numpy.linspace

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101),

np.linspace(-5, 5, 101)

numpy.linspace

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[2].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') plt.savefig('jss_figures/DFA_different_trends.png') plt.show() # plot 6b fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences Zoomed Region', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[0].set_ylim(-5.5, 5.5) axs[0].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].set_ylim(-5.5, 5.5) axs[1].set_xlim(0.95 * np.pi, 1.55 * np.pi) axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') for knot in knots_11: axs[2].plot(knot * np.ones(101),

np.linspace(-5, 5, 101)

numpy.linspace

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal =

np.cos(time)

numpy.cos

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[2].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[2].plot(1.55 * np.pi * np.ones(101),

np.linspace(-5.5, 5.5, 101)

numpy.linspace

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x =

np.linspace(minima_y[-2], maxima_y[-2], 101)

numpy.linspace

#!/usr/bin/env python3 from __future__ import absolute_import, division, print_function import curses import sys from collections import deque from datetime import datetime import numpy as np import rospy from diagnostic_msgs.msg import DiagnosticArray, DiagnosticStatus from geometry_msgs.msg import PoseStamped from mavros_msgs.msg import ExtendedState, PositionTarget, State # StatusText from scipy.spatial.transform import Rotation as R from sensor_msgs.msg import BatteryState, Image, NavSatFix GPS_FIX_DICT = { 0: ('No GPS', curses.COLOR_RED), 1: ('No fix', curses.COLOR_RED), 2: ('2D lock', curses.COLOR_BLUE), 3: ('3D lock', curses.COLOR_BLUE), 4: ('DGPS', curses.COLOR_MAGENTA), 5: ('RTK float', curses.COLOR_YELLOW), 6: ('RTK fix', curses.COLOR_GREEN) } def get_color(color): return curses.color_pair(color) def frequency_from_messages(messages): durations = [] for i in range(len(messages) - 1): duration = messages[i + 1].header.stamp - messages[i].header.stamp durations.append(duration.to_sec()) frequency = 1 / np.mean(durations) if np.isnan(frequency): return 0 return frequency class StatusNode: def __init__(self, screen): rospy.init_node('status_node', argv=sys.argv) self.rate = rospy.get_param('~rate', default=1.0) # Curses setup self.screen = curses.initscr() self.rows, self.cols = self.screen.getmaxyx() height_status = 15 self.status = curses.newwin(height_status, self.cols, 1, 2) # self.console = curses.newwin(self.rows - height_status, self.cols, 12, 2) self.lines = 0 self.text = '' self.screen.keypad(True) curses.curs_set(False) # Hide cursor colors = [curses.COLOR_BLACK, curses.COLOR_BLUE, curses.COLOR_CYAN, curses.COLOR_GREEN, curses.COLOR_MAGENTA, curses.COLOR_RED, curses.COLOR_WHITE, curses.COLOR_YELLOW] # Curses color setup curses.use_default_colors() for color in colors: curses.init_pair(color, color, -1) # Default variables self.status_battery_perc = None self.state = State() self.state_sub = rospy.Subscriber('mavros/state', State, callback=self.state_callback, queue_size=1) self.battery = BatteryState() self.battery_sub = rospy.Subscriber('mavros/battery', BatteryState, callback=self.battery_callback, queue_size=1) self.extended = ExtendedState() self.extended_sub = rospy.Subscriber('mavros/extended_state', ExtendedState, callback=self.extended_callback, queue_size=1) # self.statustext = StatusText() # self.statustext_sub = rospy.Subscriber('mavros/statustext/recv', StatusText, # callback=self.statustext_callback, # queue_size=1) self.gps = NavSatFix() self.gps_sub = rospy.Subscriber('mavros/global_position/raw/fix', NavSatFix, callback=self.gps_callback, queue_size=1) self.local_pose = PoseStamped() self.local_pose_sub = rospy.Subscriber('mavros/local_position/pose', PoseStamped, callback=self.local_pose_callback, queue_size=1) self.global_pose = PoseStamped() self.global_pose_sub = rospy.Subscriber('global_position/pose', PoseStamped, callback=self.global_pose_callback, queue_size=1) self.diagnostics = DiagnosticArray() self.diagnostic_gps = DiagnosticStatus() self.diagnostics_sub = rospy.Subscriber('/diagnostics', DiagnosticArray, callback=self.diagnostics_callback, queue_size=1) self.setpoint = PositionTarget() self.setpoint_sub = rospy.Subscriber('mavros/setpoint_raw/local', PositionTarget, callback=self.setpoint_callback, queue_size=1) self.cameras = ['front', 'right', 'back', 'left'] self.image_subscribers = [] self.images = {c: deque(maxlen=10) for c in self.cameras} for camera in self.cameras: topic = f'camera_{camera}/image_raw' subscriber = rospy.Subscriber(topic, Image, callback=self.image_callback, callback_args=camera, queue_size=1, buff_size=2 ** 24) self.image_subscribers.append(subscriber) def battery_callback(self, battery_msg): if battery_msg.location == 'id0': self.battery = battery_msg def state_callback(self, state_msg): self.state = state_msg def extended_callback(self, extended_msg): self.extended = extended_msg def diagnostics_callback(self, diagnostics_msg): for status in diagnostics_msg.status: if 'GPS' in status.name: self.diagnostic_gps = status def gps_callback(self, gps_msg): self.gps = gps_msg def local_pose_callback(self, pose_msg): self.local_pose = pose_msg def global_pose_callback(self, pose_msg): self.global_pose = pose_msg def setpoint_callback(self, setpoint_msg): self.setpoint = setpoint_msg def image_callback(self, image_msg, camera): self.images[camera].append(image_msg) def statustext_callback(self, statustext_msg): screen = self.console time_str = datetime.now().strftime('%Y-%m-%d %H:%M:%S') # time_str = datetime.datetime.fromtimestamp(unix_time) text = statustext_msg.text severity = statustext_msg.severity msg = statustext_msg severity_red = [msg.EMERGENCY, msg.ALERT, msg.CRITICAL, msg.ERROR] severity_yellow = [msg.WARNING, msg.NOTICE] severity_neutral = [msg.INFO, msg.DEBUG] color = curses.COLOR_CYAN if severity in severity_red: color = curses.COLOR_RED elif severity in severity_yellow: color = curses.COLOR_YELLOW elif severity in severity_neutral: color = curses.COLOR_WHITE self.text = f'{time_str}: {text} ({color})' # screen.addstr(self.lines, 0, log, get_color(color)) self.lines += 1 screen.refresh() def print_status(self): screen = self.status screen.clear() # rospy.loginfo(status) # print(status) x_tab = 0 x_indent = 14 row = 0 # Battery battery_percentage = int(self.battery.percentage * 100) color = curses.COLOR_CYAN if battery_percentage > 50: color = curses.COLOR_GREEN elif battery_percentage > 25: color = curses.COLOR_YELLOW elif battery_percentage > 0: color = curses.COLOR_RED status_battery = str(battery_percentage) + '%' screen.addstr(row, x_tab, 'Battery: ') screen.addstr(row, x_indent, status_battery, get_color(color)) row += 1 # Armed if self.state.armed: color = curses.COLOR_RED status_armed = 'Yes' else: color = curses.COLOR_GREEN status_armed = 'No' screen.addstr(row, x_tab, 'Armed: ') screen.addstr(row, x_indent, status_armed, get_color(color)) row += 1 # Mode color = curses.COLOR_CYAN mode = self.state.mode if mode.startswith('AUTO'): mode = mode.split('.')[-1] mode = mode.capitalize() if mode == 'Offboard': color = curses.COLOR_RED else: color = curses.COLOR_BLUE if mode == '': mode = 'None' elif mode == 'Posctl': mode = 'Position' elif mode == 'Rtl': mode = 'Return' status_mode = '{}'.format(mode) screen.addstr(row, x_tab, 'Mode: ') screen.addstr(row, x_indent, status_mode, get_color(color)) row += 1 # Extended status if self.extended.landed_state == self.extended.LANDED_STATE_IN_AIR: status_extended = 'Air' color = curses.COLOR_RED elif self.extended.landed_state == self.extended.LANDED_STATE_LANDING: status_extended = 'Landed' color = curses.COLOR_GREEN elif self.extended.landed_state == self.extended.LANDED_STATE_ON_GROUND: status_extended = 'Ground' color = curses.COLOR_GREEN elif self.extended.landed_state == self.extended.LANDED_STATE_TAKEOFF: status_extended = 'Takeoff' color = curses.COLOR_RED elif self.extended.landed_state == self.extended.LANDED_STATE_UNDEFINED: status_extended = 'Undefined' color = curses.COLOR_CYAN screen.addstr(row, x_tab, 'State: ') screen.addstr(row, x_indent, status_extended, get_color(color)) row += 1 # GPS info satellites = 0 fix_type, color = GPS_FIX_DICT[0] for value in self.diagnostic_gps.values: if value.key == 'Satellites visible': satellites = value.value elif value.key == 'Fix type': fix_type, color = GPS_FIX_DICT[int(value.value)] screen.addstr(row, x_tab, 'GPS info: ') screen.addstr(row, x_indent, f'{fix_type} ({satellites} sat)', get_color(color)) row += 2 # GPS pos latitude = self.gps.latitude longitude = self.gps.longitude altitude = round(self.gps.altitude, 2) status_gps = f'{latitude:.7f} {longitude:.7f} {altitude:.2f} (LLA)' screen.addstr(row, x_tab, 'GPS pos: ') screen.addstr(row, x_indent, status_gps) row += 1 # Local pose p = self.local_pose.pose.position q = self.local_pose.pose.orientation quaternion = [q.x, q.y, q.z, q.w] try: rot = R.from_quat(quaternion) except ValueError: rot = R.from_euler('zyx', [0.0, 0.0, 0.0]) yaw, pitch, roll = rot.as_euler('zyx', degrees=True) x, y, z = round(p.x, 2), round(p.y, 2), round(p.z, 2) yaw, pitch, roll = int(yaw), int(pitch), int(roll) screen.addstr(row, x_tab, 'Local pos: ') screen.addstr(row, x_indent, f'{x:.2f} {y:.2f} {z:.2f} (XYZ) {roll} {pitch} {yaw} (RPY)') row += 1 # Global pose p = self.global_pose.pose.position q = self.global_pose.pose.orientation quaternion = [q.x, q.y, q.z, q.w] try: rot = R.from_quat(quaternion) except ValueError: rot = R.from_euler('zyx', [0.0, 0.0, 0.0]) yaw, pitch, roll = rot.as_euler('zyx', degrees=True) x, y, z = round(p.x, 2), round(p.y, 2), round(p.z, 2) yaw, pitch, roll = int(yaw), int(pitch), int(roll) screen.addstr(row, x_tab, 'Global pos: ') screen.addstr(row, x_indent, f'{x:.2f} {y:.2f} {z:.2f} (XYZ) {roll} {pitch} {yaw} (RPY)') row += 1 # Setpoint v = self.setpoint.velocity vx, vy, vz = round(v.x, 2), round(v.y, 2), round(v.z, 2) yaw = int(

np.rad2deg(self.setpoint.yaw)

numpy.rad2deg

# pylint: disable=protected-access """ Test the wrappers for the C API. """ import os from contextlib import contextmanager import numpy as np import numpy.testing as npt import pandas as pd import pytest import xarray as xr from packaging.version import Version from pygmt import Figure, clib from pygmt.clib.conversion import dataarray_to_matrix from pygmt.clib.session import FAMILIES, VIAS from pygmt.exceptions import ( GMTCLibError, GMTCLibNoSessionError, GMTInvalidInput, GMTVersionError, ) from pygmt.helpers import GMTTempFile TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data") with clib.Session() as _lib: gmt_version = Version(_lib.info["version"]) @contextmanager def mock(session, func, returns=None, mock_func=None): """ Mock a GMT C API function to make it always return a given value. Used to test that exceptions are raised when API functions fail by producing a NULL pointer as output or non-zero status codes. Needed because it's not easy to get some API functions to fail without inducing a Segmentation Fault (which is a good thing because libgmt usually only fails with errors). """ if mock_func is None: def mock_api_function(*args): # pylint: disable=unused-argument """ A mock GMT API function that always returns a given value. """ return returns mock_func = mock_api_function get_libgmt_func = session.get_libgmt_func def mock_get_libgmt_func(name, argtypes=None, restype=None): """ Return our mock function. """ if name == func: return mock_func return get_libgmt_func(name, argtypes, restype) setattr(session, "get_libgmt_func", mock_get_libgmt_func) yield setattr(session, "get_libgmt_func", get_libgmt_func) def test_getitem(): """ Test that I can get correct constants from the C lib. """ ses = clib.Session() assert ses["GMT_SESSION_EXTERNAL"] != -99999 assert ses["GMT_MODULE_CMD"] != -99999 assert ses["GMT_PAD_DEFAULT"] != -99999 assert ses["GMT_DOUBLE"] != -99999 with pytest.raises(GMTCLibError): ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement def test_create_destroy_session(): """ Test that create and destroy session are called without errors. """ # Create two session and make sure they are not pointing to the same memory session1 = clib.Session() session1.create(name="test_session1") assert session1.session_pointer is not None session2 = clib.Session() session2.create(name="test_session2") assert session2.session_pointer is not None assert session2.session_pointer != session1.session_pointer session1.destroy() session2.destroy() # Create and destroy a session twice ses = clib.Session() for __ in range(2): with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement ses.create("session1") assert ses.session_pointer is not None ses.destroy() with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement def test_create_session_fails(): """ Check that an exception is raised when failing to create a session. """ ses = clib.Session() with mock(ses, "GMT_Create_Session", returns=None): with pytest.raises(GMTCLibError): ses.create("test-session-name") # Should fail if trying to create a session before destroying the old one. ses.create("test1") with pytest.raises(GMTCLibError): ses.create("test2") def test_destroy_session_fails(): """ Fail to destroy session when given bad input. """ ses = clib.Session() with pytest.raises(GMTCLibNoSessionError): ses.destroy() ses.create("test-session") with mock(ses, "GMT_Destroy_Session", returns=1): with pytest.raises(GMTCLibError): ses.destroy() ses.destroy() def test_call_module(): """ Run a command to see if call_module works. """ data_fname = os.path.join(TEST_DATA_DIR, "points.txt") out_fname = "test_call_module.txt" with clib.Session() as lib: with GMTTempFile() as out_fname: lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name)) assert os.path.exists(out_fname.name) output = out_fname.read().strip() assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338" def test_call_module_invalid_arguments(): """ Fails for invalid module arguments. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("info", "bogus-data.bla") def test_call_module_invalid_name(): """ Fails when given bad input. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("meh", "") def test_call_module_error_message(): """ Check is the GMT error message was captured. """ with clib.Session() as lib: try: lib.call_module("info", "bogus-data.bla") except GMTCLibError as error: assert "Module 'info' failed with status code" in str(error) assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error) def test_method_no_session(): """ Fails when not in a session. """ # Create an instance of Session without "with" so no session is created. lib = clib.Session() with pytest.raises(GMTCLibNoSessionError): lib.call_module("gmtdefaults", "") with pytest.raises(GMTCLibNoSessionError): lib.session_pointer # pylint: disable=pointless-statement def test_parse_constant_single(): """ Parsing a single family argument correctly. """ lib = clib.Session() for family in FAMILIES: parsed = lib._parse_constant(family, valid=FAMILIES) assert parsed == lib[family] def test_parse_constant_composite(): """ Parsing a composite constant argument (separated by |) correctly. """ lib = clib.Session() test_cases = ((family, via) for family in FAMILIES for via in VIAS) for family, via in test_cases: composite = "|".join([family, via]) expected = lib[family] + lib[via] parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS) assert parsed == expected def test_parse_constant_fails(): """ Check if the function fails when given bad input. """ lib = clib.Session() test_cases = [ "SOME_random_STRING", "GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR", "GMT_IS_DATASET|NOT_A_PROPER_VIA", "NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX", "NOT_A_PROPER_FAMILY|ALSO_INVALID", ] for test_case in test_cases: with pytest.raises(GMTInvalidInput): lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS) # Should also fail if not given valid modifiers but is using them anyway. # This should work... lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS ) # But this shouldn't. with pytest.raises(GMTInvalidInput): lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None ) def test_create_data_dataset(): """ Run the function to make sure it doesn't fail badly. """ with clib.Session() as lib: # Dataset from vectors data_vector = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_VECTOR", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], # columns, rows, layers, dtype ) # Dataset from matrices data_matrix = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_MATRIX", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) assert data_vector != data_matrix def test_create_data_grid_dim(): """ Create a grid ignoring range and inc. """ with clib.Session() as lib: # Grids from matrices using dim lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) def test_create_data_grid_range(): """ Create a grid specifying range and inc instead of dim. """ with clib.Session() as lib: # Grids from matrices using range and int lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) def test_create_data_fails(): """ Check that create_data raises exceptions for invalid input and output. """ # Passing in invalid mode with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="Not_a_valid_mode", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # Passing in invalid geometry with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_GRID", geometry="Not_a_valid_geometry", mode="GMT_CONTAINER_ONLY", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # If the data pointer returned is None (NULL pointer) with pytest.raises(GMTCLibError): with clib.Session() as lib: with mock(lib, "GMT_Create_Data", returns=None): lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[11, 10, 2, 0], ) def test_virtual_file(): """ Test passing in data via a virtual file with a Dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (5, 3) for dtype in dtypes: with clib.Session() as lib: family = "GMT_IS_DATASET|GMT_VIA_MATRIX" geometry = "GMT_IS_POINT" dataset = lib.create_data( family=family, geometry=geometry, mode="GMT_CONTAINER_ONLY", dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype ) data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) lib.put_matrix(dataset, matrix=data) # Add the dataset to a virtual file and pass it along to gmt info vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset) with lib.open_virtual_file(*vfargs) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtual_file_fails(): """ Check that opening and closing virtual files raises an exception for non- zero return codes. """ vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IN|GMT_IS_REFERENCE", None, ) # Mock Open_VirtualFile to test the status check when entering the context. # If the exception is raised, the code won't get to the closing of the # virtual file. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): print("Should not get to this code") # Test the status check when closing the virtual file # Mock the opening to return 0 (success) so that we don't open a file that # we won't close later. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock( lib, "GMT_Close_VirtualFile", returns=1 ): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): pass print("Shouldn't get to this code either") def test_virtual_file_bad_direction(): """ Test passing an invalid direction argument. """ with clib.Session() as lib: vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IS_GRID", # The invalid direction argument 0, ) with pytest.raises(GMTInvalidInput): with lib.open_virtual_file(*vfargs): print("This should have failed") def test_virtualfile_from_vectors(): """ Test the automation for transforming vectors to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 10 for dtype in dtypes: x = np.arange(size, dtype=dtype) y = np.arange(size, size * 2, 1, dtype=dtype) z = np.arange(size * 2, size * 3, 1, dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected @pytest.mark.parametrize("dtype", [str, object]) def test_virtualfile_from_vectors_one_string_or_object_column(dtype): """ Test passing in one column with string or object dtype into virtual file dataset. """ size = 5 x = np.arange(size, dtype=np.int32) y = np.arange(size, size * 2, 1, dtype=np.int32) strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, strings) as vfile: with GMTTempFile() as outfile: lib.call_module("convert", f"{vfile} ->{outfile.name}") output = outfile.read(keep_tabs=True) expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings)) assert output == expected @pytest.mark.parametrize("dtype", [str, object]) def test_virtualfile_from_vectors_two_string_or_object_columns(dtype): """ Test passing in two columns of string or object dtype into virtual file dataset. """ size = 5 x = np.arange(size, dtype=np.int32) y = np.arange(size, size * 2, 1, dtype=np.int32) strings1 = np.array(["a", "bc", "def", "ghij", "klmno"], dtype=dtype) strings2 = np.array(["pqrst", "uvwx", "yz!", "@#", "$"], dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, strings1, strings2) as vfile: with GMTTempFile() as outfile: lib.call_module("convert", f"{vfile} ->{outfile.name}") output = outfile.read(keep_tabs=True) expected = "".join( f"{h}\t{i}\t{j} {k}\n" for h, i, j, k in zip(x, y, strings1, strings2) ) assert output == expected def test_virtualfile_from_vectors_transpose(): """ Test transforming matrix columns to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (7, 5) for dtype in dtypes: data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) with clib.Session() as lib: with lib.virtualfile_from_vectors(*data.T) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} -C ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["{:.0f}\t{:.0f}".format(col.min(), col.max()) for col in data.T] ) expected = "{}\n".format(bounds) assert output == expected def test_virtualfile_from_vectors_diff_size(): """ Test the function fails for arrays of different sizes. """ x = np.arange(5) y = np.arange(6) with clib.Session() as lib: with pytest.raises(GMTInvalidInput): with lib.virtualfile_from_vectors(x, y): print("This should have failed") def test_virtualfile_from_matrix(): """ Test transforming a matrix to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (7, 5) for dtype in dtypes: data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) with clib.Session() as lib: with lib.virtualfile_from_matrix(data) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtualfile_from_matrix_slice(): """ Test transforming a slice of a larger array to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (10, 6) for dtype in dtypes: full_data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) rows = 5 cols = 3 data = full_data[:rows, :cols] with clib.Session() as lib: with lib.virtualfile_from_matrix(data) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(rows, bounds) assert output == expected def test_virtualfile_from_vectors_pandas(): """ Pass vectors to a dataset using pandas Series. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 13 for dtype in dtypes: data = pd.DataFrame( data=dict( x=np.arange(size, dtype=dtype), y=np.arange(size, size * 2, 1, dtype=dtype), z=np.arange(size * 2, size * 3, 1, dtype=dtype), ) ) with clib.Session() as lib: with lib.virtualfile_from_vectors(data.x, data.y, data.z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( [ "<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (data.x, data.y, data.z) ] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected def test_virtualfile_from_vectors_arraylike(): """ Pass array-like vectors to a dataset. """ size = 13 x = list(range(0, size, 1)) y = tuple(range(size, size * 2, 1)) z = range(size * 2, size * 3, 1) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(min(i), max(i)) for i in (x, y, z)] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected def test_extract_region_fails(): """ Check that extract region fails if nothing has been plotted. """ Figure() with pytest.raises(GMTCLibError): with clib.Session() as lib: lib.extract_region() def test_extract_region_two_figures(): """ Extract region should handle multiple figures existing at the same time. """ # Make two figures before calling extract_region to make sure that it's # getting from the current figure, not the last figure. fig1 = Figure() region1 = np.array([0, 10, -20, -10]) fig1.coast(region=region1, projection="M6i", frame=True, land="black") fig2 = Figure() fig2.basemap(region="US.HI+r5", projection="M6i", frame=True) # Activate the first figure and extract the region from it # Use in a different session to avoid any memory problems. with clib.Session() as lib: lib.call_module("figure", "{} -".format(fig1._name)) with clib.Session() as lib: wesn1 = lib.extract_region() npt.assert_allclose(wesn1, region1) # Now try it with the second one with clib.Session() as lib: lib.call_module("figure", "{} -".format(fig2._name)) with clib.Session() as lib: wesn2 = lib.extract_region() npt.assert_allclose(wesn2, np.array([-165.0, -150.0, 15.0, 25.0])) def test_write_data_fails(): """ Check that write data raises an exception for non-zero return codes. """ # It's hard to make the C API function fail without causing a Segmentation # Fault. Can't test this if by giving a bad file name because if # output=='', GMT will just write to stdout and spaces are valid file # names. Use a mock instead just to exercise this part of the code. with clib.Session() as lib: with mock(lib, "GMT_Write_Data", returns=1): with pytest.raises(GMTCLibError): lib.write_data( "GMT_IS_VECTOR", "GMT_IS_POINT", "GMT_WRITE_SET", [1] * 6, "some-file-name", None, ) def test_dataarray_to_matrix_works(): """ Check that dataarray_to_matrix returns correct output. """ data = np.diag(v=np.arange(3)) x = np.linspace(start=0, stop=4, num=3) y = np.linspace(start=5, stop=9, num=3) grid = xr.DataArray(data, coords=[("y", y), ("x", x)]) matrix, region, inc = dataarray_to_matrix(grid) npt.assert_allclose(actual=matrix, desired=

np.flipud(data)

numpy.flipud

############################################################################### # @todo add Pilot2-splash-app disclaimer ############################################################################### """ Get's KRAS states """ import MDAnalysis as mda from MDAnalysis.analysis import align from MDAnalysis.lib.mdamath import make_whole import os import numpy as np import math ############## Below section needs to be uncommented ############ import mummi_core import mummi_ras from mummi_core.utils import Naming # # Logger has to be initialized the first thing in the script from logging import getLogger LOGGER = getLogger(__name__) # # Innitilize MuMMI if it has not been done before # MUMMI_ROOT = mummi.init(True) # This is needed so the Naming works below #@TODO fix this so we don't have these on import make them as an init mummi_core.init() dirKRASStates = Naming.dir_res('states') dirKRASStructures = Naming.dir_res('structures') # #RAS_ONLY_macrostate = np.loadtxt(os.path.join(dirKRASStates, "RAS-ONLY.microstates.txt")) RAS_ONLY_macrostate = np.loadtxt(os.path.join(dirKRASStates, "ras-states.txt"),comments='#') # #RAS_RAF_macrostate = np.loadtxt(os.path.join(dirKRASStates, "RAS-RAF.microstates.txt")) RAS_RAF_macrostate = np.loadtxt(os.path.join(dirKRASStates, "ras-raf-states.txt"),comments='#') # Note diffrent number of columns so index change below # TODO: CS, my edits to test # RAS_ONLY_macrostate = np.loadtxt('ras-states.txt') # RAS_RAF_macrostate = np.loadtxt('ras-raf-states.txt') ############## above section needs to be uncommented ############ # TODO: CS, my edits to test # TODO: TSC, The reference structure has to currently be set as the 'RAS-ONLY-reference-structure.gro' # TODO: TSC, path to the reference structure is: mummi_resources/structures/ kras_ref_universe = mda.Universe(os.path.join(dirKRASStructures, "RAS-ONLY-reference-structure.gro")) # kras_ref_universe = mda.Universe("RAS-ONLY-reference-structure.gro") # kras_ref_universe = mda.Universe('AA_pfpatch_000000004641_RAS_RAF2_411.gro') # TODO: CS, not using these for x4 proteins; instead using protein_systems below to set num_res ######### Below hard codes the number of residues within RAS-only and RAS-RAF ########## RAS_only_num_res = 184 RAS_RAF_num_res = 320 ######### Above hard codes the number of residues within RAS-only and RAS-RAF ########## ####### This can be removed # def get_kras(syst, kras_start): # """Gets all atoms for a KRAS protein starting at 'kras_start'.""" # return syst.atoms[kras_start:kras_start+428] ####### This can be removed def get_segids(u): """Identifies the list of segments within the system. Only needs to be called x1 time""" segs = u.segments segs = segs.segids ras_segids = [] rasraf_segids = [] for i in range(len(segs)): # print(segs[i]) if segs[i][-3:] == 'RAS': ras_segids.append(segs[i]) if segs[i][-3:] == 'RAF': rasraf_segids.append(segs[i]) return ras_segids, rasraf_segids def get_protein_info(u,tag): """Uses the segments identified in get_segids to make a list of all proteins in the systems.\ Outputs a list of the first residue number of the protein, and whether it is 'RAS-ONLY', or 'RAS-RAF'.\ The 'tag' input defines what is used to identify the first residue of the protein. i.e. 'resname ACE1 and name BB'.\ Only needs to be called x1 time""" ras_segids, rasraf_segids = get_segids(u) if len(ras_segids) > 0: RAS = u.select_atoms('segid '+ras_segids[0]+' and '+str(tag)) else: RAS = [] if len(rasraf_segids) > 0: RAF = u.select_atoms('segid '+rasraf_segids[0]+' and '+str(tag)) else: RAF = [] protein_info = []#np.empty([len(RAS)+len(RAF),2]) for i in range(len(RAS)): protein_info.append((RAS[i].resid,'RAS-ONLY')) for i in range(len(RAF)): protein_info.append((RAF[i].resid,'RAS-RAF')) ######## sort protein info protein_info = sorted(protein_info) ######## sort protein info return protein_info def get_ref_kras(): """Gets the reference KRAS struct. Only called x1 time when class is loaded""" start_of_g_ref = kras_ref_universe.residues[0].resid ref_selection = 'resid '+str(start_of_g_ref)+':'+str(start_of_g_ref+24)+' ' +\ str(start_of_g_ref+38)+':'+str(start_of_g_ref+54)+' ' +\ str(start_of_g_ref+67)+':'+str(start_of_g_ref+164)+' ' +\ 'and (name CA or name BB)' r2_26r40_56r69_166_ref = kras_ref_universe.select_atoms(str(ref_selection)) return kras_ref_universe.select_atoms(str(ref_selection)).positions - kras_ref_universe.select_atoms(str(ref_selection)).center_of_mass() # Load inital ref frames (only need to do this once) ref0 = get_ref_kras() def getKRASstates(u,kras_indices): """Gets states for all KRAS proteins in path.""" # res_shift = 8 # all_glycine = u.select_atoms("resname GLY") # kras_indices = [] # for i in range(0, len(all_glycine), 26): # kras_indices.append(all_glycine[i].index) ########## Below is taken out of the function so it is only done once ######### # kras_indices = get_protein_info(u,'resname ACE1 and name BB') ########## Above is taken out of the function so it is only done once ######### # CS, for x4 cases: # [{protein_x4: (protein_type, num_res)}] protein_systems = [{'ras4a': ('RAS-ONLY', 185), 'ras4araf': ('RAS-RAF', 321), 'ras': ('RAS-ONLY', 184), 'rasraf': ('RAS-RAF', 320)}] ALLOUT = [] for k in range(len(kras_indices)): start_of_g = kras_indices[k][0] protein_x4 = str(kras_indices[k][1]) try: protein_type = [item[protein_x4] for item in protein_systems][0][0] # 'RAS-ONLY' OR 'RAS-RAF' num_res = [item[protein_x4] for item in protein_systems][0][1] except: LOGGER.error('Check KRas naming between modules') raise Exception('Error: unknown KRas name') # TODO: CS, replacing this comment section with the above, to handle x4 protein types # --------------------------------------- # ALLOUT = [] # for k in range(len(kras_indices)): # start_of_g = kras_indices[k][0] # protein_type = str(kras_indices[k][1]) # ########## BELOW SECTION TO DETERMINE WHICH RESIDUES ARE PART OF THE PROTEIN GROUP - NEEDED FOR PBC REMOVAL ############## # ########## POTENTIALLY REDO WITH A 'HARD-CODED' NUMBER OF RESIDUES PER PROTEIN GROUP (WHETHER RAS-ONLY OR RAS-RAF) ####### # ########## HAS BEEN REDONE WITH A 'HARD-CODED' NUMBER OF RESIDUES PER PROTEIN GROUP (WHETHER RAS-ONLY OR RAS-RAF) ######## # # if len(kras_indices) == 1: # # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(len(u.residues))+' and name BB') ####### HAS TO BE FIXED FOR BACKBONE ATOMS FOR SPECIFIC PROTEIN # # elif len(kras_indices) > 1: # # if k == len(kras_indices)-1: # # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(len(u.residues))+' and name BB') # # else: # # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(kras_indices[k+1][0])+' and name BB') # ########## ABOVE SECTION TO DETERMINE WHICH RESIDUES ARE PART OF THE PROTEIN GROUP - NEEDED FOR PBC REMOVAL ############## # # ########## Below hard codes the number of residues/beads in the RAS-ONLY and RAS-RAF simulations ######################### # if protein_type == 'RAS-ONLY': # num_res = RAS_only_num_res # elif protein_type == 'RAS-RAF': # num_res = RAS_RAF_num_res # ########## Above hard codes the number of residues/beads in the RAS-ONLY and RAS-RAF simulations ######################### # --------------------------------------- # TODO: TSC, I changed the selection below, which can be used for the make_whole... # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+num_res)+' and (name CA or name BB)') krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+num_res)) krases0_BB.guess_bonds() r2_26r40_56r69_166 = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+24)+' ' +\ str(start_of_g+38)+':'+str(start_of_g+54)+' ' +\ str(start_of_g+67)+':'+str(start_of_g+164)+\ ' and (name CA or name BB)') u_selection = \ 'resid '+str(start_of_g)+':'+str(start_of_g+24)+' '+str(start_of_g+38)+':'+str(start_of_g+54)+' ' +\ str(start_of_g+67)+':'+str(start_of_g+164)+' and (name CA or name BB)' mobile0 = u.select_atoms(str(u_selection)).positions - u.select_atoms(str(u_selection)).center_of_mass() # TODO: CS, something wrong with ref0 from get_kras_ref() # just making ref0 = mobile0 to test for now # ref0 = mobile0 # TSC removed this R, RMSD_junk = align.rotation_matrix(mobile0, ref0) ######## TODO: TSC, Adjusted for AA lipid names ######## # lipids = u.select_atoms('resname POPX POPC PAPC POPE DIPE DPSM PAPS PAP6 CHOL') lipids = u.select_atoms('resname POPC PAPC POPE DIPE SSM PAPS SAPI CHL1') coords = ref0 RotMat = [] OS = [] r152_165 = krases0_BB.select_atoms('resid '+str(start_of_g+150)+':'+str(start_of_g+163)+' and (name CA or name BB)') r65_74 = krases0_BB.select_atoms('resid '+str(start_of_g+63)+':'+str(start_of_g+72)+' and (name CA or name BB)') timeframes = [] # TODO: CS, for AA need bonds to run make_whole() # krases0_BB.guess_bonds() # TODO: CS, turn off for now to test beyond this point ''' *** for AA, need to bring that back on once all else runs *** ''' # @Tim and <NAME>. this was commented out - please check. #make_whole(krases0_BB) j, rmsd_junk = mda.analysis.align.rotation_matrix((r2_26r40_56r69_166.positions-r2_26r40_56r69_166.center_of_mass()), coords) RotMat.append(j) OS.append(r65_74.center_of_mass()-r152_165.center_of_mass()) timeframes.append(u.trajectory.time) if protein_type == 'RAS-RAF': z_pos = [] ############### NEED TO CONFIRM THE SELECTION OF THE RAF LOOP RESIDUES BELOW #################### ############### TODO: TSC, zshifting is set to -1 (instead of -2), as there are ACE caps that are separate residues in AA #zshifting=-1 if protein_x4 == 'rasraf': zshifting = -1 elif protein_x4 == 'ras4araf': zshifting = 0 else: zshifting = 0 LOGGER.error('Found unsupported protein_x4 type') raf_loops_selection = u.select_atoms('resid '+str(start_of_g+zshifting+291)+':'+str(start_of_g+zshifting+294)+' ' +\ str(start_of_g+zshifting+278)+':'+str(start_of_g+zshifting+281)+' ' +\ ' and (name CA or name BB)') ############### NEED TO CONFIRM THE SELECTION OF THE RAF LOOP RESIDUES ABOVE #################### diff = (lipids.center_of_mass()[2]-raf_loops_selection.center_of_mass(unwrap=True)[2])/10 if diff < 0: diff = diff+(u.dimensions[2]/10) z_pos.append(diff) z_pos = np.array(z_pos) RotMatNP =

np.array(RotMat)

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100),

np.linspace(-2.75, 2.75, 100)

numpy.linspace

# pvtrace is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # pvtrace is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import numpy as np from external.transformations import translation_matrix, rotation_matrix import external.transformations as tf from Trace import Photon from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm from Materials import Spectrum def random_spherecial_vector(): # This method of calculating isotropic vectors is taken from GNU Scientific Library LOOP = True while LOOP: x = -1. + 2. * np.random.uniform() y = -1. + 2. * np.random.uniform() s = x**2 + y**2 if s <= 1.0: LOOP = False z = -1. + 2. * s a = 2 * np.sqrt(1 - s) x = a * x y = a * y return np.array([x,y,z]) class SimpleSource(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False): super(SimpleSource, self).__init__() self.position = position self.direction = direction self.wavelength = wavelength self.use_random_polarisation = use_random_polarisation self.throw = 0 self.source_id = "SimpleSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength # If use_polarisation is set generate a random polarisation vector of the photon if self.use_random_polarisation: # Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon vec = random_spherecial_vector() vec[2] = 0. vec = norm(vec) R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1]) photon.polarisation = transform_direction(vec, R) else: photon.polarisation = None photon.id = self.throw self.throw = self.throw + 1 return photon class Laser(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None): super(Laser, self).__init__() self.position = np.array(position) self.direction = np.array(direction) self.wavelength = wavelength assert polarisation != None, "Polarisation of the Laser is not set." self.polarisation = np.array(polarisation) self.throw = 0 self.source_id = "LaserSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength photon.polarisation = self.polarisation photon.id = self.throw self.throw = self.throw + 1 return photon class PlanarSource(object): """A box that emits photons from the top surface (normal), sampled from the spectrum.""" def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05): super(PlanarSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.plane = FinitePlane(length=length, width=width) self.length = length self.width = width # direction is the direction that photons are fired out of the plane in the GLOBAL FRAME. # i.e. this is passed directly to the photon to set is's direction self.direction = direction self.throw = 0 self.source_id = "PlanarSource_" + str(id(self)) def translate(self, translation): self.plane.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.plane.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Create a point which is on the surface of the finite plane in it's local frame x = np.random.uniform(0., self.length) y = np.random.uniform(0., self.width) local_point = (x, y, 0.) # Transform the direciton photon.position = transform_point(local_point, self.plane.transform) photon.direction = self.direction photon.active = True if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSource(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint = np.array(linepoint) self.linedirection = np.array(linedirection) self.focussize = focussize self.throw = 0 self.source_id = "LensSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Position x = np.random.uniform(self.planeorigin[0],self.planeextent[0]) y = np.random.uniform(self.planeorigin[1],self.planeextent[1]) z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) photon.position = np.array((x,y,z)) # Direction focuspoint = np.array((0.,0.,0.)) focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize) focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize) focuspoint[2] = photon.position[2] direction = focuspoint - photon.position modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5 photon.direction = direction/modulus # Wavelength if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSourceAngle(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. For this lense an additional z-boost is added (Angle of incidence in z-direction). """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), angle = 0, focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSourceAngle, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint = np.array(linepoint) self.linedirection = np.array(linedirection) self.focussize = focussize self.angle = angle self.throw = 0 self.source_id = "LensSourceAngle_" + str(id(self)) def photon(self): photon = Photon() photon.id = self.throw self.throw = self.throw + 1 # Position x = np.random.uniform(self.planeorigin[0],self.planeextent[0]) y = np.random.uniform(self.planeorigin[1],self.planeextent[1]) boost = y*np.tan(self.angle) z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) - boost photon.position =

np.array((x,y,z))

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time =

np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)

numpy.linspace

# coding: utf-8 # Licensed under a 3-clause BSD style license - see LICENSE.rst """ Test the Logarithmic Units and Quantities """ from __future__ import (absolute_import, unicode_literals, division, print_function) from ...extern import six from ...extern.six.moves import zip import pickle import itertools import pytest import numpy as np from numpy.testing.utils import assert_allclose from ...tests.helper import assert_quantity_allclose from ... import units as u, constants as c lu_units = [u.dex, u.mag, u.decibel] lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit] lq_subclasses = [u.Dex, u.Magnitude, u.Decibel] pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy) class TestLogUnitCreation(object): def test_logarithmic_units(self): """Check logarithmic units are set up correctly.""" assert u.dB.to(u.dex) == 0.1 assert u.dex.to(u.mag) == -2.5 assert u.mag.to(u.dB) == -4 @pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses)) def test_callable_units(self, lu_unit, lu_cls): assert isinstance(lu_unit, u.UnitBase) assert callable(lu_unit) assert lu_unit._function_unit_class is lu_cls @pytest.mark.parametrize('lu_unit', lu_units) def test_equality_to_normal_unit_for_dimensionless(self, lu_unit): lu = lu_unit() assert lu == lu._default_function_unit # eg, MagUnit() == u.mag assert lu._default_function_unit == lu # and u.mag == MagUnit() @pytest.mark.parametrize('lu_unit, physical_unit', itertools.product(lu_units, pu_sample)) def test_call_units(self, lu_unit, physical_unit): """Create a LogUnit subclass using the callable unit and physical unit, and do basic check that output is right.""" lu1 = lu_unit(physical_unit) assert lu1.physical_unit == physical_unit assert lu1.function_unit == lu1._default_function_unit def test_call_invalid_unit(self): with pytest.raises(TypeError): u.mag([]) with pytest.raises(ValueError): u.mag(u.mag()) @pytest.mark.parametrize('lu_cls, physical_unit', itertools.product( lu_subclasses + [u.LogUnit], pu_sample)) def test_subclass_creation(self, lu_cls, physical_unit): """Create a LogUnit subclass object for given physical unit, and do basic check that output is right.""" lu1 = lu_cls(physical_unit) assert lu1.physical_unit == physical_unit assert lu1.function_unit == lu1._default_function_unit lu2 = lu_cls(physical_unit, function_unit=2*lu1._default_function_unit) assert lu2.physical_unit == physical_unit assert lu2.function_unit == u.Unit(2*lu2._default_function_unit) with pytest.raises(ValueError): lu_cls(physical_unit, u.m) def test_predefined_magnitudes(): assert_quantity_allclose((-21.1*u.STmag).physical, 1.*u.erg/u.cm**2/u.s/u.AA) assert_quantity_allclose((-48.6*u.ABmag).physical, 1.*u.erg/u.cm**2/u.s/u.Hz) assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0) assert_quantity_allclose((0*u.m_bol).physical, c.L_bol0/(4.*np.pi*(10.*c.pc)**2)) def test_predefined_reinitialisation(): assert u.mag('ST') == u.STmag assert u.mag('AB') == u.ABmag assert u.mag('Bol') == u.M_bol assert u.mag('bol') == u.m_bol def test_predefined_string_roundtrip(): """Ensure roundtripping; see #5015""" with u.magnitude_zero_points.enable(): assert u.Unit(u.STmag.to_string()) == u.STmag assert u.Unit(u.ABmag.to_string()) == u.ABmag assert u.Unit(u.M_bol.to_string()) == u.M_bol assert u.Unit(u.m_bol.to_string()) == u.m_bol def test_inequality(): """Check __ne__ works (regresssion for #5342).""" lu1 = u.mag(u.Jy) lu2 = u.dex(u.Jy) lu3 = u.mag(u.Jy**2) lu4 = lu3 - lu1 assert lu1 != lu2 assert lu1 != lu3 assert lu1 == lu4 class TestLogUnitStrings(object): def test_str(self): """Do some spot checks that str, repr, etc. work as expected.""" lu1 = u.mag(u.Jy) assert str(lu1) == 'mag(Jy)' assert repr(lu1) == 'Unit("mag(Jy)")' assert lu1.to_string('generic') == 'mag(Jy)' with pytest.raises(ValueError): lu1.to_string('fits') lu2 = u.dex() assert str(lu2) == 'dex' assert repr(lu2) == 'Unit("dex(1)")' assert lu2.to_string() == 'dex(1)' lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag) assert str(lu3) == '2 mag(Jy)' assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")' assert lu3.to_string() == '2 mag(Jy)' lu4 = u.mag(u.ct) assert lu4.to_string('generic') == 'mag(ct)' assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( ' '\\mathrm{ct} \\right)}$') assert lu4._repr_latex_() == lu4.to_string('latex') class TestLogUnitConversion(object): @pytest.mark.parametrize('lu_unit, physical_unit', itertools.product(lu_units, pu_sample)) def test_physical_unit_conversion(self, lu_unit, physical_unit): """Check various LogUnit subclasses are equivalent and convertible to their non-log counterparts.""" lu1 = lu_unit(physical_unit) assert lu1.is_equivalent(physical_unit) assert lu1.to(physical_unit, 0.) == 1. assert physical_unit.is_equivalent(lu1) assert physical_unit.to(lu1, 1.) == 0. pu = u.Unit(8.*physical_unit) assert lu1.is_equivalent(physical_unit) assert lu1.to(pu, 0.) == 0.125 assert pu.is_equivalent(lu1) assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15) # Check we round-trip. value = np.linspace(0., 10., 6) assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15) # And that we're not just returning True all the time. pu2 = u.g assert not lu1.is_equivalent(pu2) with pytest.raises(u.UnitsError): lu1.to(pu2) assert not pu2.is_equivalent(lu1) with pytest.raises(u.UnitsError): pu2.to(lu1) @pytest.mark.parametrize('lu_unit', lu_units) def test_container_unit_conversion(self, lu_unit): """Check that conversion to logarithmic units (u.mag, u.dB, u.dex) is only possible when the physical unit is dimensionless.""" values = np.linspace(0., 10., 6) lu1 = lu_unit(u.dimensionless_unscaled) assert lu1.is_equivalent(lu1.function_unit) assert_allclose(lu1.to(lu1.function_unit, values), values) lu2 = lu_unit(u.Jy) assert not lu2.is_equivalent(lu2.function_unit) with pytest.raises(u.UnitsError): lu2.to(lu2.function_unit, values) @pytest.mark.parametrize( 'flu_unit, tlu_unit, physical_unit', itertools.product(lu_units, lu_units, pu_sample)) def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit): """Check various LogUnit subclasses are equivalent and convertible to each other if they correspond to equivalent physical units.""" values = np.linspace(0., 10., 6) flu = flu_unit(physical_unit) tlu = tlu_unit(physical_unit) assert flu.is_equivalent(tlu) assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit)) assert_allclose(flu.to(tlu, values), values * flu.function_unit.to(tlu.function_unit)) tlu2 = tlu_unit(u.Unit(100.*physical_unit)) assert flu.is_equivalent(tlu2) # Check that we round-trip. assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15) tlu3 = tlu_unit(physical_unit.to_system(u.si)[0]) assert flu.is_equivalent(tlu3) assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15) tlu4 = tlu_unit(u.g) assert not flu.is_equivalent(tlu4) with pytest.raises(u.UnitsError): flu.to(tlu4, values) def test_unit_decomposition(self): lu = u.mag(u.Jy) assert lu.decompose() == u.mag(u.Jy.decompose()) assert lu.decompose().physical_unit.bases == [u.kg, u.s] assert lu.si == u.mag(u.Jy.si) assert lu.si.physical_unit.bases == [u.kg, u.s] assert lu.cgs == u.mag(u.Jy.cgs) assert lu.cgs.physical_unit.bases == [u.g, u.s] def test_unit_multiple_possible_equivalencies(self): lu = u.mag(u.Jy) assert lu.is_equivalent(pu_sample) class TestLogUnitArithmetic(object): def test_multiplication_division(self): """Check that multiplication/division with other units is only possible when the physical unit is dimensionless, and that this turns the unit into a normal one.""" lu1 = u.mag(u.Jy) with pytest.raises(u.UnitsError): lu1 * u.m with pytest.raises(u.UnitsError): u.m * lu1 with pytest.raises(u.UnitsError): lu1 / lu1 for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex): with pytest.raises(u.UnitsError): lu1 / unit lu2 = u.mag(u.dimensionless_unscaled) with pytest.raises(u.UnitsError): lu2 * lu1 with pytest.raises(u.UnitsError): lu2 / lu1 # But dimensionless_unscaled can be cancelled. assert lu2 / lu2 == u.dimensionless_unscaled # With dimensionless, normal units are OK, but we return a plain unit. tf = lu2 * u.m tr = u.m * lu2 for t in (tf, tr): assert not isinstance(t, type(lu2)) assert t == lu2.function_unit * u.m with u.set_enabled_equivalencies(u.logarithmic()): with pytest.raises(u.UnitsError): t.to(lu2.physical_unit) # Now we essentially have a LogUnit with a prefactor of 100, # so should be equivalent again. t = tf / u.cm with u.set_enabled_equivalencies(u.logarithmic()): assert t.is_equivalent(lu2.function_unit) assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.), lu2.to(lu2.physical_unit, np.arange(3.))) # If we effectively remove lu1, a normal unit should be returned. t2 = tf / lu2 assert not isinstance(t2, type(lu2)) assert t2 == u.m t3 = tf / lu2.function_unit assert not isinstance(t3, type(lu2)) assert t3 == u.m # For completeness, also ensure non-sensical operations fail with pytest.raises(TypeError): lu1 * object() with pytest.raises(TypeError): slice(None) * lu1 with pytest.raises(TypeError): lu1 / [] with pytest.raises(TypeError): 1 / lu1 @pytest.mark.parametrize('power', (2, 0.5, 1, 0)) def test_raise_to_power(self, power): """Check that raising LogUnits to some power is only possible when the physical unit is dimensionless, and that conversion is turned off when the resulting logarithmic unit (such as mag**2) is incompatible.""" lu1 = u.mag(u.Jy) if power == 0: assert lu1 ** power == u.dimensionless_unscaled elif power == 1: assert lu1 ** power == lu1 else: with pytest.raises(u.UnitsError): lu1 ** power # With dimensionless, though, it works, but returns a normal unit. lu2 = u.mag(u.dimensionless_unscaled) t = lu2**power if power == 0: assert t == u.dimensionless_unscaled elif power == 1: assert t == lu2 else: assert not isinstance(t, type(lu2)) assert t == lu2.function_unit**power # also check we roundtrip t2 = t**(1./power) assert t2 == lu2.function_unit with u.set_enabled_equivalencies(u.logarithmic()): assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)), lu2.to(lu2.physical_unit, np.arange(3.))) @pytest.mark.parametrize('other', pu_sample) def test_addition_subtraction_to_normal_units_fails(self, other): lu1 = u.mag(u.Jy) with pytest.raises(u.UnitsError): lu1 + other with pytest.raises(u.UnitsError): lu1 - other with pytest.raises(u.UnitsError): other - lu1 def test_addition_subtraction_to_non_units_fails(self): lu1 = u.mag(u.Jy) with pytest.raises(TypeError): lu1 + 1. with pytest.raises(TypeError): lu1 - [1., 2., 3.] @pytest.mark.parametrize( 'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m), u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag))) def test_addition_subtraction(self, other): """Check physical units are changed appropriately""" lu1 = u.mag(u.Jy) other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled) lu_sf = lu1 + other assert lu_sf.is_equivalent(lu1.physical_unit * other_pu) lu_sr = other + lu1 assert lu_sr.is_equivalent(lu1.physical_unit * other_pu) lu_df = lu1 - other assert lu_df.is_equivalent(lu1.physical_unit / other_pu) lu_dr = other - lu1 assert lu_dr.is_equivalent(other_pu / lu1.physical_unit) def test_complicated_addition_subtraction(self): """for fun, a more complicated example of addition and subtraction""" dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2)) lu_dm = u.mag(dm0) lu_absST = u.STmag - lu_dm assert lu_absST.is_equivalent(u.erg/u.s/u.AA) def test_neg_pos(self): lu1 = u.mag(u.Jy) neg_lu = -lu1 assert neg_lu != lu1 assert neg_lu.physical_unit == u.Jy**-1 assert -neg_lu == lu1 pos_lu = +lu1 assert pos_lu is not lu1 assert pos_lu == lu1 def test_pickle(): lu1 = u.dex(u.cm/u.s**2) s = pickle.dumps(lu1) lu2 = pickle.loads(s) assert lu1 == lu2 def test_hashable(): lu1 = u.dB(u.mW) lu2 = u.dB(u.m) lu3 = u.dB(u.mW) assert hash(lu1) != hash(lu2) assert hash(lu1) == hash(lu3) luset = {lu1, lu2, lu3} assert len(luset) == 2 class TestLogQuantityCreation(object): @pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity], lu_subclasses + [u.LogUnit])) def test_logarithmic_quantities(self, lq, lu): """Check logarithmic quantities are all set up correctly""" assert lq._unit_class == lu assert type(lu()._quantity_class(1.)) is lq @pytest.mark.parametrize('lq_cls, physical_unit', itertools.product(lq_subclasses, pu_sample)) def test_subclass_creation(self, lq_cls, physical_unit): """Create LogQuantity subclass objects for some physical units, and basic check on transformations""" value = np.arange(1., 10.) log_q = lq_cls(value * physical_unit) assert log_q.unit.physical_unit == physical_unit assert log_q.unit.function_unit == log_q.unit._default_function_unit assert_allclose(log_q.physical.value, value) with pytest.raises(ValueError): lq_cls(value, physical_unit) @pytest.mark.parametrize( 'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m), u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag), u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag))) def test_different_units(self, unit): q = u.Magnitude(1.23, unit) assert q.unit.function_unit == getattr(unit, 'function_unit', unit) assert q.unit.physical_unit is getattr(unit, 'physical_unit', u.dimensionless_unscaled) @pytest.mark.parametrize('value, unit', ( (1.*u.mag(u.Jy), None), (1.*u.dex(u.Jy), None), (1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)), (1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy)))) def test_function_values(self, value, unit): lq = u.Magnitude(value, unit) assert lq == value assert lq.unit.function_unit == u.mag assert lq.unit.physical_unit == getattr(unit, 'physical_unit', value.unit.physical_unit) @pytest.mark.parametrize( 'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag), u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag))) def test_indirect_creation(self, unit): q1 = 2.5 * unit assert isinstance(q1, u.Magnitude) assert q1.value == 2.5 assert q1.unit == unit pv = 100. * unit.physical_unit q2 = unit * pv assert q2.unit == unit assert q2.unit.physical_unit == pv.unit assert q2.to_value(unit.physical_unit) == 100. assert (q2._function_view / u.mag).to_value(1) == -5. q3 = unit / 0.4 assert q3 == q1 def test_from_view(self): # Cannot view a physical quantity as a function quantity, since the # values would change. q = [100., 1000.] * u.cm/u.s**2 with pytest.raises(TypeError): q.view(u.Dex) # But fine if we have the right magnitude. q = [2., 3.] * u.dex lq = q.view(u.Dex) assert isinstance(lq, u.Dex) assert lq.unit.physical_unit == u.dimensionless_unscaled assert np.all(q == lq) def test_using_quantity_class(self): """Check that we can use Quantity if we have subok=True""" # following issue #5851 lu = u.dex(u.AA) with pytest.raises(u.UnitTypeError): u.Quantity(1., lu) q = u.Quantity(1., lu, subok=True) assert type(q) is lu._quantity_class def test_conversion_to_and_from_physical_quantities(): """Ensures we can convert from regular quantities.""" mst = [10., 12., 14.] * u.STmag flux_lambda = mst.physical mst_roundtrip = flux_lambda.to(u.STmag) # check we return a logquantity; see #5178. assert isinstance(mst_roundtrip, u.Magnitude) assert mst_roundtrip.unit == mst.unit assert_allclose(mst_roundtrip.value, mst.value) wave = [4956.8, 4959.55, 4962.3] * u.AA flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave)) mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave)) assert isinstance(mst_roundtrip2, u.Magnitude) assert mst_roundtrip2.unit == mst.unit assert_allclose(mst_roundtrip2.value, mst.value) def test_quantity_decomposition(): lq = 10.*u.mag(u.Jy) assert lq.decompose() == lq assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s] assert lq.si == lq assert lq.si.unit.physical_unit.bases == [u.kg, u.s] assert lq.cgs == lq assert lq.cgs.unit.physical_unit.bases == [u.g, u.s] class TestLogQuantityViews(object): def setup(self): self.lq = u.Magnitude(np.arange(10.) * u.Jy) self.lq2 = u.Magnitude(np.arange(5.)) def test_value_view(self): lq_value = self.lq.value assert type(lq_value) is np.ndarray lq_value[2] = -1. assert np.all(self.lq.value == lq_value) def test_function_view(self): lq_fv = self.lq._function_view assert type(lq_fv) is u.Quantity assert lq_fv.unit is self.lq.unit.function_unit lq_fv[3] = -2. * lq_fv.unit assert np.all(self.lq.value == lq_fv.value) def test_quantity_view(self): # Cannot view as Quantity, since the unit cannot be represented. with pytest.raises(TypeError): self.lq.view(u.Quantity) # But a dimensionless one is fine. q2 = self.lq2.view(u.Quantity) assert q2.unit is u.mag assert np.all(q2.value == self.lq2.value) lq3 = q2.view(u.Magnitude) assert type(lq3.unit) is u.MagUnit assert lq3.unit.physical_unit == u.dimensionless_unscaled assert np.all(lq3 == self.lq2) class TestLogQuantitySlicing(object): def test_item_get_and_set(self): lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy) assert lq1[9] == u.Magnitude(10.*u.Jy) lq1[2] = 100.*u.Jy assert lq1[2] == u.Magnitude(100.*u.Jy) with pytest.raises(u.UnitsError): lq1[2] = 100.*u.m with pytest.raises(u.UnitsError): lq1[2] = 100.*u.mag with pytest.raises(u.UnitsError): lq1[2] = u.Magnitude(100.*u.m) assert lq1[2] == u.Magnitude(100.*u.Jy) def test_slice_get_and_set(self): lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy) lq1[2:4] = 100.*u.Jy assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy)) with pytest.raises(u.UnitsError): lq1[2:4] = 100.*u.m with pytest.raises(u.UnitsError): lq1[2:4] = 100.*u.mag with pytest.raises(u.UnitsError): lq1[2:4] = u.Magnitude(100.*u.m) assert np.all(lq1[2] == u.Magnitude(100.*u.Jy)) class TestLogQuantityArithmetic(object): def test_multiplication_division(self): """Check that multiplication/division with other quantities is only possible when the physical unit is dimensionless, and that this turns the result into a normal quantity.""" lq = u.Magnitude(np.arange(1., 11.)*u.Jy) with pytest.raises(u.UnitsError): lq * (1.*u.m) with pytest.raises(u.UnitsError): (1.*u.m) * lq with pytest.raises(u.UnitsError): lq / lq for unit in (u.m, u.mag, u.dex): with pytest.raises(u.UnitsError): lq / unit lq2 = u.Magnitude(np.arange(1, 11.)) with pytest.raises(u.UnitsError): lq2 * lq with pytest.raises(u.UnitsError): lq2 / lq with pytest.raises(u.UnitsError): lq / lq2 # but dimensionless_unscaled can be cancelled r = lq2 / u.Magnitude(2.) assert r.unit == u.dimensionless_unscaled assert np.all(r.value == lq2.value/2.) # with dimensionless, normal units OK, but return normal quantities tf = lq2 * u.m tr = u.m * lq2 for t in (tf, tr): assert not isinstance(t, type(lq2)) assert t.unit == lq2.unit.function_unit * u.m with u.set_enabled_equivalencies(u.logarithmic()): with pytest.raises(u.UnitsError): t.to(lq2.unit.physical_unit) t = tf / (50.*u.cm) # now we essentially have the same quantity but with a prefactor of 2 assert t.unit.is_equivalent(lq2.unit.function_unit) assert_allclose(t.to(lq2.unit.function_unit), lq2._function_view*2) @pytest.mark.parametrize('power', (2, 0.5, 1, 0)) def test_raise_to_power(self, power): """Check that raising LogQuantities to some power is only possible when the physical unit is dimensionless, and that conversion is turned off when the resulting logarithmic unit (say, mag**2) is incompatible.""" lq = u.Magnitude(np.arange(1., 4.)*u.Jy) if power == 0: assert np.all(lq ** power == 1.) elif power == 1: assert np.all(lq ** power == lq) else: with pytest.raises(u.UnitsError): lq ** power # with dimensionless, it works, but falls back to normal quantity # (except for power=1) lq2 = u.Magnitude(np.arange(10.)) t = lq2**power if power == 0: assert t.unit is u.dimensionless_unscaled assert np.all(t.value == 1.) elif power == 1: assert np.all(t == lq2) else: assert not isinstance(t, type(lq2)) assert t.unit == lq2.unit.function_unit ** power with u.set_enabled_equivalencies(u.logarithmic()): with pytest.raises(u.UnitsError): t.to(u.dimensionless_unscaled) def test_error_on_lq_as_power(self): lq = u.Magnitude(np.arange(1., 4.)*u.Jy) with pytest.raises(TypeError): lq ** lq @pytest.mark.parametrize('other', pu_sample) def test_addition_subtraction_to_normal_units_fails(self, other): lq = u.Magnitude(

np.arange(1., 10.)

numpy.arange

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients =

np.mean(gradients, axis=1)

numpy.mean

"""Test the search module""" from collections.abc import Iterable, Sized from io import StringIO from itertools import chain, product from functools import partial import pickle import sys from types import GeneratorType import re import numpy as np import scipy.sparse as sp import pytest from sklearn.utils.fixes import sp_version from sklearn.utils._testing import assert_raises from sklearn.utils._testing import assert_warns from sklearn.utils._testing import assert_warns_message from sklearn.utils._testing import assert_raise_message from sklearn.utils._testing import assert_array_equal from sklearn.utils._testing import assert_array_almost_equal from sklearn.utils._testing import assert_allclose from sklearn.utils._testing import assert_almost_equal from sklearn.utils._testing import ignore_warnings from sklearn.utils._mocking import CheckingClassifier, MockDataFrame from scipy.stats import bernoulli, expon, uniform from sklearn.base import BaseEstimator, ClassifierMixin from sklearn.base import clone from sklearn.exceptions import NotFittedError from sklearn.datasets import make_classification from sklearn.datasets import make_blobs from sklearn.datasets import make_multilabel_classification from sklearn.model_selection import fit_grid_point from sklearn.model_selection import train_test_split from sklearn.model_selection import KFold from sklearn.model_selection import StratifiedKFold from sklearn.model_selection import StratifiedShuffleSplit from sklearn.model_selection import LeaveOneGroupOut from sklearn.model_selection import LeavePGroupsOut from sklearn.model_selection import GroupKFold from sklearn.model_selection import GroupShuffleSplit from sklearn.model_selection import GridSearchCV from sklearn.model_selection import RandomizedSearchCV from sklearn.model_selection import ParameterGrid from sklearn.model_selection import ParameterSampler from sklearn.model_selection._search import BaseSearchCV from sklearn.model_selection._validation import FitFailedWarning from sklearn.svm import LinearSVC, SVC from sklearn.tree import DecisionTreeRegressor from sklearn.tree import DecisionTreeClassifier from sklearn.cluster import KMeans from sklearn.neighbors import KernelDensity from sklearn.neighbors import KNeighborsClassifier from sklearn.metrics import f1_score from sklearn.metrics import recall_score from sklearn.metrics import accuracy_score from sklearn.metrics import make_scorer from sklearn.metrics import roc_auc_score from sklearn.metrics.pairwise import euclidean_distances from sklearn.impute import SimpleImputer from sklearn.pipeline import Pipeline from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression from sklearn.experimental import enable_hist_gradient_boosting # noqa from sklearn.ensemble import HistGradientBoostingClassifier from sklearn.model_selection.tests.common import OneTimeSplitter # Neither of the following two estimators inherit from BaseEstimator, # to test hyperparameter search on user-defined classifiers. class MockClassifier: """Dummy classifier to test the parameter search algorithms""" def __init__(self, foo_param=0): self.foo_param = foo_param def fit(self, X, Y): assert len(X) == len(Y) self.classes_ = np.unique(Y) return self def predict(self, T): return T.shape[0] def transform(self, X): return X + self.foo_param def inverse_transform(self, X): return X - self.foo_param predict_proba = predict predict_log_proba = predict decision_function = predict def score(self, X=None, Y=None): if self.foo_param > 1: score = 1. else: score = 0. return score def get_params(self, deep=False): return {'foo_param': self.foo_param} def set_params(self, **params): self.foo_param = params['foo_param'] return self class LinearSVCNoScore(LinearSVC): """An LinearSVC classifier that has no score method.""" @property def score(self): raise AttributeError X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) y = np.array([1, 1, 2, 2]) def assert_grid_iter_equals_getitem(grid): assert list(grid) == [grid[i] for i in range(len(grid))] @pytest.mark.parametrize("klass", [ParameterGrid, partial(ParameterSampler, n_iter=10)]) @pytest.mark.parametrize( "input, error_type, error_message", [(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'), ([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'), ({'foo': 0}, TypeError, "Parameter.* value is not iterable .*" r"\(key='foo', value=0\)")] ) def test_validate_parameter_input(klass, input, error_type, error_message): with pytest.raises(error_type, match=error_message): klass(input) def test_parameter_grid(): # Test basic properties of ParameterGrid. params1 = {"foo": [1, 2, 3]} grid1 = ParameterGrid(params1) assert isinstance(grid1, Iterable) assert isinstance(grid1, Sized) assert len(grid1) == 3 assert_grid_iter_equals_getitem(grid1) params2 = {"foo": [4, 2], "bar": ["ham", "spam", "eggs"]} grid2 = ParameterGrid(params2) assert len(grid2) == 6 # loop to assert we can iterate over the grid multiple times for i in range(2): # tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2) points = set(tuple(chain(*(sorted(p.items())))) for p in grid2) assert (points == set(("bar", x, "foo", y) for x, y in product(params2["bar"], params2["foo"]))) assert_grid_iter_equals_getitem(grid2) # Special case: empty grid (useful to get default estimator settings) empty = ParameterGrid({}) assert len(empty) == 1 assert list(empty) == [{}] assert_grid_iter_equals_getitem(empty) assert_raises(IndexError, lambda: empty[1]) has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}]) assert len(has_empty) == 4 assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}] assert_grid_iter_equals_getitem(has_empty) def test_grid_search(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3) # make sure it selects the smallest parameter in case of ties old_stdout = sys.stdout sys.stdout = StringIO() grid_search.fit(X, y) sys.stdout = old_stdout assert grid_search.best_estimator_.foo_param == 2 assert_array_equal(grid_search.cv_results_["param_foo_param"].data, [1, 2, 3]) # Smoke test the score etc: grid_search.score(X, y) grid_search.predict_proba(X) grid_search.decision_function(X) grid_search.transform(X) # Test exception handling on scoring grid_search.scoring = 'sklearn' assert_raises(ValueError, grid_search.fit, X, y) def test_grid_search_pipeline_steps(): # check that parameters that are estimators are cloned before fitting pipe = Pipeline([('regressor', LinearRegression())]) param_grid = {'regressor': [LinearRegression(), Ridge()]} grid_search = GridSearchCV(pipe, param_grid, cv=2) grid_search.fit(X, y) regressor_results = grid_search.cv_results_['param_regressor'] assert isinstance(regressor_results[0], LinearRegression) assert isinstance(regressor_results[1], Ridge) assert not hasattr(regressor_results[0], 'coef_') assert not hasattr(regressor_results[1], 'coef_') assert regressor_results[0] is not grid_search.best_estimator_ assert regressor_results[1] is not grid_search.best_estimator_ # check that we didn't modify the parameter grid that was passed assert not hasattr(param_grid['regressor'][0], 'coef_') assert not hasattr(param_grid['regressor'][1], 'coef_') @pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV]) def test_SearchCV_with_fit_params(SearchCV): X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier(expected_fit_params=['spam', 'eggs']) searcher = SearchCV( clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise" ) # The CheckingClassifier generates an assertion error if # a parameter is missing or has length != len(X). err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen." with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(10)) err_msg = "Fit parameter spam has length 1; expected" with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10)) searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10)) @ignore_warnings def test_grid_search_no_score(): # Test grid-search on classifier that has no score function. clf = LinearSVC(random_state=0) X, y = make_blobs(random_state=0, centers=2) Cs = [.1, 1, 10] clf_no_score = LinearSVCNoScore(random_state=0) grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy') grid_search.fit(X, y) grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}, scoring='accuracy') # smoketest grid search grid_search_no_score.fit(X, y) # check that best params are equal assert grid_search_no_score.best_params_ == grid_search.best_params_ # check that we can call score and that it gives the correct result assert grid_search.score(X, y) == grid_search_no_score.score(X, y) # giving no scoring function raises an error grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}) assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit, [[1]]) def test_grid_search_score_method(): X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2, random_state=0) clf = LinearSVC(random_state=0) grid = {'C': [.1]} search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y) search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y) search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid, scoring='roc_auc' ).fit(X, y) search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y) # Check warning only occurs in situation where behavior changed: # estimator requires score method to compete with scoring parameter score_no_scoring = search_no_scoring.score(X, y) score_accuracy = search_accuracy.score(X, y) score_no_score_auc = search_no_score_method_auc.score(X, y) score_auc = search_auc.score(X, y) # ensure the test is sane assert score_auc < 1.0 assert score_accuracy < 1.0 assert score_auc != score_accuracy assert_almost_equal(score_accuracy, score_no_scoring) assert_almost_equal(score_auc, score_no_score_auc) def test_grid_search_groups(): # Check if ValueError (when groups is None) propagates to GridSearchCV # And also check if groups is correctly passed to the cv object rng = np.random.RandomState(0) X, y = make_classification(n_samples=15, n_classes=2, random_state=0) groups = rng.randint(0, 3, 15) clf = LinearSVC(random_state=0) grid = {'C': [1]} group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2), GroupKFold(n_splits=3), GroupShuffleSplit()] for cv in group_cvs: gs = GridSearchCV(clf, grid, cv=cv) assert_raise_message(ValueError, "The 'groups' parameter should not be None.", gs.fit, X, y) gs.fit(X, y, groups=groups) non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()] for cv in non_group_cvs: gs = GridSearchCV(clf, grid, cv=cv) # Should not raise an error gs.fit(X, y) def test_classes__property(): # Test that classes_ property matches best_estimator_.classes_ X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) Cs = [.1, 1, 10] grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) grid_search.fit(X, y) assert_array_equal(grid_search.best_estimator_.classes_, grid_search.classes_) # Test that regressors do not have a classes_ attribute grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]}) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute before it's fit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute without a refit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}, refit=False) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') def test_trivial_cv_results_attr(): # Test search over a "grid" with only one point. clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3) grid_search.fit(X, y) assert hasattr(grid_search, "cv_results_") random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3) random_search.fit(X, y) assert hasattr(grid_search, "cv_results_") def test_no_refit(): # Test that GSCV can be used for model selection alone without refitting clf = MockClassifier() for scoring in [None, ['accuracy', 'precision']]: grid_search = GridSearchCV( clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3 ) grid_search.fit(X, y) assert not hasattr(grid_search, "best_estimator_") and \ hasattr(grid_search, "best_index_") and \ hasattr(grid_search, "best_params_") # Make sure the functions predict/transform etc raise meaningful # error messages for fn_name in ('predict', 'predict_proba', 'predict_log_proba', 'transform', 'inverse_transform'): assert_raise_message(NotFittedError, ('refit=False. %s is available only after ' 'refitting on the best parameters' % fn_name), getattr(grid_search, fn_name), X) # Test that an invalid refit param raises appropriate error messages for refit in ["", 5, True, 'recall', 'accuracy']: assert_raise_message(ValueError, "For multi-metric scoring, the " "parameter refit must be set to a scorer key", GridSearchCV(clf, {}, refit=refit, scoring={'acc': 'accuracy', 'prec': 'precision'} ).fit, X, y) def test_grid_search_error(): # Test that grid search will capture errors on data with different length X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, X_[:180], y_) def test_grid_search_one_grid_point(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]} clf = SVC(gamma='auto') cv = GridSearchCV(clf, param_dict) cv.fit(X_, y_) clf = SVC(C=1.0, kernel="rbf", gamma=0.1) clf.fit(X_, y_) assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_) def test_grid_search_when_param_grid_includes_range(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = None grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3) grid_search.fit(X, y) assert grid_search.best_estimator_.foo_param == 2 def test_grid_search_bad_param_grid(): param_dict = {"C": 1} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'int'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": []} clf = SVC() assert_raise_message( ValueError, "Parameter values for parameter (C) need to be a non-empty sequence.", GridSearchCV, clf, param_dict) param_dict = {"C": "1,2,3"} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'str'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": np.ones((3, 2))} clf = SVC() assert_raises(ValueError, GridSearchCV, clf, param_dict) def test_grid_search_sparse(): # Test that grid search works with both dense and sparse matrices X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180].tocoo(), y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert np.mean(y_pred == y_pred2) >= .9 assert C == C2 def test_grid_search_sparse_scoring(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1") cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1") cv.fit(X_[:180], y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert_array_equal(y_pred, y_pred2) assert C == C2 # Smoke test the score # np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]), # cv.score(X_[:180], y[:180])) # test loss where greater is worse def f1_loss(y_true_, y_pred_): return -f1_score(y_true_, y_pred_) F1Loss = make_scorer(f1_loss, greater_is_better=False) cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss) cv.fit(X_[:180], y_[:180]) y_pred3 = cv.predict(X_[180:]) C3 = cv.best_estimator_.C assert C == C3 assert_array_equal(y_pred, y_pred3) def test_grid_search_precomputed_kernel(): # Test that grid search works when the input features are given in the # form of a precomputed kernel matrix X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) # compute the training kernel matrix corresponding to the linear kernel K_train = np.dot(X_[:180], X_[:180].T) y_train = y_[:180] clf = SVC(kernel='precomputed') cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(K_train, y_train) assert cv.best_score_ >= 0 # compute the test kernel matrix K_test = np.dot(X_[180:], X_[:180].T) y_test = y_[180:] y_pred = cv.predict(K_test) assert np.mean(y_pred == y_test) >= 0 # test error is raised when the precomputed kernel is not array-like # or sparse assert_raises(ValueError, cv.fit, K_train.tolist(), y_train) def test_grid_search_precomputed_kernel_error_nonsquare(): # Test that grid search returns an error with a non-square precomputed # training kernel matrix K_train = np.zeros((10, 20)) y_train = np.ones((10, )) clf = SVC(kernel='precomputed') cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, K_train, y_train) class BrokenClassifier(BaseEstimator): """Broken classifier that cannot be fit twice""" def __init__(self, parameter=None): self.parameter = parameter def fit(self, X, y): assert not hasattr(self, 'has_been_fit_') self.has_been_fit_ = True def predict(self, X): return np.zeros(X.shape[0]) @ignore_warnings def test_refit(): # Regression test for bug in refitting # Simulates re-fitting a broken estimator; this used to break with # sparse SVMs. X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = GridSearchCV(BrokenClassifier(), [{'parameter': [0, 1]}], scoring="precision", refit=True) clf.fit(X, y) def test_refit_callable(): """ Test refit=callable, which adds flexibility in identifying the "best" estimator. """ def refit_callable(cv_results): """ A dummy function tests `refit=callable` interface. Return the index of a model that has the least `mean_test_score`. """ # Fit a dummy clf with `refit=True` to get a list of keys in # clf.cv_results_. X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring='precision', refit=True) clf.fit(X, y) # Ensure that `best_index_ != 0` for this dummy clf assert clf.best_index_ != 0 # Assert every key matches those in `cv_results` for key in clf.cv_results_.keys(): assert key in cv_results return cv_results['mean_test_score'].argmin() X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring='precision', refit=refit_callable) clf.fit(X, y) assert clf.best_index_ == 0 # Ensure `best_score_` is disabled when using `refit=callable` assert not hasattr(clf, 'best_score_') def test_refit_callable_invalid_type(): """ Test implementation catches the errors when 'best_index_' returns an invalid result. """ def refit_callable_invalid_type(cv_results): """ A dummy function tests when returned 'best_index_' is not integer. """ return None X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.1, 1]}, scoring='precision', refit=refit_callable_invalid_type) with pytest.raises(TypeError, match='best_index_ returned is not an integer'): clf.fit(X, y) @pytest.mark.parametrize('out_bound_value', [-1, 2]) @pytest.mark.parametrize('search_cv', [RandomizedSearchCV, GridSearchCV]) def test_refit_callable_out_bound(out_bound_value, search_cv): """ Test implementation catches the errors when 'best_index_' returns an out of bound result. """ def refit_callable_out_bound(cv_results): """ A dummy function tests when returned 'best_index_' is out of bounds. """ return out_bound_value X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = search_cv(LinearSVC(random_state=42), {'C': [0.1, 1]}, scoring='precision', refit=refit_callable_out_bound) with pytest.raises(IndexError, match='best_index_ index out of range'): clf.fit(X, y) def test_refit_callable_multi_metric(): """ Test refit=callable in multiple metric evaluation setting """ def refit_callable(cv_results): """ A dummy function tests `refit=callable` interface. Return the index of a model that has the least `mean_test_prec`. """ assert 'mean_test_prec' in cv_results return cv_results['mean_test_prec'].argmin() X, y = make_classification(n_samples=100, n_features=4, random_state=42) scoring = {'Accuracy': make_scorer(accuracy_score), 'prec': 'precision'} clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring=scoring, refit=refit_callable) clf.fit(X, y) assert clf.best_index_ == 0 # Ensure `best_score_` is disabled when using `refit=callable` assert not hasattr(clf, 'best_score_') def test_gridsearch_nd(): # Pass X as list in GridSearchCV X_4d = np.arange(10 * 5 * 3 * 2).reshape(10, 5, 3, 2) y_3d = np.arange(10 * 7 * 11).reshape(10, 7, 11) check_X = lambda x: x.shape[1:] == (5, 3, 2) check_y = lambda x: x.shape[1:] == (7, 11) clf = CheckingClassifier( check_X=check_X, check_y=check_y, methods_to_check=["fit"], ) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}) grid_search.fit(X_4d, y_3d).score(X, y) assert hasattr(grid_search, "cv_results_") def test_X_as_list(): # Pass X as list in GridSearchCV X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier( check_X=lambda x: isinstance(x, list), methods_to_check=["fit"], ) cv = KFold(n_splits=3) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv) grid_search.fit(X.tolist(), y).score(X, y) assert hasattr(grid_search, "cv_results_") def test_y_as_list(): # Pass y as list in GridSearchCV X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier( check_y=lambda x: isinstance(x, list), methods_to_check=["fit"], ) cv = KFold(n_splits=3) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv) grid_search.fit(X, y.tolist()).score(X, y) assert hasattr(grid_search, "cv_results_") @ignore_warnings def test_pandas_input(): # check cross_val_score doesn't destroy pandas dataframe types = [(MockDataFrame, MockDataFrame)] try: from pandas import Series, DataFrame types.append((DataFrame, Series)) except ImportError: pass X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) for InputFeatureType, TargetType in types: # X dataframe, y series X_df, y_ser = InputFeatureType(X), TargetType(y) def check_df(x): return isinstance(x, InputFeatureType) def check_series(x): return isinstance(x, TargetType) clf = CheckingClassifier(check_X=check_df, check_y=check_series) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}) grid_search.fit(X_df, y_ser).score(X_df, y_ser) grid_search.predict(X_df) assert hasattr(grid_search, "cv_results_") def test_unsupervised_grid_search(): # test grid-search with unsupervised estimator X, y = make_blobs(n_samples=50, random_state=0) km = KMeans(random_state=0, init="random", n_init=1) # Multi-metric evaluation unsupervised scoring = ['adjusted_rand_score', 'fowlkes_mallows_score'] for refit in ['adjusted_rand_score', 'fowlkes_mallows_score']: grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]), scoring=scoring, refit=refit) grid_search.fit(X, y) # Both ARI and FMS can find the right number :) assert grid_search.best_params_["n_clusters"] == 3 # Single metric evaluation unsupervised grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]), scoring='fowlkes_mallows_score') grid_search.fit(X, y) assert grid_search.best_params_["n_clusters"] == 3 # Now without a score, and without y grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4])) grid_search.fit(X) assert grid_search.best_params_["n_clusters"] == 4 def test_gridsearch_no_predict(): # test grid-search with an estimator without predict. # slight duplication of a test from KDE def custom_scoring(estimator, X): return 42 if estimator.bandwidth == .1 else 0 X, _ = make_blobs(cluster_std=.1, random_state=1, centers=[[0, 1], [1, 0], [0, 0]]) search = GridSearchCV(KernelDensity(), param_grid=dict(bandwidth=[.01, .1, 1]), scoring=custom_scoring) search.fit(X) assert search.best_params_['bandwidth'] == .1 assert search.best_score_ == 42 def test_param_sampler(): # test basic properties of param sampler param_distributions = {"kernel": ["rbf", "linear"], "C": uniform(0, 1)} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=10, random_state=0) samples = [x for x in sampler] assert len(samples) == 10 for sample in samples: assert sample["kernel"] in ["rbf", "linear"] assert 0 <= sample["C"] <= 1 # test that repeated calls yield identical parameters param_distributions = {"C": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=3, random_state=0) assert [x for x in sampler] == [x for x in sampler] if sp_version >= (0, 16): param_distributions = {"C": uniform(0, 1)} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=10, random_state=0) assert [x for x in sampler] == [x for x in sampler] def check_cv_results_array_types(search, param_keys, score_keys): # Check if the search `cv_results`'s array are of correct types cv_results = search.cv_results_ assert all(isinstance(cv_results[param], np.ma.MaskedArray) for param in param_keys) assert all(cv_results[key].dtype == object for key in param_keys) assert not any(isinstance(cv_results[key], np.ma.MaskedArray) for key in score_keys) assert all(cv_results[key].dtype == np.float64 for key in score_keys if not key.startswith('rank')) scorer_keys = search.scorer_.keys() if search.multimetric_ else ['score'] for key in scorer_keys: assert cv_results['rank_test_%s' % key].dtype == np.int32 def check_cv_results_keys(cv_results, param_keys, score_keys, n_cand): # Test the search.cv_results_ contains all the required results assert_array_equal(sorted(cv_results.keys()), sorted(param_keys + score_keys + ('params',))) assert all(cv_results[key].shape == (n_cand,) for key in param_keys + score_keys) def test_grid_search_cv_results(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_grid_points = 6 params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]), dict(kernel=['poly', ], degree=[1, 2])] param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel') score_keys = ('mean_test_score', 'mean_train_score', 'rank_test_score', 'split0_test_score', 'split1_test_score', 'split2_test_score', 'split0_train_score', 'split1_train_score', 'split2_train_score', 'std_test_score', 'std_train_score', 'mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time') n_candidates = n_grid_points search = GridSearchCV(SVC(), cv=n_splits, param_grid=params, return_train_score=True) search.fit(X, y) cv_results = search.cv_results_ # Check if score and timing are reasonable assert all(cv_results['rank_test_score'] >= 1) assert (all(cv_results[k] >= 0) for k in score_keys if k != 'rank_test_score') assert (all(cv_results[k] <= 1) for k in score_keys if 'time' not in k and k != 'rank_test_score') # Check cv_results structure check_cv_results_array_types(search, param_keys, score_keys) check_cv_results_keys(cv_results, param_keys, score_keys, n_candidates) # Check masking cv_results = search.cv_results_ n_candidates = len(search.cv_results_['params']) assert all((cv_results['param_C'].mask[i] and cv_results['param_gamma'].mask[i] and not cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'linear') assert all((not cv_results['param_C'].mask[i] and not cv_results['param_gamma'].mask[i] and cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'rbf') def test_random_search_cv_results(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_search_iter = 30 params = [{'kernel': ['rbf'], 'C': expon(scale=10), 'gamma': expon(scale=0.1)}, {'kernel': ['poly'], 'degree': [2, 3]}] param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel') score_keys = ('mean_test_score', 'mean_train_score', 'rank_test_score', 'split0_test_score', 'split1_test_score', 'split2_test_score', 'split0_train_score', 'split1_train_score', 'split2_train_score', 'std_test_score', 'std_train_score', 'mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time') n_cand = n_search_iter search = RandomizedSearchCV(SVC(), n_iter=n_search_iter, cv=n_splits, param_distributions=params, return_train_score=True) search.fit(X, y) cv_results = search.cv_results_ # Check results structure check_cv_results_array_types(search, param_keys, score_keys) check_cv_results_keys(cv_results, param_keys, score_keys, n_cand) n_candidates = len(search.cv_results_['params']) assert all((cv_results['param_C'].mask[i] and cv_results['param_gamma'].mask[i] and not cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'linear') assert all((not cv_results['param_C'].mask[i] and not cv_results['param_gamma'].mask[i] and cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'rbf') @pytest.mark.parametrize( "SearchCV, specialized_params", [(GridSearchCV, {'param_grid': {'C': [1, 10]}}), (RandomizedSearchCV, {'param_distributions': {'C': [1, 10]}, 'n_iter': 2})] ) def test_search_default_iid(SearchCV, specialized_params): # Test the IID parameter TODO: Clearly this test does something else??? # noise-free simple 2d-data X, y = make_blobs(centers=[[0, 0], [1, 0], [0, 1], [1, 1]], random_state=0, cluster_std=0.1, shuffle=False, n_samples=80) # split dataset into two folds that are not iid # first one contains data of all 4 blobs, second only from two. mask = np.ones(X.shape[0], dtype=np.bool) mask[np.where(y == 1)[0][::2]] = 0 mask[np.where(y == 2)[0][::2]] = 0 # this leads to perfect classification on one fold and a score of 1/3 on # the other # create "cv" for splits cv = [[mask, ~mask], [~mask, mask]] common_params = {'estimator': SVC(), 'cv': cv, 'return_train_score': True} search = SearchCV(**common_params, **specialized_params) search.fit(X, y) test_cv_scores = np.array( [search.cv_results_['split%d_test_score' % s][0] for s in range(search.n_splits_)] ) test_mean = search.cv_results_['mean_test_score'][0] test_std = search.cv_results_['std_test_score'][0] train_cv_scores = np.array( [search.cv_results_['split%d_train_score' % s][0] for s in range(search.n_splits_)] ) train_mean = search.cv_results_['mean_train_score'][0] train_std = search.cv_results_['std_train_score'][0] assert search.cv_results_['param_C'][0] == 1 # scores are the same as above assert_allclose(test_cv_scores, [1, 1. / 3.]) assert_allclose(train_cv_scores, [1, 1]) # Unweighted mean/std is used assert test_mean == pytest.approx(np.mean(test_cv_scores)) assert test_std == pytest.approx(np.std(test_cv_scores)) # For the train scores, we do not take a weighted mean irrespective of # i.i.d. or not assert train_mean == pytest.approx(1) assert train_std == pytest.approx(0) def test_grid_search_cv_results_multimetric(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]), dict(kernel=['poly', ], degree=[1, 2])] grid_searches = [] for scoring in ({'accuracy': make_scorer(accuracy_score), 'recall': make_scorer(recall_score)}, 'accuracy', 'recall'): grid_search = GridSearchCV(SVC(), cv=n_splits, param_grid=params, scoring=scoring, refit=False) grid_search.fit(X, y) grid_searches.append(grid_search) compare_cv_results_multimetric_with_single(*grid_searches) def test_random_search_cv_results_multimetric(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_search_iter = 30 # Scipy 0.12's stats dists do not accept seed, hence we use param grid params = dict(C=np.logspace(-4, 1, 3), gamma=np.logspace(-5, 0, 3, base=0.1)) for refit in (True, False): random_searches = [] for scoring in (('accuracy', 'recall'), 'accuracy', 'recall'): # If True, for multi-metric pass refit='accuracy' if refit: probability = True refit = 'accuracy' if isinstance(scoring, tuple) else refit else: probability = False clf = SVC(probability=probability, random_state=42) random_search = RandomizedSearchCV(clf, n_iter=n_search_iter, cv=n_splits, param_distributions=params, scoring=scoring, refit=refit, random_state=0) random_search.fit(X, y) random_searches.append(random_search) compare_cv_results_multimetric_with_single(*random_searches) compare_refit_methods_when_refit_with_acc( random_searches[0], random_searches[1], refit) def compare_cv_results_multimetric_with_single( search_multi, search_acc, search_rec): """Compare multi-metric cv_results with the ensemble of multiple single metric cv_results from single metric grid/random search""" assert search_multi.multimetric_ assert_array_equal(sorted(search_multi.scorer_), ('accuracy', 'recall')) cv_results_multi = search_multi.cv_results_ cv_results_acc_rec = {re.sub('_score$', '_accuracy', k): v for k, v in search_acc.cv_results_.items()} cv_results_acc_rec.update({re.sub('_score$', '_recall', k): v for k, v in search_rec.cv_results_.items()}) # Check if score and timing are reasonable, also checks if the keys # are present assert all((np.all(cv_results_multi[k] <= 1) for k in ( 'mean_score_time', 'std_score_time', 'mean_fit_time', 'std_fit_time'))) # Compare the keys, other than time keys, among multi-metric and # single metric grid search results. np.testing.assert_equal performs a # deep nested comparison of the two cv_results dicts np.testing.assert_equal({k: v for k, v in cv_results_multi.items() if not k.endswith('_time')}, {k: v for k, v in cv_results_acc_rec.items() if not k.endswith('_time')}) def compare_refit_methods_when_refit_with_acc(search_multi, search_acc, refit): """Compare refit multi-metric search methods with single metric methods""" assert search_acc.refit == refit if refit: assert search_multi.refit == 'accuracy' else: assert not search_multi.refit return # search cannot predict/score without refit X, y = make_blobs(n_samples=100, n_features=4, random_state=42) for method in ('predict', 'predict_proba', 'predict_log_proba'): assert_almost_equal(getattr(search_multi, method)(X), getattr(search_acc, method)(X)) assert_almost_equal(search_multi.score(X, y), search_acc.score(X, y)) for key in ('best_index_', 'best_score_', 'best_params_'): assert getattr(search_multi, key) == getattr(search_acc, key) def test_search_cv_results_rank_tie_breaking(): X, y = make_blobs(n_samples=50, random_state=42) # The two C values are close enough to give similar models # which would result in a tie of their mean cv-scores param_grid = {'C': [1, 1.001, 0.001]} grid_search = GridSearchCV(SVC(), param_grid=param_grid, return_train_score=True) random_search = RandomizedSearchCV(SVC(), n_iter=3, param_distributions=param_grid, return_train_score=True) for search in (grid_search, random_search): search.fit(X, y) cv_results = search.cv_results_ # Check tie breaking strategy - # Check that there is a tie in the mean scores between # candidates 1 and 2 alone assert_almost_equal(cv_results['mean_test_score'][0], cv_results['mean_test_score'][1]) assert_almost_equal(cv_results['mean_train_score'][0], cv_results['mean_train_score'][1]) assert not np.allclose(cv_results['mean_test_score'][1], cv_results['mean_test_score'][2]) assert not np.allclose(cv_results['mean_train_score'][1], cv_results['mean_train_score'][2]) # 'min' rank should be assigned to the tied candidates assert_almost_equal(search.cv_results_['rank_test_score'], [1, 1, 3]) def test_search_cv_results_none_param(): X, y = [[1], [2], [3], [4], [5]], [0, 0, 0, 0, 1] estimators = (DecisionTreeRegressor(), DecisionTreeClassifier()) est_parameters = {"random_state": [0, None]} cv = KFold() for est in estimators: grid_search = GridSearchCV(est, est_parameters, cv=cv, ).fit(X, y) assert_array_equal(grid_search.cv_results_['param_random_state'], [0, None]) @ignore_warnings() def test_search_cv_timing(): svc = LinearSVC(random_state=0) X = [[1, ], [2, ], [3, ], [4, ]] y = [0, 1, 1, 0] gs = GridSearchCV(svc, {'C': [0, 1]}, cv=2, error_score=0) rs = RandomizedSearchCV(svc, {'C': [0, 1]}, cv=2, error_score=0, n_iter=2) for search in (gs, rs): search.fit(X, y) for key in ['mean_fit_time', 'std_fit_time']: # NOTE The precision of time.time in windows is not high # enough for the fit/score times to be non-zero for trivial X and y assert np.all(search.cv_results_[key] >= 0) assert

np.all(search.cv_results_[key] < 1)

numpy.all

""" YTArray class. """ from __future__ import print_function #----------------------------------------------------------------------------- # Copyright (c) 2013, yt Development Team. # # Distributed under the terms of the Modified BSD License. # # The full license is in the file COPYING.txt, distributed with this software. #----------------------------------------------------------------------------- import copy import numpy as np from distutils.version import LooseVersion from functools import wraps from numpy import \ add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \ floor_divide, negative, power, remainder, mod, absolute, rint, \ sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \ reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \ hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \ bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \ greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \ logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \ isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \ modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing try: # numpy 1.13 or newer from numpy import positive, divmod as divmod_, isnat, heaviside except ImportError: positive, divmod_, isnat, heaviside = (None,)*4 from yt.units.unit_object import Unit, UnitParseError from yt.units.unit_registry import UnitRegistry from yt.units.dimensions import \ angle, \ current_mks, \ dimensionless, \ em_dimensions from yt.utilities.exceptions import \ YTUnitOperationError, YTUnitConversionError, \ YTUfuncUnitError, YTIterableUnitCoercionError, \ YTInvalidUnitEquivalence, YTEquivalentDimsError from yt.utilities.lru_cache import lru_cache from numbers import Number as numeric_type from yt.utilities.on_demand_imports import _astropy from sympy import Rational from yt.units.unit_lookup_table import \ default_unit_symbol_lut from yt.units.equivalencies import equivalence_registry from yt.utilities.logger import ytLogger as mylog from .pint_conversions import convert_pint_units NULL_UNIT = Unit() POWER_SIGN_MAPPING = {multiply: 1, divide: -1} # redefine this here to avoid a circular import from yt.funcs def iterable(obj): try: len(obj) except: return False return True def return_arr(func): @wraps(func) def wrapped(*args, **kwargs): ret, units = func(*args, **kwargs) if ret.shape == (): return YTQuantity(ret, units) else: # This could be a subclass, so don't call YTArray directly. return type(args[0])(ret, units) return wrapped @lru_cache(maxsize=128, typed=False) def sqrt_unit(unit): return unit**0.5 @lru_cache(maxsize=128, typed=False) def multiply_units(unit1, unit2): return unit1 * unit2 def preserve_units(unit1, unit2=None): return unit1 @lru_cache(maxsize=128, typed=False) def power_unit(unit, power): return unit**power @lru_cache(maxsize=128, typed=False) def square_unit(unit): return unit*unit @lru_cache(maxsize=128, typed=False) def divide_units(unit1, unit2): return unit1/unit2 @lru_cache(maxsize=128, typed=False) def reciprocal_unit(unit): return unit**-1 def passthrough_unit(unit, unit2=None): return unit def return_without_unit(unit, unit2=None): return None def arctan2_unit(unit1, unit2): return NULL_UNIT def comparison_unit(unit1, unit2=None): return None def invert_units(unit): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def bitop_units(unit1, unit2): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def get_inp_u_unary(ufunc, inputs, out_arr=None): inp = inputs[0] u = getattr(inp, 'units', None) if u is None: u = NULL_UNIT if u.dimensions is angle and ufunc in trigonometric_operators: inp = inp.in_units('radian').v if out_arr is not None: out_arr = ufunc(inp).view(np.ndarray) return out_arr, inp, u def get_inp_u_binary(ufunc, inputs): inp1 = coerce_iterable_units(inputs[0]) inp2 = coerce_iterable_units(inputs[1]) unit1 = getattr(inp1, 'units', None) unit2 = getattr(inp2, 'units', None) ret_class = get_binary_op_return_class(type(inp1), type(inp2)) if unit1 is None: unit1 = Unit(registry=getattr(unit2, 'registry', None)) if unit2 is None and ufunc is not power: unit2 = Unit(registry=getattr(unit1, 'registry', None)) elif ufunc is power: unit2 = inp2 if isinstance(unit2, np.ndarray): if isinstance(unit2, YTArray): if unit2.units.is_dimensionless: pass else: raise YTUnitOperationError(ufunc, unit1, unit2) unit2 = 1.0 return (inp1, inp2), (unit1, unit2), ret_class def handle_preserve_units(inps, units, ufunc, ret_class): if units[0] != units[1]: any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) else: if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False): if units[0] != units[1]: u1d = units[0].is_dimensionless u2d = units[1].is_dimensionless any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) elif not any([u1d, u2d]): if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) else: if raise_error: raise YTUfuncUnitError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_multiply_divide_units(unit, units, out, out_arr): if unit.is_dimensionless and unit.base_value != 1.0: if not units[0].is_dimensionless: if units[0].dimensions == units[1].dimensions: out_arr = np.multiply(out_arr.view(np.ndarray), unit.base_value, out=out) unit = Unit(registry=unit.registry) return out, out_arr, unit def coerce_iterable_units(input_object): if isinstance(input_object, np.ndarray): return input_object if iterable(input_object): if any([isinstance(o, YTArray) for o in input_object]): ff = getattr(input_object[0], 'units', NULL_UNIT, ) if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]): raise YTIterableUnitCoercionError(input_object) # This will create a copy of the data in the iterable. return YTArray(input_object) return input_object else: return input_object def sanitize_units_mul(this_object, other_object): inp = coerce_iterable_units(this_object) ret = coerce_iterable_units(other_object) # If the other object is a YTArray and has the same dimensions as the object # under consideration, convert so we don't mix units with the same # dimensions. if isinstance(ret, YTArray): if inp.units.same_dimensions_as(ret.units): ret.in_units(inp.units) return ret def sanitize_units_add(this_object, other_object, op_string): inp = coerce_iterable_units(this_object) ret = coerce_iterable_units(other_object) # Make sure the other object is a YTArray before we use the `units` # attribute. if isinstance(ret, YTArray): if not inp.units.same_dimensions_as(ret.units): # handle special case of adding or subtracting with zero or # array filled with zero if not np.any(other_object): return ret.view(np.ndarray) elif not np.any(this_object): return ret raise YTUnitOperationError(op_string, inp.units, ret.units) ret = ret.in_units(inp.units) else: # If the other object is not a YTArray, then one of the arrays must be # dimensionless or filled with zeros if not inp.units.is_dimensionless and np.any(ret): raise YTUnitOperationError(op_string, inp.units, dimensionless) return ret def validate_comparison_units(this, other, op_string): # Check that other is a YTArray. if hasattr(other, 'units'): if this.units.expr is other.units.expr: if this.units.base_value == other.units.base_value: return other if not this.units.same_dimensions_as(other.units): raise YTUnitOperationError(op_string, this.units, other.units) return other.in_units(this.units) return other @lru_cache(maxsize=128, typed=False) def _unit_repr_check_same(my_units, other_units): """ Takes a Unit object, or string of known unit symbol, and check that it is compatible with this quantity. Returns Unit object. """ # let Unit() handle units arg if it's not already a Unit obj. if not isinstance(other_units, Unit): other_units = Unit(other_units, registry=my_units.registry) equiv_dims = em_dimensions.get(my_units.dimensions, None) if equiv_dims == other_units.dimensions: if current_mks in equiv_dims.free_symbols: base = "SI" else: base = "CGS" raise YTEquivalentDimsError(my_units, other_units, base) if not my_units.same_dimensions_as(other_units): raise YTUnitConversionError( my_units, my_units.dimensions, other_units, other_units.dimensions) return other_units unary_operators = ( negative, absolute, rint, sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, reciprocal, sin, cos, tan, arcsin, arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, invert, logical_not, isreal, iscomplex, isfinite, isinf, isnan, signbit, floor, ceil, trunc, modf, frexp, fabs, spacing, positive, isnat, ) binary_operators = ( add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, power, remainder, mod, arctan2, hypot, bitwise_and, bitwise_or, bitwise_xor, left_shift, right_shift, greater, greater_equal, less, less_equal, not_equal, equal, logical_and, logical_or, logical_xor, maximum, minimum, fmax, fmin, copysign, nextafter, ldexp, fmod, divmod_, heaviside ) trigonometric_operators = ( sin, cos, tan, ) class YTArray(np.ndarray): """ An ndarray subclass that attaches a symbolic unit object to the array data. Parameters ---------- input_array : :obj:`!iterable` A tuple, list, or array to attach units to input_units : String unit specification, unit symbol object, or astropy units The units of the array. Powers must be specified using python syntax (cm**3, not cm^3). registry : ~yt.units.unit_registry.UnitRegistry The registry to create units from. If input_units is already associated with a unit registry and this is specified, this will be used instead of the registry associated with the unit object. dtype : data-type The dtype of the array data. Defaults to the dtype of the input data, or, if none is found, uses np.float64 bypass_validation : boolean If True, all input validation is skipped. Using this option may produce corrupted, invalid units or array data, but can lead to significant speedups in the input validation logic adds significant overhead. If set, input_units *must* be a valid unit object. Defaults to False. Examples -------- >>> from yt import YTArray >>> a = YTArray([1, 2, 3], 'cm') >>> b = YTArray([4, 5, 6], 'm') >>> a + b YTArray([ 401., 502., 603.]) cm >>> b + a YTArray([ 4.01, 5.02, 6.03]) m NumPy ufuncs will pass through units where appropriate. >>> import numpy as np >>> a = YTArray(np.arange(8) - 4, 'g/cm**3') >>> np.abs(a) YTArray([4, 3, 2, 1, 0, 1, 2, 3]) g/cm**3 and strip them when it would be annoying to deal with them. >>> np.log10(a) array([ -inf, 0. , 0.30103 , 0.47712125, 0.60205999, 0.69897 , 0.77815125, 0.84509804]) YTArray is tightly integrated with yt datasets: >>> import yt >>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030') >>> a = ds.arr(np.ones(5), 'code_length') >>> a.in_cgs() YTArray([ 3.08600000e+24, 3.08600000e+24, 3.08600000e+24, 3.08600000e+24, 3.08600000e+24]) cm This is equivalent to: >>> b = YTArray(np.ones(5), 'code_length', registry=ds.unit_registry) >>> np.all(a == b) True """ _ufunc_registry = { add: preserve_units, subtract: preserve_units, multiply: multiply_units, divide: divide_units, logaddexp: return_without_unit, logaddexp2: return_without_unit, true_divide: divide_units, floor_divide: divide_units, negative: passthrough_unit, power: power_unit, remainder: preserve_units, mod: preserve_units, fmod: preserve_units, absolute: passthrough_unit, fabs: passthrough_unit, rint: return_without_unit, sign: return_without_unit, conj: passthrough_unit, exp: return_without_unit, exp2: return_without_unit, log: return_without_unit, log2: return_without_unit, log10: return_without_unit, expm1: return_without_unit, log1p: return_without_unit, sqrt: sqrt_unit, square: square_unit, reciprocal: reciprocal_unit, sin: return_without_unit, cos: return_without_unit, tan: return_without_unit, sinh: return_without_unit, cosh: return_without_unit, tanh: return_without_unit, arcsin: return_without_unit, arccos: return_without_unit, arctan: return_without_unit, arctan2: arctan2_unit, arcsinh: return_without_unit, arccosh: return_without_unit, arctanh: return_without_unit, hypot: preserve_units, deg2rad: return_without_unit, rad2deg: return_without_unit, bitwise_and: bitop_units, bitwise_or: bitop_units, bitwise_xor: bitop_units, invert: invert_units, left_shift: bitop_units, right_shift: bitop_units, greater: comparison_unit, greater_equal: comparison_unit, less: comparison_unit, less_equal: comparison_unit, not_equal: comparison_unit, equal: comparison_unit, logical_and: comparison_unit, logical_or: comparison_unit, logical_xor: comparison_unit, logical_not: return_without_unit, maximum: preserve_units, minimum: preserve_units, fmax: preserve_units, fmin: preserve_units, isreal: return_without_unit, iscomplex: return_without_unit, isfinite: return_without_unit, isinf: return_without_unit, isnan: return_without_unit, signbit: return_without_unit, copysign: passthrough_unit, nextafter: preserve_units, modf: passthrough_unit, ldexp: bitop_units, frexp: return_without_unit, floor: passthrough_unit, ceil: passthrough_unit, trunc: passthrough_unit, spacing: passthrough_unit, positive: passthrough_unit, divmod_: passthrough_unit, isnat: return_without_unit, heaviside: preserve_units, } __array_priority__ = 2.0 def __new__(cls, input_array, input_units=None, registry=None, dtype=None, bypass_validation=False): if dtype is None: dtype = getattr(input_array, 'dtype', np.float64) if bypass_validation is True: obj = np.asarray(input_array, dtype=dtype).view(cls) obj.units = input_units if registry is not None: obj.units.registry = registry return obj if input_array is NotImplemented: return input_array.view(cls) if registry is None and isinstance(input_units, (str, bytes)): if input_units.startswith('code_'): raise UnitParseError( "Code units used without referring to a dataset. \n" "Perhaps you meant to do something like this instead: \n" "ds.arr(%s, \"%s\")" % (input_array, input_units) ) if isinstance(input_array, YTArray): ret = input_array.view(cls) if input_units is None: if registry is None: ret.units = input_array.units else: units = Unit(str(input_array.units), registry=registry) ret.units = units elif isinstance(input_units, Unit): ret.units = input_units else: ret.units = Unit(input_units, registry=registry) return ret elif isinstance(input_array, np.ndarray): pass elif iterable(input_array) and input_array: if isinstance(input_array[0], YTArray): return YTArray(np.array(input_array, dtype=dtype), input_array[0].units, registry=registry) # Input array is an already formed ndarray instance # We first cast to be our class type obj = np.asarray(input_array, dtype=dtype).view(cls) # Check units type if input_units is None: # Nothing provided. Make dimensionless... units = Unit() elif isinstance(input_units, Unit): if registry and registry is not input_units.registry: units = Unit(str(input_units), registry=registry) else: units = input_units else: # units kwarg set, but it's not a Unit object. # don't handle all the cases here, let the Unit class handle if # it's a str. units = Unit(input_units, registry=registry) # Attach the units obj.units = units return obj def __repr__(self): """ """ return super(YTArray, self).__repr__()+' '+self.units.__repr__() def __str__(self): """ """ return str(self.view(np.ndarray)) + ' ' + str(self.units) # # Start unit conversion methods # def convert_to_units(self, units): """ Convert the array and units to the given units. Parameters ---------- units : Unit object or str The units you want to convert to. """ new_units = _unit_repr_check_same(self.units, units) (conversion_factor, offset) = self.units.get_conversion_factor(new_units) self.units = new_units values = self.d values *= conversion_factor if offset: np.subtract(self, offset*self.uq, self) return self def convert_to_base(self, unit_system="cgs"): """ Convert the array and units to the equivalent base units in the specified unit system. Parameters ---------- unit_system : string, optional The unit system to be used in the conversion. If not specified, the default base units of cgs are used. Examples -------- >>> E = YTQuantity(2.5, "erg/s") >>> E.convert_to_base(unit_system="galactic") """ return self.convert_to_units(self.units.get_base_equivalent(unit_system)) def convert_to_cgs(self): """ Convert the array and units to the equivalent cgs units. """ return self.convert_to_units(self.units.get_cgs_equivalent()) def convert_to_mks(self): """ Convert the array and units to the equivalent mks units. """ return self.convert_to_units(self.units.get_mks_equivalent()) def in_units(self, units, equivalence=None, **kwargs): """ Creates a copy of this array with the data in the supplied units, and returns it. Optionally, an equivalence can be specified to convert to an equivalent quantity which is not in the same dimensions. .. note:: All additional keyword arguments are passed to the equivalency, which should be used if that particular equivalency requires them. Parameters ---------- units : Unit object or string The units you want to get a new quantity in. equivalence : string, optional The equivalence you wish to use. To see which equivalencies are supported for this unitful quantity, try the :meth:`list_equivalencies` method. Default: None Returns ------- YTArray """ if equivalence is None: new_units = _unit_repr_check_same(self.units, units) (conversion_factor, offset) = self.units.get_conversion_factor(new_units) new_array = type(self)(self.ndview * conversion_factor, new_units) if offset: np.subtract(new_array, offset*new_array.uq, new_array) return new_array else: return self.to_equivalent(units, equivalence, **kwargs) def to(self, units, equivalence=None, **kwargs): """ An alias for YTArray.in_units(). See the docstrings of that function for details. """ return self.in_units(units, equivalence=equivalence, **kwargs) def to_value(self, units=None, equivalence=None, **kwargs): """ Creates a copy of this array with the data in the supplied units, and returns it without units. Output is therefore a bare NumPy array. Optionally, an equivalence can be specified to convert to an equivalent quantity which is not in the same dimensions. .. note:: All additional keyword arguments are passed to the equivalency, which should be used if that particular equivalency requires them. Parameters ---------- units : Unit object or string, optional The units you want to get the bare quantity in. If not specified, the value will be returned in the current units. equivalence : string, optional The equivalence you wish to use. To see which equivalencies are supported for this unitful quantity, try the :meth:`list_equivalencies` method. Default: None Returns ------- NumPy array """ if units is None: v = self.value else: v = self.in_units(units, equivalence=equivalence, **kwargs).value if isinstance(self, YTQuantity): return float(v) else: return v def in_base(self, unit_system="cgs"): """ Creates a copy of this array with the data in the specified unit system, and returns it in that system's base units. Parameters ---------- unit_system : string, optional The unit system to be used in the conversion. If not specified, the default base units of cgs are used. Examples -------- >>> E = YTQuantity(2.5, "erg/s") >>> E_new = E.in_base(unit_system="galactic") """ return self.in_units(self.units.get_base_equivalent(unit_system)) def in_cgs(self): """ Creates a copy of this array with the data in the equivalent cgs units, and returns it. Returns ------- Quantity object with data converted to cgs units. """ return self.in_units(self.units.get_cgs_equivalent()) def in_mks(self): """ Creates a copy of this array with the data in the equivalent mks units, and returns it. Returns ------- Quantity object with data converted to mks units. """ return self.in_units(self.units.get_mks_equivalent()) def to_equivalent(self, unit, equiv, **kwargs): """ Convert a YTArray or YTQuantity to an equivalent, e.g., something that is related by only a constant factor but not in the same units. Parameters ---------- unit : string The unit that you wish to convert to. equiv : string The equivalence you wish to use. To see which equivalencies are supported for this unitful quantity, try the :meth:`list_equivalencies` method. Examples -------- >>> a = yt.YTArray(1.0e7,"K") >>> a.to_equivalent("keV", "thermal") """ conv_unit = Unit(unit, registry=self.units.registry) if self.units.same_dimensions_as(conv_unit): return self.in_units(conv_unit) this_equiv = equivalence_registry[equiv]() oneway_or_equivalent = ( conv_unit.has_equivalent(equiv) or this_equiv._one_way) if self.has_equivalent(equiv) and oneway_or_equivalent: new_arr = this_equiv.convert( self, conv_unit.dimensions, **kwargs) if isinstance(new_arr, tuple): try: return type(self)(new_arr[0], new_arr[1]).in_units(unit) except YTUnitConversionError: raise YTInvalidUnitEquivalence(equiv, self.units, unit) else: return new_arr.in_units(unit) else: raise YTInvalidUnitEquivalence(equiv, self.units, unit) def list_equivalencies(self): """ Lists the possible equivalencies associated with this YTArray or YTQuantity. """ self.units.list_equivalencies() def has_equivalent(self, equiv): """ Check to see if this YTArray or YTQuantity has an equivalent unit in *equiv*. """ return self.units.has_equivalent(equiv) def ndarray_view(self): """ Returns a view into the array, but as an ndarray rather than ytarray. Returns ------- View of this array's data. """ return self.view(np.ndarray) def to_ndarray(self): """ Creates a copy of this array with the unit information stripped """ return np.array(self) @classmethod def from_astropy(cls, arr, unit_registry=None): """ Convert an AstroPy "Quantity" to a YTArray or YTQuantity. Parameters ---------- arr : AstroPy Quantity The Quantity to convert from. unit_registry : yt UnitRegistry, optional A yt unit registry to use in the conversion. If one is not supplied, the default one will be used. """ # Converting from AstroPy Quantity u = arr.unit ap_units = [] for base, exponent in zip(u.bases, u.powers): unit_str = base.to_string() # we have to do this because AstroPy is silly and defines # hour as "h" if unit_str == "h": unit_str = "hr" ap_units.append("%s**(%s)" % (unit_str, Rational(exponent))) ap_units = "*".join(ap_units) if isinstance(arr.value, np.ndarray): return YTArray(arr.value, ap_units, registry=unit_registry) else: return YTQuantity(arr.value, ap_units, registry=unit_registry) def to_astropy(self, **kwargs): """ Creates a new AstroPy quantity with the same unit information. """ if _astropy.units is None: raise ImportError("You don't have AstroPy installed, so you can't convert to " + "an AstroPy quantity.") return self.value*_astropy.units.Unit(str(self.units), **kwargs) @classmethod def from_pint(cls, arr, unit_registry=None): """ Convert a Pint "Quantity" to a YTArray or YTQuantity. Parameters ---------- arr : Pint Quantity The Quantity to convert from. unit_registry : yt UnitRegistry, optional A yt unit registry to use in the conversion. If one is not supplied, the default one will be used. Examples -------- >>> from pint import UnitRegistry >>> import numpy as np >>> ureg = UnitRegistry() >>> a = np.random.random(10) >>> b = ureg.Quantity(a, "erg/cm**3") >>> c = yt.YTArray.from_pint(b) """ p_units = [] for base, exponent in arr._units.items(): bs = convert_pint_units(base) p_units.append("%s**(%s)" % (bs, Rational(exponent))) p_units = "*".join(p_units) if isinstance(arr.magnitude, np.ndarray): return YTArray(arr.magnitude, p_units, registry=unit_registry) else: return YTQuantity(arr.magnitude, p_units, registry=unit_registry) def to_pint(self, unit_registry=None): """ Convert a YTArray or YTQuantity to a Pint Quantity. Parameters ---------- arr : YTArray or YTQuantity The unitful quantity to convert from. unit_registry : Pint UnitRegistry, optional The Pint UnitRegistry to use in the conversion. If one is not supplied, the default one will be used. NOTE: This is not the same as a yt UnitRegistry object. Examples -------- >>> a = YTQuantity(4.0, "cm**2/s") >>> b = a.to_pint() """ from pint import UnitRegistry if unit_registry is None: unit_registry = UnitRegistry() powers_dict = self.units.expr.as_powers_dict() units = [] for unit, pow in powers_dict.items(): # we have to do this because Pint doesn't recognize # "yr" as "year" if str(unit).endswith("yr") and len(str(unit)) in [2,3]: unit = str(unit).replace("yr","year") units.append("%s**(%s)" % (unit, Rational(pow))) units = "*".join(units) return unit_registry.Quantity(self.value, units) # # End unit conversion methods # def write_hdf5(self, filename, dataset_name=None, info=None, group_name=None): r"""Writes a YTArray to hdf5 file. Parameters ---------- filename: string The filename to create and write a dataset to dataset_name: string The name of the dataset to create in the file. info: dictionary A dictionary of supplementary info to write to append as attributes to the dataset. group_name: string An optional group to write the arrays to. If not specified, the arrays are datasets at the top level by default. Examples -------- >>> a = YTArray([1,2,3], 'cm') >>> myinfo = {'field':'dinosaurs', 'type':'field_data'} >>> a.write_hdf5('test_array_data.h5', dataset_name='dinosaurs', ... info=myinfo) """ from yt.utilities.on_demand_imports import _h5py as h5py from yt.extern.six.moves import cPickle as pickle if info is None: info = {} info['units'] = str(self.units) info['unit_registry'] = np.void(pickle.dumps(self.units.registry.lut)) if dataset_name is None: dataset_name = 'array_data' f = h5py.File(filename) if group_name is not None: if group_name in f: g = f[group_name] else: g = f.create_group(group_name) else: g = f if dataset_name in g.keys(): d = g[dataset_name] # Overwrite without deleting if we can get away with it. if d.shape == self.shape and d.dtype == self.dtype: d[...] = self for k in d.attrs.keys(): del d.attrs[k] else: del f[dataset_name] d = g.create_dataset(dataset_name, data=self) else: d = g.create_dataset(dataset_name, data=self) for k, v in info.items(): d.attrs[k] = v f.close() @classmethod def from_hdf5(cls, filename, dataset_name=None, group_name=None): r"""Attempts read in and convert a dataset in an hdf5 file into a YTArray. Parameters ---------- filename: string The filename to of the hdf5 file. dataset_name: string The name of the dataset to read from. If the dataset has a units attribute, attempt to infer units as well. group_name: string An optional group to read the arrays from. If not specified, the arrays are datasets at the top level by default. """ import h5py from yt.extern.six.moves import cPickle as pickle if dataset_name is None: dataset_name = 'array_data' f = h5py.File(filename) if group_name is not None: g = f[group_name] else: g = f dataset = g[dataset_name] data = dataset[:] units = dataset.attrs.get('units', '') if 'unit_registry' in dataset.attrs.keys(): unit_lut = pickle.loads(dataset.attrs['unit_registry'].tostring()) else: unit_lut = None f.close() registry = UnitRegistry(lut=unit_lut, add_default_symbols=False) return cls(data, units, registry=registry) # # Start convenience methods # @property def value(self): """Get a copy of the array data as a numpy ndarray""" return np.array(self) v = value @property def ndview(self): """Get a view of the array data.""" return self.ndarray_view() d = ndview @property def unit_quantity(self): """Get a YTQuantity with the same unit as this array and a value of 1.0""" return YTQuantity(1.0, self.units) uq = unit_quantity @property def unit_array(self): """Get a YTArray filled with ones with the same unit and shape as this array""" return np.ones_like(self) ua = unit_array def __getitem__(self, item): ret = super(YTArray, self).__getitem__(item) if ret.shape == (): return YTQuantity(ret, self.units, bypass_validation=True) else: if hasattr(self, 'units'): ret.units = self.units return ret # # Start operation methods # if LooseVersion(np.__version__) < LooseVersion('1.13.0'): def __add__(self, right_object): """ Add this ytarray to the object on the right of the `+` operator. Must check for the correct (same dimension) units. """ ro = sanitize_units_add(self, right_object, "addition") return super(YTArray, self).__add__(ro) def __radd__(self, left_object): """ See __add__. """ lo = sanitize_units_add(self, left_object, "addition") return super(YTArray, self).__radd__(lo) def __iadd__(self, other): """ See __add__. """ oth = sanitize_units_add(self, other, "addition") np.add(self, oth, out=self) return self def __sub__(self, right_object): """ Subtract the object on the right of the `-` from this ytarray. Must check for the correct (same dimension) units. """ ro = sanitize_units_add(self, right_object, "subtraction") return super(YTArray, self).__sub__(ro) def __rsub__(self, left_object): """ See __sub__. """ lo = sanitize_units_add(self, left_object, "subtraction") return super(YTArray, self).__rsub__(lo) def __isub__(self, other): """ See __sub__. """ oth = sanitize_units_add(self, other, "subtraction") np.subtract(self, oth, out=self) return self def __neg__(self): """ Negate the data. """ return super(YTArray, self).__neg__() def __mul__(self, right_object): """ Multiply this YTArray by the object on the right of the `*` operator. The unit objects handle being multiplied. """ ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__mul__(ro) def __rmul__(self, left_object): """ See __mul__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rmul__(lo) def __imul__(self, other): """ See __mul__. """ oth = sanitize_units_mul(self, other) np.multiply(self, oth, out=self) return self def __div__(self, right_object): """ Divide this YTArray by the object on the right of the `/` operator. """ ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__div__(ro) def __rdiv__(self, left_object): """ See __div__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rdiv__(lo) def __idiv__(self, other): """ See __div__. """ oth = sanitize_units_mul(self, other) np.divide(self, oth, out=self) return self def __truediv__(self, right_object): ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__truediv__(ro) def __rtruediv__(self, left_object): """ See __div__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rtruediv__(lo) def __itruediv__(self, other): """ See __div__. """ oth = sanitize_units_mul(self, other) np.true_divide(self, oth, out=self) return self def __floordiv__(self, right_object): ro = sanitize_units_mul(self, right_object) return super(YTArray, self).__floordiv__(ro) def __rfloordiv__(self, left_object): """ See __div__. """ lo = sanitize_units_mul(self, left_object) return super(YTArray, self).__rfloordiv__(lo) def __ifloordiv__(self, other): """ See __div__. """ oth = sanitize_units_mul(self, other) np.floor_divide(self, oth, out=self) return self def __or__(self, right_object): return super(YTArray, self).__or__(right_object) def __ror__(self, left_object): return super(YTArray, self).__ror__(left_object) def __ior__(self, other): np.bitwise_or(self, other, out=self) return self def __xor__(self, right_object): return super(YTArray, self).__xor__(right_object) def __rxor__(self, left_object): return super(YTArray, self).__rxor__(left_object) def __ixor__(self, other): np.bitwise_xor(self, other, out=self) return self def __and__(self, right_object): return super(YTArray, self).__and__(right_object) def __rand__(self, left_object): return super(YTArray, self).__rand__(left_object) def __iand__(self, other): np.bitwise_and(self, other, out=self) return self def __pow__(self, power): """ Raise this YTArray to some power. Parameters ---------- power : float or dimensionless YTArray. The pow value. """ if isinstance(power, YTArray): if not power.units.is_dimensionless: raise YTUnitOperationError('power', power.unit) # Work around a sympy issue (I think?) # # If I don't do this, super(YTArray, self).__pow__ returns a YTArray # with a unit attribute set to the sympy expression 1/1 rather than # a dimensionless Unit object. if self.units.is_dimensionless and power == -1: ret = super(YTArray, self).__pow__(power) return type(self)(ret, input_units='') return super(YTArray, self).__pow__(power) def __abs__(self): """ Return a YTArray with the abs of the data. """ return super(YTArray, self).__abs__() # # Start comparison operators. # def __lt__(self, other): """ Test if this is less than the object on the right. """ # converts if possible oth = validate_comparison_units(self, other, 'less_than') return super(YTArray, self).__lt__(oth) def __le__(self, other): """Test if this is less than or equal to the object on the right. """ oth = validate_comparison_units(self, other, 'less_than or equal') return super(YTArray, self).__le__(oth) def __eq__(self, other): """ Test if this is equal to the object on the right. """ # Check that other is a YTArray. if other is None: # self is a YTArray, so it can't be None. return False oth = validate_comparison_units(self, other, 'equal') return super(YTArray, self).__eq__(oth) def __ne__(self, other): """ Test if this is not equal to the object on the right. """ # Check that the other is a YTArray. if other is None: return True oth = validate_comparison_units(self, other, 'not equal') return super(YTArray, self).__ne__(oth) def __ge__(self, other): """ Test if this is greater than or equal to other. """ # Check that the other is a YTArray. oth = validate_comparison_units( self, other, 'greater than or equal') return super(YTArray, self).__ge__(oth) def __gt__(self, other): """ Test if this is greater than the object on the right. """ # Check that the other is a YTArray. oth = validate_comparison_units(self, other, 'greater than') return super(YTArray, self).__gt__(oth) # # End comparison operators # # # Begin reduction operators # @return_arr def prod(self, axis=None, dtype=None, out=None): if axis is not None: units = self.units**self.shape[axis] else: units = self.units**self.size return super(YTArray, self).prod(axis, dtype, out), units @return_arr def mean(self, axis=None, dtype=None, out=None): return super(YTArray, self).mean(axis, dtype, out), self.units @return_arr def sum(self, axis=None, dtype=None, out=None): return super(YTArray, self).sum(axis, dtype, out), self.units @return_arr def std(self, axis=None, dtype=None, out=None, ddof=0): return super(YTArray, self).std(axis, dtype, out, ddof), self.units def __array_wrap__(self, out_arr, context=None): ret = super(YTArray, self).__array_wrap__(out_arr, context) if isinstance(ret, YTQuantity) and ret.shape != (): ret = ret.view(YTArray) if context is None: if ret.shape == (): return ret[()] else: return ret ufunc = context[0] inputs = context[1] if ufunc in unary_operators: out_arr, inp, u = get_inp_u_unary(ufunc, inputs, out_arr) unit = self._ufunc_registry[context[0]](u) ret_class = type(self) elif ufunc in binary_operators: unit_operator = self._ufunc_registry[context[0]] inps, units, ret_class = get_inp_u_binary(ufunc, inputs) if unit_operator in (preserve_units, comparison_unit, arctan2_unit): inps, units = handle_comparison_units( inps, units, ufunc, ret_class, raise_error=True) unit = unit_operator(*units) if unit_operator in (multiply_units, divide_units): out_arr, out_arr, unit = handle_multiply_divide_units( unit, units, out_arr, out_arr) else: raise RuntimeError( "Support for the %s ufunc has not been added " "to YTArray." % str(context[0])) if unit is None: out_arr = np.array(out_arr, copy=False) return out_arr out_arr.units = unit if out_arr.size == 1: return YTQuantity(np.array(out_arr), unit) else: if ret_class is YTQuantity: # This happens if you do ndarray * YTQuantity. Explicitly # casting to YTArray avoids creating a YTQuantity with # size > 1 return YTArray(np.array(out_arr), unit) return ret_class(np.array(out_arr, copy=False), unit) else: # numpy version equal to or newer than 1.13 def __array_ufunc__(self, ufunc, method, *inputs, **kwargs): func = getattr(ufunc, method) if 'out' in kwargs: out_orig = kwargs.pop('out') out = np.asarray(out_orig[0]) else: out = None if len(inputs) == 1: _, inp, u = get_inp_u_unary(ufunc, inputs) out_arr = func(np.asarray(inp), out=out, **kwargs) if ufunc in (multiply, divide) and method == 'reduce': power_sign = POWER_SIGN_MAPPING[ufunc] if 'axis' in kwargs and kwargs['axis'] is not None: unit = u**(power_sign*inp.shape[kwargs['axis']]) else: unit = u**(power_sign*inp.size) else: unit = self._ufunc_registry[ufunc](u) ret_class = type(self) elif len(inputs) == 2: unit_operator = self._ufunc_registry[ufunc] inps, units, ret_class = get_inp_u_binary(ufunc, inputs) if unit_operator in (comparison_unit, arctan2_unit): inps, units = handle_comparison_units( inps, units, ufunc, ret_class) elif unit_operator is preserve_units: inps, units = handle_preserve_units( inps, units, ufunc, ret_class) unit = unit_operator(*units) out_arr = func(np.asarray(inps[0]), np.asarray(inps[1]), out=out, **kwargs) if unit_operator in (multiply_units, divide_units): out, out_arr, unit = handle_multiply_divide_units( unit, units, out, out_arr) else: raise RuntimeError( "Support for the %s ufunc with %i inputs has not been" "added to YTArray." % (str(ufunc), len(inputs))) if unit is None: out_arr =

np.array(out_arr, copy=False)

numpy.array

from abc import ABCMeta, abstractmethod import os from vmaf.tools.misc import make_absolute_path, run_process from vmaf.tools.stats import ListStats __copyright__ = "Copyright 2016-2018, Netflix, Inc." __license__ = "Apache, Version 2.0" import re import numpy as np import ast from vmaf import ExternalProgramCaller, to_list from vmaf.config import VmafConfig, VmafExternalConfig from vmaf.core.executor import Executor from vmaf.core.result import Result from vmaf.tools.reader import YuvReader class FeatureExtractor(Executor): """ FeatureExtractor takes in a list of assets, and run feature extraction on them, and return a list of corresponding results. A FeatureExtractor must specify a unique type and version combination (by the TYPE and VERSION attribute), so that the Result generated by it can be identified. A derived class of FeatureExtractor must: 1) Override TYPE and VERSION 2) Override _generate_result(self, asset), which call a command-line executable and generate feature scores in a log file. 3) Override _get_feature_scores(self, asset), which read the feature scores from the log file, and return the scores in a dictionary format. For an example, follow VmafFeatureExtractor. """ __metaclass__ = ABCMeta @property @abstractmethod def ATOM_FEATURES(self): raise NotImplementedError def _read_result(self, asset): result = {} result.update(self._get_feature_scores(asset)) executor_id = self.executor_id return Result(asset, executor_id, result) @classmethod def get_scores_key(cls, atom_feature): return "{type}_{atom_feature}_scores".format( type=cls.TYPE, atom_feature=atom_feature) @classmethod def get_score_key(cls, atom_feature): return "{type}_{atom_feature}_score".format( type=cls.TYPE, atom_feature=atom_feature) def _get_feature_scores(self, asset): # routine to read the feature scores from the log file, and return # the scores in a dictionary format. log_file_path = self._get_log_file_path(asset) atom_feature_scores_dict = {} atom_feature_idx_dict = {} for atom_feature in self.ATOM_FEATURES: atom_feature_scores_dict[atom_feature] = [] atom_feature_idx_dict[atom_feature] = 0 with open(log_file_path, 'rt') as log_file: for line in log_file.readlines(): for atom_feature in self.ATOM_FEATURES: re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature) mo = re.match(re_template, line) if mo: cur_idx = int(mo.group(1)) assert cur_idx == atom_feature_idx_dict[atom_feature] # parse value, allowing NaN and inf val = float(mo.group(2)) if np.isnan(val) or np.isinf(val): val = None atom_feature_scores_dict[atom_feature].append(val) atom_feature_idx_dict[atom_feature] += 1 continue len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]]) assert len_score != 0 for atom_feature in self.ATOM_FEATURES[1:]: assert len_score == len(atom_feature_scores_dict[atom_feature]), \ "Feature data possibly corrupt. Run cleanup script and try again." feature_result = {} for atom_feature in self.ATOM_FEATURES: scores_key = self.get_scores_key(atom_feature) feature_result[scores_key] = atom_feature_scores_dict[atom_feature] return feature_result class VmafFeatureExtractor(FeatureExtractor): TYPE = "VMAF_feature" # VERSION = '0.1' # vmaf_study; Anush's VIF fix # VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr # VERSION = '0.2.1' # expose vif num/den of each scale # VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case # VERSION = '0.2.2b' # expose adm_den/num_scalex # VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef # VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step # VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2 VERSION = '0.2.4c' # Modify by moving motion2 to c code ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2', 'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr', 'vif_num_scale0', 'vif_den_scale0', 'vif_num_scale1', 'vif_den_scale1', 'vif_num_scale2', 'vif_den_scale2', 'vif_num_scale3', 'vif_den_scale3', 'adm_num_scale0', 'adm_den_scale0', 'adm_num_scale1', 'adm_den_scale1', 'adm_num_scale2', 'adm_den_scale2', 'adm_num_scale3', 'adm_den_scale3', ] DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3', 'vif2', 'adm2', 'adm3', 'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3', ] ADM2_CONSTANT = 0 ADM_SCALE_CONSTANT = 0 def _generate_result(self, asset): # routine to call the command-line executable and generate feature # scores in the log file. quality_width, quality_height = asset.quality_width_height log_file_path = self._get_log_file_path(asset) yuv_type=self._get_workfile_yuv_type(asset) ref_path=asset.ref_workfile_path dis_path=asset.dis_workfile_path w=quality_width h=quality_height logger = self.logger ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger) @classmethod def _post_process_result(cls, result): # override Executor._post_process_result result = super(VmafFeatureExtractor, cls)._post_process_result(result) # adm2 = # (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT) adm2_scores_key = cls.get_scores_key('adm2') adm_num_scores_key = cls.get_scores_key('adm_num') adm_den_scores_key = cls.get_scores_key('adm_den') result.result_dict[adm2_scores_key] = list( (np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) / (np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT) ) # vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3 vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0') vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0') vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1') vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1') vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2') vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2') vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3') vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3') vif_scale0_scores_key = cls.get_scores_key('vif_scale0') vif_scale1_scores_key = cls.get_scores_key('vif_scale1') vif_scale2_scores_key = cls.get_scores_key('vif_scale2') vif_scale3_scores_key = cls.get_scores_key('vif_scale3') result.result_dict[vif_scale0_scores_key] = list( (np.array(result.result_dict[vif_num_scale0_scores_key]) / np.array(result.result_dict[vif_den_scale0_scores_key])) ) result.result_dict[vif_scale1_scores_key] = list( (np.array(result.result_dict[vif_num_scale1_scores_key]) / np.array(result.result_dict[vif_den_scale1_scores_key])) ) result.result_dict[vif_scale2_scores_key] = list( (np.array(result.result_dict[vif_num_scale2_scores_key]) / np.array(result.result_dict[vif_den_scale2_scores_key])) ) result.result_dict[vif_scale3_scores_key] = list( (np.array(result.result_dict[vif_num_scale3_scores_key]) / np.array(result.result_dict[vif_den_scale3_scores_key])) ) # vif2 = # ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) + # (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0 vif_scores_key = cls.get_scores_key('vif2') result.result_dict[vif_scores_key] = list( ( (np.array(result.result_dict[vif_num_scale0_scores_key]) / np.array(result.result_dict[vif_den_scale0_scores_key])) + (np.array(result.result_dict[vif_num_scale1_scores_key]) / np.array(result.result_dict[vif_den_scale1_scores_key])) + (np.array(result.result_dict[vif_num_scale2_scores_key]) / np.array(result.result_dict[vif_den_scale2_scores_key])) + (np.array(result.result_dict[vif_num_scale3_scores_key]) / np.array(result.result_dict[vif_den_scale3_scores_key])) ) / 4.0 ) # adm_scalei = adm_num_scalei / adm_den_scalei, i = 0, 1, 2, 3 adm_num_scale0_scores_key = cls.get_scores_key('adm_num_scale0') adm_den_scale0_scores_key = cls.get_scores_key('adm_den_scale0') adm_num_scale1_scores_key = cls.get_scores_key('adm_num_scale1') adm_den_scale1_scores_key = cls.get_scores_key('adm_den_scale1') adm_num_scale2_scores_key = cls.get_scores_key('adm_num_scale2') adm_den_scale2_scores_key = cls.get_scores_key('adm_den_scale2') adm_num_scale3_scores_key = cls.get_scores_key('adm_num_scale3') adm_den_scale3_scores_key = cls.get_scores_key('adm_den_scale3') adm_scale0_scores_key = cls.get_scores_key('adm_scale0') adm_scale1_scores_key = cls.get_scores_key('adm_scale1') adm_scale2_scores_key = cls.get_scores_key('adm_scale2') adm_scale3_scores_key = cls.get_scores_key('adm_scale3') result.result_dict[adm_scale0_scores_key] = list( (np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale1_scores_key] = list( (np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale2_scores_key] = list( (np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale3_scores_key] = list( (

np.array(result.result_dict[adm_num_scale3_scores_key])

numpy.array

# pvtrace is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # pvtrace is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import numpy as np from external.transformations import translation_matrix, rotation_matrix import external.transformations as tf from Trace import Photon from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm from Materials import Spectrum def random_spherecial_vector(): # This method of calculating isotropic vectors is taken from GNU Scientific Library LOOP = True while LOOP: x = -1. + 2. * np.random.uniform() y = -1. + 2. * np.random.uniform() s = x**2 + y**2 if s <= 1.0: LOOP = False z = -1. + 2. * s a = 2 * np.sqrt(1 - s) x = a * x y = a * y return np.array([x,y,z]) class SimpleSource(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False): super(SimpleSource, self).__init__() self.position = position self.direction = direction self.wavelength = wavelength self.use_random_polarisation = use_random_polarisation self.throw = 0 self.source_id = "SimpleSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength # If use_polarisation is set generate a random polarisation vector of the photon if self.use_random_polarisation: # Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon vec = random_spherecial_vector() vec[2] = 0. vec = norm(vec) R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1]) photon.polarisation = transform_direction(vec, R) else: photon.polarisation = None photon.id = self.throw self.throw = self.throw + 1 return photon class Laser(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None): super(Laser, self).__init__() self.position = np.array(position) self.direction = np.array(direction) self.wavelength = wavelength assert polarisation != None, "Polarisation of the Laser is not set." self.polarisation = np.array(polarisation) self.throw = 0 self.source_id = "LaserSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength photon.polarisation = self.polarisation photon.id = self.throw self.throw = self.throw + 1 return photon class PlanarSource(object): """A box that emits photons from the top surface (normal), sampled from the spectrum.""" def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05): super(PlanarSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.plane = FinitePlane(length=length, width=width) self.length = length self.width = width # direction is the direction that photons are fired out of the plane in the GLOBAL FRAME. # i.e. this is passed directly to the photon to set is's direction self.direction = direction self.throw = 0 self.source_id = "PlanarSource_" + str(id(self)) def translate(self, translation): self.plane.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.plane.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Create a point which is on the surface of the finite plane in it's local frame x = np.random.uniform(0., self.length) y = np.random.uniform(0., self.width) local_point = (x, y, 0.) # Transform the direciton photon.position = transform_point(local_point, self.plane.transform) photon.direction = self.direction photon.active = True if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSource(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint = np.array(linepoint) self.linedirection = np.array(linedirection) self.focussize = focussize self.throw = 0 self.source_id = "LensSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Position x = np.random.uniform(self.planeorigin[0],self.planeextent[0]) y = np.random.uniform(self.planeorigin[1],self.planeextent[1]) z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) photon.position = np.array((x,y,z)) # Direction focuspoint = np.array((0.,0.,0.)) focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize) focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize) focuspoint[2] = photon.position[2] direction = focuspoint - photon.position modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5 photon.direction = direction/modulus # Wavelength if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSourceAngle(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. For this lense an additional z-boost is added (Angle of incidence in z-direction). """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), angle = 0, focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSourceAngle, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint = np.array(linepoint) self.linedirection = np.array(linedirection) self.focussize = focussize self.angle = angle self.throw = 0 self.source_id = "LensSourceAngle_" + str(id(self)) def photon(self): photon = Photon() photon.id = self.throw self.throw = self.throw + 1 # Position x = np.random.uniform(self.planeorigin[0],self.planeextent[0]) y = np.random.uniform(self.planeorigin[1],self.planeextent[1]) boost = y*np.tan(self.angle) z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) - boost photon.position = np.array((x,y,z)) # Direction focuspoint = np.array((0.,0.,0.)) focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize) focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize) focuspoint[2] = photon.position[2] + boost direction = focuspoint - photon.position modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5 photon.direction = direction/modulus # Wavelength if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class CylindricalSource(object): """ A source for photons emitted in a random direction and position inside a cylinder(radius, length) """ def __init__(self, spectrum = None, wavelength = 555, radius = 1, length = 10): super(CylindricalSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.shape = Cylinder(radius = radius, length = length) self.radius = radius self.length = length self.throw = 0 self.source_id = "CylindricalSource_" + str(id(self)) def translate(self, translation): self.shape.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.shape.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Position of emission phi = np.random.uniform(0., 2*np.pi) r = np.random.uniform(0.,self.radius) x = r*np.cos(phi) y = r*np.sin(phi) z = np.random.uniform(0.,self.length) local_center = (x,y,z) photon.position = transform_point(local_center, self.shape.transform) # Direction of emission (no need to transform if meant to be isotropic) phi = np.random.uniform(0.,2*np.pi) theta =

np.random.uniform(0.,np.pi)

numpy.random.uniform

# pvtrace is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # pvtrace is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import numpy as np from external.transformations import translation_matrix, rotation_matrix import external.transformations as tf from Trace import Photon from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm from Materials import Spectrum def random_spherecial_vector(): # This method of calculating isotropic vectors is taken from GNU Scientific Library LOOP = True while LOOP: x = -1. + 2. * np.random.uniform() y = -1. + 2. * np.random.uniform() s = x**2 + y**2 if s <= 1.0: LOOP = False z = -1. + 2. * s a = 2 * np.sqrt(1 - s) x = a * x y = a * y return np.array([x,y,z]) class SimpleSource(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False): super(SimpleSource, self).__init__() self.position = position self.direction = direction self.wavelength = wavelength self.use_random_polarisation = use_random_polarisation self.throw = 0 self.source_id = "SimpleSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength # If use_polarisation is set generate a random polarisation vector of the photon if self.use_random_polarisation: # Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon vec = random_spherecial_vector() vec[2] = 0. vec = norm(vec) R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1]) photon.polarisation = transform_direction(vec, R) else: photon.polarisation = None photon.id = self.throw self.throw = self.throw + 1 return photon class Laser(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None): super(Laser, self).__init__() self.position = np.array(position) self.direction = np.array(direction) self.wavelength = wavelength assert polarisation != None, "Polarisation of the Laser is not set." self.polarisation = np.array(polarisation) self.throw = 0 self.source_id = "LaserSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength photon.polarisation = self.polarisation photon.id = self.throw self.throw = self.throw + 1 return photon class PlanarSource(object): """A box that emits photons from the top surface (normal), sampled from the spectrum.""" def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05): super(PlanarSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.plane = FinitePlane(length=length, width=width) self.length = length self.width = width # direction is the direction that photons are fired out of the plane in the GLOBAL FRAME. # i.e. this is passed directly to the photon to set is's direction self.direction = direction self.throw = 0 self.source_id = "PlanarSource_" + str(id(self)) def translate(self, translation): self.plane.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.plane.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Create a point which is on the surface of the finite plane in it's local frame x = np.random.uniform(0., self.length) y = np.random.uniform(0., self.width) local_point = (x, y, 0.) # Transform the direciton photon.position = transform_point(local_point, self.plane.transform) photon.direction = self.direction photon.active = True if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSource(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint = np.array(linepoint) self.linedirection = np.array(linedirection) self.focussize = focussize self.throw = 0 self.source_id = "LensSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Position x = np.random.uniform(self.planeorigin[0],self.planeextent[0]) y = np.random.uniform(self.planeorigin[1],self.planeextent[1]) z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) photon.position = np.array((x,y,z)) # Direction focuspoint = np.array((0.,0.,0.)) focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize) focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize) focuspoint[2] = photon.position[2] direction = focuspoint - photon.position modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5 photon.direction = direction/modulus # Wavelength if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSourceAngle(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. For this lense an additional z-boost is added (Angle of incidence in z-direction). """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), angle = 0, focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSourceAngle, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint = np.array(linepoint) self.linedirection = np.array(linedirection) self.focussize = focussize self.angle = angle self.throw = 0 self.source_id = "LensSourceAngle_" + str(id(self)) def photon(self): photon = Photon() photon.id = self.throw self.throw = self.throw + 1 # Position x = np.random.uniform(self.planeorigin[0],self.planeextent[0]) y = np.random.uniform(self.planeorigin[1],self.planeextent[1]) boost = y*np.tan(self.angle) z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) - boost photon.position = np.array((x,y,z)) # Direction focuspoint = np.array((0.,0.,0.)) focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize) focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize) focuspoint[2] = photon.position[2] + boost direction = focuspoint - photon.position modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5 photon.direction = direction/modulus # Wavelength if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class CylindricalSource(object): """ A source for photons emitted in a random direction and position inside a cylinder(radius, length) """ def __init__(self, spectrum = None, wavelength = 555, radius = 1, length = 10): super(CylindricalSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.shape = Cylinder(radius = radius, length = length) self.radius = radius self.length = length self.throw = 0 self.source_id = "CylindricalSource_" + str(id(self)) def translate(self, translation): self.shape.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.shape.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Position of emission phi = np.random.uniform(0., 2*np.pi) r = np.random.uniform(0.,self.radius) x = r*np.cos(phi) y = r*np.sin(phi) z = np.random.uniform(0.,self.length) local_center = (x,y,z) photon.position = transform_point(local_center, self.shape.transform) # Direction of emission (no need to transform if meant to be isotropic) phi = np.random.uniform(0.,2*np.pi) theta = np.random.uniform(0.,np.pi) x = np.cos(phi)*np.sin(theta) y = np.sin(phi)*np.sin(theta) z = np.cos(theta) local_direction = (x,y,z) photon.direction = local_direction # Set wavelength of photon if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength # Further initialisation photon.active = True return photon class PointSource(object): """ A point source that emits randomly in solid angle specified by phimin, ..., thetamax """ def __init__(self, spectrum = None, wavelength = 555, center = (0.,0.,0.), phimin = 0, phimax = 2*np.pi, thetamin = 0, thetamax = np.pi): super(PointSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.center = center self.phimin = phimin self.phimax = phimax self.thetamin = thetamin self.thetamax = thetamax self.throw = 0 self.source_id = "PointSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 phi = np.random.uniform(self.phimin, self.phimax) theta = np.random.uniform(self.thetamin, self.thetamax) x = np.cos(phi)*np.sin(theta) y =

np.sin(phi)

numpy.sin

""" Binary serialization NPY format ========== A simple format for saving numpy arrays to disk with the full information about them. The ``.npy`` format is the standard binary file format in NumPy for persisting a *single* arbitrary NumPy array on disk. The format stores all of the shape and dtype information necessary to reconstruct the array correctly even on another machine with a different architecture. The format is designed to be as simple as possible while achieving its limited goals. The ``.npz`` format is the standard format for persisting *multiple* NumPy arrays on disk. A ``.npz`` file is a zip file containing multiple ``.npy`` files, one for each array. Capabilities ------------ - Can represent all NumPy arrays including nested record arrays and object arrays. - Represents the data in its native binary form. - Supports Fortran-contiguous arrays directly. - Stores all of the necessary information to reconstruct the array including shape and dtype on a machine of a different architecture. Both little-endian and big-endian arrays are supported, and a file with little-endian numbers will yield a little-endian array on any machine reading the file. The types are described in terms of their actual sizes. For example, if a machine with a 64-bit C "long int" writes out an array with "long ints", a reading machine with 32-bit C "long ints" will yield an array with 64-bit integers. - Is straightforward to reverse engineer. Datasets often live longer than the programs that created them. A competent developer should be able to create a solution in their preferred programming language to read most ``.npy`` files that they have been given without much documentation. - Allows memory-mapping of the data. See `open_memmap`. - Can be read from a filelike stream object instead of an actual file. - Stores object arrays, i.e. arrays containing elements that are arbitrary Python objects. Files with object arrays are not to be mmapable, but can be read and written to disk. Limitations ----------- - Arbitrary subclasses of numpy.ndarray are not completely preserved. Subclasses will be accepted for writing, but only the array data will be written out. A regular numpy.ndarray object will be created upon reading the file. .. warning:: Due to limitations in the interpretation of structured dtypes, dtypes with fields with empty names will have the names replaced by 'f0', 'f1', etc. Such arrays will not round-trip through the format entirely accurately. The data is intact; only the field names will differ. We are working on a fix for this. This fix will not require a change in the file format. The arrays with such structures can still be saved and restored, and the correct dtype may be restored by using the ``loadedarray.view(correct_dtype)`` method. File extensions --------------- We recommend using the ``.npy`` and ``.npz`` extensions for files saved in this format. This is by no means a requirement; applications may wish to use these file formats but use an extension specific to the application. In the absence of an obvious alternative, however, we suggest using ``.npy`` and ``.npz``. Version numbering ----------------- The version numbering of these formats is independent of NumPy version numbering. If the format is upgraded, the code in `numpy.io` will still be able to read and write Version 1.0 files. Format Version 1.0 ------------------ The first 6 bytes are a magic string: exactly ``\\x93NUMPY``. The next 1 byte is an unsigned byte: the major version number of the file format, e.g. ``\\x01``. The next 1 byte is an unsigned byte: the minor version number of the file format, e.g. ``\\x00``. Note: the version of the file format is not tied to the version of the numpy package. The next 2 bytes form a little-endian unsigned short int: the length of the header data HEADER_LEN. The next HEADER_LEN bytes form the header data describing the array's format. It is an ASCII string which contains a Python literal expression of a dictionary. It is terminated by a newline (``\\n``) and padded with spaces (``\\x20``) to make the total of ``len(magic string) + 2 + len(length) + HEADER_LEN`` be evenly divisible by 64 for alignment purposes. The dictionary contains three keys: "descr" : dtype.descr An object that can be passed as an argument to the `numpy.dtype` constructor to create the array's dtype. "fortran_order" : bool Whether the array data is Fortran-contiguous or not. Since Fortran-contiguous arrays are a common form of non-C-contiguity, we allow them to be written directly to disk for efficiency. "shape" : tuple of int The shape of the array. For repeatability and readability, the dictionary keys are sorted in alphabetic order. This is for convenience only. A writer SHOULD implement this if possible. A reader MUST NOT depend on this. Following the header comes the array data. If the dtype contains Python objects (i.e. ``dtype.hasobject is True``), then the data is a Python pickle of the array. Otherwise the data is the contiguous (either C- or Fortran-, depending on ``fortran_order``) bytes of the array. Consumers can figure out the number of bytes by multiplying the number of elements given by the shape (noting that ``shape=()`` means there is 1 element) by ``dtype.itemsize``. Format Version 2.0 ------------------ The version 1.0 format only allowed the array header to have a total size of 65535 bytes. This can be exceeded by structured arrays with a large number of columns. The version 2.0 format extends the header size to 4 GiB. `numpy.save` will automatically save in 2.0 format if the data requires it, else it will always use the more compatible 1.0 format. The description of the fourth element of the header therefore has become: "The next 4 bytes form a little-endian unsigned int: the length of the header data HEADER_LEN." Format Version 3.0 ------------------ This version replaces the ASCII string (which in practice was latin1) with a utf8-encoded string, so supports structured types with any unicode field names. Notes ----- The ``.npy`` format, including motivation for creating it and a comparison of alternatives, is described in the :doc:`"npy-format" NEP <neps:nep-0001-npy-format>`, however details have evolved with time and this document is more current. """ import numpy import io import warnings from numpy.lib.utils import safe_eval from numpy.compat import ( isfileobj, os_fspath, pickle ) __all__ = [] EXPECTED_KEYS = {'descr', 'fortran_order', 'shape'} MAGIC_PREFIX = b'\x93NUMPY' MAGIC_LEN = len(MAGIC_PREFIX) + 2 ARRAY_ALIGN = 64 # plausible values are powers of 2 between 16 and 4096 BUFFER_SIZE = 2**18 # size of buffer for reading npz files in bytes # difference between version 1.0 and 2.0 is a 4 byte (I) header length # instead of 2 bytes (H) allowing storage of large structured arrays _header_size_info = { (1, 0): ('<H', 'latin1'), (2, 0): ('<I', 'latin1'), (3, 0): ('<I', 'utf8'), } def _check_version(version): if version not in [(1, 0), (2, 0), (3, 0), None]: msg = "we only support format version (1,0), (2,0), and (3,0), not %s" raise ValueError(msg % (version,)) def magic(major, minor): """ Return the magic string for the given file format version. Parameters ---------- major : int in [0, 255] minor : int in [0, 255] Returns ------- magic : str Raises ------ ValueError if the version cannot be formatted. """ if major < 0 or major > 255: raise ValueError("major version must be 0 <= major < 256") if minor < 0 or minor > 255: raise ValueError("minor version must be 0 <= minor < 256") return MAGIC_PREFIX + bytes([major, minor]) def read_magic(fp): """ Read the magic string to get the version of the file format. Parameters ---------- fp : filelike object Returns ------- major : int minor : int """ magic_str = _read_bytes(fp, MAGIC_LEN, "magic string") if magic_str[:-2] != MAGIC_PREFIX: msg = "the magic string is not correct; expected %r, got %r" raise ValueError(msg % (MAGIC_PREFIX, magic_str[:-2])) major, minor = magic_str[-2:] return major, minor def _has_metadata(dt): if dt.metadata is not None: return True elif dt.names is not None: return any(_has_metadata(dt[k]) for k in dt.names) elif dt.subdtype is not None: return _has_metadata(dt.base) else: return False def dtype_to_descr(dtype): """ Get a serializable descriptor from the dtype. The .descr attribute of a dtype object cannot be round-tripped through the dtype() constructor. Simple types, like dtype('float32'), have a descr which looks like a record array with one field with '' as a name. The dtype() constructor interprets this as a request to give a default name. Instead, we construct descriptor that can be passed to dtype(). Parameters ---------- dtype : dtype The dtype of the array that will be written to disk. Returns ------- descr : object An object that can be passed to `numpy.dtype()` in order to replicate the input dtype. """ if _has_metadata(dtype): warnings.warn("metadata on a dtype may be saved or ignored, but will " "raise if saved when read. Use another form of storage.", UserWarning, stacklevel=2) if dtype.names is not None: # This is a record array. The .descr is fine. XXX: parts of the # record array with an empty name, like padding bytes, still get # fiddled with. This needs to be fixed in the C implementation of # dtype(). return dtype.descr else: return dtype.str def descr_to_dtype(descr): """ Returns a dtype based off the given description. This is essentially the reverse of `dtype_to_descr()`. It will remove the valueless padding fields created by, i.e. simple fields like dtype('float32'), and then convert the description to its corresponding dtype. Parameters ---------- descr : object The object retreived by dtype.descr. Can be passed to `numpy.dtype()` in order to replicate the input dtype. Returns ------- dtype : dtype The dtype constructed by the description. """ if isinstance(descr, str): # No padding removal needed return numpy.dtype(descr) elif isinstance(descr, tuple): # subtype, will always have a shape descr[1] dt = descr_to_dtype(descr[0]) return numpy.dtype((dt, descr[1])) titles = [] names = [] formats = [] offsets = [] offset = 0 for field in descr: if len(field) == 2: name, descr_str = field dt = descr_to_dtype(descr_str) else: name, descr_str, shape = field dt = numpy.dtype((descr_to_dtype(descr_str), shape)) # Ignore padding bytes, which will be void bytes with '' as name # Once support for blank names is removed, only "if name == ''" needed) is_pad = (name == '' and dt.type is numpy.void and dt.names is None) if not is_pad: title, name = name if isinstance(name, tuple) else (None, name) titles.append(title) names.append(name) formats.append(dt) offsets.append(offset) offset += dt.itemsize return numpy.dtype({'names': names, 'formats': formats, 'titles': titles, 'offsets': offsets, 'itemsize': offset}) def header_data_from_array_1_0(array): """ Get the dictionary of header metadata from a numpy.ndarray. Parameters ---------- array : numpy.ndarray Returns ------- d : dict This has the appropriate entries for writing its string representation to the header of the file. """ d = {'shape': array.shape} if array.flags.c_contiguous: d['fortran_order'] = False elif array.flags.f_contiguous: d['fortran_order'] = True else: # Totally non-contiguous data. We will have to make it C-contiguous # before writing. Note that we need to test for C_CONTIGUOUS first # because a 1-D array is both C_CONTIGUOUS and F_CONTIGUOUS. d['fortran_order'] = False d['descr'] = dtype_to_descr(array.dtype) return d def _wrap_header(header, version): """ Takes a stringified header, and attaches the prefix and padding to it """ import struct assert version is not None fmt, encoding = _header_size_info[version] if not isinstance(header, bytes): # always true on python 3 header = header.encode(encoding) hlen = len(header) + 1 padlen = ARRAY_ALIGN - ((MAGIC_LEN + struct.calcsize(fmt) + hlen) % ARRAY_ALIGN) try: header_prefix = magic(*version) + struct.pack(fmt, hlen + padlen) except struct.error: msg = "Header length {} too big for version={}".format(hlen, version) raise ValueError(msg) from None # Pad the header with spaces and a final newline such that the magic # string, the header-length short and the header are aligned on a # ARRAY_ALIGN byte boundary. This supports memory mapping of dtypes # aligned up to ARRAY_ALIGN on systems like Linux where mmap() # offset must be page-aligned (i.e. the beginning of the file). return header_prefix + header + b' '*padlen + b'\n' def _wrap_header_guess_version(header): """ Like `_wrap_header`, but chooses an appropriate version given the contents """ try: return _wrap_header(header, (1, 0)) except ValueError: pass try: ret = _wrap_header(header, (2, 0)) except UnicodeEncodeError: pass else: warnings.warn("Stored array in format 2.0. It can only be" "read by NumPy >= 1.9", UserWarning, stacklevel=2) return ret header = _wrap_header(header, (3, 0)) warnings.warn("Stored array in format 3.0. It can only be " "read by NumPy >= 1.17", UserWarning, stacklevel=2) return header def _write_array_header(fp, d, version=None): """ Write the header for an array and returns the version used Parameters ---------- fp : filelike object d : dict This has the appropriate entries for writing its string representation to the header of the file. version: tuple or None None means use oldest that works explicit version will raise a ValueError if the format does not allow saving this data. Default: None """ header = ["{"] for key, value in sorted(d.items()): # Need to use repr here, since we eval these when reading header.append("'%s': %s, " % (key, repr(value))) header.append("}") header = "".join(header) if version is None: header = _wrap_header_guess_version(header) else: header = _wrap_header(header, version) fp.write(header) def write_array_header_1_0(fp, d): """ Write the header for an array using the 1.0 format. Parameters ---------- fp : filelike object d : dict This has the appropriate entries for writing its string representation to the header of the file. """ _write_array_header(fp, d, (1, 0)) def write_array_header_2_0(fp, d): """ Write the header for an array using the 2.0 format. The 2.0 format allows storing very large structured arrays. .. versionadded:: 1.9.0 Parameters ---------- fp : filelike object d : dict This has the appropriate entries for writing its string representation to the header of the file. """ _write_array_header(fp, d, (2, 0)) def read_array_header_1_0(fp): """ Read an array header from a filelike object using the 1.0 file format version. This will leave the file object located just after the header. Parameters ---------- fp : filelike object A file object or something with a `.read()` method like a file. Returns ------- shape : tuple of int The shape of the array. fortran_order : bool The array data will be written out directly if it is either C-contiguous or Fortran-contiguous. Otherwise, it will be made contiguous before writing it out. dtype : dtype The dtype of the file's data. Raises ------ ValueError If the data is invalid. """ return _read_array_header(fp, version=(1, 0)) def read_array_header_2_0(fp): """ Read an array header from a filelike object using the 2.0 file format version. This will leave the file object located just after the header. .. versionadded:: 1.9.0 Parameters ---------- fp : filelike object A file object or something with a `.read()` method like a file. Returns ------- shape : tuple of int The shape of the array. fortran_order : bool The array data will be written out directly if it is either C-contiguous or Fortran-contiguous. Otherwise, it will be made contiguous before writing it out. dtype : dtype The dtype of the file's data. Raises ------ ValueError If the data is invalid. """ return _read_array_header(fp, version=(2, 0)) def _filter_header(s): """Clean up 'L' in npz header ints. Cleans up the 'L' in strings representing integers. Needed to allow npz headers produced in Python2 to be read in Python3. Parameters ---------- s : string Npy file header. Returns ------- header : str Cleaned up header. """ import tokenize from io import StringIO tokens = [] last_token_was_number = False for token in tokenize.generate_tokens(StringIO(s).readline): token_type = token[0] token_string = token[1] if (last_token_was_number and token_type == tokenize.NAME and token_string == "L"): continue else: tokens.append(token) last_token_was_number = (token_type == tokenize.NUMBER) return tokenize.untokenize(tokens) def _read_array_header(fp, version): """ see read_array_header_1_0 """ # Read an unsigned, little-endian short int which has the length of the # header. import struct hinfo = _header_size_info.get(version) if hinfo is None: raise ValueError("Invalid version {!r}".format(version)) hlength_type, encoding = hinfo hlength_str = _read_bytes(fp, struct.calcsize(hlength_type), "array header length") header_length = struct.unpack(hlength_type, hlength_str)[0] header = _read_bytes(fp, header_length, "array header") header = header.decode(encoding) # The header is a pretty-printed string representation of a literal # Python dictionary with trailing newlines padded to a ARRAY_ALIGN byte # boundary. The keys are strings. # "shape" : tuple of int # "fortran_order" : bool # "descr" : dtype.descr # Versions (2, 0) and (1, 0) could have been created by a Python 2 # implementation before header filtering was implemented. if version <= (2, 0): header = _filter_header(header) try: d = safe_eval(header) except SyntaxError as e: msg = "Cannot parse header: {!r}" raise ValueError(msg.format(header)) from e if not isinstance(d, dict): msg = "Header is not a dictionary: {!r}" raise ValueError(msg.format(d)) if EXPECTED_KEYS != d.keys(): keys = sorted(d.keys()) msg = "Header does not contain the correct keys: {!r}" raise ValueError(msg.format(keys)) # Sanity-check the values. if (not isinstance(d['shape'], tuple) or not all(isinstance(x, int) for x in d['shape'])): msg = "shape is not valid: {!r}" raise ValueError(msg.format(d['shape'])) if not isinstance(d['fortran_order'], bool): msg = "fortran_order is not a valid bool: {!r}" raise ValueError(msg.format(d['fortran_order'])) try: dtype = descr_to_dtype(d['descr']) except TypeError as e: msg = "descr is not a valid dtype descriptor: {!r}" raise ValueError(msg.format(d['descr'])) from e return d['shape'], d['fortran_order'], dtype def write_array(fp, array, version=None, allow_pickle=True, pickle_kwargs=None): """ Write an array to an NPY file, including a header. If the array is neither C-contiguous nor Fortran-contiguous AND the file_like object is not a real file object, this function will have to copy data in memory. Parameters ---------- fp : file_like object An open, writable file object, or similar object with a ``.write()`` method. array : ndarray The array to write to disk. version : (int, int) or None, optional The version number of the format. None means use the oldest supported version that is able to store the data. Default: None allow_pickle : bool, optional Whether to allow writing pickled data. Default: True pickle_kwargs : dict, optional Additional keyword arguments to pass to pickle.dump, excluding 'protocol'. These are only useful when pickling objects in object arrays on Python 3 to Python 2 compatible format. Raises ------ ValueError If the array cannot be persisted. This includes the case of allow_pickle=False and array being an object array. Various other errors If the array contains Python objects as part of its dtype, the process of pickling them may raise various errors if the objects are not picklable. """ _check_version(version) _write_array_header(fp, header_data_from_array_1_0(array), version) if array.itemsize == 0: buffersize = 0 else: # Set buffer size to 16 MiB to hide the Python loop overhead. buffersize = max(16 * 1024 ** 2 // array.itemsize, 1) if array.dtype.hasobject: # We contain Python objects so we cannot write out the data # directly. Instead, we will pickle it out if not allow_pickle: raise ValueError("Object arrays cannot be saved when " "allow_pickle=False") if pickle_kwargs is None: pickle_kwargs = {} pickle.dump(array, fp, protocol=3, **pickle_kwargs) elif array.flags.f_contiguous and not array.flags.c_contiguous: if isfileobj(fp): array.T.tofile(fp) else: for chunk in numpy.nditer( array, flags=['external_loop', 'buffered', 'zerosize_ok'], buffersize=buffersize, order='F'): fp.write(chunk.tobytes('C')) else: if isfileobj(fp): array.tofile(fp) else: for chunk in numpy.nditer( array, flags=['external_loop', 'buffered', 'zerosize_ok'], buffersize=buffersize, order='C'): fp.write(chunk.tobytes('C')) def read_array(fp, allow_pickle=False, pickle_kwargs=None): """ Read an array from an NPY file. Parameters ---------- fp : file_like object If this is not a real file object, then this may take extra memory and time. allow_pickle : bool, optional Whether to allow writing pickled data. Default: False .. versionchanged:: 1.16.3 Made default False in response to CVE-2019-6446. pickle_kwargs : dict Additional keyword arguments to pass to pickle.load. These are only useful when loading object arrays saved on Python 2 when using Python 3. Returns ------- array : ndarray The array from the data on disk. Raises ------ ValueError If the data is invalid, or allow_pickle=False and the file contains an object array. """ version = read_magic(fp) _check_version(version) shape, fortran_order, dtype = _read_array_header(fp, version) if len(shape) == 0: count = 1 else: count = numpy.multiply.reduce(shape, dtype=numpy.int64) # Now read the actual data. if dtype.hasobject: # The array contained Python objects. We need to unpickle the data. if not allow_pickle: raise ValueError("Object arrays cannot be loaded when " "allow_pickle=False") if pickle_kwargs is None: pickle_kwargs = {} try: array =

pickle.load(fp, **pickle_kwargs)

numpy.compat.pickle.load

import numpy as np import tensorflow as tf H = 2 N = 2 M = 3 BS = 10 def my_softmax(arr): max_elements = np.reshape(np.max(arr, axis = 2), (BS, N, 1)) arr = arr - max_elements exp_array = np.exp(arr) print (exp_array) sum_array = np.reshape(np.sum(exp_array, axis=2), (BS, N, 1)) return exp_array /sum_array def masked_softmax(logits, mask, dim): """ Takes masked softmax over given dimension of logits. Inputs: logits: Numpy array. We want to take softmax over dimension dim. mask: Numpy array of same shape as logits. Has 1s where there's real data in logits, 0 where there's padding dim: int. dimension over which to take softmax Returns: masked_logits: Numpy array same shape as logits. This is the same as logits, but with 1e30 subtracted (i.e. very large negative number) in the padding locations. prob_dist: Numpy array same shape as logits. The result of taking softmax over masked_logits in given dimension. Should be 0 in padding locations. Should sum to 1 over given dimension. """ exp_mask = (1 - tf.cast(mask, 'float64')) * (-1e30) # -large where there's padding, 0 elsewhere print (exp_mask) masked_logits = tf.add(logits, exp_mask) # where there's padding, set logits to -large prob_dist = tf.nn.softmax(masked_logits, dim) return masked_logits, prob_dist def test_build_similarity(contexts, questions): w_sim_1 = tf.get_variable('w_sim_1', initializer=w_1) # 2 * H w_sim_2 = tf.get_variable('w_sim_2', initializer=w_2) # 2 * self.hidden_size w_sim_3 = tf.get_variable('w_sim_3', initializer=w_3) # 2 * self.hidden_size q_tile = tf.tile(tf.expand_dims(questions, 0), [N, 1, 1, 1]) # N x BS x M x 2H q_tile = tf.transpose(q_tile, (1, 0, 3, 2)) # BS x N x 2H x M contexts = tf.expand_dims(contexts, -1) # BS x N x 2H x 1 result = (contexts * q_tile) # BS x N x 2H x M tf.assert_equal(tf.shape(result), [BS, N, 2 * H, M]) result = tf.transpose(result, (0, 1, 3, 2)) # BS x N x M x 2H result = tf.reshape(result, (-1, N * M, 2 * H)) # BS x (NxM) x 2H tf.assert_equal(tf.shape(result), [BS, N*M, 2*H]) # w_sim_1 = tf.tile(tf.expand_dims(w_sim_1, 0), [BS, 1]) # w_sim_2 = tf.tile(tf.expand_dims(w_sim_2, 0), [BS, 1]) # w_sim_3 = tf.tile(tf.expand_dims(w_sim_3, 0), [BS, 1]) term1 = tf.matmul(tf.reshape(contexts, (BS * N, 2*H)), tf.expand_dims(w_sim_1, -1)) # BS x N term1 = tf.reshape(term1, (-1, N)) term2 = tf.matmul(tf.reshape(questions, (BS * M, 2*H)), tf.expand_dims(w_sim_2, -1)) # BS x M term2 = tf.reshape(term2, (-1, M)) term3 = tf.matmul(tf.reshape(result, (BS * N * M, 2* H)), tf.expand_dims(w_sim_3, -1)) term3 = tf.reshape(term3, (-1, N, M)) # BS x N x M S = tf.reshape(term1,(-1, N, 1)) + term3 + tf.reshape(term2, (-1, 1, M)) return S def test_build_sim_mask(): context_mask = np.array([True, True]) # BS x N question_mask = np.array([True, True, False]) # BS x M context_mask =

np.tile(context_mask, [BS, 1])

numpy.tile

# # Copyright (c) 2021 The GPflux Contributors. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # import abc import numpy as np import pytest import tensorflow as tf import tensorflow_probability as tfp from gpflow.kullback_leiblers import gauss_kl from gpflux.encoders import DirectlyParameterizedNormalDiag from gpflux.layers import LatentVariableLayer, LayerWithObservations, TrackableLayer tf.keras.backend.set_floatx("float64") ############ # Utilities ############ def _zero_one_normal_prior(w_dim): """ N(0, I) prior """ return tfp.distributions.MultivariateNormalDiag(loc=np.zeros(w_dim), scale_diag=

np.ones(w_dim)

numpy.ones

# -*- coding: utf-8 -*- """ Created on Thu Nov 28 12:10:11 2019 @author: Omer """ ## File handler ## This file was initially intended purely to generate the matrices for the near earth code found in: https://public.ccsds.org/Pubs/131x1o2e2s.pdf ## The values from the above pdf were copied manually to a txt file, and it is the purpose of this file to parse it. ## The emphasis here is on correctness, I currently do not see a reason to generalise this file, since matrices will be saved in either json or some matrix friendly format. import numpy as np from scipy.linalg import circulant #import matplotlib.pyplot as plt import scipy.io import common import hashlib import os projectDir = os.environ.get('LDPC') if projectDir == None: import pathlib projectDir = pathlib.Path(__file__).parent.absolute() ## <NAME>: added on 01/12/2020, need to make sure this doesn't break anything. import sys sys.path.insert(1, projectDir) FILE_HANDLER_INT_DATA_TYPE = np.int32 GENERAL_CODE_MATRIX_DATA_TYPE = np.int32 NIBBLE_CONVERTER = np.array([8, 4, 2, 1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) def nibbleToHex(inputArray): n = NIBBLE_CONVERTER.dot(inputArray) if n == 10: h = 'A' elif n== 11: h = 'B' elif n== 12: h = 'C' elif n== 13: h = 'D' elif n== 14: h = 'E' elif n== 15: h = 'F' else: h = str(n) return h def binaryArraytoHex(inputArray): d1 = len(inputArray) assert (d1 % 4 == 0) outputArray = np.zeros(d1//4, dtype = str) outputString = '' for j in range(d1//4): nibble = inputArray[4 * j : 4 * j + 4] h = nibbleToHex(nibble) outputArray[j] = h outputString = outputString + h return outputArray, outputString def hexStringToBinaryArray(hexString): outputBinary = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) for i in hexString: if i == '0': nibble = np.array([0,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '1': nibble = np.array([0,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '2': nibble = np.array([0,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '3': nibble = np.array([0,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '4': nibble = np.array([0,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '5': nibble = np.array([0,1,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '6': nibble = np.array([0,1,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '7': nibble = np.array([0,1,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '8': nibble = np.array([1,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == '9': nibble = np.array([1,0,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'A': nibble = np.array([1,0,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'B': nibble = np.array([1,0,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'C': nibble = np.array([1,1,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'D': nibble = np.array([1,1,0,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'E': nibble = np.array([1,1,1,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) elif i == 'F': nibble = np.array([1,1,1,1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) else: #print('Error, 0-9 or A-F') pass nibble = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) outputBinary = np.hstack((outputBinary, nibble)) return outputBinary def hexToCirculant(hexStr, circulantSize): binaryArray = hexStringToBinaryArray(hexStr) if len(binaryArray) < circulantSize: binaryArray = np.hstack(np.zeros(circulantSize-len(binaryArray), dtype = GENERAL_CODE_MATRIX_DATA_TYPE)) else: binaryArray = binaryArray[1:] circulantMatrix = circulant(binaryArray) circulantMatrix = circulantMatrix.T return circulantMatrix def hotLocationsToCirculant(locationList, circulantSize): generatingVector = np.zeros(circulantSize, dtype = GENERAL_CODE_MATRIX_DATA_TYPE) generatingVector[locationList] = 1 newCirculant = circulant(generatingVector) newCirculant = newCirculant.T return newCirculant def readMatrixFromFile(fileName, dim0, dim1, circulantSize, isRow = True, isHex = True, isGenerator = True ): # This function assumes that each line in the file contains the non zero locations of the first row of a circulant. # Each line in the file then defines a circulant, and the order in which they are defined is top to bottom left to right, i.e.: # line 0 defines circulant 0,0 with open(fileName) as fid: lines = fid.readlines() if isGenerator: for i in range((dim0 // circulantSize) ): bLeft = hexToCirculant(lines[2 * i], circulantSize) bRight = hexToCirculant(lines[2 * i + 1], circulantSize) newBlock =

np.hstack((bLeft, bRight))

numpy.hstack

from itertools import product import numpy as np import pytest from alibi_detect.utils.discretizer import Discretizer x = np.random.rand(10, 4) n_features = x.shape[1] feature_names = [str(_) for _ in range(n_features)] categorical_features = [[], [1, 3]] percentiles = [list(

np.arange(25, 100, 25)

numpy.arange

"""Test the search module""" from collections.abc import Iterable, Sized from io import StringIO from itertools import chain, product from functools import partial import pickle import sys from types import GeneratorType import re import numpy as np import scipy.sparse as sp import pytest from sklearn.utils.fixes import sp_version from sklearn.utils._testing import assert_raises from sklearn.utils._testing import assert_warns from sklearn.utils._testing import assert_warns_message from sklearn.utils._testing import assert_raise_message from sklearn.utils._testing import assert_array_equal from sklearn.utils._testing import assert_array_almost_equal from sklearn.utils._testing import assert_allclose from sklearn.utils._testing import assert_almost_equal from sklearn.utils._testing import ignore_warnings from sklearn.utils._mocking import CheckingClassifier, MockDataFrame from scipy.stats import bernoulli, expon, uniform from sklearn.base import BaseEstimator, ClassifierMixin from sklearn.base import clone from sklearn.exceptions import NotFittedError from sklearn.datasets import make_classification from sklearn.datasets import make_blobs from sklearn.datasets import make_multilabel_classification from sklearn.model_selection import fit_grid_point from sklearn.model_selection import train_test_split from sklearn.model_selection import KFold from sklearn.model_selection import StratifiedKFold from sklearn.model_selection import StratifiedShuffleSplit from sklearn.model_selection import LeaveOneGroupOut from sklearn.model_selection import LeavePGroupsOut from sklearn.model_selection import GroupKFold from sklearn.model_selection import GroupShuffleSplit from sklearn.model_selection import GridSearchCV from sklearn.model_selection import RandomizedSearchCV from sklearn.model_selection import ParameterGrid from sklearn.model_selection import ParameterSampler from sklearn.model_selection._search import BaseSearchCV from sklearn.model_selection._validation import FitFailedWarning from sklearn.svm import LinearSVC, SVC from sklearn.tree import DecisionTreeRegressor from sklearn.tree import DecisionTreeClassifier from sklearn.cluster import KMeans from sklearn.neighbors import KernelDensity from sklearn.neighbors import KNeighborsClassifier from sklearn.metrics import f1_score from sklearn.metrics import recall_score from sklearn.metrics import accuracy_score from sklearn.metrics import make_scorer from sklearn.metrics import roc_auc_score from sklearn.metrics.pairwise import euclidean_distances from sklearn.impute import SimpleImputer from sklearn.pipeline import Pipeline from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression from sklearn.experimental import enable_hist_gradient_boosting # noqa from sklearn.ensemble import HistGradientBoostingClassifier from sklearn.model_selection.tests.common import OneTimeSplitter # Neither of the following two estimators inherit from BaseEstimator, # to test hyperparameter search on user-defined classifiers. class MockClassifier: """Dummy classifier to test the parameter search algorithms""" def __init__(self, foo_param=0): self.foo_param = foo_param def fit(self, X, Y): assert len(X) == len(Y) self.classes_ = np.unique(Y) return self def predict(self, T): return T.shape[0] def transform(self, X): return X + self.foo_param def inverse_transform(self, X): return X - self.foo_param predict_proba = predict predict_log_proba = predict decision_function = predict def score(self, X=None, Y=None): if self.foo_param > 1: score = 1. else: score = 0. return score def get_params(self, deep=False): return {'foo_param': self.foo_param} def set_params(self, **params): self.foo_param = params['foo_param'] return self class LinearSVCNoScore(LinearSVC): """An LinearSVC classifier that has no score method.""" @property def score(self): raise AttributeError X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) y = np.array([1, 1, 2, 2]) def assert_grid_iter_equals_getitem(grid): assert list(grid) == [grid[i] for i in range(len(grid))] @pytest.mark.parametrize("klass", [ParameterGrid, partial(ParameterSampler, n_iter=10)]) @pytest.mark.parametrize( "input, error_type, error_message", [(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'), ([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'), ({'foo': 0}, TypeError, "Parameter.* value is not iterable .*" r"\(key='foo', value=0\)")] ) def test_validate_parameter_input(klass, input, error_type, error_message): with pytest.raises(error_type, match=error_message): klass(input) def test_parameter_grid(): # Test basic properties of ParameterGrid. params1 = {"foo": [1, 2, 3]} grid1 = ParameterGrid(params1) assert isinstance(grid1, Iterable) assert isinstance(grid1, Sized) assert len(grid1) == 3 assert_grid_iter_equals_getitem(grid1) params2 = {"foo": [4, 2], "bar": ["ham", "spam", "eggs"]} grid2 = ParameterGrid(params2) assert len(grid2) == 6 # loop to assert we can iterate over the grid multiple times for i in range(2): # tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2) points = set(tuple(chain(*(sorted(p.items())))) for p in grid2) assert (points == set(("bar", x, "foo", y) for x, y in product(params2["bar"], params2["foo"]))) assert_grid_iter_equals_getitem(grid2) # Special case: empty grid (useful to get default estimator settings) empty = ParameterGrid({}) assert len(empty) == 1 assert list(empty) == [{}] assert_grid_iter_equals_getitem(empty) assert_raises(IndexError, lambda: empty[1]) has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}]) assert len(has_empty) == 4 assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}] assert_grid_iter_equals_getitem(has_empty) def test_grid_search(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3) # make sure it selects the smallest parameter in case of ties old_stdout = sys.stdout sys.stdout = StringIO() grid_search.fit(X, y) sys.stdout = old_stdout assert grid_search.best_estimator_.foo_param == 2 assert_array_equal(grid_search.cv_results_["param_foo_param"].data, [1, 2, 3]) # Smoke test the score etc: grid_search.score(X, y) grid_search.predict_proba(X) grid_search.decision_function(X) grid_search.transform(X) # Test exception handling on scoring grid_search.scoring = 'sklearn' assert_raises(ValueError, grid_search.fit, X, y) def test_grid_search_pipeline_steps(): # check that parameters that are estimators are cloned before fitting pipe = Pipeline([('regressor', LinearRegression())]) param_grid = {'regressor': [LinearRegression(), Ridge()]} grid_search = GridSearchCV(pipe, param_grid, cv=2) grid_search.fit(X, y) regressor_results = grid_search.cv_results_['param_regressor'] assert isinstance(regressor_results[0], LinearRegression) assert isinstance(regressor_results[1], Ridge) assert not hasattr(regressor_results[0], 'coef_') assert not hasattr(regressor_results[1], 'coef_') assert regressor_results[0] is not grid_search.best_estimator_ assert regressor_results[1] is not grid_search.best_estimator_ # check that we didn't modify the parameter grid that was passed assert not hasattr(param_grid['regressor'][0], 'coef_') assert not hasattr(param_grid['regressor'][1], 'coef_') @pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV]) def test_SearchCV_with_fit_params(SearchCV): X = np.arange(100).reshape(10, 10) y =

np.array([0] * 5 + [1] * 5)

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 =

np.linspace(slope_based_maximum, slope_based_minimum)

numpy.linspace

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101),

np.linspace(-5, 5, 101)

numpy.linspace

import os import numpy as np import pandas as pd import tensorflow as tf from keras.preprocessing.image import ImageDataGenerator from keras.preprocessing.image import img_to_array, load_img from keras.utils.np_utils import to_categorical from sklearn.model_selection import StratifiedShuffleSplit from sklearn.preprocessing import LabelEncoder, StandardScaler def load_numeric_training(standardize=True): data = pd.read_csv('../train.csv') ID = data.pop('id') y = data.pop('species') y = LabelEncoder().fit(y).transform(y) X = StandardScaler().fit(data).transform(data) if standardize else data.values return ID.values, X, y def load_numeric_test(standardize=True): data = pd.read_csv('../test.csv') ID = data.pop('id') test = StandardScaler().fit(data).transform(data) if standardize else data.values return ID.values, test def resize_img(img, max_dim=96): max_axis = np.argmax(img.size) scale = max_dim / img.size[max_axis] return img.resize((int(img.size[0] * scale), int(img.size[1] * scale))) def load_img_data(ids, max_dim=96, center=True): X = np.empty((len(ids), max_dim, max_dim, 1)) for i, id in enumerate(ids): img = load_img('../images/{}.jpg'.format(id), grayscale=True) img = resize_img(img, max_dim=max_dim) x = img_to_array(img) h, w = x.shape[:2] if center: h1 = (max_dim - h) >> 1 h2 = h1 + h w1 = (max_dim - w) >> 1 w2 = w1 + w else: h1, h2, w1, w2 = 0, h, 0, w X[i][h1:h2, w1:w2][:] = x return np.around(X / 255) def load_train_data(split=0.9, random_state=7): ID, X_num_train, y = load_numeric_training() X_img_train = load_img_data(ID) sss = StratifiedShuffleSplit(n_splits=1, train_size=split, test_size=1 - split, random_state=random_state) train_idx, val_idx = next(sss.split(X_num_train, y)) ID_tr, X_num_tr, X_img_tr, y_tr = ID[train_idx], X_num_train[train_idx], X_img_train[train_idx], y[train_idx] ID_val, X_num_val, X_img_val, y_val = ID[val_idx], X_num_train[val_idx], X_img_train[val_idx], y[val_idx] return (ID_tr, X_num_tr, X_img_tr, y_tr), (ID_val, X_num_val, X_img_val, y_val) def load_test_data(): ID, X_num_test = load_numeric_test() X_img_test = load_img_data(ID) return ID, X_num_test, X_img_test print('Loading train data ...') (ID_train, X_num_tr, X_img_tr, y_tr), (ID_val, X_num_val, X_img_val, y_val) = load_train_data() # Prepare ID-to-label and ID-to-numerical dictionary ID_y_dic, ID_num_dic = {}, {} for i in range(len(ID_train)): ID_y_dic[ID_train[i]] = y_tr[i] ID_num_dic[ID_train[i]] = X_num_tr[i, :] print('Loading test data ...') ID_test, X_num_test, X_img_test = load_test_data() # Convert label to categorical/one-hot ID_train, y_tr, y_val = to_categorical(ID_train), to_categorical(y_tr), to_categorical((y_val)) def _bytes_feature(value): return tf.train.Feature(bytes_list=tf.train.BytesList(value=[value])) def _int64_feature(value): return tf.train.Feature(int64_list=tf.train.Int64List(value=[value])) def _float32_feature(value): return tf.train.Feature(float_list=tf.train.FloatList(value=value)) def write_val_data(): val_data_path = '../tfrecords/val_data_1.tfrecords' if os.path.exists(val_data_path): print('Warning: old file exists, removed.') os.remove(val_data_path) val_image, val_num, val_label = X_img_val.astype(np.bool), X_num_val.astype(np.float64), y_val.astype(np.bool) print(val_image.shape, val_num.shape, val_label.shape) val_writer = tf.python_io.TFRecordWriter(val_data_path) print('Writing data into tfrecord ...') for i in range(len(val_image)): image, num, label = val_image[i], val_num[i], val_label[i] feature = {'image': _bytes_feature(image.tostring()), 'num': _bytes_feature(num.tostring()), 'label': _bytes_feature(label.tostring())} example = tf.train.Example(features=tf.train.Features(feature=feature)) val_writer.write(example.SerializeToString()) print('Done!') def write_train_data(): imgen = ImageDataGenerator(rotation_range=20, zoom_range=0.2, horizontal_flip=True, vertical_flip=True, fill_mode='nearest') imgen_train = imgen.flow(X_img_tr, ID_train, batch_size=32, seed=7) print('Generating augmented images') all_images = [] all_ID = [] p = True for i in range(28 * 200): print('Generating augmented images for epoch {}, batch {}'.format(i // 28, i % 28)) X, ID = imgen_train.next() all_images.append(X) all_ID.append(np.argmax(ID, axis=1)) all_images = np.concatenate(all_images).astype(np.bool) all_ID = np.concatenate(all_ID) all_y =

np.zeros(all_ID.shape)

numpy.zeros

import cv2 import torch import yaml import imageio import throttle import numpy as np import matplotlib.pyplot as plt from argparse import ArgumentParser from skimage.transform import resize from scipy.spatial import ConvexHull from modules.generator import OcclusionAwareGenerator from modules.keypoint_detector import KPDetector from sync_batchnorm import DataParallelWithCallback #from animate import normalize_kp # command = [ffmpeg, # '-y', # '-f', 'rawvideo', # '-vcodec','rawvideo', # '-pix_fmt', 'bgr24', # '-s', dimension, # '-i', '-', # '-c:v', 'libx264', # '-pix_fmt', 'yuv420p', # '-preset', 'ultrafast', # '-f', 'flv', # 'rtmp://10.10.10.80/live/mystream'] def normalize_kp(kp_source, kp_driving, kp_driving_initial, adapt_movement_scale=False, use_relative_movement=False, use_relative_jacobian=False): if adapt_movement_scale: source_area = ConvexHull(kp_source['value'][0].data.cpu().numpy()).volume driving_area = ConvexHull(kp_driving_initial['value'][0].data.cpu().numpy()).volume adapt_movement_scale = np.sqrt(source_area) / np.sqrt(driving_area) else: adapt_movement_scale = 1 kp_new = {k: v for k, v in kp_driving.items()} if use_relative_movement: kp_value_diff = (kp_driving['value'] - kp_driving_initial['value']) kp_value_diff *= adapt_movement_scale kp_new['value'] = kp_value_diff + kp_source['value'] if use_relative_jacobian: jacobian_diff = torch.matmul(kp_driving['jacobian'], torch.inverse(kp_driving_initial['jacobian'])) kp_new['jacobian'] = torch.matmul(jacobian_diff, kp_source['jacobian']) return kp_new def load_checkpoints(config_path, checkpoint_path, cpu=False): with open(config_path) as f: config = yaml.load(f) generator = OcclusionAwareGenerator(**config['model_params']['generator_params'], **config['model_params']['common_params']) if not cpu: generator.cuda() kp_detector = KPDetector(**config['model_params']['kp_detector_params'], **config['model_params']['common_params']) if not cpu: kp_detector.cuda() if cpu: checkpoint = torch.load(checkpoint_path, map_location=torch.device('cpu')) else: checkpoint = torch.load(checkpoint_path) generator.load_state_dict(checkpoint['generator']) kp_detector.load_state_dict(checkpoint['kp_detector']) if not cpu: generator = DataParallelWithCallback(generator) kp_detector = DataParallelWithCallback(kp_detector) generator.eval() kp_detector.eval() return generator, kp_detector @throttle.wrap(1, 2) def forward(source_image, driving_frame, kp_source, kp_driving_initial, generator, kp_detector, relative=True, adapt_scale=True, cpu=True): kp_driving = kp_detector(driving_frame) kp_norm = normalize_kp( kp_source=kp_source, kp_driving=kp_driving, kp_driving_initial=kp_driving_initial, use_relative_movement=relative, use_relative_jacobian=relative, adapt_movement_scale=adapt_scale ) out = generator(source_image, kp_source=kp_source, kp_driving=kp_norm) return np.transpose(out["prediction"].data.cpu().numpy(), [0, 2, 3, 1])[0] if __name__ == "__main__": parser = ArgumentParser() parser.add_argument("--config", required=True, help="path to config") parser.add_argument("--source_image", required=True, help="path to source image") parser.add_argument("--checkpoint", default="vox-cpk.pth.tar", help="path to checkpoint") parser.add_argument("--relative", dest="relative", action="store_true", help="use relative or absolute keypoint coordinates") parser.add_argument("--adapt_scale", dest="adapt_scale", action="store_true", help="adapt movement scale based on convex hull of keypoints") parser.add_argument("--cpu", dest="cpu", action="store_true", help="CPU mode") parser.set_defaults(relative=False) parser.set_defaults(adapt_scale=False) opt = parser.parse_args() generator, kp_detector = load_checkpoints(config_path=opt.config, checkpoint_path=opt.checkpoint, cpu=opt.cpu) source_image = imageio.imread(opt.source_image) source_image = resize(source_image, (256, 256))[..., :3] source = torch.tensor(source_image[np.newaxis].astype(np.float32)).permute(0, 3, 1, 2) if not opt.cpu: source = source.cuda() kp_source = kp_detector(source) #out = cv2.VideoWriter('outpy.avi', cv2.VideoWriter_fourcc('M','J','P','G'), 30, (256, 256)) kp_driving_initial = None camera = cv2.VideoCapture(0) ret, frame = camera.read() while True: ret, frame = camera.read() resized = resize(frame, (256, 256))[..., :3] if not opt.cpu: resized = resized.cuda() # y = torch.tensor(np.array(resized)) # x = y.cpu().numpy() # image = cv2.cvtColor(x, cv2.COLOR_BGR2RGB) # # x = y.permute(1, 2, 0) # plt.imshow(np.array(image)) # plt.show() driving_resized = torch.tensor(

np.array(resized)

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100),

np.linspace(-0.2, 1.2, 100)

numpy.linspace

import argparse import json import numpy as np import pandas as pd import os from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split from sklearn.metrics import classification_report,f1_score from keras.models import Sequential from keras.layers import Dense, Dropout from keras import backend as K from keras.utils.vis_utils import plot_model from sklearn.externals import joblib import time def f1(y_true, y_pred): def recall(y_true, y_pred): """Recall metric. Only computes a batch-wise average of recall. Computes the recall, a metric for multi-label classification of how many relevant items are selected. """ true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1))) possible_positives = K.sum(K.round(K.clip(y_true, 0, 1))) recall = true_positives / (possible_positives + K.epsilon()) return recall def precision(y_true, y_pred): """Precision metric. Only computes a batch-wise average of precision. Computes the precision, a metric for multi-label classification of how many selected items are relevant. """ true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1))) predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1))) precision = true_positives / (predicted_positives + K.epsilon()) return precision precision = precision(y_true, y_pred) recall = recall(y_true, y_pred) return 2*((precision*recall)/(precision+recall+K.epsilon())) def get_embeddings(sentences_list,layer_json): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :return: Dictionary with key each sentence of the sentences_list and as value the embedding ''' sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence embeddings = dict()##dict with key the index of each sentence and as value the its embedding sentence_emb = dict()#key:sentence,value:its embedding with open(sentences_list,'r') as file: for index,line in enumerate(file): sentences[index] = line.strip() with open(layer_json, 'r',encoding='utf-8') as f: for line in f: embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features']) for key,value in sentences.items(): sentence_emb[value] = embeddings[key] return sentence_emb def train_classifier(sentences_list,layer_json,dataset_csv,filename): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :param dataset_csv: the path of the dataset :param filename: The path of the pickle file that the model will be stored :return: ''' dataset = pd.read_csv(dataset_csv) bert_dict = get_embeddings(sentences_list,layer_json) length = list() sentence_emb = list() previous_emb = list() next_list = list() section_list = list() label = list() errors = 0 for row in dataset.iterrows(): sentence = row[1][0].strip() previous = row[1][1].strip() nexts = row[1][2].strip() section = row[1][3].strip() if sentence in bert_dict: sentence_emb.append(bert_dict[sentence]) else: sentence_emb.append(np.zeros(768)) print(sentence) errors += 1 if previous in bert_dict: previous_emb.append(bert_dict[previous]) else: previous_emb.append(np.zeros(768)) if nexts in bert_dict: next_list.append(bert_dict[nexts]) else: next_list.append(np.zeros(768)) if section in bert_dict: section_list.append(bert_dict[section]) else: section_list.append(np.zeros(768)) length.append(row[1][4]) label.append(row[1][5]) sentence_emb = np.asarray(sentence_emb) print(sentence_emb.shape) next_emb = np.asarray(next_list) print(next_emb.shape) previous_emb = np.asarray(previous_emb) print(previous_emb.shape) section_emb = np.asarray(section_list) print(sentence_emb.shape) length = np.asarray(length) print(length.shape) label = np.asarray(label) print(errors) features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1) features = np.column_stack([features, length]) # np.append(features,length,axis=1) print(features.shape) X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42) log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1) log.fit(X_train, y_train) #save the model _ = joblib.dump(log, filename, compress=9) predictions = log.predict(X_val) print("###########################################") print("Results using embeddings from the",layer_json,"file") print(classification_report(y_val, predictions)) print("F1 score using Logistic Regression:",f1_score(y_val, predictions)) print("###########################################") #train a DNN f1_results = list() for i in range(3): model = Sequential() model.add(Dense(64, activation='relu', trainable=True)) model.add(Dense(128, activation='relu', trainable=True)) model.add(Dropout(0.30)) model.add(Dense(64, activation='relu', trainable=True)) model.add(Dropout(0.25)) model.add(Dense(64, activation='relu', trainable=True)) model.add(Dropout(0.35)) model.add(Dense(1, activation='sigmoid')) # compile network model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1]) # fit network model.fit(X_train, y_train, epochs=100, batch_size=64) loss, f_1 = model.evaluate(X_val, y_val, verbose=1) print('\nTest F1: %f' % (f_1 * 100)) f1_results.append(f_1) model = None print("###########################################") print("Results using embeddings from the", layer_json, "file") # evaluate print(np.mean(f1_results)) print("###########################################") def parameter_tuning_LR(sentences_list,layer_json,dataset_csv): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :param dataset_csv: the path of the dataset :return: ''' dataset = pd.read_csv(dataset_csv) bert_dict = get_embeddings(sentences_list,layer_json) length = list() sentence_emb = list() previous_emb = list() next_list = list() section_list = list() label = list() errors = 0 for row in dataset.iterrows(): sentence = row[1][0].strip() previous = row[1][1].strip() nexts = row[1][2].strip() section = row[1][3].strip() if sentence in bert_dict: sentence_emb.append(bert_dict[sentence]) else: sentence_emb.append(np.zeros(768)) print(sentence) errors += 1 if previous in bert_dict: previous_emb.append(bert_dict[previous]) else: previous_emb.append(np.zeros(768)) if nexts in bert_dict: next_list.append(bert_dict[nexts]) else: next_list.append(np.zeros(768)) if section in bert_dict: section_list.append(bert_dict[section]) else: section_list.append(np.zeros(768)) length.append(row[1][4]) label.append(row[1][5]) sentence_emb = np.asarray(sentence_emb) print(sentence_emb.shape) next_emb =

np.asarray(next_list)

numpy.asarray

"""Test the search module""" from collections.abc import Iterable, Sized from io import StringIO from itertools import chain, product from functools import partial import pickle import sys from types import GeneratorType import re import numpy as np import scipy.sparse as sp import pytest from sklearn.utils.fixes import sp_version from sklearn.utils._testing import assert_raises from sklearn.utils._testing import assert_warns from sklearn.utils._testing import assert_warns_message from sklearn.utils._testing import assert_raise_message from sklearn.utils._testing import assert_array_equal from sklearn.utils._testing import assert_array_almost_equal from sklearn.utils._testing import assert_allclose from sklearn.utils._testing import assert_almost_equal from sklearn.utils._testing import ignore_warnings from sklearn.utils._mocking import CheckingClassifier, MockDataFrame from scipy.stats import bernoulli, expon, uniform from sklearn.base import BaseEstimator, ClassifierMixin from sklearn.base import clone from sklearn.exceptions import NotFittedError from sklearn.datasets import make_classification from sklearn.datasets import make_blobs from sklearn.datasets import make_multilabel_classification from sklearn.model_selection import fit_grid_point from sklearn.model_selection import train_test_split from sklearn.model_selection import KFold from sklearn.model_selection import StratifiedKFold from sklearn.model_selection import StratifiedShuffleSplit from sklearn.model_selection import LeaveOneGroupOut from sklearn.model_selection import LeavePGroupsOut from sklearn.model_selection import GroupKFold from sklearn.model_selection import GroupShuffleSplit from sklearn.model_selection import GridSearchCV from sklearn.model_selection import RandomizedSearchCV from sklearn.model_selection import ParameterGrid from sklearn.model_selection import ParameterSampler from sklearn.model_selection._search import BaseSearchCV from sklearn.model_selection._validation import FitFailedWarning from sklearn.svm import LinearSVC, SVC from sklearn.tree import DecisionTreeRegressor from sklearn.tree import DecisionTreeClassifier from sklearn.cluster import KMeans from sklearn.neighbors import KernelDensity from sklearn.neighbors import KNeighborsClassifier from sklearn.metrics import f1_score from sklearn.metrics import recall_score from sklearn.metrics import accuracy_score from sklearn.metrics import make_scorer from sklearn.metrics import roc_auc_score from sklearn.metrics.pairwise import euclidean_distances from sklearn.impute import SimpleImputer from sklearn.pipeline import Pipeline from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression from sklearn.experimental import enable_hist_gradient_boosting # noqa from sklearn.ensemble import HistGradientBoostingClassifier from sklearn.model_selection.tests.common import OneTimeSplitter # Neither of the following two estimators inherit from BaseEstimator, # to test hyperparameter search on user-defined classifiers. class MockClassifier: """Dummy classifier to test the parameter search algorithms""" def __init__(self, foo_param=0): self.foo_param = foo_param def fit(self, X, Y): assert len(X) == len(Y) self.classes_ = np.unique(Y) return self def predict(self, T): return T.shape[0] def transform(self, X): return X + self.foo_param def inverse_transform(self, X): return X - self.foo_param predict_proba = predict predict_log_proba = predict decision_function = predict def score(self, X=None, Y=None): if self.foo_param > 1: score = 1. else: score = 0. return score def get_params(self, deep=False): return {'foo_param': self.foo_param} def set_params(self, **params): self.foo_param = params['foo_param'] return self class LinearSVCNoScore(LinearSVC): """An LinearSVC classifier that has no score method.""" @property def score(self): raise AttributeError X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) y = np.array([1, 1, 2, 2]) def assert_grid_iter_equals_getitem(grid): assert list(grid) == [grid[i] for i in range(len(grid))] @pytest.mark.parametrize("klass", [ParameterGrid, partial(ParameterSampler, n_iter=10)]) @pytest.mark.parametrize( "input, error_type, error_message", [(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'), ([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'), ({'foo': 0}, TypeError, "Parameter.* value is not iterable .*" r"\(key='foo', value=0\)")] ) def test_validate_parameter_input(klass, input, error_type, error_message): with pytest.raises(error_type, match=error_message): klass(input) def test_parameter_grid(): # Test basic properties of ParameterGrid. params1 = {"foo": [1, 2, 3]} grid1 = ParameterGrid(params1) assert isinstance(grid1, Iterable) assert isinstance(grid1, Sized) assert len(grid1) == 3 assert_grid_iter_equals_getitem(grid1) params2 = {"foo": [4, 2], "bar": ["ham", "spam", "eggs"]} grid2 = ParameterGrid(params2) assert len(grid2) == 6 # loop to assert we can iterate over the grid multiple times for i in range(2): # tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2) points = set(tuple(chain(*(sorted(p.items())))) for p in grid2) assert (points == set(("bar", x, "foo", y) for x, y in product(params2["bar"], params2["foo"]))) assert_grid_iter_equals_getitem(grid2) # Special case: empty grid (useful to get default estimator settings) empty = ParameterGrid({}) assert len(empty) == 1 assert list(empty) == [{}] assert_grid_iter_equals_getitem(empty) assert_raises(IndexError, lambda: empty[1]) has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}]) assert len(has_empty) == 4 assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}] assert_grid_iter_equals_getitem(has_empty) def test_grid_search(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3) # make sure it selects the smallest parameter in case of ties old_stdout = sys.stdout sys.stdout = StringIO() grid_search.fit(X, y) sys.stdout = old_stdout assert grid_search.best_estimator_.foo_param == 2 assert_array_equal(grid_search.cv_results_["param_foo_param"].data, [1, 2, 3]) # Smoke test the score etc: grid_search.score(X, y) grid_search.predict_proba(X) grid_search.decision_function(X) grid_search.transform(X) # Test exception handling on scoring grid_search.scoring = 'sklearn' assert_raises(ValueError, grid_search.fit, X, y) def test_grid_search_pipeline_steps(): # check that parameters that are estimators are cloned before fitting pipe = Pipeline([('regressor', LinearRegression())]) param_grid = {'regressor': [LinearRegression(), Ridge()]} grid_search = GridSearchCV(pipe, param_grid, cv=2) grid_search.fit(X, y) regressor_results = grid_search.cv_results_['param_regressor'] assert isinstance(regressor_results[0], LinearRegression) assert isinstance(regressor_results[1], Ridge) assert not hasattr(regressor_results[0], 'coef_') assert not hasattr(regressor_results[1], 'coef_') assert regressor_results[0] is not grid_search.best_estimator_ assert regressor_results[1] is not grid_search.best_estimator_ # check that we didn't modify the parameter grid that was passed assert not hasattr(param_grid['regressor'][0], 'coef_') assert not hasattr(param_grid['regressor'][1], 'coef_') @pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV]) def test_SearchCV_with_fit_params(SearchCV): X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier(expected_fit_params=['spam', 'eggs']) searcher = SearchCV( clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise" ) # The CheckingClassifier generates an assertion error if # a parameter is missing or has length != len(X). err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen." with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(10)) err_msg = "Fit parameter spam has length 1; expected" with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10)) searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10)) @ignore_warnings def test_grid_search_no_score(): # Test grid-search on classifier that has no score function. clf = LinearSVC(random_state=0) X, y = make_blobs(random_state=0, centers=2) Cs = [.1, 1, 10] clf_no_score = LinearSVCNoScore(random_state=0) grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy') grid_search.fit(X, y) grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}, scoring='accuracy') # smoketest grid search grid_search_no_score.fit(X, y) # check that best params are equal assert grid_search_no_score.best_params_ == grid_search.best_params_ # check that we can call score and that it gives the correct result assert grid_search.score(X, y) == grid_search_no_score.score(X, y) # giving no scoring function raises an error grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}) assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit, [[1]]) def test_grid_search_score_method(): X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2, random_state=0) clf = LinearSVC(random_state=0) grid = {'C': [.1]} search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y) search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y) search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid, scoring='roc_auc' ).fit(X, y) search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y) # Check warning only occurs in situation where behavior changed: # estimator requires score method to compete with scoring parameter score_no_scoring = search_no_scoring.score(X, y) score_accuracy = search_accuracy.score(X, y) score_no_score_auc = search_no_score_method_auc.score(X, y) score_auc = search_auc.score(X, y) # ensure the test is sane assert score_auc < 1.0 assert score_accuracy < 1.0 assert score_auc != score_accuracy assert_almost_equal(score_accuracy, score_no_scoring) assert_almost_equal(score_auc, score_no_score_auc) def test_grid_search_groups(): # Check if ValueError (when groups is None) propagates to GridSearchCV # And also check if groups is correctly passed to the cv object rng = np.random.RandomState(0) X, y = make_classification(n_samples=15, n_classes=2, random_state=0) groups = rng.randint(0, 3, 15) clf = LinearSVC(random_state=0) grid = {'C': [1]} group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2), GroupKFold(n_splits=3), GroupShuffleSplit()] for cv in group_cvs: gs = GridSearchCV(clf, grid, cv=cv) assert_raise_message(ValueError, "The 'groups' parameter should not be None.", gs.fit, X, y) gs.fit(X, y, groups=groups) non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()] for cv in non_group_cvs: gs = GridSearchCV(clf, grid, cv=cv) # Should not raise an error gs.fit(X, y) def test_classes__property(): # Test that classes_ property matches best_estimator_.classes_ X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) Cs = [.1, 1, 10] grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) grid_search.fit(X, y) assert_array_equal(grid_search.best_estimator_.classes_, grid_search.classes_) # Test that regressors do not have a classes_ attribute grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]}) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute before it's fit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute without a refit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}, refit=False) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') def test_trivial_cv_results_attr(): # Test search over a "grid" with only one point. clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3) grid_search.fit(X, y) assert hasattr(grid_search, "cv_results_") random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3) random_search.fit(X, y) assert hasattr(grid_search, "cv_results_") def test_no_refit(): # Test that GSCV can be used for model selection alone without refitting clf = MockClassifier() for scoring in [None, ['accuracy', 'precision']]: grid_search = GridSearchCV( clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3 ) grid_search.fit(X, y) assert not hasattr(grid_search, "best_estimator_") and \ hasattr(grid_search, "best_index_") and \ hasattr(grid_search, "best_params_") # Make sure the functions predict/transform etc raise meaningful # error messages for fn_name in ('predict', 'predict_proba', 'predict_log_proba', 'transform', 'inverse_transform'): assert_raise_message(NotFittedError, ('refit=False. %s is available only after ' 'refitting on the best parameters' % fn_name), getattr(grid_search, fn_name), X) # Test that an invalid refit param raises appropriate error messages for refit in ["", 5, True, 'recall', 'accuracy']: assert_raise_message(ValueError, "For multi-metric scoring, the " "parameter refit must be set to a scorer key", GridSearchCV(clf, {}, refit=refit, scoring={'acc': 'accuracy', 'prec': 'precision'} ).fit, X, y) def test_grid_search_error(): # Test that grid search will capture errors on data with different length X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, X_[:180], y_) def test_grid_search_one_grid_point(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]} clf = SVC(gamma='auto') cv = GridSearchCV(clf, param_dict) cv.fit(X_, y_) clf = SVC(C=1.0, kernel="rbf", gamma=0.1) clf.fit(X_, y_) assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_) def test_grid_search_when_param_grid_includes_range(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = None grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3) grid_search.fit(X, y) assert grid_search.best_estimator_.foo_param == 2 def test_grid_search_bad_param_grid(): param_dict = {"C": 1} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'int'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": []} clf = SVC() assert_raise_message( ValueError, "Parameter values for parameter (C) need to be a non-empty sequence.", GridSearchCV, clf, param_dict) param_dict = {"C": "1,2,3"} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'str'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": np.ones((3, 2))} clf = SVC() assert_raises(ValueError, GridSearchCV, clf, param_dict) def test_grid_search_sparse(): # Test that grid search works with both dense and sparse matrices X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180].tocoo(), y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert np.mean(y_pred == y_pred2) >= .9 assert C == C2 def test_grid_search_sparse_scoring(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1") cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1") cv.fit(X_[:180], y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert_array_equal(y_pred, y_pred2) assert C == C2 # Smoke test the score # np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]), # cv.score(X_[:180], y[:180])) # test loss where greater is worse def f1_loss(y_true_, y_pred_): return -f1_score(y_true_, y_pred_) F1Loss = make_scorer(f1_loss, greater_is_better=False) cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss) cv.fit(X_[:180], y_[:180]) y_pred3 = cv.predict(X_[180:]) C3 = cv.best_estimator_.C assert C == C3 assert_array_equal(y_pred, y_pred3) def test_grid_search_precomputed_kernel(): # Test that grid search works when the input features are given in the # form of a precomputed kernel matrix X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) # compute the training kernel matrix corresponding to the linear kernel K_train = np.dot(X_[:180], X_[:180].T) y_train = y_[:180] clf = SVC(kernel='precomputed') cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(K_train, y_train) assert cv.best_score_ >= 0 # compute the test kernel matrix K_test = np.dot(X_[180:], X_[:180].T) y_test = y_[180:] y_pred = cv.predict(K_test) assert np.mean(y_pred == y_test) >= 0 # test error is raised when the precomputed kernel is not array-like # or sparse assert_raises(ValueError, cv.fit, K_train.tolist(), y_train) def test_grid_search_precomputed_kernel_error_nonsquare(): # Test that grid search returns an error with a non-square precomputed # training kernel matrix K_train = np.zeros((10, 20)) y_train = np.ones((10, )) clf = SVC(kernel='precomputed') cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, K_train, y_train) class BrokenClassifier(BaseEstimator): """Broken classifier that cannot be fit twice""" def __init__(self, parameter=None): self.parameter = parameter def fit(self, X, y): assert not hasattr(self, 'has_been_fit_') self.has_been_fit_ = True def predict(self, X): return np.zeros(X.shape[0]) @ignore_warnings def test_refit(): # Regression test for bug in refitting # Simulates re-fitting a broken estimator; this used to break with # sparse SVMs. X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = GridSearchCV(BrokenClassifier(), [{'parameter': [0, 1]}], scoring="precision", refit=True) clf.fit(X, y) def test_refit_callable(): """ Test refit=callable, which adds flexibility in identifying the "best" estimator. """ def refit_callable(cv_results): """ A dummy function tests `refit=callable` interface. Return the index of a model that has the least `mean_test_score`. """ # Fit a dummy clf with `refit=True` to get a list of keys in # clf.cv_results_. X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring='precision', refit=True) clf.fit(X, y) # Ensure that `best_index_ != 0` for this dummy clf assert clf.best_index_ != 0 # Assert every key matches those in `cv_results` for key in clf.cv_results_.keys(): assert key in cv_results return cv_results['mean_test_score'].argmin() X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring='precision', refit=refit_callable) clf.fit(X, y) assert clf.best_index_ == 0 # Ensure `best_score_` is disabled when using `refit=callable` assert not hasattr(clf, 'best_score_') def test_refit_callable_invalid_type(): """ Test implementation catches the errors when 'best_index_' returns an invalid result. """ def refit_callable_invalid_type(cv_results): """ A dummy function tests when returned 'best_index_' is not integer. """ return None X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.1, 1]}, scoring='precision', refit=refit_callable_invalid_type) with pytest.raises(TypeError, match='best_index_ returned is not an integer'): clf.fit(X, y) @pytest.mark.parametrize('out_bound_value', [-1, 2]) @pytest.mark.parametrize('search_cv', [RandomizedSearchCV, GridSearchCV]) def test_refit_callable_out_bound(out_bound_value, search_cv): """ Test implementation catches the errors when 'best_index_' returns an out of bound result. """ def refit_callable_out_bound(cv_results): """ A dummy function tests when returned 'best_index_' is out of bounds. """ return out_bound_value X, y = make_classification(n_samples=100, n_features=4, random_state=42) clf = search_cv(LinearSVC(random_state=42), {'C': [0.1, 1]}, scoring='precision', refit=refit_callable_out_bound) with pytest.raises(IndexError, match='best_index_ index out of range'): clf.fit(X, y) def test_refit_callable_multi_metric(): """ Test refit=callable in multiple metric evaluation setting """ def refit_callable(cv_results): """ A dummy function tests `refit=callable` interface. Return the index of a model that has the least `mean_test_prec`. """ assert 'mean_test_prec' in cv_results return cv_results['mean_test_prec'].argmin() X, y = make_classification(n_samples=100, n_features=4, random_state=42) scoring = {'Accuracy': make_scorer(accuracy_score), 'prec': 'precision'} clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]}, scoring=scoring, refit=refit_callable) clf.fit(X, y) assert clf.best_index_ == 0 # Ensure `best_score_` is disabled when using `refit=callable` assert not hasattr(clf, 'best_score_') def test_gridsearch_nd(): # Pass X as list in GridSearchCV X_4d = np.arange(10 * 5 * 3 * 2).reshape(10, 5, 3, 2) y_3d = np.arange(10 * 7 * 11).reshape(10, 7, 11) check_X = lambda x: x.shape[1:] == (5, 3, 2) check_y = lambda x: x.shape[1:] == (7, 11) clf = CheckingClassifier( check_X=check_X, check_y=check_y, methods_to_check=["fit"], ) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}) grid_search.fit(X_4d, y_3d).score(X, y) assert hasattr(grid_search, "cv_results_") def test_X_as_list(): # Pass X as list in GridSearchCV X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier( check_X=lambda x: isinstance(x, list), methods_to_check=["fit"], ) cv = KFold(n_splits=3) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv) grid_search.fit(X.tolist(), y).score(X, y) assert hasattr(grid_search, "cv_results_") def test_y_as_list(): # Pass y as list in GridSearchCV X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier( check_y=lambda x: isinstance(x, list), methods_to_check=["fit"], ) cv = KFold(n_splits=3) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv) grid_search.fit(X, y.tolist()).score(X, y) assert hasattr(grid_search, "cv_results_") @ignore_warnings def test_pandas_input(): # check cross_val_score doesn't destroy pandas dataframe types = [(MockDataFrame, MockDataFrame)] try: from pandas import Series, DataFrame types.append((DataFrame, Series)) except ImportError: pass X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) for InputFeatureType, TargetType in types: # X dataframe, y series X_df, y_ser = InputFeatureType(X), TargetType(y) def check_df(x): return isinstance(x, InputFeatureType) def check_series(x): return isinstance(x, TargetType) clf = CheckingClassifier(check_X=check_df, check_y=check_series) grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}) grid_search.fit(X_df, y_ser).score(X_df, y_ser) grid_search.predict(X_df) assert hasattr(grid_search, "cv_results_") def test_unsupervised_grid_search(): # test grid-search with unsupervised estimator X, y = make_blobs(n_samples=50, random_state=0) km = KMeans(random_state=0, init="random", n_init=1) # Multi-metric evaluation unsupervised scoring = ['adjusted_rand_score', 'fowlkes_mallows_score'] for refit in ['adjusted_rand_score', 'fowlkes_mallows_score']: grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]), scoring=scoring, refit=refit) grid_search.fit(X, y) # Both ARI and FMS can find the right number :) assert grid_search.best_params_["n_clusters"] == 3 # Single metric evaluation unsupervised grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]), scoring='fowlkes_mallows_score') grid_search.fit(X, y) assert grid_search.best_params_["n_clusters"] == 3 # Now without a score, and without y grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4])) grid_search.fit(X) assert grid_search.best_params_["n_clusters"] == 4 def test_gridsearch_no_predict(): # test grid-search with an estimator without predict. # slight duplication of a test from KDE def custom_scoring(estimator, X): return 42 if estimator.bandwidth == .1 else 0 X, _ = make_blobs(cluster_std=.1, random_state=1, centers=[[0, 1], [1, 0], [0, 0]]) search = GridSearchCV(KernelDensity(), param_grid=dict(bandwidth=[.01, .1, 1]), scoring=custom_scoring) search.fit(X) assert search.best_params_['bandwidth'] == .1 assert search.best_score_ == 42 def test_param_sampler(): # test basic properties of param sampler param_distributions = {"kernel": ["rbf", "linear"], "C": uniform(0, 1)} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=10, random_state=0) samples = [x for x in sampler] assert len(samples) == 10 for sample in samples: assert sample["kernel"] in ["rbf", "linear"] assert 0 <= sample["C"] <= 1 # test that repeated calls yield identical parameters param_distributions = {"C": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=3, random_state=0) assert [x for x in sampler] == [x for x in sampler] if sp_version >= (0, 16): param_distributions = {"C": uniform(0, 1)} sampler = ParameterSampler(param_distributions=param_distributions, n_iter=10, random_state=0) assert [x for x in sampler] == [x for x in sampler] def check_cv_results_array_types(search, param_keys, score_keys): # Check if the search `cv_results`'s array are of correct types cv_results = search.cv_results_ assert all(isinstance(cv_results[param], np.ma.MaskedArray) for param in param_keys) assert all(cv_results[key].dtype == object for key in param_keys) assert not any(isinstance(cv_results[key], np.ma.MaskedArray) for key in score_keys) assert all(cv_results[key].dtype == np.float64 for key in score_keys if not key.startswith('rank')) scorer_keys = search.scorer_.keys() if search.multimetric_ else ['score'] for key in scorer_keys: assert cv_results['rank_test_%s' % key].dtype == np.int32 def check_cv_results_keys(cv_results, param_keys, score_keys, n_cand): # Test the search.cv_results_ contains all the required results assert_array_equal(sorted(cv_results.keys()), sorted(param_keys + score_keys + ('params',))) assert all(cv_results[key].shape == (n_cand,) for key in param_keys + score_keys) def test_grid_search_cv_results(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_grid_points = 6 params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]), dict(kernel=['poly', ], degree=[1, 2])] param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel') score_keys = ('mean_test_score', 'mean_train_score', 'rank_test_score', 'split0_test_score', 'split1_test_score', 'split2_test_score', 'split0_train_score', 'split1_train_score', 'split2_train_score', 'std_test_score', 'std_train_score', 'mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time') n_candidates = n_grid_points search = GridSearchCV(SVC(), cv=n_splits, param_grid=params, return_train_score=True) search.fit(X, y) cv_results = search.cv_results_ # Check if score and timing are reasonable assert all(cv_results['rank_test_score'] >= 1) assert (all(cv_results[k] >= 0) for k in score_keys if k != 'rank_test_score') assert (all(cv_results[k] <= 1) for k in score_keys if 'time' not in k and k != 'rank_test_score') # Check cv_results structure check_cv_results_array_types(search, param_keys, score_keys) check_cv_results_keys(cv_results, param_keys, score_keys, n_candidates) # Check masking cv_results = search.cv_results_ n_candidates = len(search.cv_results_['params']) assert all((cv_results['param_C'].mask[i] and cv_results['param_gamma'].mask[i] and not cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'linear') assert all((not cv_results['param_C'].mask[i] and not cv_results['param_gamma'].mask[i] and cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'rbf') def test_random_search_cv_results(): X, y = make_classification(n_samples=50, n_features=4, random_state=42) n_splits = 3 n_search_iter = 30 params = [{'kernel': ['rbf'], 'C': expon(scale=10), 'gamma': expon(scale=0.1)}, {'kernel': ['poly'], 'degree': [2, 3]}] param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel') score_keys = ('mean_test_score', 'mean_train_score', 'rank_test_score', 'split0_test_score', 'split1_test_score', 'split2_test_score', 'split0_train_score', 'split1_train_score', 'split2_train_score', 'std_test_score', 'std_train_score', 'mean_fit_time', 'std_fit_time', 'mean_score_time', 'std_score_time') n_cand = n_search_iter search = RandomizedSearchCV(SVC(), n_iter=n_search_iter, cv=n_splits, param_distributions=params, return_train_score=True) search.fit(X, y) cv_results = search.cv_results_ # Check results structure check_cv_results_array_types(search, param_keys, score_keys) check_cv_results_keys(cv_results, param_keys, score_keys, n_cand) n_candidates = len(search.cv_results_['params']) assert all((cv_results['param_C'].mask[i] and cv_results['param_gamma'].mask[i] and not cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'linear') assert all((not cv_results['param_C'].mask[i] and not cv_results['param_gamma'].mask[i] and cv_results['param_degree'].mask[i]) for i in range(n_candidates) if cv_results['param_kernel'][i] == 'rbf') @pytest.mark.parametrize( "SearchCV, specialized_params", [(GridSearchCV, {'param_grid': {'C': [1, 10]}}), (RandomizedSearchCV, {'param_distributions': {'C': [1, 10]}, 'n_iter': 2})] ) def test_search_default_iid(SearchCV, specialized_params): # Test the IID parameter TODO: Clearly this test does something else??? # noise-free simple 2d-data X, y = make_blobs(centers=[[0, 0], [1, 0], [0, 1], [1, 1]], random_state=0, cluster_std=0.1, shuffle=False, n_samples=80) # split dataset into two folds that are not iid # first one contains data of all 4 blobs, second only from two. mask = np.ones(X.shape[0], dtype=np.bool) mask[np.where(y == 1)[0][::2]] = 0 mask[

np.where(y == 2)

numpy.where

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(

np.linspace(0.95 * np.pi, 1.55 * np.pi, 101)

numpy.linspace

from abc import ABCMeta, abstractmethod import os from vmaf.tools.misc import make_absolute_path, run_process from vmaf.tools.stats import ListStats __copyright__ = "Copyright 2016-2018, Netflix, Inc." __license__ = "Apache, Version 2.0" import re import numpy as np import ast from vmaf import ExternalProgramCaller, to_list from vmaf.config import VmafConfig, VmafExternalConfig from vmaf.core.executor import Executor from vmaf.core.result import Result from vmaf.tools.reader import YuvReader class FeatureExtractor(Executor): """ FeatureExtractor takes in a list of assets, and run feature extraction on them, and return a list of corresponding results. A FeatureExtractor must specify a unique type and version combination (by the TYPE and VERSION attribute), so that the Result generated by it can be identified. A derived class of FeatureExtractor must: 1) Override TYPE and VERSION 2) Override _generate_result(self, asset), which call a command-line executable and generate feature scores in a log file. 3) Override _get_feature_scores(self, asset), which read the feature scores from the log file, and return the scores in a dictionary format. For an example, follow VmafFeatureExtractor. """ __metaclass__ = ABCMeta @property @abstractmethod def ATOM_FEATURES(self): raise NotImplementedError def _read_result(self, asset): result = {} result.update(self._get_feature_scores(asset)) executor_id = self.executor_id return Result(asset, executor_id, result) @classmethod def get_scores_key(cls, atom_feature): return "{type}_{atom_feature}_scores".format( type=cls.TYPE, atom_feature=atom_feature) @classmethod def get_score_key(cls, atom_feature): return "{type}_{atom_feature}_score".format( type=cls.TYPE, atom_feature=atom_feature) def _get_feature_scores(self, asset): # routine to read the feature scores from the log file, and return # the scores in a dictionary format. log_file_path = self._get_log_file_path(asset) atom_feature_scores_dict = {} atom_feature_idx_dict = {} for atom_feature in self.ATOM_FEATURES: atom_feature_scores_dict[atom_feature] = [] atom_feature_idx_dict[atom_feature] = 0 with open(log_file_path, 'rt') as log_file: for line in log_file.readlines(): for atom_feature in self.ATOM_FEATURES: re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature) mo = re.match(re_template, line) if mo: cur_idx = int(mo.group(1)) assert cur_idx == atom_feature_idx_dict[atom_feature] # parse value, allowing NaN and inf val = float(mo.group(2)) if np.isnan(val) or np.isinf(val): val = None atom_feature_scores_dict[atom_feature].append(val) atom_feature_idx_dict[atom_feature] += 1 continue len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]]) assert len_score != 0 for atom_feature in self.ATOM_FEATURES[1:]: assert len_score == len(atom_feature_scores_dict[atom_feature]), \ "Feature data possibly corrupt. Run cleanup script and try again." feature_result = {} for atom_feature in self.ATOM_FEATURES: scores_key = self.get_scores_key(atom_feature) feature_result[scores_key] = atom_feature_scores_dict[atom_feature] return feature_result class VmafFeatureExtractor(FeatureExtractor): TYPE = "VMAF_feature" # VERSION = '0.1' # vmaf_study; Anush's VIF fix # VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr # VERSION = '0.2.1' # expose vif num/den of each scale # VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case # VERSION = '0.2.2b' # expose adm_den/num_scalex # VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef # VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step # VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2 VERSION = '0.2.4c' # Modify by moving motion2 to c code ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2', 'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr', 'vif_num_scale0', 'vif_den_scale0', 'vif_num_scale1', 'vif_den_scale1', 'vif_num_scale2', 'vif_den_scale2', 'vif_num_scale3', 'vif_den_scale3', 'adm_num_scale0', 'adm_den_scale0', 'adm_num_scale1', 'adm_den_scale1', 'adm_num_scale2', 'adm_den_scale2', 'adm_num_scale3', 'adm_den_scale3', ] DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3', 'vif2', 'adm2', 'adm3', 'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3', ] ADM2_CONSTANT = 0 ADM_SCALE_CONSTANT = 0 def _generate_result(self, asset): # routine to call the command-line executable and generate feature # scores in the log file. quality_width, quality_height = asset.quality_width_height log_file_path = self._get_log_file_path(asset) yuv_type=self._get_workfile_yuv_type(asset) ref_path=asset.ref_workfile_path dis_path=asset.dis_workfile_path w=quality_width h=quality_height logger = self.logger ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger) @classmethod def _post_process_result(cls, result): # override Executor._post_process_result result = super(VmafFeatureExtractor, cls)._post_process_result(result) # adm2 = # (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT) adm2_scores_key = cls.get_scores_key('adm2') adm_num_scores_key = cls.get_scores_key('adm_num') adm_den_scores_key = cls.get_scores_key('adm_den') result.result_dict[adm2_scores_key] = list( (np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) / (np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT) ) # vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3 vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0') vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0') vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1') vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1') vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2') vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2') vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3') vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3') vif_scale0_scores_key = cls.get_scores_key('vif_scale0') vif_scale1_scores_key = cls.get_scores_key('vif_scale1') vif_scale2_scores_key = cls.get_scores_key('vif_scale2') vif_scale3_scores_key = cls.get_scores_key('vif_scale3') result.result_dict[vif_scale0_scores_key] = list( (np.array(result.result_dict[vif_num_scale0_scores_key]) / np.array(result.result_dict[vif_den_scale0_scores_key])) ) result.result_dict[vif_scale1_scores_key] = list( (np.array(result.result_dict[vif_num_scale1_scores_key]) / np.array(result.result_dict[vif_den_scale1_scores_key])) ) result.result_dict[vif_scale2_scores_key] = list( (np.array(result.result_dict[vif_num_scale2_scores_key]) / np.array(result.result_dict[vif_den_scale2_scores_key])) ) result.result_dict[vif_scale3_scores_key] = list( (np.array(result.result_dict[vif_num_scale3_scores_key]) / np.array(result.result_dict[vif_den_scale3_scores_key])) ) # vif2 = # ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) + # (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0 vif_scores_key = cls.get_scores_key('vif2') result.result_dict[vif_scores_key] = list( ( (np.array(result.result_dict[vif_num_scale0_scores_key]) / np.array(result.result_dict[vif_den_scale0_scores_key])) + (np.array(result.result_dict[vif_num_scale1_scores_key]) / np.array(result.result_dict[vif_den_scale1_scores_key])) + (np.array(result.result_dict[vif_num_scale2_scores_key]) / np.array(result.result_dict[vif_den_scale2_scores_key])) + (np.array(result.result_dict[vif_num_scale3_scores_key]) / np.array(result.result_dict[vif_den_scale3_scores_key])) ) / 4.0 ) # adm_scalei = adm_num_scalei / adm_den_scalei, i = 0, 1, 2, 3 adm_num_scale0_scores_key = cls.get_scores_key('adm_num_scale0') adm_den_scale0_scores_key = cls.get_scores_key('adm_den_scale0') adm_num_scale1_scores_key = cls.get_scores_key('adm_num_scale1') adm_den_scale1_scores_key = cls.get_scores_key('adm_den_scale1') adm_num_scale2_scores_key = cls.get_scores_key('adm_num_scale2') adm_den_scale2_scores_key = cls.get_scores_key('adm_den_scale2') adm_num_scale3_scores_key = cls.get_scores_key('adm_num_scale3') adm_den_scale3_scores_key = cls.get_scores_key('adm_den_scale3') adm_scale0_scores_key = cls.get_scores_key('adm_scale0') adm_scale1_scores_key = cls.get_scores_key('adm_scale1') adm_scale2_scores_key = cls.get_scores_key('adm_scale2') adm_scale3_scores_key = cls.get_scores_key('adm_scale3') result.result_dict[adm_scale0_scores_key] = list( (np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale1_scores_key] = list( (np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale2_scores_key] = list( (np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale3_scores_key] = list( (np.array(result.result_dict[adm_num_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT) ) # adm3 = \ # (((adm_num_scale0 + ADM_SCALE_CONSTANT) / (adm_den_scale0 + ADM_SCALE_CONSTANT)) # + ((adm_num_scale1 + ADM_SCALE_CONSTANT) / (adm_den_scale1 + ADM_SCALE_CONSTANT)) # + ((adm_num_scale2 + ADM_SCALE_CONSTANT) / (adm_den_scale2 + ADM_SCALE_CONSTANT)) # + ((adm_num_scale3 + ADM_SCALE_CONSTANT) / (adm_den_scale3 + ADM_SCALE_CONSTANT))) / 4.0 adm3_scores_key = cls.get_scores_key('adm3') result.result_dict[adm3_scores_key] = list( ( ((np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)) + ((np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) / (

np.array(result.result_dict[adm_den_scale1_scores_key])

numpy.array

import copy import functools import itertools import numbers import warnings from collections import defaultdict from datetime import timedelta from distutils.version import LooseVersion from typing import ( Any, Dict, Hashable, Mapping, Optional, Sequence, Tuple, TypeVar, Union, ) import numpy as np import pandas as pd import xarray as xr # only for Dataset and DataArray from . import arithmetic, common, dtypes, duck_array_ops, indexing, nputils, ops, utils from .indexing import ( BasicIndexer, OuterIndexer, PandasIndexAdapter, VectorizedIndexer, as_indexable, ) from .npcompat import IS_NEP18_ACTIVE from .options import _get_keep_attrs from .pycompat import ( cupy_array_type, dask_array_type, integer_types, is_duck_dask_array, ) from .utils import ( OrderedSet, _default, decode_numpy_dict_values, drop_dims_from_indexers, either_dict_or_kwargs, ensure_us_time_resolution, infix_dims, is_duck_array, ) NON_NUMPY_SUPPORTED_ARRAY_TYPES = ( ( indexing.ExplicitlyIndexed, pd.Index, ) + dask_array_type + cupy_array_type ) # https://github.com/python/mypy/issues/224 BASIC_INDEXING_TYPES = integer_types + (slice,) # type: ignore VariableType = TypeVar("VariableType", bound="Variable") """Type annotation to be used when methods of Variable return self or a copy of self. When called from an instance of a subclass, e.g. IndexVariable, mypy identifies the output as an instance of the subclass. Usage:: class Variable: def f(self: VariableType, ...) -> VariableType: ... """ class MissingDimensionsError(ValueError): """Error class used when we can't safely guess a dimension name.""" # inherits from ValueError for backward compatibility # TODO: move this to an xarray.exceptions module? def as_variable(obj, name=None) -> "Union[Variable, IndexVariable]": """Convert an object into a Variable. Parameters ---------- obj : object Object to convert into a Variable. - If the object is already a Variable, return a shallow copy. - Otherwise, if the object has 'dims' and 'data' attributes, convert it into a new Variable. - If all else fails, attempt to convert the object into a Variable by unpacking it into the arguments for creating a new Variable. name : str, optional If provided: - `obj` can be a 1D array, which is assumed to label coordinate values along a dimension of this given name. - Variables with name matching one of their dimensions are converted into `IndexVariable` objects. Returns ------- var : Variable The newly created variable. """ from .dataarray import DataArray # TODO: consider extending this method to automatically handle Iris and if isinstance(obj, DataArray): # extract the primary Variable from DataArrays obj = obj.variable if isinstance(obj, Variable): obj = obj.copy(deep=False) elif isinstance(obj, tuple): try: obj = Variable(*obj) except (TypeError, ValueError) as error: # use .format() instead of % because it handles tuples consistently raise error.__class__( "Could not convert tuple of form " "(dims, data[, attrs, encoding]): " "{} to Variable.".format(obj) ) elif utils.is_scalar(obj): obj = Variable([], obj) elif isinstance(obj, (pd.Index, IndexVariable)) and obj.name is not None: obj = Variable(obj.name, obj) elif isinstance(obj, (set, dict)): raise TypeError("variable {!r} has invalid type {!r}".format(name, type(obj))) elif name is not None: data = as_compatible_data(obj) if data.ndim != 1: raise MissingDimensionsError( "cannot set variable %r with %r-dimensional data " "without explicit dimension names. Pass a tuple of " "(dims, data) instead." % (name, data.ndim) ) obj = Variable(name, data, fastpath=True) else: raise TypeError( "unable to convert object into a variable without an " "explicit list of dimensions: %r" % obj ) if name is not None and name in obj.dims: # convert the Variable into an Index if obj.ndim != 1: raise MissingDimensionsError( "%r has more than 1-dimension and the same name as one of its " "dimensions %r. xarray disallows such variables because they " "conflict with the coordinates used to label " "dimensions." % (name, obj.dims) ) obj = obj.to_index_variable() return obj def _maybe_wrap_data(data): """ Put pandas.Index and numpy.ndarray arguments in adapter objects to ensure they can be indexed properly. NumpyArrayAdapter, PandasIndexAdapter and LazilyOuterIndexedArray should all pass through unmodified. """ if isinstance(data, pd.Index): return PandasIndexAdapter(data) return data def _possibly_convert_objects(values): """Convert arrays of datetime.datetime and datetime.timedelta objects into datetime64 and timedelta64, according to the pandas convention. Also used for validating that datetime64 and timedelta64 objects are within the valid date range for ns precision, as pandas will raise an error if they are not. """ return np.asarray(pd.Series(values.ravel())).reshape(values.shape) def as_compatible_data(data, fastpath=False): """Prepare and wrap data to put in a Variable. - If data does not have the necessary attributes, convert it to ndarray. - If data has dtype=datetime64, ensure that it has ns precision. If it's a pandas.Timestamp, convert it to datetime64. - If data is already a pandas or xarray object (other than an Index), just use the values. Finally, wrap it up with an adapter if necessary. """ if fastpath and getattr(data, "ndim", 0) > 0: # can't use fastpath (yet) for scalars return _maybe_wrap_data(data) if isinstance(data, Variable): return data.data if isinstance(data, NON_NUMPY_SUPPORTED_ARRAY_TYPES): return _maybe_wrap_data(data) if isinstance(data, tuple): data = utils.to_0d_object_array(data) if isinstance(data, pd.Timestamp): # TODO: convert, handle datetime objects, too data = np.datetime64(data.value, "ns") if isinstance(data, timedelta): data = np.timedelta64(getattr(data, "value", data), "ns") # we don't want nested self-described arrays data = getattr(data, "values", data) if isinstance(data, np.ma.MaskedArray): mask = np.ma.getmaskarray(data) if mask.any(): dtype, fill_value = dtypes.maybe_promote(data.dtype) data = np.asarray(data, dtype=dtype) data[mask] = fill_value else: data = np.asarray(data) if not isinstance(data, np.ndarray): if hasattr(data, "__array_function__"): if IS_NEP18_ACTIVE: return data else: raise TypeError( "Got an NumPy-like array type providing the " "__array_function__ protocol but NEP18 is not enabled. " "Check that numpy >= v1.16 and that the environment " 'variable "NUMPY_EXPERIMENTAL_ARRAY_FUNCTION" is set to ' '"1"' ) # validate whether the data is valid data types. data = np.asarray(data) if isinstance(data, np.ndarray): if data.dtype.kind == "O": data = _possibly_convert_objects(data) elif data.dtype.kind == "M": data = _possibly_convert_objects(data) elif data.dtype.kind == "m": data = _possibly_convert_objects(data) return _maybe_wrap_data(data) def _as_array_or_item(data): """Return the given values as a numpy array, or as an individual item if it's a 0d datetime64 or timedelta64 array. Importantly, this function does not copy data if it is already an ndarray - otherwise, it will not be possible to update Variable values in place. This function mostly exists because 0-dimensional ndarrays with dtype=datetime64 are broken :( https://github.com/numpy/numpy/issues/4337 https://github.com/numpy/numpy/issues/7619 TODO: remove this (replace with np.asarray) once these issues are fixed """ if isinstance(data, cupy_array_type): data = data.get() else: data = np.asarray(data) if data.ndim == 0: if data.dtype.kind == "M": data = np.datetime64(data, "ns") elif data.dtype.kind == "m": data = np.timedelta64(data, "ns") return data class Variable( common.AbstractArray, arithmetic.SupportsArithmetic, utils.NdimSizeLenMixin ): """A netcdf-like variable consisting of dimensions, data and attributes which describe a single Array. A single Variable object is not fully described outside the context of its parent Dataset (if you want such a fully described object, use a DataArray instead). The main functional difference between Variables and numpy arrays is that numerical operations on Variables implement array broadcasting by dimension name. For example, adding an Variable with dimensions `('time',)` to another Variable with dimensions `('space',)` results in a new Variable with dimensions `('time', 'space')`. Furthermore, numpy reduce operations like ``mean`` or ``sum`` are overwritten to take a "dimension" argument instead of an "axis". Variables are light-weight objects used as the building block for datasets. They are more primitive objects, so operations with them provide marginally higher performance than using DataArrays. However, manipulating data in the form of a Dataset or DataArray should almost always be preferred, because they can use more complete metadata in context of coordinate labels. """ __slots__ = ("_dims", "_data", "_attrs", "_encoding") def __init__(self, dims, data, attrs=None, encoding=None, fastpath=False): """ Parameters ---------- dims : str or sequence of str Name(s) of the the data dimension(s). Must be either a string (only for 1D data) or a sequence of strings with length equal to the number of dimensions. data : array_like Data array which supports numpy-like data access. attrs : dict_like or None, optional Attributes to assign to the new variable. If None (default), an empty attribute dictionary is initialized. encoding : dict_like or None, optional Dictionary specifying how to encode this array's data into a serialized format like netCDF4. Currently used keys (for netCDF) include '_FillValue', 'scale_factor', 'add_offset' and 'dtype'. Well-behaved code to serialize a Variable should ignore unrecognized encoding items. """ self._data = as_compatible_data(data, fastpath=fastpath) self._dims = self._parse_dimensions(dims) self._attrs = None self._encoding = None if attrs is not None: self.attrs = attrs if encoding is not None: self.encoding = encoding @property def dtype(self): return self._data.dtype @property def shape(self): return self._data.shape @property def nbytes(self): return self.size * self.dtype.itemsize @property def _in_memory(self): return isinstance(self._data, (np.ndarray, np.number, PandasIndexAdapter)) or ( isinstance(self._data, indexing.MemoryCachedArray) and isinstance(self._data.array, indexing.NumpyIndexingAdapter) ) @property def data(self): if is_duck_array(self._data): return self._data else: return self.values @data.setter def data(self, data): data = as_compatible_data(data) if data.shape != self.shape: raise ValueError( f"replacement data must match the Variable's shape. " f"replacement data has shape {data.shape}; Variable has shape {self.shape}" ) self._data = data def astype( self: VariableType, dtype, *, order=None, casting=None, subok=None, copy=None, keep_attrs=True, ) -> VariableType: """ Copy of the Variable object, with data cast to a specified type. Parameters ---------- dtype : str or dtype Typecode or data-type to which the array is cast. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout order of the result. ‘C’ means C order, ‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to the order the array elements appear in memory as possible. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array. copy : bool, optional By default, astype always returns a newly allocated array. If this is set to False and the `dtype` requirement is satisfied, the input array is returned instead of a copy. keep_attrs : bool, optional By default, astype keeps attributes. Set to False to remove attributes in the returned object. Returns ------- out : same as object New object with data cast to the specified type. Notes ----- The ``order``, ``casting``, ``subok`` and ``copy`` arguments are only passed through to the ``astype`` method of the underlying array when a value different than ``None`` is supplied. Make sure to only supply these arguments if the underlying array class supports them. See also -------- numpy.ndarray.astype dask.array.Array.astype sparse.COO.astype """ from .computation import apply_ufunc kwargs = dict(order=order, casting=casting, subok=subok, copy=copy) kwargs = {k: v for k, v in kwargs.items() if v is not None} return apply_ufunc( duck_array_ops.astype, self, dtype, kwargs=kwargs, keep_attrs=keep_attrs, dask="allowed", ) def load(self, **kwargs): """Manually trigger loading of this variable's data from disk or a remote source into memory and return this variable. Normally, it should not be necessary to call this method in user code, because all xarray functions should either work on deferred data or load data automatically. Parameters ---------- **kwargs : dict Additional keyword arguments passed on to ``dask.array.compute``. See Also -------- dask.array.compute """ if is_duck_dask_array(self._data): self._data = as_compatible_data(self._data.compute(**kwargs)) elif not is_duck_array(self._data): self._data = np.asarray(self._data) return self def compute(self, **kwargs): """Manually trigger loading of this variable's data from disk or a remote source into memory and return a new variable. The original is left unaltered. Normally, it should not be necessary to call this method in user code, because all xarray functions should either work on deferred data or load data automatically. Parameters ---------- **kwargs : dict Additional keyword arguments passed on to ``dask.array.compute``. See Also -------- dask.array.compute """ new = self.copy(deep=False) return new.load(**kwargs) def __dask_tokenize__(self): # Use v.data, instead of v._data, in order to cope with the wrappers # around NetCDF and the like from dask.base import normalize_token return normalize_token((type(self), self._dims, self.data, self._attrs)) def __dask_graph__(self): if is_duck_dask_array(self._data): return self._data.__dask_graph__() else: return None def __dask_keys__(self): return self._data.__dask_keys__() def __dask_layers__(self): return self._data.__dask_layers__() @property def __dask_optimize__(self): return self._data.__dask_optimize__ @property def __dask_scheduler__(self): return self._data.__dask_scheduler__ def __dask_postcompute__(self): array_func, array_args = self._data.__dask_postcompute__() return ( self._dask_finalize, (array_func, array_args, self._dims, self._attrs, self._encoding), ) def __dask_postpersist__(self): array_func, array_args = self._data.__dask_postpersist__() return ( self._dask_finalize, (array_func, array_args, self._dims, self._attrs, self._encoding), ) @staticmethod def _dask_finalize(results, array_func, array_args, dims, attrs, encoding): data = array_func(results, *array_args) return Variable(dims, data, attrs=attrs, encoding=encoding) @property def values(self): """The variable's data as a numpy.ndarray""" return _as_array_or_item(self._data) @values.setter def values(self, values): self.data = values def to_base_variable(self): """Return this variable as a base xarray.Variable""" return Variable( self.dims, self._data, self._attrs, encoding=self._encoding, fastpath=True ) to_variable = utils.alias(to_base_variable, "to_variable") def to_index_variable(self): """Return this variable as an xarray.IndexVariable""" return IndexVariable( self.dims, self._data, self._attrs, encoding=self._encoding, fastpath=True ) to_coord = utils.alias(to_index_variable, "to_coord") def to_index(self): """Convert this variable to a pandas.Index""" return self.to_index_variable().to_index() def to_dict(self, data=True): """Dictionary representation of variable.""" item = {"dims": self.dims, "attrs": decode_numpy_dict_values(self.attrs)} if data: item["data"] = ensure_us_time_resolution(self.values).tolist() else: item.update({"dtype": str(self.dtype), "shape": self.shape}) return item @property def dims(self): """Tuple of dimension names with which this variable is associated.""" return self._dims @dims.setter def dims(self, value): self._dims = self._parse_dimensions(value) def _parse_dimensions(self, dims): if isinstance(dims, str): dims = (dims,) dims = tuple(dims) if len(dims) != self.ndim: raise ValueError( "dimensions %s must have the same length as the " "number of data dimensions, ndim=%s" % (dims, self.ndim) ) return dims def _item_key_to_tuple(self, key): if utils.is_dict_like(key): return tuple(key.get(dim, slice(None)) for dim in self.dims) else: return key def _broadcast_indexes(self, key): """Prepare an indexing key for an indexing operation. Parameters ----------- key: int, slice, array-like, dict or tuple of integer, slice and array-like Any valid input for indexing. Returns ------- dims : tuple Dimension of the resultant variable. indexers : IndexingTuple subclass Tuple of integer, array-like, or slices to use when indexing self._data. The type of this argument indicates the type of indexing to perform, either basic, outer or vectorized. new_order : Optional[Sequence[int]] Optional reordering to do on the result of indexing. If not None, the first len(new_order) indexing should be moved to these positions. """ key = self._item_key_to_tuple(key) # key is a tuple # key is a tuple of full size key = indexing.expanded_indexer(key, self.ndim) # Convert a scalar Variable to an integer key = tuple( k.data.item() if isinstance(k, Variable) and k.ndim == 0 else k for k in key ) # Convert a 0d-array to an integer key = tuple( k.item() if isinstance(k, np.ndarray) and k.ndim == 0 else k for k in key ) if all(isinstance(k, BASIC_INDEXING_TYPES) for k in key): return self._broadcast_indexes_basic(key) self._validate_indexers(key) # Detect it can be mapped as an outer indexer # If all key is unlabeled, or # key can be mapped as an OuterIndexer. if all(not isinstance(k, Variable) for k in key): return self._broadcast_indexes_outer(key) # If all key is 1-dimensional and there are no duplicate labels, # key can be mapped as an OuterIndexer. dims = [] for k, d in zip(key, self.dims): if isinstance(k, Variable): if len(k.dims) > 1: return self._broadcast_indexes_vectorized(key) dims.append(k.dims[0]) elif not isinstance(k, integer_types): dims.append(d) if len(set(dims)) == len(dims): return self._broadcast_indexes_outer(key) return self._broadcast_indexes_vectorized(key) def _broadcast_indexes_basic(self, key): dims = tuple( dim for k, dim in zip(key, self.dims) if not isinstance(k, integer_types) ) return dims, BasicIndexer(key), None def _validate_indexers(self, key): """ Make sanity checks """ for dim, k in zip(self.dims, key): if isinstance(k, BASIC_INDEXING_TYPES): pass else: if not isinstance(k, Variable): k = np.asarray(k) if k.ndim > 1: raise IndexError( "Unlabeled multi-dimensional array cannot be " "used for indexing: {}".format(k) ) if k.dtype.kind == "b": if self.shape[self.get_axis_num(dim)] != len(k): raise IndexError( "Boolean array size {:d} is used to index array " "with shape {:s}.".format(len(k), str(self.shape)) ) if k.ndim > 1: raise IndexError( "{}-dimensional boolean indexing is " "not supported. ".format(k.ndim) ) if getattr(k, "dims", (dim,)) != (dim,): raise IndexError( "Boolean indexer should be unlabeled or on the " "same dimension to the indexed array. Indexer is " "on {:s} but the target dimension is {:s}.".format( str(k.dims), dim ) ) def _broadcast_indexes_outer(self, key): dims = tuple( k.dims[0] if isinstance(k, Variable) else dim for k, dim in zip(key, self.dims) if not isinstance(k, integer_types) ) new_key = [] for k in key: if isinstance(k, Variable): k = k.data if not isinstance(k, BASIC_INDEXING_TYPES): k = np.asarray(k) if k.size == 0: # Slice by empty list; numpy could not infer the dtype k = k.astype(int) elif k.dtype.kind == "b": (k,) = np.nonzero(k) new_key.append(k) return dims, OuterIndexer(tuple(new_key)), None def _nonzero(self): """ Equivalent numpy's nonzero but returns a tuple of Varibles. """ # TODO we should replace dask's native nonzero # after https://github.com/dask/dask/issues/1076 is implemented. nonzeros = np.nonzero(self.data) return tuple(Variable((dim), nz) for nz, dim in zip(nonzeros, self.dims)) def _broadcast_indexes_vectorized(self, key): variables = [] out_dims_set = OrderedSet() for dim, value in zip(self.dims, key): if isinstance(value, slice): out_dims_set.add(dim) else: variable = ( value if isinstance(value, Variable) else as_variable(value, name=dim) ) if variable.dtype.kind == "b": # boolean indexing case (variable,) = variable._nonzero() variables.append(variable) out_dims_set.update(variable.dims) variable_dims = set() for variable in variables: variable_dims.update(variable.dims) slices = [] for i, (dim, value) in enumerate(zip(self.dims, key)): if isinstance(value, slice): if dim in variable_dims: # We only convert slice objects to variables if they share # a dimension with at least one other variable. Otherwise, # we can equivalently leave them as slices aknd transpose # the result. This is significantly faster/more efficient # for most array backends. values = np.arange(*value.indices(self.sizes[dim])) variables.insert(i - len(slices), Variable((dim,), values)) else: slices.append((i, value)) try: variables = _broadcast_compat_variables(*variables) except ValueError: raise IndexError(f"Dimensions of indexers mismatch: {key}") out_key = [variable.data for variable in variables] out_dims = tuple(out_dims_set) slice_positions = set() for i, value in slices: out_key.insert(i, value) new_position = out_dims.index(self.dims[i]) slice_positions.add(new_position) if slice_positions: new_order = [i for i in range(len(out_dims)) if i not in slice_positions] else: new_order = None return out_dims, VectorizedIndexer(tuple(out_key)), new_order def __getitem__(self: VariableType, key) -> VariableType: """Return a new Variable object whose contents are consistent with getting the provided key from the underlying data. NB. __getitem__ and __setitem__ implement xarray-style indexing, where if keys are unlabeled arrays, we index the array orthogonally with them. If keys are labeled array (such as Variables), they are broadcasted with our usual scheme and then the array is indexed with the broadcasted key, like numpy's fancy indexing. If you really want to do indexing like `x[x > 0]`, manipulate the numpy array `x.values` directly. """ dims, indexer, new_order = self._broadcast_indexes(key) data = as_indexable(self._data)[indexer] if new_order: data = duck_array_ops.moveaxis(data, range(len(new_order)), new_order) return self._finalize_indexing_result(dims, data) def _finalize_indexing_result(self: VariableType, dims, data) -> VariableType: """Used by IndexVariable to return IndexVariable objects when possible.""" return type(self)(dims, data, self._attrs, self._encoding, fastpath=True) def _getitem_with_mask(self, key, fill_value=dtypes.NA): """Index this Variable with -1 remapped to fill_value.""" # TODO(shoyer): expose this method in public API somewhere (isel?) and # use it for reindex. # TODO(shoyer): add a sanity check that all other integers are # non-negative # TODO(shoyer): add an optimization, remapping -1 to an adjacent value # that is actually indexed rather than mapping it to the last value # along each axis. if fill_value is dtypes.NA: fill_value = dtypes.get_fill_value(self.dtype) dims, indexer, new_order = self._broadcast_indexes(key) if self.size: if is_duck_dask_array(self._data): # dask's indexing is faster this way; also vindex does not # support negative indices yet: # https://github.com/dask/dask/pull/2967 actual_indexer = indexing.posify_mask_indexer(indexer) else: actual_indexer = indexer data = as_indexable(self._data)[actual_indexer] mask = indexing.create_mask(indexer, self.shape, data) # we need to invert the mask in order to pass data first. This helps # pint to choose the correct unit # TODO: revert after https://github.com/hgrecco/pint/issues/1019 is fixed data = duck_array_ops.where(np.logical_not(mask), data, fill_value) else: # array cannot be indexed along dimensions of size 0, so just # build the mask directly instead. mask = indexing.create_mask(indexer, self.shape) data = np.broadcast_to(fill_value, getattr(mask, "shape", ())) if new_order: data = duck_array_ops.moveaxis(data, range(len(new_order)), new_order) return self._finalize_indexing_result(dims, data) def __setitem__(self, key, value): """__setitem__ is overloaded to access the underlying numpy values with orthogonal indexing. See __getitem__ for more details. """ dims, index_tuple, new_order = self._broadcast_indexes(key) if not isinstance(value, Variable): value = as_compatible_data(value) if value.ndim > len(dims): raise ValueError( "shape mismatch: value array of shape %s could not be " "broadcast to indexing result with %s dimensions" % (value.shape, len(dims)) ) if value.ndim == 0: value = Variable((), value) else: value = Variable(dims[-value.ndim :], value) # broadcast to become assignable value = value.set_dims(dims).data if new_order: value = duck_array_ops.asarray(value) value = value[(len(dims) - value.ndim) * (np.newaxis,) + (Ellipsis,)] value = duck_array_ops.moveaxis(value, new_order, range(len(new_order))) indexable = as_indexable(self._data) indexable[index_tuple] = value @property def attrs(self) -> Dict[Hashable, Any]: """Dictionary of local attributes on this variable.""" if self._attrs is None: self._attrs = {} return self._attrs @attrs.setter def attrs(self, value: Mapping[Hashable, Any]) -> None: self._attrs = dict(value) @property def encoding(self): """Dictionary of encodings on this variable.""" if self._encoding is None: self._encoding = {} return self._encoding @encoding.setter def encoding(self, value): try: self._encoding = dict(value) except ValueError: raise ValueError("encoding must be castable to a dictionary") def copy(self, deep=True, data=None): """Returns a copy of this object. If `deep=True`, the data array is loaded into memory and copied onto the new object. Dimensions, attributes and encodings are always copied. Use `data` to create a new object with the same structure as original but entirely new data. Parameters ---------- deep : bool, optional Whether the data array is loaded into memory and copied onto the new object. Default is True. data : array_like, optional Data to use in the new object. Must have same shape as original. When `data` is used, `deep` is ignored. Returns ------- object : Variable New object with dimensions, attributes, encodings, and optionally data copied from original. Examples -------- Shallow copy versus deep copy >>> var = xr.Variable(data=[1, 2, 3], dims="x") >>> var.copy() <xarray.Variable (x: 3)> array([1, 2, 3]) >>> var_0 = var.copy(deep=False) >>> var_0[0] = 7 >>> var_0 <xarray.Variable (x: 3)> array([7, 2, 3]) >>> var <xarray.Variable (x: 3)> array([7, 2, 3]) Changing the data using the ``data`` argument maintains the structure of the original object, but with the new data. Original object is unaffected. >>> var.copy(data=[0.1, 0.2, 0.3]) <xarray.Variable (x: 3)> array([0.1, 0.2, 0.3]) >>> var <xarray.Variable (x: 3)> array([7, 2, 3]) See Also -------- pandas.DataFrame.copy """ if data is None: data = self._data if isinstance(data, indexing.MemoryCachedArray): # don't share caching between copies data = indexing.MemoryCachedArray(data.array) if deep: data = copy.deepcopy(data) else: data = as_compatible_data(data) if self.shape != data.shape: raise ValueError( "Data shape {} must match shape of object {}".format( data.shape, self.shape ) ) # note: # dims is already an immutable tuple # attributes and encoding will be copied when the new Array is created return self._replace(data=data) def _replace( self, dims=_default, data=_default, attrs=_default, encoding=_default ) -> "Variable": if dims is _default: dims = copy.copy(self._dims) if data is _default: data = copy.copy(self.data) if attrs is _default: attrs = copy.copy(self._attrs) if encoding is _default: encoding = copy.copy(self._encoding) return type(self)(dims, data, attrs, encoding, fastpath=True) def __copy__(self): return self.copy(deep=False) def __deepcopy__(self, memo=None): # memo does nothing but is required for compatibility with # copy.deepcopy return self.copy(deep=True) # mutable objects should not be hashable # https://github.com/python/mypy/issues/4266 __hash__ = None # type: ignore @property def chunks(self): """Block dimensions for this array's data or None if it's not a dask array. """ return getattr(self._data, "chunks", None) _array_counter = itertools.count() def chunk(self, chunks={}, name=None, lock=False): """Coerce this array's data into a dask arrays with the given chunks. If this variable is a non-dask array, it will be converted to dask array. If it's a dask array, it will be rechunked to the given chunk sizes. If neither chunks is not provided for one or more dimensions, chunk sizes along that dimension will not be updated; non-dask arrays will be converted into dask arrays with a single block. Parameters ---------- chunks : int, tuple or dict, optional Chunk sizes along each dimension, e.g., ``5``, ``(5, 5)`` or ``{'x': 5, 'y': 5}``. name : str, optional Used to generate the name for this array in the internal dask graph. Does not need not be unique. lock : optional Passed on to :py:func:`dask.array.from_array`, if the array is not already as dask array. Returns ------- chunked : xarray.Variable """ import dask import dask.array as da if chunks is None: warnings.warn( "None value for 'chunks' is deprecated. " "It will raise an error in the future. Use instead '{}'", category=FutureWarning, ) chunks = {} if utils.is_dict_like(chunks): chunks = {self.get_axis_num(dim): chunk for dim, chunk in chunks.items()} data = self._data if is_duck_dask_array(data): data = data.rechunk(chunks) else: if isinstance(data, indexing.ExplicitlyIndexed): # Unambiguously handle array storage backends (like NetCDF4 and h5py) # that can't handle general array indexing. For example, in netCDF4 you # can do "outer" indexing along two dimensions independent, which works # differently from how NumPy handles it. # da.from_array works by using lazy indexing with a tuple of slices. # Using OuterIndexer is a pragmatic choice: dask does not yet handle # different indexing types in an explicit way: # https://github.com/dask/dask/issues/2883 data = indexing.ImplicitToExplicitIndexingAdapter( data, indexing.OuterIndexer ) if LooseVersion(dask.__version__) < "2.0.0": kwargs = {} else: # All of our lazily loaded backend array classes should use NumPy # array operations. kwargs = {"meta": np.ndarray} else: kwargs = {} if utils.is_dict_like(chunks): chunks = tuple(chunks.get(n, s) for n, s in enumerate(self.shape)) data = da.from_array(data, chunks, name=name, lock=lock, **kwargs) return type(self)(self.dims, data, self._attrs, self._encoding, fastpath=True) def _as_sparse(self, sparse_format=_default, fill_value=dtypes.NA): """ use sparse-array as backend. """ import sparse # TODO: what to do if dask-backended? if fill_value is dtypes.NA: dtype, fill_value = dtypes.maybe_promote(self.dtype) else: dtype = dtypes.result_type(self.dtype, fill_value) if sparse_format is _default: sparse_format = "coo" try: as_sparse = getattr(sparse, f"as_{sparse_format.lower()}") except AttributeError: raise ValueError(f"{sparse_format} is not a valid sparse format") data = as_sparse(self.data.astype(dtype), fill_value=fill_value) return self._replace(data=data) def _to_dense(self): """ Change backend from sparse to np.array """ if hasattr(self._data, "todense"): return self._replace(data=self._data.todense()) return self.copy(deep=False) def isel( self: VariableType, indexers: Mapping[Hashable, Any] = None, missing_dims: str = "raise", **indexers_kwargs: Any, ) -> VariableType: """Return a new array indexed along the specified dimension(s). Parameters ---------- **indexers : {dim: indexer, ...} Keyword arguments with names matching dimensions and values given by integers, slice objects or arrays. missing_dims : {"raise", "warn", "ignore"}, default: "raise" What to do if dimensions that should be selected from are not present in the DataArray: - "raise": raise an exception - "warning": raise a warning, and ignore the missing dimensions - "ignore": ignore the missing dimensions Returns ------- obj : Array object A new Array with the selected data and dimensions. In general, the new variable's data will be a view of this variable's data, unless numpy fancy indexing was triggered by using an array indexer, in which case the data will be a copy. """ indexers = either_dict_or_kwargs(indexers, indexers_kwargs, "isel") indexers = drop_dims_from_indexers(indexers, self.dims, missing_dims) key = tuple(indexers.get(dim, slice(None)) for dim in self.dims) return self[key] def squeeze(self, dim=None): """Return a new object with squeezed data. Parameters ---------- dim : None or str or tuple of str, optional Selects a subset of the length one dimensions. If a dimension is selected with length greater than one, an error is raised. If None, all length one dimensions are squeezed. Returns ------- squeezed : same type as caller This object, but with with all or a subset of the dimensions of length 1 removed. See Also -------- numpy.squeeze """ dims = common.get_squeeze_dims(self, dim) return self.isel({d: 0 for d in dims}) def _shift_one_dim(self, dim, count, fill_value=dtypes.NA): axis = self.get_axis_num(dim) if count > 0: keep = slice(None, -count) elif count < 0: keep = slice(-count, None) else: keep = slice(None) trimmed_data = self[(slice(None),) * axis + (keep,)].data if fill_value is dtypes.NA: dtype, fill_value = dtypes.maybe_promote(self.dtype) else: dtype = self.dtype width = min(abs(count), self.shape[axis]) dim_pad = (width, 0) if count >= 0 else (0, width) pads = [(0, 0) if d != dim else dim_pad for d in self.dims] data = duck_array_ops.pad( trimmed_data.astype(dtype), pads, mode="constant", constant_values=fill_value, ) if is_duck_dask_array(data): # chunked data should come out with the same chunks; this makes # it feasible to combine shifted and unshifted data # TODO: remove this once dask.array automatically aligns chunks data = data.rechunk(self.data.chunks) return type(self)(self.dims, data, self._attrs, fastpath=True) def shift(self, shifts=None, fill_value=dtypes.NA, **shifts_kwargs): """ Return a new Variable with shifted data. Parameters ---------- shifts : mapping of the form {dim: offset} Integer offset to shift along each of the given dimensions. Positive offsets shift to the right; negative offsets shift to the left. fill_value: scalar, optional Value to use for newly missing values **shifts_kwargs The keyword arguments form of ``shifts``. One of shifts or shifts_kwargs must be provided. Returns ------- shifted : Variable Variable with the same dimensions and attributes but shifted data. """ shifts = either_dict_or_kwargs(shifts, shifts_kwargs, "shift") result = self for dim, count in shifts.items(): result = result._shift_one_dim(dim, count, fill_value=fill_value) return result def _pad_options_dim_to_index( self, pad_option: Mapping[Hashable, Union[int, Tuple[int, int]]], fill_with_shape=False, ): if fill_with_shape: return [ (n, n) if d not in pad_option else pad_option[d] for d, n in zip(self.dims, self.data.shape) ] return [(0, 0) if d not in pad_option else pad_option[d] for d in self.dims] def pad( self, pad_width: Mapping[Hashable, Union[int, Tuple[int, int]]] = None, mode: str = "constant", stat_length: Union[ int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]] ] = None, constant_values: Union[ int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]] ] = None, end_values: Union[ int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]] ] = None, reflect_type: str = None, **pad_width_kwargs: Any, ): """ Return a new Variable with padded data. Parameters ---------- pad_width : mapping of hashable to tuple of int Mapping with the form of {dim: (pad_before, pad_after)} describing the number of values padded along each dimension. {dim: pad} is a shortcut for pad_before = pad_after = pad mode : str, default: "constant" See numpy / Dask docs stat_length : int, tuple or mapping of hashable to tuple Used in 'maximum', 'mean', 'median', and 'minimum'. Number of values at edge of each axis used to calculate the statistic value. constant_values : scalar, tuple or mapping of hashable to tuple Used in 'constant'. The values to set the padded values for each axis. end_values : scalar, tuple or mapping of hashable to tuple Used in 'linear_ramp'. The values used for the ending value of the linear_ramp and that will form the edge of the padded array. reflect_type : {"even", "odd"}, optional Used in "reflect", and "symmetric". The "even" style is the default with an unaltered reflection around the edge value. For the "odd" style, the extended part of the array is created by subtracting the reflected values from two times the edge value. **pad_width_kwargs One of pad_width or pad_width_kwargs must be provided. Returns ------- padded : Variable Variable with the same dimensions and attributes but padded data. """ pad_width = either_dict_or_kwargs(pad_width, pad_width_kwargs, "pad") # change default behaviour of pad with mode constant if mode == "constant" and ( constant_values is None or constant_values is dtypes.NA ): dtype, constant_values = dtypes.maybe_promote(self.dtype) else: dtype = self.dtype # create pad_options_kwargs, numpy requires only relevant kwargs to be nonempty if isinstance(stat_length, dict): stat_length = self._pad_options_dim_to_index( stat_length, fill_with_shape=True ) if isinstance(constant_values, dict): constant_values = self._pad_options_dim_to_index(constant_values) if isinstance(end_values, dict): end_values = self._pad_options_dim_to_index(end_values) # workaround for bug in Dask's default value of stat_length https://github.com/dask/dask/issues/5303 if stat_length is None and mode in ["maximum", "mean", "median", "minimum"]: stat_length = [(n, n) for n in self.data.shape] # type: ignore # change integer values to a tuple of two of those values and change pad_width to index for k, v in pad_width.items(): if isinstance(v, numbers.Number): pad_width[k] = (v, v) pad_width_by_index = self._pad_options_dim_to_index(pad_width) # create pad_options_kwargs, numpy/dask requires only relevant kwargs to be nonempty pad_option_kwargs = {} if stat_length is not None: pad_option_kwargs["stat_length"] = stat_length if constant_values is not None: pad_option_kwargs["constant_values"] = constant_values if end_values is not None: pad_option_kwargs["end_values"] = end_values if reflect_type is not None: pad_option_kwargs["reflect_type"] = reflect_type # type: ignore array = duck_array_ops.pad( self.data.astype(dtype, copy=False), pad_width_by_index, mode=mode, **pad_option_kwargs, ) return type(self)(self.dims, array) def _roll_one_dim(self, dim, count): axis = self.get_axis_num(dim) count %= self.shape[axis] if count != 0: indices = [slice(-count, None), slice(None, -count)] else: indices = [slice(None)] arrays = [self[(slice(None),) * axis + (idx,)].data for idx in indices] data = duck_array_ops.concatenate(arrays, axis) if is_duck_dask_array(data): # chunked data should come out with the same chunks; this makes # it feasible to combine shifted and unshifted data # TODO: remove this once dask.array automatically aligns chunks data = data.rechunk(self.data.chunks) return type(self)(self.dims, data, self._attrs, fastpath=True) def roll(self, shifts=None, **shifts_kwargs): """ Return a new Variable with rolld data. Parameters ---------- shifts : mapping of hashable to int Integer offset to roll along each of the given dimensions. Positive offsets roll to the right; negative offsets roll to the left. **shifts_kwargs The keyword arguments form of ``shifts``. One of shifts or shifts_kwargs must be provided. Returns ------- shifted : Variable Variable with the same dimensions and attributes but rolled data. """ shifts = either_dict_or_kwargs(shifts, shifts_kwargs, "roll") result = self for dim, count in shifts.items(): result = result._roll_one_dim(dim, count) return result def transpose(self, *dims) -> "Variable": """Return a new Variable object with transposed dimensions. Parameters ---------- *dims : str, optional By default, reverse the dimensions. Otherwise, reorder the dimensions to this order. Returns ------- transposed : Variable The returned object has transposed data and dimensions with the same attributes as the original. Notes ----- This operation returns a view of this variable's data. It is lazy for dask-backed Variables but not for numpy-backed Variables. See Also -------- numpy.transpose """ if len(dims) == 0: dims = self.dims[::-1] dims = tuple(infix_dims(dims, self.dims)) axes = self.get_axis_num(dims) if len(dims) < 2 or dims == self.dims: # no need to transpose if only one dimension # or dims are in same order return self.copy(deep=False) data = as_indexable(self._data).transpose(axes) return type(self)(dims, data, self._attrs, self._encoding, fastpath=True) @property def T(self) -> "Variable": return self.transpose() def set_dims(self, dims, shape=None): """Return a new variable with given set of dimensions. This method might be used to attach new dimension(s) to variable. When possible, this operation does not copy this variable's data. Parameters ---------- dims : str or sequence of str or dict Dimensions to include on the new variable. If a dict, values are used to provide the sizes of new dimensions; otherwise, new dimensions are inserted with length 1. Returns ------- Variable """ if isinstance(dims, str): dims = [dims] if shape is None and utils.is_dict_like(dims): shape = dims.values() missing_dims = set(self.dims) - set(dims) if missing_dims: raise ValueError( "new dimensions %r must be a superset of " "existing dimensions %r" % (dims, self.dims) ) self_dims = set(self.dims) expanded_dims = tuple(d for d in dims if d not in self_dims) + self.dims if self.dims == expanded_dims: # don't use broadcast_to unless necessary so the result remains # writeable if possible expanded_data = self.data elif shape is not None: dims_map = dict(zip(dims, shape)) tmp_shape = tuple(dims_map[d] for d in expanded_dims) expanded_data = duck_array_ops.broadcast_to(self.data, tmp_shape) else: expanded_data = self.data[(None,) * (len(expanded_dims) - self.ndim)] expanded_var = Variable( expanded_dims, expanded_data, self._attrs, self._encoding, fastpath=True ) return expanded_var.transpose(*dims) def _stack_once(self, dims, new_dim): if not set(dims) <= set(self.dims): raise ValueError("invalid existing dimensions: %s" % dims) if new_dim in self.dims: raise ValueError( "cannot create a new dimension with the same " "name as an existing dimension" ) if len(dims) == 0: # don't stack return self.copy(deep=False) other_dims = [d for d in self.dims if d not in dims] dim_order = other_dims + list(dims) reordered = self.transpose(*dim_order) new_shape = reordered.shape[: len(other_dims)] + (-1,) new_data = reordered.data.reshape(new_shape) new_dims = reordered.dims[: len(other_dims)] + (new_dim,) return Variable(new_dims, new_data, self._attrs, self._encoding, fastpath=True) def stack(self, dimensions=None, **dimensions_kwargs): """ Stack any number of existing dimensions into a single new dimension. New dimensions will be added at the end, and the order of the data along each new dimension will be in contiguous (C) order. Parameters ---------- dimensions : mapping of hashable to tuple of hashable Mapping of form new_name=(dim1, dim2, ...) describing the names of new dimensions, and the existing dimensions that they replace. **dimensions_kwargs The keyword arguments form of ``dimensions``. One of dimensions or dimensions_kwargs must be provided. Returns ------- stacked : Variable Variable with the same attributes but stacked data. See also -------- Variable.unstack """ dimensions = either_dict_or_kwargs(dimensions, dimensions_kwargs, "stack") result = self for new_dim, dims in dimensions.items(): result = result._stack_once(dims, new_dim) return result def _unstack_once(self, dims, old_dim): new_dim_names = tuple(dims.keys()) new_dim_sizes = tuple(dims.values()) if old_dim not in self.dims: raise ValueError("invalid existing dimension: %s" % old_dim) if set(new_dim_names).intersection(self.dims): raise ValueError( "cannot create a new dimension with the same " "name as an existing dimension" ) if np.prod(new_dim_sizes) != self.sizes[old_dim]: raise ValueError( "the product of the new dimension sizes must " "equal the size of the old dimension" ) other_dims = [d for d in self.dims if d != old_dim] dim_order = other_dims + [old_dim] reordered = self.transpose(*dim_order) new_shape = reordered.shape[: len(other_dims)] + new_dim_sizes new_data = reordered.data.reshape(new_shape) new_dims = reordered.dims[: len(other_dims)] + new_dim_names return Variable(new_dims, new_data, self._attrs, self._encoding, fastpath=True) def unstack(self, dimensions=None, **dimensions_kwargs): """ Unstack an existing dimension into multiple new dimensions. New dimensions will be added at the end, and the order of the data along each new dimension will be in contiguous (C) order. Parameters ---------- dimensions : mapping of hashable to mapping of hashable to int Mapping of the form old_dim={dim1: size1, ...} describing the names of existing dimensions, and the new dimensions and sizes that they map to. **dimensions_kwargs The keyword arguments form of ``dimensions``. One of dimensions or dimensions_kwargs must be provided. Returns ------- unstacked : Variable Variable with the same attributes but unstacked data. See also -------- Variable.stack """ dimensions = either_dict_or_kwargs(dimensions, dimensions_kwargs, "unstack") result = self for old_dim, dims in dimensions.items(): result = result._unstack_once(dims, old_dim) return result def fillna(self, value): return ops.fillna(self, value) def where(self, cond, other=dtypes.NA): return ops.where_method(self, cond, other) def reduce( self, func, dim=None, axis=None, keep_attrs=None, keepdims=False, **kwargs, ): """Reduce this array by applying `func` along some dimension(s). Parameters ---------- func : callable Function which can be called in the form `func(x, axis=axis, **kwargs)` to return the result of reducing an np.ndarray over an integer valued axis. dim : str or sequence of str, optional Dimension(s) over which to apply `func`. axis : int or sequence of int, optional Axis(es) over which to apply `func`. Only one of the 'dim' and 'axis' arguments can be supplied. If neither are supplied, then the reduction is calculated over the flattened array (by calling `func(x)` without an axis argument). keep_attrs : bool, optional If True, the variable's attributes (`attrs`) will be copied from the original object to the new one. If False (default), the new object will be returned without attributes. keepdims : bool, default: False If True, the dimensions which are reduced are left in the result as dimensions of size one **kwargs : dict Additional keyword arguments passed on to `func`. Returns ------- reduced : Array Array with summarized data and the indicated dimension(s) removed. """ if dim == ...: dim = None if dim is not None and axis is not None: raise ValueError("cannot supply both 'axis' and 'dim' arguments") if dim is not None: axis = self.get_axis_num(dim) with warnings.catch_warnings(): warnings.filterwarnings( "ignore", r"Mean of empty slice", category=RuntimeWarning ) if axis is not None: data = func(self.data, axis=axis, **kwargs) else: data = func(self.data, **kwargs) if getattr(data, "shape", ()) == self.shape: dims = self.dims else: removed_axes = ( range(self.ndim) if axis is None else np.atleast_1d(axis) % self.ndim ) if keepdims: # Insert np.newaxis for removed dims slices = tuple( np.newaxis if i in removed_axes else slice(None, None) for i in range(self.ndim) ) if getattr(data, "shape", None) is None: # Reduce has produced a scalar value, not an array-like data = np.asanyarray(data)[slices] else: data = data[slices] dims = self.dims else: dims = [ adim for n, adim in enumerate(self.dims) if n not in removed_axes ] if keep_attrs is None: keep_attrs = _get_keep_attrs(default=False) attrs = self._attrs if keep_attrs else None return Variable(dims, data, attrs=attrs) @classmethod def concat(cls, variables, dim="concat_dim", positions=None, shortcut=False): """Concatenate variables along a new or existing dimension. Parameters ---------- variables : iterable of Variable Arrays to stack together. Each variable is expected to have matching dimensions and shape except for along the stacked dimension. dim : str or DataArray, optional Name of the dimension to stack along. This can either be a new dimension name, in which case it is added along axis=0, or an existing dimension name, in which case the location of the dimension is unchanged. Where to insert the new dimension is determined by the first variable. positions : None or list of array-like, optional List of integer arrays which specifies the integer positions to which to assign each dataset along the concatenated dimension. If not supplied, objects are concatenated in the provided order. shortcut : bool, optional This option is used internally to speed-up groupby operations. If `shortcut` is True, some checks of internal consistency between arrays to concatenate are skipped. Returns ------- stacked : Variable Concatenated Variable formed by stacking all the supplied variables along the given dimension. """ if not isinstance(dim, str): (dim,) = dim.dims # can't do this lazily: we need to loop through variables at least # twice variables = list(variables) first_var = variables[0] arrays = [v.data for v in variables] if dim in first_var.dims: axis = first_var.get_axis_num(dim) dims = first_var.dims data = duck_array_ops.concatenate(arrays, axis=axis) if positions is not None: # TODO: deprecate this option -- we don't need it for groupby # any more. indices = nputils.inverse_permutation(np.concatenate(positions)) data = duck_array_ops.take(data, indices, axis=axis) else: axis = 0 dims = (dim,) + first_var.dims data = duck_array_ops.stack(arrays, axis=axis) attrs = dict(first_var.attrs) encoding = dict(first_var.encoding) if not shortcut: for var in variables: if var.dims != first_var.dims: raise ValueError( f"Variable has dimensions {list(var.dims)} but first Variable has dimensions {list(first_var.dims)}" ) return cls(dims, data, attrs, encoding) def equals(self, other, equiv=duck_array_ops.array_equiv): """True if two Variables have the same dimensions and values; otherwise False. Variables can still be equal (like pandas objects) if they have NaN values in the same locations. This method is necessary because `v1 == v2` for Variables does element-wise comparisons (like numpy.ndarrays). """ other = getattr(other, "variable", other) try: return self.dims == other.dims and ( self._data is other._data or equiv(self.data, other.data) ) except (TypeError, AttributeError): return False def broadcast_equals(self, other, equiv=duck_array_ops.array_equiv): """True if two Variables have the values after being broadcast against each other; otherwise False. Variables can still be equal (like pandas objects) if they have NaN values in the same locations. """ try: self, other = broadcast_variables(self, other) except (ValueError, AttributeError): return False return self.equals(other, equiv=equiv) def identical(self, other, equiv=duck_array_ops.array_equiv): """Like equals, but also checks attributes.""" try: return utils.dict_equiv(self.attrs, other.attrs) and self.equals( other, equiv=equiv ) except (TypeError, AttributeError): return False def no_conflicts(self, other, equiv=duck_array_ops.array_notnull_equiv): """True if the intersection of two Variable's non-null data is equal; otherwise false. Variables can thus still be equal if there are locations where either, or both, contain NaN values. """ return self.broadcast_equals(other, equiv=equiv) def quantile( self, q, dim=None, interpolation="linear", keep_attrs=None, skipna=True ): """Compute the qth quantile of the data along the specified dimension. Returns the qth quantiles(s) of the array elements. Parameters ---------- q : float or sequence of float Quantile to compute, which must be between 0 and 1 inclusive. dim : str or sequence of str, optional Dimension(s) over which to apply quantile. interpolation : {"linear", "lower", "higher", "midpoint", "nearest"}, default: "linear" This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points ``i < j``: * linear: ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. * lower: ``i``. * higher: ``j``. * nearest: ``i`` or ``j``, whichever is nearest. * midpoint: ``(i + j) / 2``. keep_attrs : bool, optional If True, the variable's attributes (`attrs`) will be copied from the original object to the new one. If False (default), the new object will be returned without attributes. Returns ------- quantiles : Variable If `q` is a single quantile, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the quantile and a quantile dimension is added to the return array. The other dimensions are the dimensions that remain after the reduction of the array. See Also -------- numpy.nanquantile, pandas.Series.quantile, Dataset.quantile, DataArray.quantile """ from .computation import apply_ufunc _quantile_func = np.nanquantile if skipna else np.quantile if keep_attrs is None: keep_attrs = _get_keep_attrs(default=False) scalar = utils.is_scalar(q) q = np.atleast_1d(np.asarray(q, dtype=np.float64)) if dim is None: dim = self.dims if utils.is_scalar(dim): dim = [dim] def _wrapper(npa, **kwargs): # move quantile axis to end. required for apply_ufunc return np.moveaxis(_quantile_func(npa, **kwargs), 0, -1) axis = np.arange(-1, -1 * len(dim) - 1, -1) result = apply_ufunc( _wrapper, self, input_core_dims=[dim], exclude_dims=set(dim), output_core_dims=[["quantile"]], output_dtypes=[np.float64], dask_gufunc_kwargs=dict(output_sizes={"quantile": len(q)}), dask="parallelized", kwargs={"q": q, "axis": axis, "interpolation": interpolation}, ) # for backward compatibility result = result.transpose("quantile", ...) if scalar: result = result.squeeze("quantile") if keep_attrs: result.attrs = self._attrs return result def rank(self, dim, pct=False): """Ranks the data. Equal values are assigned a rank that is the average of the ranks that would have been otherwise assigned to all of the values within that set. Ranks begin at 1, not 0. If `pct`, computes percentage ranks. NaNs in the input array are returned as NaNs. The `bottleneck` library is required. Parameters ---------- dim : str Dimension over which to compute rank. pct : bool, optional If True, compute percentage ranks, otherwise compute integer ranks. Returns ------- ranked : Variable See Also -------- Dataset.rank, DataArray.rank """ import bottleneck as bn data = self.data if is_duck_dask_array(data): raise TypeError( "rank does not work for arrays stored as dask " "arrays. Load the data via .compute() or .load() " "prior to calling this method." ) elif not isinstance(data, np.ndarray): raise TypeError( "rank is not implemented for {} objects.".format(type(data)) ) axis = self.get_axis_num(dim) func = bn.nanrankdata if self.dtype.kind == "f" else bn.rankdata ranked = func(data, axis=axis) if pct: count = np.sum(~np.isnan(data), axis=axis, keepdims=True) ranked /= count return Variable(self.dims, ranked) def rolling_window( self, dim, window, window_dim, center=False, fill_value=dtypes.NA ): """ Make a rolling_window along dim and add a new_dim to the last place. Parameters ---------- dim : str Dimension over which to compute rolling_window. For nd-rolling, should be list of dimensions. window : int Window size of the rolling For nd-rolling, should be list of integers. window_dim : str New name of the window dimension. For nd-rolling, should be list of integers. center : bool, default: False If True, pad fill_value for both ends. Otherwise, pad in the head of the axis. fill_value value to be filled. Returns ------- Variable that is a view of the original array with a added dimension of size w. The return dim: self.dims + (window_dim, ) The return shape: self.shape + (window, ) Examples -------- >>> v = Variable(("a", "b"), np.arange(8).reshape((2, 4))) >>> v.rolling_window("b", 3, "window_dim") <xarray.Variable (a: 2, b: 4, window_dim: 3)> array([[[nan, nan, 0.], [nan, 0., 1.], [ 0., 1., 2.], [ 1., 2., 3.]], <BLANKLINE> [[nan, nan, 4.], [nan, 4., 5.], [ 4., 5., 6.], [ 5., 6., 7.]]]) >>> v.rolling_window("b", 3, "window_dim", center=True) <xarray.Variable (a: 2, b: 4, window_dim: 3)> array([[[nan, 0., 1.], [ 0., 1., 2.], [ 1., 2., 3.], [ 2., 3., nan]], <BLANKLINE> [[nan, 4., 5.], [ 4., 5., 6.], [ 5., 6., 7.], [ 6., 7., nan]]]) """ if fill_value is dtypes.NA: # np.nan is passed dtype, fill_value = dtypes.maybe_promote(self.dtype) array = self.astype(dtype, copy=False).data else: dtype = self.dtype array = self.data if isinstance(dim, list): assert len(dim) == len(window) assert len(dim) == len(window_dim) assert len(dim) == len(center) else: dim = [dim] window = [window] window_dim = [window_dim] center = [center] axis = [self.get_axis_num(d) for d in dim] new_dims = self.dims + tuple(window_dim) return Variable( new_dims, duck_array_ops.rolling_window( array, axis=axis, window=window, center=center, fill_value=fill_value ), ) def coarsen( self, windows, func, boundary="exact", side="left", keep_attrs=None, **kwargs ): """ Apply reduction function. """ windows = {k: v for k, v in windows.items() if k in self.dims} if not windows: return self.copy() if keep_attrs is None: keep_attrs = _get_keep_attrs(default=False) if keep_attrs: _attrs = self.attrs else: _attrs = None reshaped, axes = self._coarsen_reshape(windows, boundary, side) if isinstance(func, str): name = func func = getattr(duck_array_ops, name, None) if func is None: raise NameError(f"{name} is not a valid method.") return self._replace(data=func(reshaped, axis=axes, **kwargs), attrs=_attrs) def _coarsen_reshape(self, windows, boundary, side): """ Construct a reshaped-array for coarsen """ if not utils.is_dict_like(boundary): boundary = {d: boundary for d in windows.keys()} if not utils.is_dict_like(side): side = {d: side for d in windows.keys()} # remove unrelated dimensions boundary = {k: v for k, v in boundary.items() if k in windows} side = {k: v for k, v in side.items() if k in windows} for d, window in windows.items(): if window <= 0: raise ValueError(f"window must be > 0. Given {window}") variable = self for d, window in windows.items(): # trim or pad the object size = variable.shape[self._get_axis_num(d)] n = int(size / window) if boundary[d] == "exact": if n * window != size: raise ValueError( "Could not coarsen a dimension of size {} with " "window {}".format(size, window) ) elif boundary[d] == "trim": if side[d] == "left": variable = variable.isel({d: slice(0, window * n)}) else: excess = size - window * n variable = variable.isel({d: slice(excess, None)}) elif boundary[d] == "pad": # pad pad = window * n - size if pad < 0: pad += window if side[d] == "left": pad_width = {d: (0, pad)} else: pad_width = {d: (pad, 0)} variable = variable.pad(pad_width, mode="constant") else: raise TypeError( "{} is invalid for boundary. Valid option is 'exact', " "'trim' and 'pad'".format(boundary[d]) ) shape = [] axes = [] axis_count = 0 for i, d in enumerate(variable.dims): if d in windows: size = variable.shape[i] shape.append(int(size / windows[d])) shape.append(windows[d]) axis_count += 1 axes.append(i + axis_count) else: shape.append(variable.shape[i]) return variable.data.reshape(shape), tuple(axes) def isnull(self, keep_attrs: bool = None): """Test each value in the array for whether it is a missing value. Returns ------- isnull : Variable Same type and shape as object, but the dtype of the data is bool. See Also -------- pandas.isnull Examples -------- >>> var = xr.Variable("x", [1, np.nan, 3]) >>> var <xarray.Variable (x: 3)> array([ 1., nan, 3.]) >>> var.isnull() <xarray.Variable (x: 3)> array([False, True, False]) """ from .computation import apply_ufunc if keep_attrs is None: keep_attrs = _get_keep_attrs(default=False) return apply_ufunc( duck_array_ops.isnull, self, dask="allowed", keep_attrs=keep_attrs, ) def notnull(self, keep_attrs: bool = None): """Test each value in the array for whether it is not a missing value. Returns ------- notnull : Variable Same type and shape as object, but the dtype of the data is bool. See Also -------- pandas.notnull Examples -------- >>> var = xr.Variable("x", [1, np.nan, 3]) >>> var <xarray.Variable (x: 3)> array([ 1., nan, 3.]) >>> var.notnull() <xarray.Variable (x: 3)> array([ True, False, True]) """ from .computation import apply_ufunc if keep_attrs is None: keep_attrs = _get_keep_attrs(default=False) return apply_ufunc( duck_array_ops.notnull, self, dask="allowed", keep_attrs=keep_attrs, ) @property def real(self): return type(self)(self.dims, self.data.real, self._attrs) @property def imag(self): return type(self)(self.dims, self.data.imag, self._attrs) def __array_wrap__(self, obj, context=None): return Variable(self.dims, obj) @staticmethod def _unary_op(f): @functools.wraps(f) def func(self, *args, **kwargs): keep_attrs = kwargs.pop("keep_attrs", None) if keep_attrs is None: keep_attrs = _get_keep_attrs(default=True) with

np.errstate(all="ignore")

numpy.errstate

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 *

np.ones(101)

numpy.ones

""" Random Variables. This module implements random variables. Random variables are the main in- and outputs of probabilistic numerical methods. """ from typing import Any, Callable, Dict, Generic, Optional, Tuple, TypeVar, Union import numpy as np from probnum import utils as _utils from probnum.type import ( ArrayLikeGetitemArgType, DTypeArgType, FloatArgType, RandomStateArgType, RandomStateType, ShapeArgType, ShapeType, ) try: # functools.cached_property is only available in Python >=3.8 from functools import cached_property except ImportError: from cached_property import cached_property _ValueType = TypeVar("ValueType") class RandomVariable(Generic[_ValueType]): """ Random variables are the main objects used by probabilistic numerical methods. Every probabilistic numerical method takes a random variable encoding the prior distribution as input and outputs a random variable whose distribution encodes the uncertainty arising from finite computation. The generic signature of a probabilistic numerical method is: ``output_rv = probnum_method(input_rv, method_params)`` In practice, most random variables used by methods in ProbNum have Dirac or Gaussian measure. Instances of :class:`RandomVariable` can be added, multiplied, etc. with arrays and linear operators. This may change their ``distribution`` and not necessarily all previously available methods are retained. The internals of :class:`RandomVariable` objects are assumed to be constant over their whole lifecycle. This is due to the caches used to make certain computations more efficient. As a consequence, altering the internal state of a :class:`RandomVariable` (e.g. its mean, cov, sampling function, etc.) will result in undefined behavior. In particular, this should be kept in mind when subclassing :class:`RandomVariable` or any of its descendants. Parameters ---------- shape : Shape of realizations of this random variable. dtype : Data type of realizations of this random variable. If ``object`` will be converted to ``numpy.dtype``. as_value_type : Function which can be used to transform user-supplied arguments, interpreted as realizations of this random variable, to an easy-to-process, normalized format. Will be called internally to transform the argument of functions like ``in_support``, ``cdf`` and ``logcdf``, ``pmf`` and ``logpmf`` (in :class:`DiscreteRandomVariable`), ``pdf`` and ``logpdf`` (in :class:`ContinuousRandomVariable`), and potentially by similar functions in subclasses. For instance, this method is useful if (``log``)``cdf`` and (``log``)``pdf`` both only work on :class:`np.float_` arguments, but we still want the user to be able to pass Python :class:`float`. Then ``as_value_type`` should be set to something like ``lambda x: np.float64(x)``. See Also -------- asrandvar : Transform into a :class:`RandomVariable`. Examples -------- """ # pylint: disable=too-many-instance-attributes,too-many-public-methods def __init__( self, shape: ShapeArgType, dtype: DTypeArgType, random_state: RandomStateArgType = None, parameters: Optional[Dict[str, Any]] = None, sample: Optional[Callable[[ShapeType], _ValueType]] = None, in_support: Optional[Callable[[_ValueType], bool]] = None, cdf: Optional[Callable[[_ValueType], np.float_]] = None, logcdf: Optional[Callable[[_ValueType], np.float_]] = None, quantile: Optional[Callable[[FloatArgType], _ValueType]] = None, mode: Optional[Callable[[], _ValueType]] = None, median: Optional[Callable[[], _ValueType]] = None, mean: Optional[Callable[[], _ValueType]] = None, cov: Optional[Callable[[], _ValueType]] = None, var: Optional[Callable[[], _ValueType]] = None, std: Optional[Callable[[], _ValueType]] = None, entropy: Optional[Callable[[], np.float_]] = None, as_value_type: Optional[Callable[[Any], _ValueType]] = None, ): # pylint: disable=too-many-arguments,too-many-locals """Create a new random variable.""" self.__shape = _utils.as_shape(shape) # Data Types self.__dtype = np.dtype(dtype) self.__median_dtype = RandomVariable.infer_median_dtype(self.__dtype) self.__moment_dtype = RandomVariable.infer_moment_dtype(self.__dtype) self._random_state = _utils.as_random_state(random_state) # Probability distribution of the random variable self.__parameters = parameters.copy() if parameters is not None else {} self.__sample = sample self.__in_support = in_support self.__cdf = cdf self.__logcdf = logcdf self.__quantile = quantile # Properties of the random variable self.__mode = mode self.__median = median self.__mean = mean self.__cov = cov self.__var = var self.__std = std self.__entropy = entropy # Utilities self.__as_value_type = as_value_type def __repr__(self) -> str: return f"<{self.shape} {self.__class__.__name__} with dtype={self.dtype}>" @property def shape(self) -> ShapeType: """Shape of realizations of the random variable.""" return self.__shape @cached_property def ndim(self) -> int: return len(self.__shape) @cached_property def size(self) -> int: return int(np.prod(self.__shape)) @property def dtype(self) -> np.dtype: """Data type of (elements of) a realization of this random variable.""" return self.__dtype @property def median_dtype(self) -> np.dtype: """The dtype of the :attr:`median`. It will be set to the dtype arising from the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`. This is motivated by the fact that, even for discrete random variables, e.g. integer-valued random variables, the :attr:`median` might lie in between two values in which case these values are averaged. For example, a uniform random variable on :math:`\\{ 1, 2, 3, 4 \\}` will have a median of :math:`2.5`. """ return self.__median_dtype @property def moment_dtype(self) -> np.dtype: """The dtype of any (function of a) moment of the random variable, e.g. its :attr:`mean`, :attr:`cov`, :attr:`var`, or :attr:`std`. It will be set to the dtype arising from the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`. This is motivated by the mathematical definition of a moment as a sum or an integral over products of probabilities and values of the random variable, which are represented as using the dtypes :class:`np.float_` and :attr:`dtype`, respectively. """ return self.__moment_dtype @property def random_state(self) -> RandomStateType: """Random state of the random variable. This attribute defines the RandomState object to use for drawing realizations from this random variable. If None (or np.random), the global np.random state is used. If integer, it is used to seed the local :class:`~numpy.random.RandomState` instance. """ return self._random_state @random_state.setter def random_state(self, seed: RandomStateArgType): """Get or set the RandomState object of the underlying distribution. This can be either None or an existing RandomState object. If None (or np.random), use the RandomState singleton used by np.random. If already a RandomState instance, use it. If an int, use a new RandomState instance seeded with seed. """ self._random_state = _utils.as_random_state(seed) @property def parameters(self) -> Dict[str, Any]: """ Parameters of the probability distribution. The parameters of the distribution such as mean, variance, et cetera stored in a ``dict``. """ return self.__parameters.copy() @cached_property def mode(self) -> _ValueType: """ Mode of the random variable. Returns ------- mode : float The mode of the random variable. """ if self.__mode is None: raise NotImplementedError mode = self.__mode() RandomVariable._check_property_value( "mode", mode, shape=self.__shape, dtype=self.__dtype, ) # Make immutable if isinstance(mode, np.ndarray): mode.setflags(write=False) return mode @cached_property def median(self) -> _ValueType: """ Median of the random variable. To learn about the dtype of the median, see :attr:`median_dtype`. Returns ------- median : float The median of the distribution. """ if self.__shape != (): raise NotImplementedError( "The median is only defined for scalar random variables." ) median = self.__median() RandomVariable._check_property_value( "median", median, shape=self.__shape, dtype=self.__median_dtype, ) # Make immutable if isinstance(median, np.ndarray): median.setflags(write=False) return median @cached_property def mean(self) -> _ValueType: """ Mean :math:`\\mathbb{E}(X)` of the distribution. To learn about the dtype of the mean, see :attr:`moment_dtype`. Returns ------- mean : array-like The mean of the distribution. """ if self.__mean is None: raise NotImplementedError mean = self.__mean() RandomVariable._check_property_value( "mean", mean, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(mean, np.ndarray): mean.setflags(write=False) return mean @cached_property def cov(self) -> _ValueType: """ Covariance :math:`\\operatorname{Cov}(X) = \\mathbb{E}((X-\\mathbb{E}(X))(X-\\mathbb{E}(X))^\\top)` of the random variable. To learn about the dtype of the covariance, see :attr:`moment_dtype`. Returns ------- cov : array-like The kernels of the random variable. """ # pylint: disable=line-too-long if self.__cov is None: raise NotImplementedError cov = self.__cov() RandomVariable._check_property_value( "covariance", cov, shape=(self.size, self.size) if self.ndim > 0 else (), dtype=self.__moment_dtype, ) # Make immutable if isinstance(cov, np.ndarray): cov.setflags(write=False) return cov @cached_property def var(self) -> _ValueType: """ Variance :math:`\\operatorname{Var}(X) = \\mathbb{E}((X-\\mathbb{E}(X))^2)` of the distribution. To learn about the dtype of the variance, see :attr:`moment_dtype`. Returns ------- var : array-like The variance of the distribution. """ if self.__var is None: try: var = np.diag(self.cov).reshape(self.__shape).copy() except NotImplementedError as exc: raise NotImplementedError from exc else: var = self.__var() RandomVariable._check_property_value( "variance", var, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(var, np.ndarray): var.setflags(write=False) return var @cached_property def std(self) -> _ValueType: """ Standard deviation of the distribution. To learn about the dtype of the standard deviation, see :attr:`moment_dtype`. Returns ------- std : array-like The standard deviation of the distribution. """ if self.__std is None: try: std = np.sqrt(self.var) except NotImplementedError as exc: raise NotImplementedError from exc else: std = self.__std() RandomVariable._check_property_value( "standard deviation", std, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(std, np.ndarray): std.setflags(write=False) return std @cached_property def entropy(self) -> np.float_: if self.__entropy is None: raise NotImplementedError entropy = self.__entropy() entropy = RandomVariable._ensure_numpy_float( "entropy", entropy, force_scalar=True ) return entropy def in_support(self, x: _ValueType) -> bool: if self.__in_support is None: raise NotImplementedError in_support = self.__in_support(self._as_value_type(x)) if not isinstance(in_support, bool): raise ValueError( f"The function `in_support` must return a `bool`, but its return value " f"is of type `{type(x)}`." ) return in_support def sample(self, size: ShapeArgType = ()) -> _ValueType: """ Draw realizations from a random variable. Parameters ---------- size : tuple Size of the drawn sample of realizations. Returns ------- sample : array-like Sample of realizations with the given ``size`` and the inherent ``shape``. """ if self.__sample is None: raise NotImplementedError("No sampling method provided.") return self.__sample(size=_utils.as_shape(size)) def cdf(self, x: _ValueType) -> np.float_: """ Cumulative distribution function. Parameters ---------- x : array-like Evaluation points of the cumulative distribution function. The shape of this argument should be :code:`(..., S1, ..., SN)`, where :code:`(S1, ..., SN)` is the :attr:`shape` of the random variable. The cdf evaluation will be broadcast over all additional dimensions. Returns ------- q : array-like Value of the cumulative density function at the given points. """ if self.__cdf is not None: return RandomVariable._ensure_numpy_float( "cdf", self.__cdf(self._as_value_type(x)) ) elif self.__logcdf is not None: cdf = np.exp(self.logcdf(self._as_value_type(x))) assert isinstance(cdf, np.float_) return cdf else: raise NotImplementedError( f"Neither the `cdf` nor the `logcdf` of the random variable object " f"with type `{type(self).__name__}` is implemented." ) def logcdf(self, x: _ValueType) -> np.float_: """ Log-cumulative distribution function. Parameters ---------- x : array-like Evaluation points of the cumulative distribution function. The shape of this argument should be :code:`(..., S1, ..., SN)`, where :code:`(S1, ..., SN)` is the :attr:`shape` of the random variable. The logcdf evaluation will be broadcast over all additional dimensions. Returns ------- q : array-like Value of the log-cumulative density function at the given points. """ if self.__logcdf is not None: return RandomVariable._ensure_numpy_float( "logcdf", self.__logcdf(self._as_value_type(x)) ) elif self.__cdf is not None: logcdf = np.log(self.__cdf(x)) assert isinstance(logcdf, np.float_) return logcdf else: raise NotImplementedError( f"Neither the `logcdf` nor the `cdf` of the random variable object " f"with type `{type(self).__name__}` is implemented." ) def quantile(self, p: FloatArgType) -> _ValueType: """Quantile function. The quantile function :math:`Q \\colon [0, 1] \\to \\mathbb{R}` of a random variable :math:`X` is defined as :math:`Q(p) = \\inf\\{ x \\in \\mathbb{R} \\colon p \\le F_X(x) \\}`, where :math:`F_X \\colon \\mathbb{R} \\to [0, 1]` is the :meth:`cdf` of the random variable. From the definition it follows that the quantile function always returns values of the same dtype as the random variable. For instance, for a discrete distribution over the integers, the returned quantiles will also be integers. This means that, in general, :math:`Q(0.5)` is not equal to the :attr:`median` as it is defined in this class. See https://en.wikipedia.org/wiki/Quantile_function for more details and examples. """ if self.__shape != (): raise NotImplementedError( "The quantile function is only defined for scalar random variables." ) if self.__quantile is None: raise NotImplementedError try: p = _utils.as_numpy_scalar(p, dtype=np.floating) except TypeError as exc: raise TypeError( "The given argument `p` can not be cast to a `np.floating` object." ) from exc quantile = self.__quantile(p) if quantile.shape != self.__shape: raise ValueError( f"The quantile function should return values of the same shape as the " f"random variable, i.e. {self.__shape}, but it returned a value with " f"{quantile.shape}." ) if quantile.dtype != self.__dtype: raise ValueError( f"The quantile function should return values of the same dtype as the " f"random variable, i.e. `{self.__dtype.name}`, but it returned a value " f"with dtype `{quantile.dtype.name}`." ) return quantile def __getitem__(self, key: ArrayLikeGetitemArgType) -> "RandomVariable": return RandomVariable( shape=np.empty(shape=self.shape)[key].shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: self.sample(size)[key], mode=lambda: self.mode[key], mean=lambda: self.mean[key], var=lambda: self.var[key], std=lambda: self.std[key], entropy=lambda: self.entropy, as_value_type=self.__as_value_type, ) def reshape(self, newshape: ShapeArgType) -> "RandomVariable": """ Give a new shape to a random variable. Parameters ---------- newshape : int or tuple of ints New shape for the random variable. It must be compatible with the original shape. Returns ------- reshaped_rv : ``self`` with the new dimensions of ``shape``. """ newshape = _utils.as_shape(newshape) return RandomVariable( shape=newshape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: self.sample(size).reshape(size + newshape), mode=lambda: self.mode.reshape(newshape), median=lambda: self.median.reshape(newshape), mean=lambda: self.mean.reshape(newshape), cov=lambda: self.cov, var=lambda: self.var.reshape(newshape), std=lambda: self.std.reshape(newshape), entropy=lambda: self.entropy, as_value_type=self.__as_value_type, ) def transpose(self, *axes: int) -> "RandomVariable": """ Transpose the random variable. Parameters ---------- axes : None, tuple of ints, or n ints See documentation of numpy.ndarray.transpose. Returns ------- transposed_rv : The transposed random variable. """ return RandomVariable( shape=np.empty(shape=self.shape).transpose(*axes).shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: self.sample(size).transpose(*axes), mode=lambda: self.mode.transpose(*axes), median=lambda: self.median.transpose(*axes), mean=lambda: self.mean.transpose(*axes), cov=lambda: self.cov, var=lambda: self.var.transpose(*axes), std=lambda: self.std.transpose(*axes), entropy=lambda: self.entropy, as_value_type=self.__as_value_type, ) T = property(transpose) # Unary arithmetic operations def __neg__(self) -> "RandomVariable": return RandomVariable( shape=self.shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: -self.sample(size=size), in_support=lambda x: self.in_support(-x), mode=lambda: -self.mode, median=lambda: -self.median, mean=lambda: -self.mean, cov=lambda: self.cov, var=lambda: self.var, std=lambda: self.std, as_value_type=self.__as_value_type, ) def __pos__(self) -> "RandomVariable": return RandomVariable( shape=self.shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: +self.sample(size=size), in_support=lambda x: self.in_support(+x), mode=lambda: +self.mode, median=lambda: +self.median, mean=lambda: +self.mean, cov=lambda: self.cov, var=lambda: self.var, std=lambda: self.std, as_value_type=self.__as_value_type, ) def __abs__(self) -> "RandomVariable": return RandomVariable( shape=self.shape, dtype=self.dtype, random_state=_utils.derive_random_seed(self.random_state), sample=lambda size: abs(self.sample(size=size)), ) # Binary arithmetic operations __array_ufunc__ = None """ This prevents numpy from calling elementwise arithmetic operations allowing expressions like: y = np.array([1, 1]) + RV to call the arithmetic operations defined by RandomVariable instead of elementwise. Thus no array of RandomVariables but a RandomVariable with the correct shape is returned. """ def __add__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import add return add(self, other) def __radd__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import add return add(other, self) def __sub__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import sub return sub(self, other) def __rsub__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import sub return sub(other, self) def __mul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mul return mul(self, other) def __rmul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mul return mul(other, self) def __matmul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import matmul return matmul(self, other) def __rmatmul__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import matmul return matmul(other, self) def __truediv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import truediv return truediv(self, other) def __rtruediv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import truediv return truediv(other, self) def __floordiv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import floordiv return floordiv(self, other) def __rfloordiv__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import floordiv return floordiv(other, self) def __mod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mod return mod(self, other) def __rmod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import mod return mod(other, self) def __divmod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import divmod_ return divmod_(self, other) def __rdivmod__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import divmod_ return divmod_(other, self) def __pow__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import pow_ return pow_(self, other) def __rpow__(self, other: Any) -> "RandomVariable": # pylint: disable=import-outside-toplevel,cyclic-import from ._arithmetic import pow_ return pow_(other, self) @staticmethod def infer_median_dtype(value_dtype: DTypeArgType) -> np.dtype: return RandomVariable.infer_moment_dtype(value_dtype) @staticmethod def infer_moment_dtype(value_dtype: DTypeArgType) -> np.dtype: return np.promote_types(value_dtype, np.float_) def _as_value_type(self, x: Any) -> _ValueType: if self.__as_value_type is not None: return self.__as_value_type(x) return x @staticmethod def _check_property_value( name: str, value: Any, shape: Optional[Tuple[int, ...]] = None, dtype: Optional[np.dtype] = None, ): if shape is not None: if value.shape != shape: raise ValueError( f"The {name} of the random variable does not have the correct " f"shape. Expected {shape} but got {value.shape}." ) if dtype is not None: if not

np.issubdtype(value.dtype, dtype)

numpy.issubdtype

import numpy as np import pytest import theano import theano.tensor as tt # Don't import test classes otherwise they get tested as part of the file from tests import unittest_tools as utt from tests.gpuarray.config import mode_with_gpu, mode_without_gpu, test_ctx_name from tests.tensor.test_basic import ( TestAlloc, TestComparison, TestJoinAndSplit, TestReshape, ) from tests.tensor.utils import rand, safe_make_node from theano.gpuarray.basic_ops import ( GpuAlloc, GpuAllocEmpty, GpuContiguous, GpuEye, GpuFromHost, GpuJoin, GpuReshape, GpuSplit, GpuToGpu, GpuTri, HostFromGpu, gpu_contiguous, gpu_join, host_from_gpu, ) from theano.gpuarray.elemwise import GpuDimShuffle, GpuElemwise from theano.gpuarray.subtensor import GpuSubtensor from theano.gpuarray.type import GpuArrayType, get_context, gpuarray_shared_constructor from theano.tensor import TensorType from theano.tensor.basic import alloc pygpu = pytest.importorskip("pygpu") gpuarray = pygpu.gpuarray utt.seed_rng() rng = np.random.RandomState(seed=utt.fetch_seed()) def inplace_func( inputs, outputs, mode=None, allow_input_downcast=False, on_unused_input="raise", name=None, ): if mode is None: mode = mode_with_gpu return theano.function( inputs, outputs, mode=mode, allow_input_downcast=allow_input_downcast, accept_inplace=True, on_unused_input=on_unused_input, name=name, ) def fake_shared(value, name=None, strict=False, allow_downcast=None, **kwargs): from theano.tensor.sharedvar import scalar_constructor, tensor_constructor for c in (gpuarray_shared_constructor, tensor_constructor, scalar_constructor): try: return c( value, name=name, strict=strict, allow_downcast=allow_downcast, **kwargs ) except TypeError: continue def rand_gpuarray(*shape, **kwargs): r = rng.rand(*shape) * 2 - 1 dtype = kwargs.pop("dtype", theano.config.floatX) cls = kwargs.pop("cls", None) if len(kwargs) != 0: raise TypeError("Unexpected argument %s", list(kwargs.keys())[0]) return gpuarray.array(r, dtype=dtype, cls=cls, context=get_context(test_ctx_name)) def makeTester( name, op, gpu_op, cases, checks=None, mode_gpu=mode_with_gpu, mode_nogpu=mode_without_gpu, skip=False, eps=1e-10, ): if checks is None: checks = {} _op = op _gpu_op = gpu_op _cases = cases _skip = skip _checks = checks class Checker(utt.OptimizationTestMixin): op = staticmethod(_op) gpu_op = staticmethod(_gpu_op) cases = _cases skip = _skip checks = _checks def setup_method(self): eval(self.__class__.__module__ + "." + self.__class__.__name__) def test_all(self): if skip: pytest.skip(skip) for testname, inputs in cases.items(): for _ in range(len(inputs)): if type(inputs[_]) is float: inputs[_] = np.asarray(inputs[_], dtype=theano.config.floatX) self.run_case(testname, inputs) def run_case(self, testname, inputs): inputs_ref = [theano.shared(inp) for inp in inputs] inputs_tst = [theano.shared(inp) for inp in inputs] try: node_ref = safe_make_node(self.op, *inputs_ref) node_tst = safe_make_node(self.op, *inputs_tst) except Exception as exc: err_msg = ( "Test %s::%s: Error occurred while making " "a node with inputs %s" ) % (self.gpu_op, testname, inputs) exc.args += (err_msg,) raise try: f_ref = inplace_func([], node_ref.outputs, mode=mode_nogpu) f_tst = inplace_func([], node_tst.outputs, mode=mode_gpu) except Exception as exc: err_msg = ( "Test %s::%s: Error occurred while trying to " "make a Function" ) % (self.gpu_op, testname) exc.args += (err_msg,) raise self.assertFunctionContains1(f_tst, self.gpu_op) ref_e = None try: expecteds = f_ref() except Exception as exc: ref_e = exc try: variables = f_tst() except Exception as exc: if ref_e is None: err_msg = ( "Test %s::%s: exception when calling the " "Function" ) % (self.gpu_op, testname) exc.args += (err_msg,) raise else: # if we raised an exception of the same type we're good. if isinstance(exc, type(ref_e)): return else: err_msg = ( "Test %s::%s: exception raised during test " "call was not the same as the reference " "call (got: %s, expected %s)" % (self.gpu_op, testname, type(exc), type(ref_e)) ) exc.args += (err_msg,) raise for i, (variable, expected) in enumerate(zip(variables, expecteds)): condition = ( variable.dtype != expected.dtype or variable.shape != expected.shape or not TensorType.values_eq_approx(variable, expected) ) assert not condition, ( "Test %s::%s: Output %s gave the wrong " "value. With inputs %s, expected %s " "(dtype %s), got %s (dtype %s)." % ( self.op, testname, i, inputs, expected, expected.dtype, variable, variable.dtype, ) ) for description, check in self.checks.items(): assert check(inputs, variables), ( "Test %s::%s: Failed check: %s " "(inputs were %s, ouputs were %s)" ) % (self.op, testname, description, inputs, variables) Checker.__name__ = name if hasattr(Checker, "__qualname__"): Checker.__qualname__ = name return Checker def test_transfer_cpu_gpu(): a = tt.fmatrix("a") g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g") av = np.asarray(rng.rand(5, 4), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) f = theano.function([a], GpuFromHost(test_ctx_name)(a)) fv = f(av) assert GpuArrayType.values_eq(fv, gv) f = theano.function([g], host_from_gpu(g)) fv = f(gv) assert np.all(fv == av) def test_transfer_gpu_gpu(): g = GpuArrayType( dtype="float32", broadcastable=(False, False), context_name=test_ctx_name )() av = np.asarray(rng.rand(5, 4), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) mode = mode_with_gpu.excluding( "cut_gpua_host_transfers", "local_cut_gpua_host_gpua" ) f = theano.function([g], GpuToGpu(test_ctx_name)(g), mode=mode) topo = f.maker.fgraph.toposort() assert len(topo) == 1 assert isinstance(topo[0].op, GpuToGpu) fv = f(gv) assert GpuArrayType.values_eq(fv, gv) def test_transfer_strided(): # This is just to ensure that it works in theano # libgpuarray has a much more comprehensive suit of tests to # ensure correctness a = tt.fmatrix("a") g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g") av = np.asarray(rng.rand(5, 8), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) av = av[:, ::2] gv = gv[:, ::2] f = theano.function([a], GpuFromHost(test_ctx_name)(a)) fv = f(av) assert GpuArrayType.values_eq(fv, gv) f = theano.function([g], host_from_gpu(g)) fv = f(gv) assert np.all(fv == av) def gpu_alloc_expected(x, *shp): g = gpuarray.empty(shp, dtype=x.dtype, context=get_context(test_ctx_name)) g[:] = x return g TestGpuAlloc = makeTester( name="GpuAllocTester", # The +1 is there to allow the lift to the GPU. op=lambda *args: alloc(*args) + 1, gpu_op=GpuAlloc(test_ctx_name), cases=dict( correct01=(rand(), np.int32(7)), # just gives a DeepCopyOp with possibly wrong results on the CPU # correct01_bcast=(rand(1), np.int32(7)), correct02=(rand(), np.int32(4), np.int32(7)), correct12=(rand(7), np.int32(4), np.int32(7)), correct13=(rand(7), np.int32(2), np.int32(4), np.int32(7)), correct23=(rand(4, 7), np.int32(2), np.int32(4), np.int32(7)), bad_shape12=(rand(7), np.int32(7), np.int32(5)), ), ) class TestGPUAlloc(TestAlloc): dtype = "float32" mode = mode_with_gpu shared = staticmethod(gpuarray_shared_constructor) allocs = [GpuAlloc(test_ctx_name), GpuAlloc(test_ctx_name), tt.Alloc()] def test_alloc_empty(): for dt in ["float32", "int8"]: f = theano.function([], GpuAllocEmpty(dt, context_name=test_ctx_name)(2, 3)) assert len(f.maker.fgraph.apply_nodes) == 1 out = f() assert out.shape == (2, 3) assert out.dtype == dt f = theano.function( [], [ GpuAllocEmpty("uint64", test_ctx_name)(3, 2), GpuAllocEmpty("uint64", test_ctx_name)(3, 2), ], ) out = f() assert out[0].shape == (3, 2) assert out[0].dtype == "uint64" assert out[1].shape == (3, 2) assert out[1].dtype == "uint64" assert ( len( [ node for node in f.maker.fgraph.apply_nodes if isinstance(node.op, GpuAllocEmpty) ] ) == 1 ) def test_shape(): x = GpuArrayType(dtype="float32", broadcastable=[False, False, False])() v = gpuarray.zeros((3, 4, 5), dtype="float32", context=get_context(test_ctx_name)) f = theano.function([x], x.shape) topo = f.maker.fgraph.toposort() assert np.all(f(v) == (3, 4, 5)) if theano.config.mode != "FAST_COMPILE": assert len(topo) == 4 assert isinstance(topo[0].op, tt.opt.Shape_i) assert isinstance(topo[1].op, tt.opt.Shape_i) assert isinstance(topo[2].op, tt.opt.Shape_i) assert isinstance(topo[3].op, tt.opt.MakeVector) mode = mode_with_gpu.excluding("local_shape_to_shape_i") f = theano.function([x], x.shape, mode=mode) topo = f.maker.fgraph.toposort() assert np.all(f(v) == (3, 4, 5)) assert len(topo) == 1 assert isinstance(topo[0].op, tt.Shape) def test_gpu_contiguous(): a = tt.fmatrix("a") i = tt.iscalar("i") a_val = np.asarray(np.random.rand(4, 5), dtype="float32") # The reshape is needed otherwise we make the subtensor on the CPU # to transfer less data. f = theano.function( [a, i], gpu_contiguous(a.reshape((5, 4))[::i]), mode=mode_with_gpu ) topo = f.maker.fgraph.toposort() assert any([isinstance(node.op, GpuSubtensor) for node in topo]) assert any([isinstance(node.op, GpuContiguous) for node in topo]) assert f(a_val, 1).flags.c_contiguous assert f(a_val, 2).flags.c_contiguous assert f(a_val, 2).flags.c_contiguous class TestGPUReshape(TestReshape): def setup_method(self): self.shared = gpuarray_shared_constructor self.op = GpuReshape self.mode = mode_with_gpu self.ignore_topo = ( HostFromGpu, GpuFromHost, theano.compile.DeepCopyOp, GpuDimShuffle, GpuElemwise, tt.opt.Shape_i, tt.opt.MakeVector, ) assert self.op == GpuReshape class TestGPUComparison(TestComparison): def setup_method(self): utt.seed_rng() self.mode = mode_with_gpu self.shared = gpuarray_shared_constructor self.dtypes = ["float64", "float32"] class TestGPUJoinAndSplit(TestJoinAndSplit): def setup_method(self): self.mode = mode_with_gpu.excluding("constant_folding") self.join_op = GpuJoin() self.split_op_class = GpuSplit # Use join instead of MakeVector since there is no MakeVector on GPU self.make_vector_op = GpuJoin() # this is to avoid errors with limited devices self.floatX = "float32" self.hide_error = theano.config.mode not in ["DebugMode", "DEBUG_MODE"] def shared(x, **kwargs): return gpuarray_shared_constructor(x, target=test_ctx_name, **kwargs) self.shared = shared def test_gpusplit_opt(self): # Test that we move the node to the GPU # Also test float16 computation at the same time. rng = np.random.RandomState(seed=utt.fetch_seed()) m = self.shared(rng.rand(4, 6).astype("float16")) o = tt.Split(2)(m, 0, [2, 2]) assert o[0].dtype == "float16" f = theano.function([], o, mode=self.mode) assert any( [ isinstance(node.op, self.split_op_class) for node in f.maker.fgraph.toposort() ] ) o1, o2 = f() assert np.allclose(o1, m.get_value(borrow=True)[:2]) assert np.allclose(o2, m.get_value(borrow=True)[2:]) def test_gpujoin_gpualloc(): a = tt.fmatrix("a") a_val = np.asarray(np.random.rand(4, 5), dtype="float32") b = tt.fmatrix("b") b_val = np.asarray(np.random.rand(3, 5), dtype="float32") f = theano.function( [a, b], tt.join(0, tt.zeros_like(a), tt.ones_like(b)) + 4, mode=mode_without_gpu ) f_gpu = theano.function( [a, b], tt.join(0, tt.zeros_like(a), tt.ones_like(b)), mode=mode_with_gpu ) f_gpu2 = theano.function( [a, b], tt.join(0, tt.zeros_like(a), tt.ones_like(b)) + 4, mode=mode_with_gpu ) assert sum([node.op == tt.alloc for node in f.maker.fgraph.toposort()]) == 2 assert sum([node.op == tt.join_ for node in f.maker.fgraph.toposort()]) == 1 assert ( sum([isinstance(node.op, GpuAlloc) for node in f_gpu.maker.fgraph.toposort()]) == 2 ) assert sum([node.op == gpu_join for node in f_gpu.maker.fgraph.toposort()]) == 1 assert ( sum([isinstance(node.op, GpuAlloc) for node in f_gpu2.maker.fgraph.toposort()]) == 2 ) assert sum([node.op == gpu_join for node in f_gpu2.maker.fgraph.toposort()]) == 1 assert np.allclose(f(a_val, b_val), f_gpu2(a_val, b_val)) def test_gpueye(): def check(dtype, N, M_=None, k=0): # Theano does not accept None as a tensor. # So we must use a real value. M = M_ # Currently DebugMode does not support None as inputs even if this is # allowed. if M is None: M = N N_symb = tt.iscalar() M_symb = tt.iscalar() k_symb = tt.iscalar() out = tt.eye(N_symb, M_symb, k_symb, dtype=dtype) + np.array(1).astype(dtype) f = theano.function([N_symb, M_symb, k_symb], out, mode=mode_with_gpu) result = np.asarray(f(N, M, k)) - np.array(1).astype(dtype) assert np.allclose(result, np.eye(N, M_, k, dtype=dtype)) assert result.dtype == np.dtype(dtype) assert any([isinstance(node.op, GpuEye) for node in f.maker.fgraph.toposort()]) for dtype in ["float32", "int32", "float16"]: check(dtype, 3) # M != N, k = 0 check(dtype, 3, 5) check(dtype, 5, 3) # N == M, k != 0 check(dtype, 3, 3, 1) check(dtype, 3, 3, -1) # N < M, k != 0 check(dtype, 3, 5, 1) check(dtype, 3, 5, -1) # N > M, k != 0 check(dtype, 5, 3, 1) check(dtype, 5, 3, -1) # k > M, -k > N, k > M, k > N check(dtype, 5, 3, 3) check(dtype, 3, 5, 3) check(dtype, 5, 3, -3) check(dtype, 3, 5, -3) check(dtype, 5, 3, 6) check(dtype, 3, 5, -6) def test_hostfromgpu_shape_i(): # Test that the shape is lifted over hostfromgpu m = mode_with_gpu.including( "local_dot_to_dot22", "local_dot22_to_dot22scalar", "specialize" ) a = tt.fmatrix("a") ca = theano.gpuarray.type.GpuArrayType("float32", (False, False))() av = np.asarray(np.random.rand(5, 4), dtype="float32") cv = gpuarray.asarray(

np.random.rand(5, 4)

numpy.random.rand

# pylint: disable=protected-access """ Test the wrappers for the C API. """ import os from contextlib import contextmanager import numpy as np import numpy.testing as npt import pandas as pd import pytest import xarray as xr from packaging.version import Version from pygmt import Figure, clib from pygmt.clib.conversion import dataarray_to_matrix from pygmt.clib.session import FAMILIES, VIAS from pygmt.exceptions import ( GMTCLibError, GMTCLibNoSessionError, GMTInvalidInput, GMTVersionError, ) from pygmt.helpers import GMTTempFile TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data") with clib.Session() as _lib: gmt_version = Version(_lib.info["version"]) @contextmanager def mock(session, func, returns=None, mock_func=None): """ Mock a GMT C API function to make it always return a given value. Used to test that exceptions are raised when API functions fail by producing a NULL pointer as output or non-zero status codes. Needed because it's not easy to get some API functions to fail without inducing a Segmentation Fault (which is a good thing because libgmt usually only fails with errors). """ if mock_func is None: def mock_api_function(*args): # pylint: disable=unused-argument """ A mock GMT API function that always returns a given value. """ return returns mock_func = mock_api_function get_libgmt_func = session.get_libgmt_func def mock_get_libgmt_func(name, argtypes=None, restype=None): """ Return our mock function. """ if name == func: return mock_func return get_libgmt_func(name, argtypes, restype) setattr(session, "get_libgmt_func", mock_get_libgmt_func) yield setattr(session, "get_libgmt_func", get_libgmt_func) def test_getitem(): """ Test that I can get correct constants from the C lib. """ ses = clib.Session() assert ses["GMT_SESSION_EXTERNAL"] != -99999 assert ses["GMT_MODULE_CMD"] != -99999 assert ses["GMT_PAD_DEFAULT"] != -99999 assert ses["GMT_DOUBLE"] != -99999 with pytest.raises(GMTCLibError): ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement def test_create_destroy_session(): """ Test that create and destroy session are called without errors. """ # Create two session and make sure they are not pointing to the same memory session1 = clib.Session() session1.create(name="test_session1") assert session1.session_pointer is not None session2 = clib.Session() session2.create(name="test_session2") assert session2.session_pointer is not None assert session2.session_pointer != session1.session_pointer session1.destroy() session2.destroy() # Create and destroy a session twice ses = clib.Session() for __ in range(2): with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement ses.create("session1") assert ses.session_pointer is not None ses.destroy() with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement def test_create_session_fails(): """ Check that an exception is raised when failing to create a session. """ ses = clib.Session() with mock(ses, "GMT_Create_Session", returns=None): with pytest.raises(GMTCLibError): ses.create("test-session-name") # Should fail if trying to create a session before destroying the old one. ses.create("test1") with pytest.raises(GMTCLibError): ses.create("test2") def test_destroy_session_fails(): """ Fail to destroy session when given bad input. """ ses = clib.Session() with pytest.raises(GMTCLibNoSessionError): ses.destroy() ses.create("test-session") with mock(ses, "GMT_Destroy_Session", returns=1): with pytest.raises(GMTCLibError): ses.destroy() ses.destroy() def test_call_module(): """ Run a command to see if call_module works. """ data_fname = os.path.join(TEST_DATA_DIR, "points.txt") out_fname = "test_call_module.txt" with clib.Session() as lib: with GMTTempFile() as out_fname: lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name)) assert os.path.exists(out_fname.name) output = out_fname.read().strip() assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338" def test_call_module_invalid_arguments(): """ Fails for invalid module arguments. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("info", "bogus-data.bla") def test_call_module_invalid_name(): """ Fails when given bad input. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("meh", "") def test_call_module_error_message(): """ Check is the GMT error message was captured. """ with clib.Session() as lib: try: lib.call_module("info", "bogus-data.bla") except GMTCLibError as error: assert "Module 'info' failed with status code" in str(error) assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error) def test_method_no_session(): """ Fails when not in a session. """ # Create an instance of Session without "with" so no session is created. lib = clib.Session() with pytest.raises(GMTCLibNoSessionError): lib.call_module("gmtdefaults", "") with pytest.raises(GMTCLibNoSessionError): lib.session_pointer # pylint: disable=pointless-statement def test_parse_constant_single(): """ Parsing a single family argument correctly. """ lib = clib.Session() for family in FAMILIES: parsed = lib._parse_constant(family, valid=FAMILIES) assert parsed == lib[family] def test_parse_constant_composite(): """ Parsing a composite constant argument (separated by |) correctly. """ lib = clib.Session() test_cases = ((family, via) for family in FAMILIES for via in VIAS) for family, via in test_cases: composite = "|".join([family, via]) expected = lib[family] + lib[via] parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS) assert parsed == expected def test_parse_constant_fails(): """ Check if the function fails when given bad input. """ lib = clib.Session() test_cases = [ "SOME_random_STRING", "GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR", "GMT_IS_DATASET|NOT_A_PROPER_VIA", "NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX", "NOT_A_PROPER_FAMILY|ALSO_INVALID", ] for test_case in test_cases: with pytest.raises(GMTInvalidInput): lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS) # Should also fail if not given valid modifiers but is using them anyway. # This should work... lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS ) # But this shouldn't. with pytest.raises(GMTInvalidInput): lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None ) def test_create_data_dataset(): """ Run the function to make sure it doesn't fail badly. """ with clib.Session() as lib: # Dataset from vectors data_vector = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_VECTOR", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], # columns, rows, layers, dtype ) # Dataset from matrices data_matrix = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_MATRIX", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) assert data_vector != data_matrix def test_create_data_grid_dim(): """ Create a grid ignoring range and inc. """ with clib.Session() as lib: # Grids from matrices using dim lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) def test_create_data_grid_range(): """ Create a grid specifying range and inc instead of dim. """ with clib.Session() as lib: # Grids from matrices using range and int lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) def test_create_data_fails(): """ Check that create_data raises exceptions for invalid input and output. """ # Passing in invalid mode with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="Not_a_valid_mode", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # Passing in invalid geometry with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_GRID", geometry="Not_a_valid_geometry", mode="GMT_CONTAINER_ONLY", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # If the data pointer returned is None (NULL pointer) with pytest.raises(GMTCLibError): with clib.Session() as lib: with mock(lib, "GMT_Create_Data", returns=None): lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[11, 10, 2, 0], ) def test_virtual_file(): """ Test passing in data via a virtual file with a Dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (5, 3) for dtype in dtypes: with clib.Session() as lib: family = "GMT_IS_DATASET|GMT_VIA_MATRIX" geometry = "GMT_IS_POINT" dataset = lib.create_data( family=family, geometry=geometry, mode="GMT_CONTAINER_ONLY", dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype ) data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) lib.put_matrix(dataset, matrix=data) # Add the dataset to a virtual file and pass it along to gmt info vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset) with lib.open_virtual_file(*vfargs) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtual_file_fails(): """ Check that opening and closing virtual files raises an exception for non- zero return codes. """ vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IN|GMT_IS_REFERENCE", None, ) # Mock Open_VirtualFile to test the status check when entering the context. # If the exception is raised, the code won't get to the closing of the # virtual file. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): print("Should not get to this code") # Test the status check when closing the virtual file # Mock the opening to return 0 (success) so that we don't open a file that # we won't close later. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock( lib, "GMT_Close_VirtualFile", returns=1 ): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): pass print("Shouldn't get to this code either") def test_virtual_file_bad_direction(): """ Test passing an invalid direction argument. """ with clib.Session() as lib: vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IS_GRID", # The invalid direction argument 0, ) with pytest.raises(GMTInvalidInput): with lib.open_virtual_file(*vfargs): print("This should have failed") def test_virtualfile_from_vectors(): """ Test the automation for transforming vectors to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 10 for dtype in dtypes: x =

np.arange(size, dtype=dtype)

numpy.arange

# -*- coding: utf-8 -*- """ Created on Thu Nov 28 12:10:11 2019 @author: Omer """ ## File handler ## This file was initially intended purely to generate the matrices for the near earth code found in: https://public.ccsds.org/Pubs/131x1o2e2s.pdf ## The values from the above pdf were copied manually to a txt file, and it is the purpose of this file to parse it. ## The emphasis here is on correctness, I currently do not see a reason to generalise this file, since matrices will be saved in either json or some matrix friendly format. import numpy as np from scipy.linalg import circulant #import matplotlib.pyplot as plt import scipy.io import common import hashlib import os projectDir = os.environ.get('LDPC') if projectDir == None: import pathlib projectDir = pathlib.Path(__file__).parent.absolute() ## <NAME>: added on 01/12/2020, need to make sure this doesn't break anything. import sys sys.path.insert(1, projectDir) FILE_HANDLER_INT_DATA_TYPE = np.int32 GENERAL_CODE_MATRIX_DATA_TYPE = np.int32 NIBBLE_CONVERTER = np.array([8, 4, 2, 1], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) def nibbleToHex(inputArray): n = NIBBLE_CONVERTER.dot(inputArray) if n == 10: h = 'A' elif n== 11: h = 'B' elif n== 12: h = 'C' elif n== 13: h = 'D' elif n== 14: h = 'E' elif n== 15: h = 'F' else: h = str(n) return h def binaryArraytoHex(inputArray): d1 = len(inputArray) assert (d1 % 4 == 0) outputArray = np.zeros(d1//4, dtype = str) outputString = '' for j in range(d1//4): nibble = inputArray[4 * j : 4 * j + 4] h = nibbleToHex(nibble) outputArray[j] = h outputString = outputString + h return outputArray, outputString def hexStringToBinaryArray(hexString): outputBinary = np.array([], dtype = GENERAL_CODE_MATRIX_DATA_TYPE) for i in hexString: if i == '0': nibble =

np.array([0,0,0,0], dtype = GENERAL_CODE_MATRIX_DATA_TYPE)

numpy.array

''' ------------------------------------------------------------------------------------------------- This code accompanies the paper titled "Human injury-based safety decision of automated vehicles" Author: <NAME>, <NAME>, <NAME>, <NAME> Corresponding author: <NAME> (<EMAIL>) ------------------------------------------------------------------------------------------------- ''' import torch import numpy as np from torch import nn from torch.nn.utils import weight_norm __author__ = "<NAME>" def Collision_cond(veh_striking_list, V1_v, V2_v, delta_angle, veh_param): ''' Estimate the collision condition. ''' (veh_l, veh_w, veh_cgf, veh_cgs, veh_k, veh_m) = veh_param delta_angle_2 = np.arccos(np.abs(np.cos(delta_angle))) if -1e-6 < delta_angle_2 < 1e-6: delta_angle_2 = 1e-6 delta_v1_list = [] delta_v2_list = [] # Estimate the collision condition (delat-v) according to the principal impact direction. for veh_striking in veh_striking_list: if veh_striking[0] == 1: veh_ca = np.arctan(veh_cgf[0] / veh_cgs[0]) veh_a2 = np.abs(veh_cgs[1] - veh_striking[3]) veh_RDS = np.abs(V1_v * np.cos(delta_angle) - V2_v) veh_a1 = np.abs(np.sqrt(veh_cgf[0] ** 2 + veh_cgs[0] ** 2) * np.cos(veh_ca + delta_angle_2)) if (veh_striking[1]+1) in [16, 1, 2, 3, 17, 20, 21] and (veh_striking[2]+1) in [16, 1, 2, 3, 17, 20, 21]: veh_e = 2 / veh_RDS else: veh_e = 0.5 / veh_RDS elif veh_striking[0] == 2: veh_ca = np.arctan(veh_cgf[0] / veh_cgs[0]) veh_a2 = np.abs(veh_cgf[1] - veh_striking[3]) veh_a1 = np.abs(np.sqrt(veh_cgf[0] ** 2 + veh_cgs[0] ** 2) * np.cos(delta_angle_2 - veh_ca + np.pi / 2)) veh_RDS = V1_v * np.sin(delta_angle_2) veh_e = 1.5 / veh_RDS elif veh_striking[0] == 3: veh_ca = np.arctan(veh_cgf[1] / veh_cgs[1]) veh_a1 = np.abs(veh_cgs[0] - veh_striking[3]) veh_RDS = np.abs(V2_v * np.cos(delta_angle) - V1_v) veh_a2 = np.abs(np.sqrt(veh_cgf[1] ** 2 + veh_cgs[1] ** 2) *

np.cos(veh_ca + delta_angle_2)

numpy.cos

""" YTArray class. """ from __future__ import print_function #----------------------------------------------------------------------------- # Copyright (c) 2013, yt Development Team. # # Distributed under the terms of the Modified BSD License. # # The full license is in the file COPYING.txt, distributed with this software. #----------------------------------------------------------------------------- import copy import numpy as np from distutils.version import LooseVersion from functools import wraps from numpy import \ add, subtract, multiply, divide, logaddexp, logaddexp2, true_divide, \ floor_divide, negative, power, remainder, mod, absolute, rint, \ sign, conj, exp, exp2, log, log2, log10, expm1, log1p, sqrt, square, \ reciprocal, sin, cos, tan, arcsin, arccos, arctan, arctan2, \ hypot, sinh, cosh, tanh, arcsinh, arccosh, arctanh, deg2rad, rad2deg, \ bitwise_and, bitwise_or, bitwise_xor, invert, left_shift, right_shift, \ greater, greater_equal, less, less_equal, not_equal, equal, logical_and, \ logical_or, logical_xor, logical_not, maximum, minimum, fmax, fmin, \ isreal, iscomplex, isfinite, isinf, isnan, signbit, copysign, nextafter, \ modf, ldexp, frexp, fmod, floor, ceil, trunc, fabs, spacing try: # numpy 1.13 or newer from numpy import positive, divmod as divmod_, isnat, heaviside except ImportError: positive, divmod_, isnat, heaviside = (None,)*4 from yt.units.unit_object import Unit, UnitParseError from yt.units.unit_registry import UnitRegistry from yt.units.dimensions import \ angle, \ current_mks, \ dimensionless, \ em_dimensions from yt.utilities.exceptions import \ YTUnitOperationError, YTUnitConversionError, \ YTUfuncUnitError, YTIterableUnitCoercionError, \ YTInvalidUnitEquivalence, YTEquivalentDimsError from yt.utilities.lru_cache import lru_cache from numbers import Number as numeric_type from yt.utilities.on_demand_imports import _astropy from sympy import Rational from yt.units.unit_lookup_table import \ default_unit_symbol_lut from yt.units.equivalencies import equivalence_registry from yt.utilities.logger import ytLogger as mylog from .pint_conversions import convert_pint_units NULL_UNIT = Unit() POWER_SIGN_MAPPING = {multiply: 1, divide: -1} # redefine this here to avoid a circular import from yt.funcs def iterable(obj): try: len(obj) except: return False return True def return_arr(func): @wraps(func) def wrapped(*args, **kwargs): ret, units = func(*args, **kwargs) if ret.shape == (): return YTQuantity(ret, units) else: # This could be a subclass, so don't call YTArray directly. return type(args[0])(ret, units) return wrapped @lru_cache(maxsize=128, typed=False) def sqrt_unit(unit): return unit**0.5 @lru_cache(maxsize=128, typed=False) def multiply_units(unit1, unit2): return unit1 * unit2 def preserve_units(unit1, unit2=None): return unit1 @lru_cache(maxsize=128, typed=False) def power_unit(unit, power): return unit**power @lru_cache(maxsize=128, typed=False) def square_unit(unit): return unit*unit @lru_cache(maxsize=128, typed=False) def divide_units(unit1, unit2): return unit1/unit2 @lru_cache(maxsize=128, typed=False) def reciprocal_unit(unit): return unit**-1 def passthrough_unit(unit, unit2=None): return unit def return_without_unit(unit, unit2=None): return None def arctan2_unit(unit1, unit2): return NULL_UNIT def comparison_unit(unit1, unit2=None): return None def invert_units(unit): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def bitop_units(unit1, unit2): raise TypeError( "Bit-twiddling operators are not defined for YTArray instances") def get_inp_u_unary(ufunc, inputs, out_arr=None): inp = inputs[0] u = getattr(inp, 'units', None) if u is None: u = NULL_UNIT if u.dimensions is angle and ufunc in trigonometric_operators: inp = inp.in_units('radian').v if out_arr is not None: out_arr = ufunc(inp).view(np.ndarray) return out_arr, inp, u def get_inp_u_binary(ufunc, inputs): inp1 = coerce_iterable_units(inputs[0]) inp2 = coerce_iterable_units(inputs[1]) unit1 = getattr(inp1, 'units', None) unit2 = getattr(inp2, 'units', None) ret_class = get_binary_op_return_class(type(inp1), type(inp2)) if unit1 is None: unit1 = Unit(registry=getattr(unit2, 'registry', None)) if unit2 is None and ufunc is not power: unit2 = Unit(registry=getattr(unit1, 'registry', None)) elif ufunc is power: unit2 = inp2 if isinstance(unit2, np.ndarray): if isinstance(unit2, YTArray): if unit2.units.is_dimensionless: pass else: raise YTUnitOperationError(ufunc, unit1, unit2) unit2 = 1.0 return (inp1, inp2), (unit1, unit2), ret_class def handle_preserve_units(inps, units, ufunc, ret_class): if units[0] != units[1]: any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) else: if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_comparison_units(inps, units, ufunc, ret_class, raise_error=False): if units[0] != units[1]: u1d = units[0].is_dimensionless u2d = units[1].is_dimensionless any_nonzero = [np.any(inps[0]), np.any(inps[1])] if any_nonzero[0] == np.bool_(False): units = (units[1], units[1]) elif any_nonzero[1] == np.bool_(False): units = (units[0], units[0]) elif not any([u1d, u2d]): if not units[0].same_dimensions_as(units[1]): raise YTUnitOperationError(ufunc, *units) else: if raise_error: raise YTUfuncUnitError(ufunc, *units) inps = (inps[0], ret_class(inps[1]).to( ret_class(inps[0]).units)) return inps, units def handle_multiply_divide_units(unit, units, out, out_arr): if unit.is_dimensionless and unit.base_value != 1.0: if not units[0].is_dimensionless: if units[0].dimensions == units[1].dimensions: out_arr = np.multiply(out_arr.view(np.ndarray), unit.base_value, out=out) unit = Unit(registry=unit.registry) return out, out_arr, unit def coerce_iterable_units(input_object): if isinstance(input_object, np.ndarray): return input_object if iterable(input_object): if any([isinstance(o, YTArray) for o in input_object]): ff = getattr(input_object[0], 'units', NULL_UNIT, ) if any([ff != getattr(_, 'units', NULL_UNIT) for _ in input_object]): raise YTIterableUnitCoercionError(input_object) # This will create a copy of the data in the iterable. return YTArray(input_object) return input_object else: return input_object def sanitize_units_mul(this_object, other_object): inp = coerce_iterable_units(this_object) ret = coerce_iterable_units(other_object) # If the other object is a YTArray and has the same dimensions as the object # under consideration, convert so we don't mix units with the same # dimensions. if isinstance(ret, YTArray): if inp.units.same_dimensions_as(ret.units): ret.in_units(inp.units) return ret def sanitize_units_add(this_object, other_object, op_string): inp = coerce_iterable_units(this_object) ret = coerce_iterable_units(other_object) # Make sure the other object is a YTArray before we use the `units` # attribute. if isinstance(ret, YTArray): if not inp.units.same_dimensions_as(ret.units): # handle special case of adding or subtracting with zero or # array filled with zero if not np.any(other_object): return ret.view(np.ndarray) elif not np.any(this_object): return ret raise YTUnitOperationError(op_string, inp.units, ret.units) ret = ret.in_units(inp.units) else: # If the other object is not a YTArray, then one of the arrays must be # dimensionless or filled with zeros if not inp.units.is_dimensionless and

np.any(ret)

numpy.any

""" Random Variables. This module implements random variables. Random variables are the main in- and outputs of probabilistic numerical methods. """ from typing import Any, Callable, Dict, Generic, Optional, Tuple, TypeVar, Union import numpy as np from probnum import utils as _utils from probnum.type import ( ArrayLikeGetitemArgType, DTypeArgType, FloatArgType, RandomStateArgType, RandomStateType, ShapeArgType, ShapeType, ) try: # functools.cached_property is only available in Python >=3.8 from functools import cached_property except ImportError: from cached_property import cached_property _ValueType = TypeVar("ValueType") class RandomVariable(Generic[_ValueType]): """ Random variables are the main objects used by probabilistic numerical methods. Every probabilistic numerical method takes a random variable encoding the prior distribution as input and outputs a random variable whose distribution encodes the uncertainty arising from finite computation. The generic signature of a probabilistic numerical method is: ``output_rv = probnum_method(input_rv, method_params)`` In practice, most random variables used by methods in ProbNum have Dirac or Gaussian measure. Instances of :class:`RandomVariable` can be added, multiplied, etc. with arrays and linear operators. This may change their ``distribution`` and not necessarily all previously available methods are retained. The internals of :class:`RandomVariable` objects are assumed to be constant over their whole lifecycle. This is due to the caches used to make certain computations more efficient. As a consequence, altering the internal state of a :class:`RandomVariable` (e.g. its mean, cov, sampling function, etc.) will result in undefined behavior. In particular, this should be kept in mind when subclassing :class:`RandomVariable` or any of its descendants. Parameters ---------- shape : Shape of realizations of this random variable. dtype : Data type of realizations of this random variable. If ``object`` will be converted to ``numpy.dtype``. as_value_type : Function which can be used to transform user-supplied arguments, interpreted as realizations of this random variable, to an easy-to-process, normalized format. Will be called internally to transform the argument of functions like ``in_support``, ``cdf`` and ``logcdf``, ``pmf`` and ``logpmf`` (in :class:`DiscreteRandomVariable`), ``pdf`` and ``logpdf`` (in :class:`ContinuousRandomVariable`), and potentially by similar functions in subclasses. For instance, this method is useful if (``log``)``cdf`` and (``log``)``pdf`` both only work on :class:`np.float_` arguments, but we still want the user to be able to pass Python :class:`float`. Then ``as_value_type`` should be set to something like ``lambda x: np.float64(x)``. See Also -------- asrandvar : Transform into a :class:`RandomVariable`. Examples -------- """ # pylint: disable=too-many-instance-attributes,too-many-public-methods def __init__( self, shape: ShapeArgType, dtype: DTypeArgType, random_state: RandomStateArgType = None, parameters: Optional[Dict[str, Any]] = None, sample: Optional[Callable[[ShapeType], _ValueType]] = None, in_support: Optional[Callable[[_ValueType], bool]] = None, cdf: Optional[Callable[[_ValueType], np.float_]] = None, logcdf: Optional[Callable[[_ValueType], np.float_]] = None, quantile: Optional[Callable[[FloatArgType], _ValueType]] = None, mode: Optional[Callable[[], _ValueType]] = None, median: Optional[Callable[[], _ValueType]] = None, mean: Optional[Callable[[], _ValueType]] = None, cov: Optional[Callable[[], _ValueType]] = None, var: Optional[Callable[[], _ValueType]] = None, std: Optional[Callable[[], _ValueType]] = None, entropy: Optional[Callable[[], np.float_]] = None, as_value_type: Optional[Callable[[Any], _ValueType]] = None, ): # pylint: disable=too-many-arguments,too-many-locals """Create a new random variable.""" self.__shape = _utils.as_shape(shape) # Data Types self.__dtype = np.dtype(dtype) self.__median_dtype = RandomVariable.infer_median_dtype(self.__dtype) self.__moment_dtype = RandomVariable.infer_moment_dtype(self.__dtype) self._random_state = _utils.as_random_state(random_state) # Probability distribution of the random variable self.__parameters = parameters.copy() if parameters is not None else {} self.__sample = sample self.__in_support = in_support self.__cdf = cdf self.__logcdf = logcdf self.__quantile = quantile # Properties of the random variable self.__mode = mode self.__median = median self.__mean = mean self.__cov = cov self.__var = var self.__std = std self.__entropy = entropy # Utilities self.__as_value_type = as_value_type def __repr__(self) -> str: return f"<{self.shape} {self.__class__.__name__} with dtype={self.dtype}>" @property def shape(self) -> ShapeType: """Shape of realizations of the random variable.""" return self.__shape @cached_property def ndim(self) -> int: return len(self.__shape) @cached_property def size(self) -> int: return int(np.prod(self.__shape)) @property def dtype(self) -> np.dtype: """Data type of (elements of) a realization of this random variable.""" return self.__dtype @property def median_dtype(self) -> np.dtype: """The dtype of the :attr:`median`. It will be set to the dtype arising from the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`. This is motivated by the fact that, even for discrete random variables, e.g. integer-valued random variables, the :attr:`median` might lie in between two values in which case these values are averaged. For example, a uniform random variable on :math:`\\{ 1, 2, 3, 4 \\}` will have a median of :math:`2.5`. """ return self.__median_dtype @property def moment_dtype(self) -> np.dtype: """The dtype of any (function of a) moment of the random variable, e.g. its :attr:`mean`, :attr:`cov`, :attr:`var`, or :attr:`std`. It will be set to the dtype arising from the multiplication of values with dtypes :attr:`dtype` and :class:`np.float_`. This is motivated by the mathematical definition of a moment as a sum or an integral over products of probabilities and values of the random variable, which are represented as using the dtypes :class:`np.float_` and :attr:`dtype`, respectively. """ return self.__moment_dtype @property def random_state(self) -> RandomStateType: """Random state of the random variable. This attribute defines the RandomState object to use for drawing realizations from this random variable. If None (or np.random), the global np.random state is used. If integer, it is used to seed the local :class:`~numpy.random.RandomState` instance. """ return self._random_state @random_state.setter def random_state(self, seed: RandomStateArgType): """Get or set the RandomState object of the underlying distribution. This can be either None or an existing RandomState object. If None (or np.random), use the RandomState singleton used by np.random. If already a RandomState instance, use it. If an int, use a new RandomState instance seeded with seed. """ self._random_state = _utils.as_random_state(seed) @property def parameters(self) -> Dict[str, Any]: """ Parameters of the probability distribution. The parameters of the distribution such as mean, variance, et cetera stored in a ``dict``. """ return self.__parameters.copy() @cached_property def mode(self) -> _ValueType: """ Mode of the random variable. Returns ------- mode : float The mode of the random variable. """ if self.__mode is None: raise NotImplementedError mode = self.__mode() RandomVariable._check_property_value( "mode", mode, shape=self.__shape, dtype=self.__dtype, ) # Make immutable if isinstance(mode, np.ndarray): mode.setflags(write=False) return mode @cached_property def median(self) -> _ValueType: """ Median of the random variable. To learn about the dtype of the median, see :attr:`median_dtype`. Returns ------- median : float The median of the distribution. """ if self.__shape != (): raise NotImplementedError( "The median is only defined for scalar random variables." ) median = self.__median() RandomVariable._check_property_value( "median", median, shape=self.__shape, dtype=self.__median_dtype, ) # Make immutable if isinstance(median, np.ndarray): median.setflags(write=False) return median @cached_property def mean(self) -> _ValueType: """ Mean :math:`\\mathbb{E}(X)` of the distribution. To learn about the dtype of the mean, see :attr:`moment_dtype`. Returns ------- mean : array-like The mean of the distribution. """ if self.__mean is None: raise NotImplementedError mean = self.__mean() RandomVariable._check_property_value( "mean", mean, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(mean, np.ndarray): mean.setflags(write=False) return mean @cached_property def cov(self) -> _ValueType: """ Covariance :math:`\\operatorname{Cov}(X) = \\mathbb{E}((X-\\mathbb{E}(X))(X-\\mathbb{E}(X))^\\top)` of the random variable. To learn about the dtype of the covariance, see :attr:`moment_dtype`. Returns ------- cov : array-like The kernels of the random variable. """ # pylint: disable=line-too-long if self.__cov is None: raise NotImplementedError cov = self.__cov() RandomVariable._check_property_value( "covariance", cov, shape=(self.size, self.size) if self.ndim > 0 else (), dtype=self.__moment_dtype, ) # Make immutable if isinstance(cov, np.ndarray): cov.setflags(write=False) return cov @cached_property def var(self) -> _ValueType: """ Variance :math:`\\operatorname{Var}(X) = \\mathbb{E}((X-\\mathbb{E}(X))^2)` of the distribution. To learn about the dtype of the variance, see :attr:`moment_dtype`. Returns ------- var : array-like The variance of the distribution. """ if self.__var is None: try: var = np.diag(self.cov).reshape(self.__shape).copy() except NotImplementedError as exc: raise NotImplementedError from exc else: var = self.__var() RandomVariable._check_property_value( "variance", var, shape=self.__shape, dtype=self.__moment_dtype, ) # Make immutable if isinstance(var, np.ndarray): var.setflags(write=False) return var @cached_property def std(self) -> _ValueType: """ Standard deviation of the distribution. To learn about the dtype of the standard deviation, see :attr:`moment_dtype`. Returns ------- std : array-like The standard deviation of the distribution. """ if self.__std is None: try: std =

np.sqrt(self.var)

numpy.sqrt

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time *

np.ones_like(maxima_dash)

numpy.ones_like

""" Greedy Word Swap with Word Importance Ranking =================================================== When WIR method is set to ``unk``, this is a reimplementation of the search method from the paper: Is BERT Really Robust? A Strong Baseline for Natural Language Attack on Text Classification and Entailment by Jin et. al, 2019. See https://arxiv.org/abs/1907.11932 and https://github.com/jind11/TextFooler. """ import numpy as np import torch from torch.nn.functional import softmax from textattack.goal_function_results import GoalFunctionResultStatus from textattack.search_methods import SearchMethod from textattack.shared.validators import ( transformation_consists_of_word_swaps_and_deletions, ) class GreedyWordSwapWIR(SearchMethod): """An attack that greedily chooses from a list of possible perturbations in order of index, after ranking indices by importance. Args: wir_method: method for ranking most important words """ def __init__(self, wir_method="unk"): self.wir_method = wir_method def _get_index_order(self, initial_text): """Returns word indices of ``initial_text`` in descending order of importance.""" len_text = len(initial_text.words) if self.wir_method == "unk": leave_one_texts = [ initial_text.replace_word_at_index(i, "[UNK]") for i in range(len_text) ] leave_one_results, search_over = self.get_goal_results(leave_one_texts) index_scores = np.array([result.score for result in leave_one_results]) elif self.wir_method == "weighted-saliency": # first, compute word saliency leave_one_texts = [ initial_text.replace_word_at_index(i, "[UNK]") for i in range(len_text) ] leave_one_results, search_over = self.get_goal_results(leave_one_texts) saliency_scores = np.array([result.score for result in leave_one_results]) softmax_saliency_scores = softmax( torch.Tensor(saliency_scores), dim=0 ).numpy() # compute the largest change in score we can find by swapping each word delta_ps = [] for idx in range(len_text): transformed_text_candidates = self.get_transformations( initial_text, original_text=initial_text, indices_to_modify=[idx], ) if not transformed_text_candidates: # no valid synonym substitutions for this word delta_ps.append(0.0) continue swap_results, _ = self.get_goal_results(transformed_text_candidates) score_change = [result.score for result in swap_results] max_score_change = np.max(score_change) delta_ps.append(max_score_change) index_scores = softmax_saliency_scores * np.array(delta_ps) elif self.wir_method == "delete": leave_one_texts = [ initial_text.delete_word_at_index(i) for i in range(len_text) ] leave_one_results, search_over = self.get_goal_results(leave_one_texts) index_scores = np.array([result.score for result in leave_one_results]) elif self.wir_method == "random": index_order = np.arange(len_text)

np.random.shuffle(index_order)

numpy.random.shuffle

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) *

np.ones(100)

numpy.ones

#!/usr/bin/env python # encoding: utf-8 -*- """ This module contains unit tests of the rmgpy.reaction module. """ import numpy import unittest from external.wip import work_in_progress from rmgpy.species import Species, TransitionState from rmgpy.reaction import Reaction from rmgpy.statmech.translation import Translation, IdealGasTranslation from rmgpy.statmech.rotation import Rotation, LinearRotor, NonlinearRotor, KRotor, SphericalTopRotor from rmgpy.statmech.vibration import Vibration, HarmonicOscillator from rmgpy.statmech.torsion import Torsion, HinderedRotor from rmgpy.statmech.conformer import Conformer from rmgpy.kinetics import Arrhenius from rmgpy.thermo import Wilhoit import rmgpy.constants as constants ################################################################################ class PseudoSpecies: """ Can be used in place of a :class:`rmg.species.Species` for isomorphism checks. PseudoSpecies('a') is isomorphic with PseudoSpecies('A') but nothing else. """ def __init__(self, label): self.label = label def __repr__(self): return "PseudoSpecies('{0}')".format(self.label) def __str__(self): return self.label def isIsomorphic(self, other): return self.label.lower() == other.label.lower() class TestReactionIsomorphism(unittest.TestCase): """ Contains unit tests of the isomorphism testing of the Reaction class. """ def makeReaction(self,reaction_string): """" Make a Reaction (containing PseudoSpecies) of from a string like 'Ab=CD' """ reactants, products = reaction_string.split('=') reactants = [PseudoSpecies(i) for i in reactants] products = [PseudoSpecies(i) for i in products] return Reaction(reactants=reactants, products=products) def test1to1(self): r1 = self.makeReaction('A=B') self.assertTrue(r1.isIsomorphic(self.makeReaction('a=B'))) self.assertTrue(r1.isIsomorphic(self.makeReaction('b=A'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('B=a'),eitherDirection=False)) self.assertFalse(r1.isIsomorphic(self.makeReaction('A=C'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('A=BB'))) def test1to2(self): r1 = self.makeReaction('A=BC') self.assertTrue(r1.isIsomorphic(self.makeReaction('a=Bc'))) self.assertTrue(r1.isIsomorphic(self.makeReaction('cb=a'))) self.assertTrue(r1.isIsomorphic(self.makeReaction('a=cb'),eitherDirection=False)) self.assertFalse(r1.isIsomorphic(self.makeReaction('bc=a'),eitherDirection=False)) self.assertFalse(r1.isIsomorphic(self.makeReaction('a=c'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('ab=c'))) def test2to2(self): r1 = self.makeReaction('AB=CD') self.assertTrue(r1.isIsomorphic(self.makeReaction('ab=cd'))) self.assertTrue(r1.isIsomorphic(self.makeReaction('ab=dc'),eitherDirection=False)) self.assertTrue(r1.isIsomorphic(self.makeReaction('dc=ba'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('cd=ab'),eitherDirection=False)) self.assertFalse(r1.isIsomorphic(self.makeReaction('ab=ab'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('ab=cde'))) def test2to3(self): r1 = self.makeReaction('AB=CDE') self.assertTrue(r1.isIsomorphic(self.makeReaction('ab=cde'))) self.assertTrue(r1.isIsomorphic(self.makeReaction('ba=edc'),eitherDirection=False)) self.assertTrue(r1.isIsomorphic(self.makeReaction('dec=ba'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('cde=ab'),eitherDirection=False)) self.assertFalse(r1.isIsomorphic(self.makeReaction('ab=abc'))) self.assertFalse(r1.isIsomorphic(self.makeReaction('abe=cde'))) class TestReaction(unittest.TestCase): """ Contains unit tests of the Reaction class. """ def setUp(self): """ A method that is called prior to each unit test in this class. """ ethylene = Species( label = 'C2H4', conformer = Conformer( E0 = (44.7127, 'kJ/mol'), modes = [ IdealGasTranslation( mass = (28.0313, 'amu'), ), NonlinearRotor( inertia = ( [3.41526, 16.6498, 20.065], 'amu*angstrom^2', ), symmetry = 4, ), HarmonicOscillator( frequencies = ( [828.397, 970.652, 977.223, 1052.93, 1233.55, 1367.56, 1465.09, 1672.25, 3098.46, 3111.7, 3165.79, 3193.54], 'cm^-1', ), ), ], spinMultiplicity = 1, opticalIsomers = 1, ), ) hydrogen = Species( label = 'H', conformer = Conformer( E0 = (211.794, 'kJ/mol'), modes = [ IdealGasTranslation( mass = (1.00783, 'amu'), ), ], spinMultiplicity = 2, opticalIsomers = 1, ), ) ethyl = Species( label = 'C2H5', conformer = Conformer( E0 = (111.603, 'kJ/mol'), modes = [ IdealGasTranslation( mass = (29.0391, 'amu'), ), NonlinearRotor( inertia = ( [4.8709, 22.2353, 23.9925], 'amu*angstrom^2', ), symmetry = 1, ), HarmonicOscillator( frequencies = ( [482.224, 791.876, 974.355, 1051.48, 1183.21, 1361.36, 1448.65, 1455.07, 1465.48, 2688.22, 2954.51, 3033.39, 3101.54, 3204.73], 'cm^-1', ), ), HinderedRotor( inertia = (1.11481, 'amu*angstrom^2'), symmetry = 6, barrier = (0.244029, 'kJ/mol'), semiclassical = None, ), ], spinMultiplicity = 2, opticalIsomers = 1, ), ) TS = TransitionState( label = 'TS', conformer = Conformer( E0 = (266.694, 'kJ/mol'), modes = [ IdealGasTranslation( mass = (29.0391, 'amu'), ), NonlinearRotor( inertia = ( [6.78512, 22.1437, 22.2114], 'amu*angstrom^2', ), symmetry = 1, ), HarmonicOscillator( frequencies = ( [412.75, 415.206, 821.495, 924.44, 982.714, 1024.16, 1224.21, 1326.36, 1455.06, 1600.35, 3101.46, 3110.55, 3175.34, 3201.88], 'cm^-1', ), ), ], spinMultiplicity = 2, opticalIsomers = 1, ), frequency = (-750.232, 'cm^-1'), ) self.reaction = Reaction( reactants = [hydrogen, ethylene], products = [ethyl], kinetics = Arrhenius( A = (501366000.0, 'cm^3/(mol*s)'), n = 1.637, Ea = (4.32508, 'kJ/mol'), T0 = (1, 'K'), Tmin = (300, 'K'), Tmax = (2500, 'K'), ), transitionState = TS, ) # CC(=O)O[O] acetylperoxy = Species( label='acetylperoxy', thermo=Wilhoit(Cp0=(4.0*constants.R,"J/(mol*K)"), CpInf=(21.0*constants.R,"J/(mol*K)"), a0=-3.95, a1=9.26, a2=-15.6, a3=8.55, B=(500.0,"K"), H0=(-6.151e+04,"J/mol"), S0=(-790.2,"J/(mol*K)")), ) # C[C]=O acetyl = Species( label='acetyl', thermo=Wilhoit(Cp0=(4.0*constants.R,"J/(mol*K)"), CpInf=(15.5*constants.R,"J/(mol*K)"), a0=0.2541, a1=-0.4712, a2=-4.434, a3=2.25, B=(500.0,"K"), H0=(-1.439e+05,"J/mol"), S0=(-524.6,"J/(mol*K)")), ) # [O][O] oxygen = Species( label='oxygen', thermo=Wilhoit(Cp0=(3.5*constants.R,"J/(mol*K)"), CpInf=(4.5*constants.R,"J/(mol*K)"), a0=-0.9324, a1=26.18, a2=-70.47, a3=44.12, B=(500.0,"K"), H0=(1.453e+04,"J/mol"), S0=(-12.19,"J/(mol*K)")), ) self.reaction2 = Reaction( reactants=[acetyl, oxygen], products=[acetylperoxy], kinetics = Arrhenius( A = (2.65e12, 'cm^3/(mol*s)'), n = 0.0, Ea = (0.0, 'kJ/mol'), T0 = (1, 'K'), Tmin = (300, 'K'), Tmax = (2000, 'K'), ), ) def testIsIsomerization(self): """ Test the Reaction.isIsomerization() method. """ isomerization = Reaction(reactants=[Species()], products=[Species()]) association = Reaction(reactants=[Species(),Species()], products=[Species()]) dissociation = Reaction(reactants=[Species()], products=[Species(),Species()]) bimolecular = Reaction(reactants=[Species(),Species()], products=[Species(),Species()]) self.assertTrue(isomerization.isIsomerization()) self.assertFalse(association.isIsomerization()) self.assertFalse(dissociation.isIsomerization()) self.assertFalse(bimolecular.isIsomerization()) def testIsAssociation(self): """ Test the Reaction.isAssociation() method. """ isomerization = Reaction(reactants=[Species()], products=[Species()]) association = Reaction(reactants=[Species(),Species()], products=[Species()]) dissociation = Reaction(reactants=[Species()], products=[Species(),Species()]) bimolecular = Reaction(reactants=[Species(),Species()], products=[Species(),Species()]) self.assertFalse(isomerization.isAssociation()) self.assertTrue(association.isAssociation()) self.assertFalse(dissociation.isAssociation()) self.assertFalse(bimolecular.isAssociation()) def testIsDissociation(self): """ Test the Reaction.isDissociation() method. """ isomerization = Reaction(reactants=[Species()], products=[Species()]) association = Reaction(reactants=[Species(),Species()], products=[Species()]) dissociation = Reaction(reactants=[Species()], products=[Species(),Species()]) bimolecular = Reaction(reactants=[Species(),Species()], products=[Species(),Species()]) self.assertFalse(isomerization.isDissociation()) self.assertFalse(association.isDissociation()) self.assertTrue(dissociation.isDissociation()) self.assertFalse(bimolecular.isDissociation()) def testHasTemplate(self): """ Test the Reaction.hasTemplate() method. """ reactants = self.reaction.reactants[:] products = self.reaction.products[:] self.assertTrue(self.reaction.hasTemplate(reactants, products)) self.assertTrue(self.reaction.hasTemplate(products, reactants)) self.assertFalse(self.reaction2.hasTemplate(reactants, products)) self.assertFalse(self.reaction2.hasTemplate(products, reactants)) reactants.reverse() products.reverse() self.assertTrue(self.reaction.hasTemplate(reactants, products)) self.assertTrue(self.reaction.hasTemplate(products, reactants)) self.assertFalse(self.reaction2.hasTemplate(reactants, products)) self.assertFalse(self.reaction2.hasTemplate(products, reactants)) reactants = self.reaction2.reactants[:] products = self.reaction2.products[:] self.assertFalse(self.reaction.hasTemplate(reactants, products)) self.assertFalse(self.reaction.hasTemplate(products, reactants)) self.assertTrue(self.reaction2.hasTemplate(reactants, products)) self.assertTrue(self.reaction2.hasTemplate(products, reactants)) reactants.reverse() products.reverse() self.assertFalse(self.reaction.hasTemplate(reactants, products)) self.assertFalse(self.reaction.hasTemplate(products, reactants)) self.assertTrue(self.reaction2.hasTemplate(reactants, products)) self.assertTrue(self.reaction2.hasTemplate(products, reactants)) def testEnthalpyOfReaction(self): """ Test the Reaction.getEnthalpyOfReaction() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) Hlist0 = [float(v) for v in ['-146007', '-145886', '-144195', '-141973', '-139633', '-137341', '-135155', '-133093', '-131150', '-129316']] Hlist = self.reaction2.getEnthalpiesOfReaction(Tlist) for i in range(len(Tlist)): self.assertAlmostEqual(Hlist[i] / 1000., Hlist0[i] / 1000., 2) def testEntropyOfReaction(self): """ Test the Reaction.getEntropyOfReaction() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) Slist0 = [float(v) for v in ['-156.793', '-156.872', '-153.504', '-150.317', '-147.707', '-145.616', '-143.93', '-142.552', '-141.407', '-140.441']] Slist = self.reaction2.getEntropiesOfReaction(Tlist) for i in range(len(Tlist)): self.assertAlmostEqual(Slist[i], Slist0[i], 2) def testFreeEnergyOfReaction(self): """ Test the Reaction.getFreeEnergyOfReaction() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) Glist0 = [float(v) for v in ['-114648', '-83137.2', '-52092.4', '-21719.3', '8073.53', '37398.1', '66346.8', '94990.6', '123383', '151565']] Glist = self.reaction2.getFreeEnergiesOfReaction(Tlist) for i in range(len(Tlist)): self.assertAlmostEqual(Glist[i] / 1000., Glist0[i] / 1000., 2) def testEquilibriumConstantKa(self): """ Test the Reaction.getEquilibriumConstant() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) Kalist0 = [float(v) for v in ['8.75951e+29', '7.1843e+10', '34272.7', '26.1877', '0.378696', '0.0235579', '0.00334673', '0.000792389', '0.000262777', '0.000110053']] Kalist = self.reaction2.getEquilibriumConstants(Tlist, type='Ka') for i in range(len(Tlist)): self.assertAlmostEqual(Kalist[i] / Kalist0[i], 1.0, 4) def testEquilibriumConstantKc(self): """ Test the Reaction.getEquilibriumConstant() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) Kclist0 = [float(v) for v in ['1.45661e+28', '2.38935e+09', '1709.76', '1.74189', '0.0314866', '0.00235045', '0.000389568', '0.000105413', '3.93273e-05', '1.83006e-05']] Kclist = self.reaction2.getEquilibriumConstants(Tlist, type='Kc') for i in range(len(Tlist)): self.assertAlmostEqual(Kclist[i] / Kclist0[i], 1.0, 4) def testEquilibriumConstantKp(self): """ Test the Reaction.getEquilibriumConstant() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) Kplist0 = [float(v) for v in ['8.75951e+24', '718430', '0.342727', '0.000261877', '3.78696e-06', '2.35579e-07', '3.34673e-08', '7.92389e-09', '2.62777e-09', '1.10053e-09']] Kplist = self.reaction2.getEquilibriumConstants(Tlist, type='Kp') for i in range(len(Tlist)): self.assertAlmostEqual(Kplist[i] / Kplist0[i], 1.0, 4) def testStoichiometricCoefficient(self): """ Test the Reaction.getStoichiometricCoefficient() method. """ for reactant in self.reaction.reactants: self.assertEqual(self.reaction.getStoichiometricCoefficient(reactant), -1) for product in self.reaction.products: self.assertEqual(self.reaction.getStoichiometricCoefficient(product), 1) for reactant in self.reaction2.reactants: self.assertEqual(self.reaction.getStoichiometricCoefficient(reactant), 0) for product in self.reaction2.products: self.assertEqual(self.reaction.getStoichiometricCoefficient(product), 0) def testRateCoefficient(self): """ Test the Reaction.getRateCoefficient() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) P = 1e5 for T in Tlist: self.assertAlmostEqual(self.reaction.getRateCoefficient(T, P) / self.reaction.kinetics.getRateCoefficient(T), 1.0, 6) def testGenerateReverseRateCoefficient(self): """ Test the Reaction.generateReverseRateCoefficient() method. """ Tlist = numpy.arange(200.0, 2001.0, 200.0, numpy.float64) P = 1e5 reverseKinetics = self.reaction2.generateReverseRateCoefficient() for T in Tlist: kr0 = self.reaction2.getRateCoefficient(T, P) / self.reaction2.getEquilibriumConstant(T) kr = reverseKinetics.getRateCoefficient(T) self.assertAlmostEqual(kr0 / kr, 1.0, 0) def testGenerateReverseRateCoefficientArrhenius(self): """ Test the Reaction.generateReverseRateCoefficient() method works for the Arrhenius format. """ original_kinetics = Arrhenius( A = (2.65e12, 'cm^3/(mol*s)'), n = 0.0, Ea = (0.0, 'kJ/mol'), T0 = (1, 'K'), Tmin = (300, 'K'), Tmax = (2000, 'K'), ) self.reaction2.kinetics = original_kinetics reverseKinetics = self.reaction2.generateReverseRateCoefficient() self.reaction2.kinetics = reverseKinetics # reverse reactants, products to ensure Keq is correctly computed self.reaction2.reactants, self.reaction2.products = self.reaction2.products, self.reaction2.reactants reversereverseKinetics = self.reaction2.generateReverseRateCoefficient() # check that reverting the reverse yields the original Tlist =

numpy.arange(original_kinetics.Tmin.value_si, original_kinetics.Tmax.value_si, 200.0, numpy.float64)

numpy.arange

import json import logging import sys import numpy as np import torch from task_config import SuperGLUE_LABEL_MAPPING from snorkel.mtl.data import MultitaskDataset sys.path.append("..") # Adds higher directory to python modules path. logger = logging.getLogger(__name__) TASK_NAME = "WSC" def get_char_index(text, span_text, span_index): tokens = text.replace("\n", " ").lower().split(" ") span_tokens = span_text.replace("\n", " ").lower().split(" ") # Token exact match if tokens[span_index : span_index + len(span_tokens)] == span_tokens: st = len(" ".join(tokens[:span_index])) + 1 if span_index != 0 else 0 ed = st + len(span_text) return st, ed if span_index < len(tokens): # Token fuzzy match with extra chars char_in_text = " ".join(tokens[span_index : span_index + len(span_tokens)]) char_in_span = " ".join(span_tokens) if char_in_text.startswith(char_in_span): st = len(" ".join(tokens[:span_index])) + 1 if span_index != 0 else 0 # ed = st + len(char_in_span) ed = st + len(char_in_text) return st, ed # Token fuzzy match with extra chars char_in_text = " ".join(tokens[span_index : span_index + len(span_tokens)]) char_in_span = " ".join(span_tokens) if char_in_span.startswith(char_in_text): st = len(" ".join(tokens[:span_index])) + 1 if span_index != 0 else 0 ed = st + len(char_in_text) return st, ed # Index out of range if span_index >= len(tokens): span_index -= 10 # Token fuzzy match with different position for idx in range(span_index, len(tokens)): if tokens[idx : idx + len(span_tokens)] == span_tokens: st = len(" ".join(tokens[:idx])) + 1 if idx != 0 else 0 ed = st + len(span_text) return st, ed # Token best fuzzy match with different position for idx in range(span_index, len(tokens)): if tokens[idx] == span_tokens[0]: for length in range(1, len(span_tokens)): if tokens[idx : idx + length] != span_tokens[:length]: st = len(" ".join(tokens[:idx])) + 1 if idx != 0 else 0 ed = st + len(" ".join(span_tokens[: length - 1])) return st, ed return None def parse(jsonl_path, tokenizer, max_data_samples, max_sequence_length): logger.info(f"Loading data from {jsonl_path}.") rows = [json.loads(row) for row in open(jsonl_path, encoding="utf-8")] for i in range(2): logger.info(f"Sample {i}: {rows[i]}") # Truncate to max_data_samples if max_data_samples: rows = rows[:max_data_samples] logger.info(f"Truncating to {max_data_samples} samples.") # sentence text sentences = [] # span1 span1s = [] # span2 span2s = [] # span1 idx span1_idxs = [] # span2 idx span2_idxs = [] # label labels = [] token1_idxs = [] token2_idxs = [] xlnet_tokens = [] xlnet_token_ids = [] xlnet_token_masks = [] xlnet_token_segments = [] # Check the maximum token length max_len = -1 for row in rows: index = row["idx"] text = row["text"] span1_text = row["target"]["span1_text"] span2_text = row["target"]["span2_text"] span1_index = row["target"]["span1_index"] span2_index = row["target"]["span2_index"] label = row["label"] if "label" in row else True span1_char_index = get_char_index(text, span1_text, span1_index) span2_char_index = get_char_index(text, span2_text, span2_index) assert span1_char_index is not None, f"Check example {id} in {jsonl_path}" assert span2_char_index is not None, f"Check example {id} in {jsonl_path}" # Tokenize sentences xlnet_tokens_sub1 = tokenizer.tokenize( text[: min(span1_char_index[0], span2_char_index[0])] ) if span1_char_index[0] < span2_char_index[0]: xlnet_tokens_sub2 = tokenizer.tokenize( text[span1_char_index[0] : span1_char_index[1]] ) token1_idx = [ len(xlnet_tokens_sub1) + 1, len(xlnet_tokens_sub1) + len(xlnet_tokens_sub2), ] else: xlnet_tokens_sub2 = tokenizer.tokenize( text[span2_char_index[0] : span2_char_index[1]] ) token2_idx = [ len(xlnet_tokens_sub1) + 1, len(xlnet_tokens_sub1) + len(xlnet_tokens_sub2), ] sub3_st = ( span1_char_index[1] if span1_char_index[0] < span2_char_index[0] else span2_char_index[1] ) sub3_ed = ( span1_char_index[0] if span1_char_index[0] > span2_char_index[0] else span2_char_index[0] ) xlnet_tokens_sub3 = tokenizer.tokenize(text[sub3_st:sub3_ed]) if span1_char_index[0] < span2_char_index[0]: xlnet_tokens_sub4 = tokenizer.tokenize( text[span2_char_index[0] : span2_char_index[1]] ) cur_len = ( len(xlnet_tokens_sub1) + len(xlnet_tokens_sub2) + len(xlnet_tokens_sub3) ) token2_idx = [cur_len + 1, cur_len + len(xlnet_tokens_sub4)] else: xlnet_tokens_sub4 = tokenizer.tokenize( text[span1_char_index[0] : span1_char_index[1]] ) cur_len = ( len(xlnet_tokens_sub1) + len(xlnet_tokens_sub2) + len(xlnet_tokens_sub3) ) token1_idx = [cur_len + 1, cur_len + len(xlnet_tokens_sub4)] if span1_char_index[0] < span2_char_index[0]: xlnet_tokens_sub5 = tokenizer.tokenize(text[span2_char_index[1] :]) else: xlnet_tokens_sub5 = tokenizer.tokenize(text[span1_char_index[1] :]) tokens = ( ["[CLS]"] + xlnet_tokens_sub1 + xlnet_tokens_sub2 + xlnet_tokens_sub3 + xlnet_tokens_sub4 + xlnet_tokens_sub5 + ["[SEP]"] ) if len(tokens) > max_len: max_len = len(tokens) token_ids = tokenizer.convert_tokens_to_ids(tokens) token_segments = [0] * len(token_ids) # Generate mask where 1 for real tokens and 0 for padding tokens token_masks = [1] * len(token_ids) token1_idxs.append(token1_idx) token2_idxs.append(token2_idx) sentences.append(text) span1s.append(span1_text) span2s.append(span2_text) span1_idxs.append(span1_index) span2_idxs.append(span2_index) labels.append(SuperGLUE_LABEL_MAPPING[TASK_NAME][label]) xlnet_tokens.append(tokens) xlnet_token_ids.append(torch.LongTensor(token_ids)) xlnet_token_masks.append(torch.LongTensor(token_masks)) xlnet_token_segments.append(torch.LongTensor(token_segments)) token1_idxs = torch.from_numpy(np.array(token1_idxs)) token2_idxs = torch.from_numpy(

np.array(token2_idxs)

numpy.array

#!/usr/bin/env python3 import tensorflow as tf physical_devices = tf.config.list_physical_devices('GPU') try: tf.config.experimental.set_memory_growth(physical_devices[0], True) except: # Invalid device or cannot modify virtual devices once initialized. pass import numpy as np import os, time, csv import tqdm import umap import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt import datetime import signal import net from matplotlib import rcParams rcParams['font.family'] = 'sans-serif' rcParams['font.sans-serif'] = ['Hiragino Maru Gothic Pro', 'Yu Gothic', 'Meirio', 'Takao', 'IPAexGothic', 'IPAPGothic', 'Noto Sans CJK JP'] import net class SimpleEncodeDecoder: def __init__(self): self.save_dir = './result/step1/' self.result_dir = './result/plot/' os.makedirs(self.result_dir, exist_ok=True) checkpoint_dir = self.save_dir self.max_epoch = 300 self.steps_per_epoch = 1000 self.batch_size = 64 lr = tf.keras.optimizers.schedules.ExponentialDecay(1e-3, 1e5, 0.5) self.optimizer = tf.keras.optimizers.Adam(lr) self.encoder = net.FeatureBlock() self.encoder.summary() self.decoder = net.SimpleDecoderBlock() self.decoder.summary() inputs = { 'image': tf.keras.Input(shape=(128,128,3)), } feature_out = self.encoder(inputs) outputs = self.decoder(feature_out) self.model = tf.keras.Model(inputs, outputs, name='SimpleEncodeDecoder') checkpoint = tf.train.Checkpoint(optimizer=self.optimizer, model=self.model) last = tf.train.latest_checkpoint(checkpoint_dir) checkpoint.restore(last) self.manager = tf.train.CheckpointManager( checkpoint, directory=checkpoint_dir, max_to_keep=2) if not last is None: self.init_epoch = int(os.path.basename(last).split('-')[1]) print('loaded %d epoch'%self.init_epoch) else: self.init_epoch = 0 self.model.summary() def eval(self): self.data = net.FontData() print("Plot: ", self.init_epoch + 1) acc = self.make_plot(self.data.test_data(self.batch_size), (self.init_epoch + 1)) print('acc', acc) @tf.function def eval_substep(self, inputs): input_data = { 'image': inputs['input'], } feature = self.encoder(input_data) outputs = self.decoder(feature) target_id = inputs['index'] target_id1 = inputs['idx1'] target_id2 = inputs['idx2'] pred_id1 = tf.nn.softmax(outputs['id1'], -1) pred_id2 = tf.nn.softmax(outputs['id2'], -1) return { 'feature': feature, 'pred_id1': pred_id1, 'pred_id2': pred_id2, 'target_id': target_id, 'target_id1': target_id1, 'target_id2': target_id2, } def make_plot(self, test_ds, epoch): result = [] labels = [] with open(os.path.join(self.result_dir,'test_result-%d.txt'%epoch),'w') as txt: correct_count = 0 failed_count = 0 with tqdm.tqdm(total=len(self.data.test_keys)) as pbar: for inputs in test_ds: pred = self.eval_substep(inputs) result += [pred['feature']] labels += [pred['target_id']] for i in range(pred['target_id1'].shape[0]): txt.write('---\n') target = pred['target_id'][i].numpy() txt.write('target: id %d = %s\n'%(target, self.data.glyphs[target-1])) predid1 = np.argmax(pred['pred_id1'][i]) predid2 = np.argmax(pred['pred_id2'][i]) predid = predid1 * 100 + predid2 if predid == 0: txt.write('predict: id %d nothing (p=%f)\n'%(predid, pred['pred_id1'][i][predid1] * pred['pred_id2'][i][predid2])) elif predid > self.data.id_count + 1: txt.write('predict: id %d nothing (p=%f)\n'%(predid, pred['pred_id1'][i][predid1] * pred['pred_id2'][i][predid2])) else: txt.write('predict: id %d = %s (p=%f)\n'%(predid, self.data.glyphs[predid-1], pred['pred_id1'][i][predid1] * pred['pred_id2'][i][predid2])) if target == predid: txt.write('Correct!\n') correct_count += 1 else: txt.write('Failed!\n') failed_count += 1 pbar.update(1) acc = correct_count / (correct_count + failed_count) txt.write('==============\n') txt.write('Correct = %d\n'%correct_count) txt.write('Failed = %d\n'%failed_count) txt.write('accuracy = %f\n'%acc) result =

np.concatenate(result)

numpy.concatenate

"""Test the search module""" from collections.abc import Iterable, Sized from io import StringIO from itertools import chain, product from functools import partial import pickle import sys from types import GeneratorType import re import numpy as np import scipy.sparse as sp import pytest from sklearn.utils.fixes import sp_version from sklearn.utils._testing import assert_raises from sklearn.utils._testing import assert_warns from sklearn.utils._testing import assert_warns_message from sklearn.utils._testing import assert_raise_message from sklearn.utils._testing import assert_array_equal from sklearn.utils._testing import assert_array_almost_equal from sklearn.utils._testing import assert_allclose from sklearn.utils._testing import assert_almost_equal from sklearn.utils._testing import ignore_warnings from sklearn.utils._mocking import CheckingClassifier, MockDataFrame from scipy.stats import bernoulli, expon, uniform from sklearn.base import BaseEstimator, ClassifierMixin from sklearn.base import clone from sklearn.exceptions import NotFittedError from sklearn.datasets import make_classification from sklearn.datasets import make_blobs from sklearn.datasets import make_multilabel_classification from sklearn.model_selection import fit_grid_point from sklearn.model_selection import train_test_split from sklearn.model_selection import KFold from sklearn.model_selection import StratifiedKFold from sklearn.model_selection import StratifiedShuffleSplit from sklearn.model_selection import LeaveOneGroupOut from sklearn.model_selection import LeavePGroupsOut from sklearn.model_selection import GroupKFold from sklearn.model_selection import GroupShuffleSplit from sklearn.model_selection import GridSearchCV from sklearn.model_selection import RandomizedSearchCV from sklearn.model_selection import ParameterGrid from sklearn.model_selection import ParameterSampler from sklearn.model_selection._search import BaseSearchCV from sklearn.model_selection._validation import FitFailedWarning from sklearn.svm import LinearSVC, SVC from sklearn.tree import DecisionTreeRegressor from sklearn.tree import DecisionTreeClassifier from sklearn.cluster import KMeans from sklearn.neighbors import KernelDensity from sklearn.neighbors import KNeighborsClassifier from sklearn.metrics import f1_score from sklearn.metrics import recall_score from sklearn.metrics import accuracy_score from sklearn.metrics import make_scorer from sklearn.metrics import roc_auc_score from sklearn.metrics.pairwise import euclidean_distances from sklearn.impute import SimpleImputer from sklearn.pipeline import Pipeline from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression from sklearn.experimental import enable_hist_gradient_boosting # noqa from sklearn.ensemble import HistGradientBoostingClassifier from sklearn.model_selection.tests.common import OneTimeSplitter # Neither of the following two estimators inherit from BaseEstimator, # to test hyperparameter search on user-defined classifiers. class MockClassifier: """Dummy classifier to test the parameter search algorithms""" def __init__(self, foo_param=0): self.foo_param = foo_param def fit(self, X, Y): assert len(X) == len(Y) self.classes_ = np.unique(Y) return self def predict(self, T): return T.shape[0] def transform(self, X): return X + self.foo_param def inverse_transform(self, X): return X - self.foo_param predict_proba = predict predict_log_proba = predict decision_function = predict def score(self, X=None, Y=None): if self.foo_param > 1: score = 1. else: score = 0. return score def get_params(self, deep=False): return {'foo_param': self.foo_param} def set_params(self, **params): self.foo_param = params['foo_param'] return self class LinearSVCNoScore(LinearSVC): """An LinearSVC classifier that has no score method.""" @property def score(self): raise AttributeError X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) y = np.array([1, 1, 2, 2]) def assert_grid_iter_equals_getitem(grid): assert list(grid) == [grid[i] for i in range(len(grid))] @pytest.mark.parametrize("klass", [ParameterGrid, partial(ParameterSampler, n_iter=10)]) @pytest.mark.parametrize( "input, error_type, error_message", [(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'), ([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'), ({'foo': 0}, TypeError, "Parameter.* value is not iterable .*" r"\(key='foo', value=0\)")] ) def test_validate_parameter_input(klass, input, error_type, error_message): with pytest.raises(error_type, match=error_message): klass(input) def test_parameter_grid(): # Test basic properties of ParameterGrid. params1 = {"foo": [1, 2, 3]} grid1 = ParameterGrid(params1) assert isinstance(grid1, Iterable) assert isinstance(grid1, Sized) assert len(grid1) == 3 assert_grid_iter_equals_getitem(grid1) params2 = {"foo": [4, 2], "bar": ["ham", "spam", "eggs"]} grid2 = ParameterGrid(params2) assert len(grid2) == 6 # loop to assert we can iterate over the grid multiple times for i in range(2): # tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2) points = set(tuple(chain(*(sorted(p.items())))) for p in grid2) assert (points == set(("bar", x, "foo", y) for x, y in product(params2["bar"], params2["foo"]))) assert_grid_iter_equals_getitem(grid2) # Special case: empty grid (useful to get default estimator settings) empty = ParameterGrid({}) assert len(empty) == 1 assert list(empty) == [{}] assert_grid_iter_equals_getitem(empty) assert_raises(IndexError, lambda: empty[1]) has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}]) assert len(has_empty) == 4 assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}] assert_grid_iter_equals_getitem(has_empty) def test_grid_search(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3) # make sure it selects the smallest parameter in case of ties old_stdout = sys.stdout sys.stdout = StringIO() grid_search.fit(X, y) sys.stdout = old_stdout assert grid_search.best_estimator_.foo_param == 2 assert_array_equal(grid_search.cv_results_["param_foo_param"].data, [1, 2, 3]) # Smoke test the score etc: grid_search.score(X, y) grid_search.predict_proba(X) grid_search.decision_function(X) grid_search.transform(X) # Test exception handling on scoring grid_search.scoring = 'sklearn' assert_raises(ValueError, grid_search.fit, X, y) def test_grid_search_pipeline_steps(): # check that parameters that are estimators are cloned before fitting pipe = Pipeline([('regressor', LinearRegression())]) param_grid = {'regressor': [LinearRegression(), Ridge()]} grid_search = GridSearchCV(pipe, param_grid, cv=2) grid_search.fit(X, y) regressor_results = grid_search.cv_results_['param_regressor'] assert isinstance(regressor_results[0], LinearRegression) assert isinstance(regressor_results[1], Ridge) assert not hasattr(regressor_results[0], 'coef_') assert not hasattr(regressor_results[1], 'coef_') assert regressor_results[0] is not grid_search.best_estimator_ assert regressor_results[1] is not grid_search.best_estimator_ # check that we didn't modify the parameter grid that was passed assert not hasattr(param_grid['regressor'][0], 'coef_') assert not hasattr(param_grid['regressor'][1], 'coef_') @pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV]) def test_SearchCV_with_fit_params(SearchCV): X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) clf = CheckingClassifier(expected_fit_params=['spam', 'eggs']) searcher = SearchCV( clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise" ) # The CheckingClassifier generates an assertion error if # a parameter is missing or has length != len(X). err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen." with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(10)) err_msg = "Fit parameter spam has length 1; expected" with pytest.raises(AssertionError, match=err_msg): searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10)) searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10)) @ignore_warnings def test_grid_search_no_score(): # Test grid-search on classifier that has no score function. clf = LinearSVC(random_state=0) X, y = make_blobs(random_state=0, centers=2) Cs = [.1, 1, 10] clf_no_score = LinearSVCNoScore(random_state=0) grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy') grid_search.fit(X, y) grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}, scoring='accuracy') # smoketest grid search grid_search_no_score.fit(X, y) # check that best params are equal assert grid_search_no_score.best_params_ == grid_search.best_params_ # check that we can call score and that it gives the correct result assert grid_search.score(X, y) == grid_search_no_score.score(X, y) # giving no scoring function raises an error grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs}) assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit, [[1]]) def test_grid_search_score_method(): X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2, random_state=0) clf = LinearSVC(random_state=0) grid = {'C': [.1]} search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y) search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y) search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid, scoring='roc_auc' ).fit(X, y) search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y) # Check warning only occurs in situation where behavior changed: # estimator requires score method to compete with scoring parameter score_no_scoring = search_no_scoring.score(X, y) score_accuracy = search_accuracy.score(X, y) score_no_score_auc = search_no_score_method_auc.score(X, y) score_auc = search_auc.score(X, y) # ensure the test is sane assert score_auc < 1.0 assert score_accuracy < 1.0 assert score_auc != score_accuracy assert_almost_equal(score_accuracy, score_no_scoring) assert_almost_equal(score_auc, score_no_score_auc) def test_grid_search_groups(): # Check if ValueError (when groups is None) propagates to GridSearchCV # And also check if groups is correctly passed to the cv object rng = np.random.RandomState(0) X, y = make_classification(n_samples=15, n_classes=2, random_state=0) groups = rng.randint(0, 3, 15) clf = LinearSVC(random_state=0) grid = {'C': [1]} group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2), GroupKFold(n_splits=3), GroupShuffleSplit()] for cv in group_cvs: gs = GridSearchCV(clf, grid, cv=cv) assert_raise_message(ValueError, "The 'groups' parameter should not be None.", gs.fit, X, y) gs.fit(X, y, groups=groups) non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()] for cv in non_group_cvs: gs = GridSearchCV(clf, grid, cv=cv) # Should not raise an error gs.fit(X, y) def test_classes__property(): # Test that classes_ property matches best_estimator_.classes_ X = np.arange(100).reshape(10, 10) y = np.array([0] * 5 + [1] * 5) Cs = [.1, 1, 10] grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) grid_search.fit(X, y) assert_array_equal(grid_search.best_estimator_.classes_, grid_search.classes_) # Test that regressors do not have a classes_ attribute grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]}) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute before it's fit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}) assert not hasattr(grid_search, 'classes_') # Test that the grid searcher has no classes_ attribute without a refit grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs}, refit=False) grid_search.fit(X, y) assert not hasattr(grid_search, 'classes_') def test_trivial_cv_results_attr(): # Test search over a "grid" with only one point. clf = MockClassifier() grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3) grid_search.fit(X, y) assert hasattr(grid_search, "cv_results_") random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3) random_search.fit(X, y) assert hasattr(grid_search, "cv_results_") def test_no_refit(): # Test that GSCV can be used for model selection alone without refitting clf = MockClassifier() for scoring in [None, ['accuracy', 'precision']]: grid_search = GridSearchCV( clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3 ) grid_search.fit(X, y) assert not hasattr(grid_search, "best_estimator_") and \ hasattr(grid_search, "best_index_") and \ hasattr(grid_search, "best_params_") # Make sure the functions predict/transform etc raise meaningful # error messages for fn_name in ('predict', 'predict_proba', 'predict_log_proba', 'transform', 'inverse_transform'): assert_raise_message(NotFittedError, ('refit=False. %s is available only after ' 'refitting on the best parameters' % fn_name), getattr(grid_search, fn_name), X) # Test that an invalid refit param raises appropriate error messages for refit in ["", 5, True, 'recall', 'accuracy']: assert_raise_message(ValueError, "For multi-metric scoring, the " "parameter refit must be set to a scorer key", GridSearchCV(clf, {}, refit=refit, scoring={'acc': 'accuracy', 'prec': 'precision'} ).fit, X, y) def test_grid_search_error(): # Test that grid search will capture errors on data with different length X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) assert_raises(ValueError, cv.fit, X_[:180], y_) def test_grid_search_one_grid_point(): X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]} clf = SVC(gamma='auto') cv = GridSearchCV(clf, param_dict) cv.fit(X_, y_) clf = SVC(C=1.0, kernel="rbf", gamma=0.1) clf.fit(X_, y_) assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_) def test_grid_search_when_param_grid_includes_range(): # Test that the best estimator contains the right value for foo_param clf = MockClassifier() grid_search = None grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3) grid_search.fit(X, y) assert grid_search.best_estimator_.foo_param == 2 def test_grid_search_bad_param_grid(): param_dict = {"C": 1} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'int'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": []} clf = SVC() assert_raise_message( ValueError, "Parameter values for parameter (C) need to be a non-empty sequence.", GridSearchCV, clf, param_dict) param_dict = {"C": "1,2,3"} clf = SVC(gamma='auto') assert_raise_message( ValueError, "Parameter grid for parameter (C) needs to" " be a list or numpy array, but got (<class 'str'>)." " Single values need to be wrapped in a list" " with one element.", GridSearchCV, clf, param_dict) param_dict = {"C": np.ones((3, 2))} clf = SVC() assert_raises(ValueError, GridSearchCV, clf, param_dict) def test_grid_search_sparse(): # Test that grid search works with both dense and sparse matrices X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180], y_[:180]) y_pred = cv.predict(X_[180:]) C = cv.best_estimator_.C X_ = sp.csr_matrix(X_) clf = LinearSVC() cv = GridSearchCV(clf, {'C': [0.1, 1.0]}) cv.fit(X_[:180].tocoo(), y_[:180]) y_pred2 = cv.predict(X_[180:]) C2 = cv.best_estimator_.C assert

np.mean(y_pred == y_pred2)

numpy.mean

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash) maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash) maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash) maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101) maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time) minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101) minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash) minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash) minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash) minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101) minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time) # slightly edit signal to make difference between slope-based method and improved slope-based method more clear time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \ time_series[time == minima_x[-1]] improved_slope_based_maximum_time = time[-1] improved_slope_based_maximum = time_series[-1] improved_slope_based_minimum_time = slope_based_minimum_time improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time - improved_slope_based_maximum_time) min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101) min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4) dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101) dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101) ax = plt.subplot(111) figure_size = plt.gcf().get_size_inches() factor = 0.9 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Slope-Based Edge Effects Example') plt.plot(max_dash_time_1, max_dash_1, 'k-') plt.plot(max_dash_time_2, max_dash_2, 'k-') plt.plot(max_dash_time_3, max_dash_3, 'k-') plt.plot(min_dash_time_1, min_dash_1, 'k-') plt.plot(min_dash_time_2, min_dash_2, 'k-') plt.plot(min_dash_time_3, min_dash_3, 'k-') plt.plot(min_dash_time_4, min_dash_4, 'k-') plt.plot(maxima_dash_time_1, maxima_dash, 'k-') plt.plot(maxima_dash_time_2, maxima_dash, 'k-') plt.plot(maxima_dash_time_3, maxima_dash, 'k-') plt.plot(minima_dash_time_1, minima_dash, 'k-') plt.plot(minima_dash_time_2, minima_dash, 'k-') plt.plot(minima_dash_time_3, minima_dash, 'k-') plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$') plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$') plt.text(4.30 * np.pi, 0.35, r'$s_1$') plt.text(4.43 * np.pi, -0.20, r'$s_2$') plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$') plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]), -0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]), 1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$') plt.plot(minima_line_dash_time, minima_line_dash, 'k--') plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(dash_3_time, dash_3, 'k--') plt.plot(dash_4_time, dash_4, 'k--') plt.plot(dash_final_time, dash_final, 'k--') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4, label=textwrap.fill('Slope-based maximum', 11)) plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4, label=textwrap.fill('Slope-based minimum', 11)) plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4, label=textwrap.fill('Improved slope-based maximum', 11)) plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4, label=textwrap.fill('Improved slope-based minimum', 11)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_slope_based.png') plt.show() # plot 5 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2 A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2 P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2]) P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1]) Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1] Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1] Coughlin_time = Huang_time Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0])) Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) Average_max = (maxima_y[-2] + maxima_y[-1]) / 2 Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) Average_min = (minima_y[-2] + minima_y[-1]) / 2 utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave) Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd() Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd() utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave) Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd() Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd() Huang_max_time = Huang_time[Huang_max_bool] Huang_max = Huang_wave[Huang_max_bool] Huang_min_time = Huang_time[Huang_min_bool] Huang_min = Huang_wave[Huang_min_bool] Coughlin_max_time = Coughlin_time[Coughlin_max_bool] Coughlin_max = Coughlin_wave[Coughlin_max_bool] Coughlin_min_time = Coughlin_time[Coughlin_min_bool] Coughlin_min = Coughlin_wave[Coughlin_min_bool] max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101) max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time) min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101) min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101) min_2_x = minima_y[-2] * np.ones_like(min_2_x_time) dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101) dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x) max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y) min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101) min_2_y_time = minima_x[-2] * np.ones_like(min_2_y) dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101) dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time) max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time) min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101) min_1_x = minima_y[-1] * np.ones_like(min_1_x_time) dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101) dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x) max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y) min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101) min_1_y_time = minima_x[-1] * np.ones_like(min_1_y) dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101) dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Characteristic Wave Effects Example') plt.plot(time, time_series, LineWidth=2, label='Signal') plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10)) plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10)) plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4, label=textwrap.fill('Coughlin maximum', 14)) plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4, label=textwrap.fill('Coughlin minimum', 14)) plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4, label=textwrap.fill('Average maximum', 14)) plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4, label=textwrap.fill('Average minimum', 14)) plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14)) plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14)) plt.plot(max_2_x_time, max_2_x, 'k-') plt.plot(max_2_x_time_side, max_2_x, 'k-') plt.plot(min_2_x_time, min_2_x, 'k-') plt.plot(min_2_x_time_side, min_2_x, 'k-') plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--') plt.text(5.16 * np.pi, 0.85, r'$2a_2$') plt.plot(max_2_y_time, max_2_y, 'k-') plt.plot(max_2_y_time, max_2_y_side, 'k-') plt.plot(min_2_y_time, min_2_y, 'k-') plt.plot(min_2_y_time, min_2_y_side, 'k-') plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--') plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$') plt.plot(max_1_x_time, max_1_x, 'k-') plt.plot(max_1_x_time_side, max_1_x, 'k-') plt.plot(min_1_x_time, min_1_x, 'k-') plt.plot(min_1_x_time_side, min_1_x, 'k-') plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--') plt.text(5.42 * np.pi, -0.1, r'$2a_1$') plt.plot(max_1_y_time, max_1_y, 'k-') plt.plot(max_1_y_time, max_1_y_side, 'k-') plt.plot(min_1_y_time, min_1_y, 'k-') plt.plot(min_1_y_time, min_1_y_side, 'k-') plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--') plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$') plt.xlim(3.9 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_characteristic_wave.png') plt.show() # plot 6 t = np.linspace(5, 95, 100) signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200) util_nn = emd_utils.Utility(time=t, time_series=signal_orig) maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()] minima = signal_orig[util_nn.min_bool_func_1st_order_fd()] cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima) cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima) time = np.linspace(0, 5 * np.pi, 1001) lsq_signal = np.cos(time) + np.cos(5 * time) knots = np.linspace(0, 5 * np.pi, 101) time_extended = time_extension(time) time_series_extended = np.zeros_like(time_extended) / 0 time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal neural_network_m = 200 neural_network_k = 100 # forward -> P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))] P[-1, col] = 1 # for additive constant t = lsq_signal[-neural_network_m:] # test - top seed_weights = np.ones(neural_network_k) / neural_network_k weights = 0 * seed_weights.copy() train_input = P[:-1, :] lr = 0.01 for iterations in range(1000): output = np.matmul(weights, train_input) error = (t - output) gradients = error * (- train_input) # guess average gradients average_gradients = np.mean(gradients, axis=1) # steepest descent max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients))) adjustment = - lr * average_gradients # adjustment = - lr * max_gradient_vector weights += adjustment # test - bottom weights_right = np.hstack((weights, 0)) max_count_right = 0 min_count_right = 0 i_right = 0 while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1): time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \ sum(weights_right * np.hstack((time_series_extended[ int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right): int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1))) i_right += 1 if i_right > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_right += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)], time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1): int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_right += 1 # backward <- P = np.zeros((int(neural_network_k + 1), neural_network_m)) for col in range(neural_network_m): P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)] P[-1, col] = 1 # for additive constant t = lsq_signal[:neural_network_m] vx = cvx.Variable(int(neural_network_k + 1)) objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary prob = cvx.Problem(objective) result = prob.solve(verbose=True, solver=cvx.ECOS) weights_left = np.array(vx.value) max_count_left = 0 min_count_left = 0 i_left = 0 while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1): time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \ 2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left): int(len(lsq_signal) - 1 - i_left + neural_network_k)], 1))) + 1 i_left += 1 if i_left > 1: emd_utils_max = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0: max_count_left += 1 emd_utils_min = \ emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))], time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))]) if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0: min_count_left += 1 lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal) utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended) maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()] maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()] maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1] maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1] minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()] minima_time = time[lsq_utils.min_bool_func_1st_order_fd()] minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:] ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('Single Neuron Neural Network Example') plt.plot(time, lsq_signal, zorder=2, label='Signal') plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12)) plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima') plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima') plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3, label=textwrap.fill('Extrapolated maxima', 12)) plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4, label=textwrap.fill('Extrapolated minima', 12)) plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k', label=textwrap.fill('Neural network inputs', 13)) plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2), ((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k') plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k') plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed', label=textwrap.fill('Neural network targets', 13)) plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray') plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2), ((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray') plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed') plt.xlim(3.4 * np.pi, 5.6 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/neural_network.png') plt.show() # plot 6a np.random.seed(0) time = np.linspace(0, 5 * np.pi, 1001) knots_51 = np.linspace(0, 5 * np.pi, 51) time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time) noise = np.random.normal(0, 1, len(time_series)) time_series += noise advemdpy = EMD(time=time, time_series=time_series) imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3, edge_effect='symmetric_anchor', verbose=False)[:3] knots_31 = np.linspace(0, 5 * np.pi, 31) imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2, edge_effect='symmetric_anchor', verbose=False)[:3] knots_11 = np.linspace(0, 5 * np.pi, 11) imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1, edge_effect='symmetric_anchor', verbose=False)[:3] fig, axs = plt.subplots(3, 1) plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40)) plt.subplots_adjust(hspace=0.1) axs[0].plot(time, time_series, label='Time series') axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21)) print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}') for knot in knots_51: axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[0].set_xticklabels(['', '', '', '', '', '']) axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(time, time_series, label='Time series') axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19)) axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19)) print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}') for knot in knots_31: axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[1].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[1].set_xticklabels(['', '', '', '', '', '']) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) axs[1].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--') axs[1].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--') axs[1].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--') axs[1].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region') axs[2].plot(time, time_series, label='Time series') axs[2].plot(time, imfs_11[1, :], label='IMF 1 with 11 knots') axs[2].plot(time, imfs_31[2, :], label='IMF 2 with 31 knots') axs[2].plot(time, imfs_51[3, :], label='IMF 3 with 51 knots') print(f'DFA fluctuation with 11 knots: {np.round(np.var(time_series - imfs_51[3, :]), 3)}') for knot in knots_11: axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1) axs[2].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots') axs[2].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi]) axs[2].set_xticklabels(['$0$', r'$\pi$', r'$2\pi$', r'$3\pi$', r'$4\pi$', r'$5\pi$']) box_2 = axs[2].get_position() axs[2].set_position([box_2.x0 - 0.05, box_2.y0, box_2.width * 0.85, box_2.height]) axs[2].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8) axs[2].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 *

np.ones(101)

numpy.ones

import numpy as np from typing import Tuple, Union, Optional from autoarray.structures.arrays.two_d import array_2d_util from autoarray.geometry import geometry_util from autoarray import numba_util from autoarray.mask import mask_2d_util @numba_util.jit() def grid_2d_centre_from(grid_2d_slim: np.ndarray) -> Tuple[float, float]: """ Returns the centre of a grid from a 1D grid. Parameters ---------- grid_2d_slim The 1D grid of values which are mapped to a 2D array. Returns ------- (float, float) The (y,x) central coordinates of the grid. """ centre_y = (np.max(grid_2d_slim[:, 0]) + np.min(grid_2d_slim[:, 0])) / 2.0 centre_x = (np.max(grid_2d_slim[:, 1]) + np.min(grid_2d_slim[:, 1])) / 2.0 return centre_y, centre_x @numba_util.jit() def grid_2d_slim_via_mask_from( mask_2d: np.ndarray, pixel_scales: Union[float, Tuple[float, float]], sub_size: int, origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into a finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x) scaled coordinates a the centre of every sub-pixel defined by this 2D mask array. The sub-grid is returned on an array of shape (total_unmasked_pixels*sub_size**2, 2). y coordinates are stored in the 0 index of the second dimension, x coordinates in the 1 index. Masked coordinates are therefore removed and not included in the slimmed grid. Grid2D are defined from the top-left corner, where the first unmasked sub-pixel corresponds to index 0. Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth. Parameters ---------- mask_2d A 2D array of bools, where `False` values are unmasked and therefore included as part of the calculated sub-grid. pixel_scales The (y,x) scaled units to pixel units conversion factor of the 2D mask array. sub_size The size of the sub-grid that each pixel of the 2D mask array is divided into. origin : (float, flloat) The (y,x) origin of the 2D array, which the sub-grid is shifted around. Returns ------- ndarray A slimmed sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask array. The sub grid array has dimensions (total_unmasked_pixels*sub_size**2, 2). Examples -------- mask = np.array([[True, False, True], [False, False, False] [True, False, True]]) grid_slim = grid_2d_slim_via_mask_from(mask=mask, pixel_scales=(0.5, 0.5), sub_size=1, origin=(0.0, 0.0)) """ total_sub_pixels = mask_2d_util.total_sub_pixels_2d_from(mask_2d, sub_size) grid_slim = np.zeros(shape=(total_sub_pixels, 2)) centres_scaled = geometry_util.central_scaled_coordinate_2d_from( shape_native=mask_2d.shape, pixel_scales=pixel_scales, origin=origin ) sub_index = 0 y_sub_half = pixel_scales[0] / 2 y_sub_step = pixel_scales[0] / (sub_size) x_sub_half = pixel_scales[1] / 2 x_sub_step = pixel_scales[1] / (sub_size) for y in range(mask_2d.shape[0]): for x in range(mask_2d.shape[1]): if not mask_2d[y, x]: y_scaled = (y - centres_scaled[0]) * pixel_scales[0] x_scaled = (x - centres_scaled[1]) * pixel_scales[1] for y1 in range(sub_size): for x1 in range(sub_size): grid_slim[sub_index, 0] = -( y_scaled - y_sub_half + y1 * y_sub_step + (y_sub_step / 2.0) ) grid_slim[sub_index, 1] = ( x_scaled - x_sub_half + x1 * x_sub_step + (x_sub_step / 2.0) ) sub_index += 1 return grid_slim def grid_2d_via_mask_from( mask_2d: np.ndarray, pixel_scales: Union[float, Tuple[float, float]], sub_size: int, origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into a finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x) scaled coordinates at the centre of every sub-pixel defined by this 2D mask array. The sub-grid is returned in its native dimensions with shape (total_y_pixels*sub_size, total_x_pixels*sub_size). y coordinates are stored in the 0 index of the second dimension, x coordinates in the 1 index. Masked pixels are given values (0.0, 0.0). Grids are defined from the top-left corner, where the first unmasked sub-pixel corresponds to index 0. Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth. Parameters ---------- mask_2d A 2D array of bools, where `False` values are unmasked and therefore included as part of the calculated sub-grid. pixel_scales The (y,x) scaled units to pixel units conversion factor of the 2D mask array. sub_size The size of the sub-grid that each pixel of the 2D mask array is divided into. origin : (float, flloat) The (y,x) origin of the 2D array, which the sub-grid is shifted around. Returns ------- ndarray A sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask array. The sub grid array has dimensions (total_y_pixels*sub_size, total_x_pixels*sub_size). Examples -------- mask = np.array([[True, False, True], [False, False, False] [True, False, True]]) grid_2d = grid_2d_via_mask_from(mask=mask, pixel_scales=(0.5, 0.5), sub_size=1, origin=(0.0, 0.0)) """ grid_2d_slim = grid_2d_slim_via_mask_from( mask_2d=mask_2d, pixel_scales=pixel_scales, sub_size=sub_size, origin=origin ) return grid_2d_native_from( grid_2d_slim=grid_2d_slim, mask_2d=mask_2d, sub_size=sub_size ) def grid_2d_slim_via_shape_native_from( shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], sub_size: int, origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into a finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x) scaled coordinates at the centre of every sub-pixel defined by this 2D mask array. The sub-grid is returned in its slimmed dimensions with shape (total_pixels**2*sub_size**2, 2). y coordinates are stored in the 0 index of the second dimension, x coordinates in the 1 index. Grid2D are defined from the top-left corner, where the first sub-pixel corresponds to index [0,0]. Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth. Parameters ---------- shape_native The (y,x) shape of the 2D array the sub-grid of coordinates is computed for. pixel_scales The (y,x) scaled units to pixel units conversion factor of the 2D mask array. sub_size The size of the sub-grid that each pixel of the 2D mask array is divided into. origin The (y,x) origin of the 2D array, which the sub-grid is shifted around. Returns ------- ndarray A sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask array. The sub grid is slimmed and has dimensions (total_unmasked_pixels*sub_size**2, 2). Examples -------- mask = np.array([[True, False, True], [False, False, False] [True, False, True]]) grid_2d_slim = grid_2d_slim_via_shape_native_from(shape_native=(3,3), pixel_scales=(0.5, 0.5), sub_size=2, origin=(0.0, 0.0)) """ return grid_2d_slim_via_mask_from( mask_2d=np.full(fill_value=False, shape=shape_native), pixel_scales=pixel_scales, sub_size=sub_size, origin=origin, ) def grid_2d_via_shape_native_from( shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], sub_size: int, origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ For a sub-grid, every unmasked pixel of its 2D mask with shape (total_y_pixels, total_x_pixels) is divided into a finer uniform grid of shape (total_y_pixels*sub_size, total_x_pixels*sub_size). This routine computes the (y,x) scaled coordinates at the centre of every sub-pixel defined by this 2D mask array. The sub-grid is returned in its native dimensions with shape (total_y_pixels*sub_size, total_x_pixels*sub_size). y coordinates are stored in the 0 index of the second dimension, x coordinates in the 1 index. Grids are defined from the top-left corner, where the first sub-pixel corresponds to index [0,0]. Sub-pixels that are part of the same mask array pixel are indexed next to one another, such that the second sub-pixel in the first pixel has index 1, its next sub-pixel has index 2, and so forth. Parameters ---------- shape_native The (y,x) shape of the 2D array the sub-grid of coordinates is computed for. pixel_scales The (y,x) scaled units to pixel units conversion factor of the 2D mask array. sub_size The size of the sub-grid that each pixel of the 2D mask array is divided into. origin : (float, flloat) The (y,x) origin of the 2D array, which the sub-grid is shifted around. Returns ------- ndarray A sub grid of (y,x) scaled coordinates at the centre of every pixel unmasked pixel on the 2D mask array. The sub grid array has dimensions (total_y_pixels*sub_size, total_x_pixels*sub_size). Examples -------- grid_2d = grid_2d_via_shape_native_from(shape_native=(3, 3), pixel_scales=(1.0, 1.0), sub_size=2, origin=(0.0, 0.0)) """ return grid_2d_via_mask_from( mask_2d=np.full(fill_value=False, shape=shape_native), pixel_scales=pixel_scales, sub_size=sub_size, origin=origin, ) @numba_util.jit() def grid_scaled_2d_slim_radial_projected_from( extent: np.ndarray, centre: Tuple[float, float], pixel_scales: Union[float, Tuple[float, float]], sub_size: int, shape_slim: Optional[int] = 0, ) -> np.ndarray: """ Determine a projected radial grid of points from a 2D region of coordinates defined by an extent [xmin, xmax, ymin, ymax] and with a (y,x) centre. This functions operates as follows: 1) Given the region defined by the extent [xmin, xmax, ymin, ymax], the algorithm finds the longest 1D distance of the 4 paths from the (y,x) centre to the edge of the region (e.g. following the positive / negative y and x axes). 2) Use the pixel-scale corresponding to the direction chosen (e.g. if the positive x-axis was the longest, the pixel_scale in the x dimension is used). 3) Determine the number of pixels between the centre and the edge of the region using the longest path between the two chosen above. 4) Create a (y,x) grid of radial points where all points are at the centre's y value = 0.0 and the x values iterate from the centre in increasing steps of the pixel-scale. 5) Rotate these radial coordinates by the input `angle` clockwise. A schematric is shown below: ------------------- | | |<- - - - ->x | x = centre | | <-> = longest radial path from centre to extent edge | | ------------------- Using the centre x above, this function finds the longest radial path to the edge of the extent window. The returned `grid_radii` represents a radial set of points that in 1D sample the 2D grid outwards from its centre. This grid stores the radial coordinates as (y,x) values (where all y values are the same) as opposed to a 1D data structure so that it can be used in functions which require that a 2D grid structure is input. Parameters ---------- extent The extent of the grid the radii grid is computed using, with format [xmin, xmax, ymin, ymax] centre : (float, flloat) The (y,x) central coordinate which the radial grid is traced outwards from. pixel_scales The (y,x) scaled units to pixel units conversion factor of the 2D mask array. sub_size The size of the sub-grid that each pixel of the 2D mask array is divided into. shape_slim Manually choose the shape of the 1D projected grid that is returned. If 0, the border based on the 2D grid is used (due to numba None cannot be used as a default value). Returns ------- ndarray A radial set of points sampling the longest distance from the centre to the edge of the extent in along the positive x-axis. """ distance_to_positive_x = extent[1] - centre[1] distance_to_positive_y = extent[3] - centre[0] distance_to_negative_x = centre[1] - extent[0] distance_to_negative_y = centre[0] - extent[2] scaled_distance = max( [ distance_to_positive_x, distance_to_positive_y, distance_to_negative_x, distance_to_negative_y, ] ) if (scaled_distance == distance_to_positive_y) or ( scaled_distance == distance_to_negative_y ): pixel_scale = pixel_scales[0] else: pixel_scale = pixel_scales[1] if shape_slim == 0: shape_slim = sub_size * int((scaled_distance / pixel_scale)) + 1 grid_scaled_2d_slim_radii = np.zeros((shape_slim, 2)) grid_scaled_2d_slim_radii[:, 0] += centre[0] radii = centre[1] for slim_index in range(shape_slim): grid_scaled_2d_slim_radii[slim_index, 1] = radii radii += pixel_scale / sub_size return grid_scaled_2d_slim_radii @numba_util.jit() def grid_pixels_2d_slim_from( grid_scaled_2d_slim: np.ndarray, shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ Convert a slimmed grid of 2d (y,x) scaled coordinates to a slimmed grid of 2d (y,x) pixel coordinate values. Pixel coordinates are returned as floats such that they include the decimal offset from each pixel's top-left corner relative to the input scaled coordinate. The input and output grids are both slimmed and therefore shape (total_pixels, 2). The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird. The scaled grid is defined by an origin and coordinates are shifted to this origin before computing their 1D grid pixel coordinate values. Parameters ---------- grid_scaled_2d_slim: np.ndarray The slimmed grid of 2D (y,x) coordinates in scaled units which are converted to pixel value coordinates. shape_native The (y,x) shape of the original 2D array the scaled coordinates were computed on. pixel_scales The (y,x) scaled units to pixel units conversion factor of the original 2D array. origin : (float, flloat) The (y,x) origin of the grid, which the scaled grid is shifted to. Returns ------- ndarray A slimmed grid of 2D (y,x) pixel-value coordinates with dimensions (total_pixels, 2). Examples -------- grid_scaled_2d_slim = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]]) grid_pixels_2d_slim = grid_scaled_2d_slim_from(grid_scaled_2d_slim=grid_scaled_2d_slim, shape=(2,2), pixel_scales=(0.5, 0.5), origin=(0.0, 0.0)) """ grid_pixels_2d_slim = np.zeros((grid_scaled_2d_slim.shape[0], 2)) centres_scaled = geometry_util.central_scaled_coordinate_2d_from( shape_native=shape_native, pixel_scales=pixel_scales, origin=origin ) for slim_index in range(grid_scaled_2d_slim.shape[0]): grid_pixels_2d_slim[slim_index, 0] = ( (-grid_scaled_2d_slim[slim_index, 0] / pixel_scales[0]) + centres_scaled[0] + 0.5 ) grid_pixels_2d_slim[slim_index, 1] = ( (grid_scaled_2d_slim[slim_index, 1] / pixel_scales[1]) + centres_scaled[1] + 0.5 ) return grid_pixels_2d_slim @numba_util.jit() def grid_pixel_centres_2d_slim_from( grid_scaled_2d_slim: np.ndarray, shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ Convert a slimmed grid of 2D (y,x) scaled coordinates to a slimmed grid of 2D (y,x) pixel values. Pixel coordinates are returned as integers such that they map directly to the pixel they are contained within. The input and output grids are both slimmed and therefore shape (total_pixels, 2). The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird. The scaled coordinate grid is defined by the class attribute origin, and coordinates are shifted to this origin before computing their 1D grid pixel indexes. Parameters ---------- grid_scaled_2d_slim: np.ndarray The slimmed grid of 2D (y,x) coordinates in scaled units which is converted to pixel indexes. shape_native The (y,x) shape of the original 2D array the scaled coordinates were computed on. pixel_scales The (y,x) scaled units to pixel units conversion factor of the original 2D array. origin : (float, flloat) The (y,x) origin of the grid, which the scaled grid is shifted Returns ------- ndarray A slimmed grid of 2D (y,x) pixel indexes with dimensions (total_pixels, 2). Examples -------- grid_scaled_2d_slim = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]]) grid_pixels_2d_slim = grid_scaled_2d_slim_from(grid_scaled_2d_slim=grid_scaled_2d_slim, shape=(2,2), pixel_scales=(0.5, 0.5), origin=(0.0, 0.0)) """ grid_pixels_2d_slim = np.zeros((grid_scaled_2d_slim.shape[0], 2)) centres_scaled = geometry_util.central_scaled_coordinate_2d_from( shape_native=shape_native, pixel_scales=pixel_scales, origin=origin ) for slim_index in range(grid_scaled_2d_slim.shape[0]): grid_pixels_2d_slim[slim_index, 0] = int( (-grid_scaled_2d_slim[slim_index, 0] / pixel_scales[0]) + centres_scaled[0] + 0.5 ) grid_pixels_2d_slim[slim_index, 1] = int( (grid_scaled_2d_slim[slim_index, 1] / pixel_scales[1]) + centres_scaled[1] + 0.5 ) return grid_pixels_2d_slim @numba_util.jit() def grid_pixel_indexes_2d_slim_from( grid_scaled_2d_slim: np.ndarray, shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ Convert a slimmed grid of 2D (y,x) scaled coordinates to a slimmed grid of pixel indexes. Pixel coordinates are returned as integers such that they are the pixel from the top-left of the 2D grid going rights and then downwards. The input and output grids are both slimmed and have shapes (total_pixels, 2) and (total_pixels,). For example: The pixel at the top-left, whose native index is [0,0], corresponds to slimmed pixel index 0. The fifth pixel on the top row, whose native index is [0,5], corresponds to slimmed pixel index 4. The first pixel on the second row, whose native index is [0,1], has slimmed pixel index 10 if a row has 10 pixels. The scaled coordinate grid is defined by the class attribute origin, and coordinates are shifted to this origin before computing their 1D grid pixel indexes. The input and output grids are both of shape (total_pixels, 2). Parameters ---------- grid_scaled_2d_slim: np.ndarray The slimmed grid of 2D (y,x) coordinates in scaled units which is converted to slimmed pixel indexes. shape_native The (y,x) shape of the original 2D array the scaled coordinates were computed on. pixel_scales The (y,x) scaled units to pixel units conversion factor of the original 2D array. origin : (float, flloat) The (y,x) origin of the grid, which the scaled grid is shifted. Returns ------- ndarray A grid of slimmed pixel indexes with dimensions (total_pixels,). Examples -------- grid_scaled_2d_slim = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]]) grid_pixel_indexes_2d_slim = grid_pixel_indexes_2d_slim_from(grid_scaled_2d_slim=grid_scaled_2d_slim, shape=(2,2), pixel_scales=(0.5, 0.5), origin=(0.0, 0.0)) """ grid_pixels_2d_slim = grid_pixel_centres_2d_slim_from( grid_scaled_2d_slim=grid_scaled_2d_slim, shape_native=shape_native, pixel_scales=pixel_scales, origin=origin, ) grid_pixel_indexes_2d_slim = np.zeros(grid_pixels_2d_slim.shape[0]) for slim_index in range(grid_pixels_2d_slim.shape[0]): grid_pixel_indexes_2d_slim[slim_index] = int( grid_pixels_2d_slim[slim_index, 0] * shape_native[1] + grid_pixels_2d_slim[slim_index, 1] ) return grid_pixel_indexes_2d_slim @numba_util.jit() def grid_scaled_2d_slim_from( grid_pixels_2d_slim: np.ndarray, shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ Convert a slimmed grid of 2D (y,x) pixel coordinates to a slimmed grid of 2D (y,x) scaled values. The input and output grids are both slimmed and therefore shape (total_pixels, 2). The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird. The scaled coordinate origin is defined by the class attribute origin, and coordinates are shifted to this origin after computing their values from the 1D grid pixel indexes. Parameters ---------- grid_pixels_2d_slim: np.ndarray The slimmed grid of (y,x) coordinates in pixel values which is converted to scaled coordinates. shape_native The (y,x) shape of the original 2D array the scaled coordinates were computed on. pixel_scales The (y,x) scaled units to pixel units conversion factor of the original 2D array. origin : (float, flloat) The (y,x) origin of the grid, which the scaled grid is shifted. Returns ------- ndarray A slimmed grid of 2d scaled coordinates with dimensions (total_pixels, 2). Examples -------- grid_pixels_2d_slim = np.array([[0,0], [0,1], [1,0], [1,1]) grid_pixels_2d_slim = grid_scaled_2d_slim_from(grid_pixels_2d_slim=grid_pixels_2d_slim, shape=(2,2), pixel_scales=(0.5, 0.5), origin=(0.0, 0.0)) """ grid_scaled_2d_slim = np.zeros((grid_pixels_2d_slim.shape[0], 2)) centres_scaled = geometry_util.central_scaled_coordinate_2d_from( shape_native=shape_native, pixel_scales=pixel_scales, origin=origin ) for slim_index in range(grid_scaled_2d_slim.shape[0]): grid_scaled_2d_slim[slim_index, 0] = ( -(grid_pixels_2d_slim[slim_index, 0] - centres_scaled[0] - 0.5) * pixel_scales[0] ) grid_scaled_2d_slim[slim_index, 1] = ( grid_pixels_2d_slim[slim_index, 1] - centres_scaled[1] - 0.5 ) * pixel_scales[1] return grid_scaled_2d_slim @numba_util.jit() def grid_pixel_centres_2d_from( grid_scaled_2d: np.ndarray, shape_native: Tuple[int, int], pixel_scales: Union[float, Tuple[float, float]], origin: Tuple[float, float] = (0.0, 0.0), ) -> np.ndarray: """ Convert a native grid of 2D (y,x) scaled coordinates to a native grid of 2D (y,x) pixel values. Pixel coordinates are returned as integers such that they map directly to the pixel they are contained within. The input and output grids are both native resolution and therefore have shape (y_pixels, x_pixels, 2). The pixel coordinate origin is at the top left corner of the grid, such that the pixel [0,0] corresponds to the highest (most positive) y scaled coordinate and lowest (most negative) x scaled coordinate on the gird. The scaled coordinate grid is defined by the class attribute origin, and coordinates are shifted to this origin before computing their 1D grid pixel indexes. Parameters ---------- grid_scaled_2d: np.ndarray The native grid of 2D (y,x) coordinates in scaled units which is converted to pixel indexes. shape_native The (y,x) shape of the original 2D array the scaled coordinates were computed on. pixel_scales The (y,x) scaled units to pixel units conversion factor of the original 2D array. origin : (float, flloat) The (y,x) origin of the grid, which the scaled grid is shifted Returns ------- ndarray A native grid of 2D (y,x) pixel indexes with dimensions (y_pixels, x_pixels, 2). Examples -------- grid_scaled_2d = np.array([[1.0, 1.0], [2.0, 2.0], [3.0, 3.0], [4.0, 4.0]]) grid_pixel_centres_2d = grid_pixel_centres_2d_from(grid_scaled_2d=grid_scaled_2d, shape=(2,2), pixel_scales=(0.5, 0.5), origin=(0.0, 0.0)) """ grid_pixels_2d = np.zeros((grid_scaled_2d.shape[0], grid_scaled_2d.shape[1], 2)) centres_scaled = geometry_util.central_scaled_coordinate_2d_from( shape_native=shape_native, pixel_scales=pixel_scales, origin=origin ) for y in range(grid_scaled_2d.shape[0]): for x in range(grid_scaled_2d.shape[1]): grid_pixels_2d[y, x, 0] = int( (-grid_scaled_2d[y, x, 0] / pixel_scales[0]) + centres_scaled[0] + 0.5 ) grid_pixels_2d[y, x, 1] = int( (grid_scaled_2d[y, x, 1] / pixel_scales[1]) + centres_scaled[1] + 0.5 ) return grid_pixels_2d @numba_util.jit() def relocated_grid_via_jit_from(grid, border_grid): """ Relocate the coordinates of a grid to its border if they are outside the border, where the border is defined as all pixels at the edge of the grid's mask (see *mask._border_1d_indexes*). This is performed as follows: 1: Use the mean value of the grid's y and x coordinates to determine the origin of the grid. 2: Compute the radial distance of every grid coordinate from the origin. 3: For every coordinate, find its nearest pixel in the border. 4: Determine if it is outside the border, by comparing its radial distance from the origin to its paired border pixel's radial distance. 5: If its radial distance is larger, use the ratio of radial distances to move the coordinate to the border (if its inside the border, do nothing). The method can be used on uniform or irregular grids, however for irregular grids the border of the 'image-plane' mask is used to define border pixels. Parameters ---------- grid : Grid2D The grid (uniform or irregular) whose pixels are to be relocated to the border edge if outside it. border_grid : Grid2D The grid of border (y,x) coordinates. """ grid_relocated = np.zeros(grid.shape) grid_relocated[:, :] = grid[:, :] border_origin = np.zeros(2) border_origin[0] = np.mean(border_grid[:, 0]) border_origin[1] = np.mean(border_grid[:, 1]) border_grid_radii = np.sqrt( np.add( np.square(np.subtract(border_grid[:, 0], border_origin[0])), np.square(np.subtract(border_grid[:, 1], border_origin[1])), ) ) border_min_radii = np.min(border_grid_radii) grid_radii = np.sqrt( np.add( np.square(np.subtract(grid[:, 0], border_origin[0])), np.square(

np.subtract(grid[:, 1], border_origin[1])

numpy.subtract

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 *

np.ones(101)

numpy.ones

import numpy as np import pytest import theano import theano.tensor as tt # Don't import test classes otherwise they get tested as part of the file from tests import unittest_tools as utt from tests.gpuarray.config import mode_with_gpu, mode_without_gpu, test_ctx_name from tests.tensor.test_basic import ( TestAlloc, TestComparison, TestJoinAndSplit, TestReshape, ) from tests.tensor.utils import rand, safe_make_node from theano.gpuarray.basic_ops import ( GpuAlloc, GpuAllocEmpty, GpuContiguous, GpuEye, GpuFromHost, GpuJoin, GpuReshape, GpuSplit, GpuToGpu, GpuTri, HostFromGpu, gpu_contiguous, gpu_join, host_from_gpu, ) from theano.gpuarray.elemwise import GpuDimShuffle, GpuElemwise from theano.gpuarray.subtensor import GpuSubtensor from theano.gpuarray.type import GpuArrayType, get_context, gpuarray_shared_constructor from theano.tensor import TensorType from theano.tensor.basic import alloc pygpu = pytest.importorskip("pygpu") gpuarray = pygpu.gpuarray utt.seed_rng() rng = np.random.RandomState(seed=utt.fetch_seed()) def inplace_func( inputs, outputs, mode=None, allow_input_downcast=False, on_unused_input="raise", name=None, ): if mode is None: mode = mode_with_gpu return theano.function( inputs, outputs, mode=mode, allow_input_downcast=allow_input_downcast, accept_inplace=True, on_unused_input=on_unused_input, name=name, ) def fake_shared(value, name=None, strict=False, allow_downcast=None, **kwargs): from theano.tensor.sharedvar import scalar_constructor, tensor_constructor for c in (gpuarray_shared_constructor, tensor_constructor, scalar_constructor): try: return c( value, name=name, strict=strict, allow_downcast=allow_downcast, **kwargs ) except TypeError: continue def rand_gpuarray(*shape, **kwargs): r = rng.rand(*shape) * 2 - 1 dtype = kwargs.pop("dtype", theano.config.floatX) cls = kwargs.pop("cls", None) if len(kwargs) != 0: raise TypeError("Unexpected argument %s", list(kwargs.keys())[0]) return gpuarray.array(r, dtype=dtype, cls=cls, context=get_context(test_ctx_name)) def makeTester( name, op, gpu_op, cases, checks=None, mode_gpu=mode_with_gpu, mode_nogpu=mode_without_gpu, skip=False, eps=1e-10, ): if checks is None: checks = {} _op = op _gpu_op = gpu_op _cases = cases _skip = skip _checks = checks class Checker(utt.OptimizationTestMixin): op = staticmethod(_op) gpu_op = staticmethod(_gpu_op) cases = _cases skip = _skip checks = _checks def setup_method(self): eval(self.__class__.__module__ + "." + self.__class__.__name__) def test_all(self): if skip: pytest.skip(skip) for testname, inputs in cases.items(): for _ in range(len(inputs)): if type(inputs[_]) is float: inputs[_] = np.asarray(inputs[_], dtype=theano.config.floatX) self.run_case(testname, inputs) def run_case(self, testname, inputs): inputs_ref = [theano.shared(inp) for inp in inputs] inputs_tst = [theano.shared(inp) for inp in inputs] try: node_ref = safe_make_node(self.op, *inputs_ref) node_tst = safe_make_node(self.op, *inputs_tst) except Exception as exc: err_msg = ( "Test %s::%s: Error occurred while making " "a node with inputs %s" ) % (self.gpu_op, testname, inputs) exc.args += (err_msg,) raise try: f_ref = inplace_func([], node_ref.outputs, mode=mode_nogpu) f_tst = inplace_func([], node_tst.outputs, mode=mode_gpu) except Exception as exc: err_msg = ( "Test %s::%s: Error occurred while trying to " "make a Function" ) % (self.gpu_op, testname) exc.args += (err_msg,) raise self.assertFunctionContains1(f_tst, self.gpu_op) ref_e = None try: expecteds = f_ref() except Exception as exc: ref_e = exc try: variables = f_tst() except Exception as exc: if ref_e is None: err_msg = ( "Test %s::%s: exception when calling the " "Function" ) % (self.gpu_op, testname) exc.args += (err_msg,) raise else: # if we raised an exception of the same type we're good. if isinstance(exc, type(ref_e)): return else: err_msg = ( "Test %s::%s: exception raised during test " "call was not the same as the reference " "call (got: %s, expected %s)" % (self.gpu_op, testname, type(exc), type(ref_e)) ) exc.args += (err_msg,) raise for i, (variable, expected) in enumerate(zip(variables, expecteds)): condition = ( variable.dtype != expected.dtype or variable.shape != expected.shape or not TensorType.values_eq_approx(variable, expected) ) assert not condition, ( "Test %s::%s: Output %s gave the wrong " "value. With inputs %s, expected %s " "(dtype %s), got %s (dtype %s)." % ( self.op, testname, i, inputs, expected, expected.dtype, variable, variable.dtype, ) ) for description, check in self.checks.items(): assert check(inputs, variables), ( "Test %s::%s: Failed check: %s " "(inputs were %s, ouputs were %s)" ) % (self.op, testname, description, inputs, variables) Checker.__name__ = name if hasattr(Checker, "__qualname__"): Checker.__qualname__ = name return Checker def test_transfer_cpu_gpu(): a = tt.fmatrix("a") g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g") av = np.asarray(rng.rand(5, 4), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) f = theano.function([a], GpuFromHost(test_ctx_name)(a)) fv = f(av) assert GpuArrayType.values_eq(fv, gv) f = theano.function([g], host_from_gpu(g)) fv = f(gv) assert np.all(fv == av) def test_transfer_gpu_gpu(): g = GpuArrayType( dtype="float32", broadcastable=(False, False), context_name=test_ctx_name )() av = np.asarray(rng.rand(5, 4), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) mode = mode_with_gpu.excluding( "cut_gpua_host_transfers", "local_cut_gpua_host_gpua" ) f = theano.function([g], GpuToGpu(test_ctx_name)(g), mode=mode) topo = f.maker.fgraph.toposort() assert len(topo) == 1 assert isinstance(topo[0].op, GpuToGpu) fv = f(gv) assert GpuArrayType.values_eq(fv, gv) def test_transfer_strided(): # This is just to ensure that it works in theano # libgpuarray has a much more comprehensive suit of tests to # ensure correctness a = tt.fmatrix("a") g = GpuArrayType(dtype="float32", broadcastable=(False, False))("g") av = np.asarray(rng.rand(5, 8), dtype="float32") gv = gpuarray.array(av, context=get_context(test_ctx_name)) av = av[:, ::2] gv = gv[:, ::2] f = theano.function([a], GpuFromHost(test_ctx_name)(a)) fv = f(av) assert GpuArrayType.values_eq(fv, gv) f = theano.function([g], host_from_gpu(g)) fv = f(gv) assert np.all(fv == av) def gpu_alloc_expected(x, *shp): g = gpuarray.empty(shp, dtype=x.dtype, context=get_context(test_ctx_name)) g[:] = x return g TestGpuAlloc = makeTester( name="GpuAllocTester", # The +1 is there to allow the lift to the GPU. op=lambda *args: alloc(*args) + 1, gpu_op=GpuAlloc(test_ctx_name), cases=dict( correct01=(rand(), np.int32(7)), # just gives a DeepCopyOp with possibly wrong results on the CPU # correct01_bcast=(rand(1), np.int32(7)), correct02=(rand(), np.int32(4), np.int32(7)), correct12=(rand(7), np.int32(4), np.int32(7)), correct13=(rand(7), np.int32(2), np.int32(4), np.int32(7)), correct23=(rand(4, 7), np.int32(2), np.int32(4), np.int32(7)), bad_shape12=(rand(7), np.int32(7), np.int32(5)), ), ) class TestGPUAlloc(TestAlloc): dtype = "float32" mode = mode_with_gpu shared = staticmethod(gpuarray_shared_constructor) allocs = [GpuAlloc(test_ctx_name), GpuAlloc(test_ctx_name), tt.Alloc()] def test_alloc_empty(): for dt in ["float32", "int8"]: f = theano.function([], GpuAllocEmpty(dt, context_name=test_ctx_name)(2, 3)) assert len(f.maker.fgraph.apply_nodes) == 1 out = f() assert out.shape == (2, 3) assert out.dtype == dt f = theano.function( [], [ GpuAllocEmpty("uint64", test_ctx_name)(3, 2), GpuAllocEmpty("uint64", test_ctx_name)(3, 2), ], ) out = f() assert out[0].shape == (3, 2) assert out[0].dtype == "uint64" assert out[1].shape == (3, 2) assert out[1].dtype == "uint64" assert ( len( [ node for node in f.maker.fgraph.apply_nodes if isinstance(node.op, GpuAllocEmpty) ] ) == 1 ) def test_shape(): x = GpuArrayType(dtype="float32", broadcastable=[False, False, False])() v = gpuarray.zeros((3, 4, 5), dtype="float32", context=get_context(test_ctx_name)) f = theano.function([x], x.shape) topo = f.maker.fgraph.toposort() assert np.all(f(v) == (3, 4, 5)) if theano.config.mode != "FAST_COMPILE": assert len(topo) == 4 assert isinstance(topo[0].op, tt.opt.Shape_i) assert isinstance(topo[1].op, tt.opt.Shape_i) assert isinstance(topo[2].op, tt.opt.Shape_i) assert isinstance(topo[3].op, tt.opt.MakeVector) mode = mode_with_gpu.excluding("local_shape_to_shape_i") f = theano.function([x], x.shape, mode=mode) topo = f.maker.fgraph.toposort() assert np.all(f(v) == (3, 4, 5)) assert len(topo) == 1 assert isinstance(topo[0].op, tt.Shape) def test_gpu_contiguous(): a = tt.fmatrix("a") i = tt.iscalar("i") a_val = np.asarray(np.random.rand(4, 5), dtype="float32") # The reshape is needed otherwise we make the subtensor on the CPU # to transfer less data. f = theano.function( [a, i], gpu_contiguous(a.reshape((5, 4))[::i]), mode=mode_with_gpu ) topo = f.maker.fgraph.toposort() assert any([isinstance(node.op, GpuSubtensor) for node in topo]) assert any([isinstance(node.op, GpuContiguous) for node in topo]) assert f(a_val, 1).flags.c_contiguous assert f(a_val, 2).flags.c_contiguous assert f(a_val, 2).flags.c_contiguous class TestGPUReshape(TestReshape): def setup_method(self): self.shared = gpuarray_shared_constructor self.op = GpuReshape self.mode = mode_with_gpu self.ignore_topo = ( HostFromGpu, GpuFromHost, theano.compile.DeepCopyOp, GpuDimShuffle, GpuElemwise, tt.opt.Shape_i, tt.opt.MakeVector, ) assert self.op == GpuReshape class TestGPUComparison(TestComparison): def setup_method(self): utt.seed_rng() self.mode = mode_with_gpu self.shared = gpuarray_shared_constructor self.dtypes = ["float64", "float32"] class TestGPUJoinAndSplit(TestJoinAndSplit): def setup_method(self): self.mode = mode_with_gpu.excluding("constant_folding") self.join_op = GpuJoin() self.split_op_class = GpuSplit # Use join instead of MakeVector since there is no MakeVector on GPU self.make_vector_op = GpuJoin() # this is to avoid errors with limited devices self.floatX = "float32" self.hide_error = theano.config.mode not in ["DebugMode", "DEBUG_MODE"] def shared(x, **kwargs): return gpuarray_shared_constructor(x, target=test_ctx_name, **kwargs) self.shared = shared def test_gpusplit_opt(self): # Test that we move the node to the GPU # Also test float16 computation at the same time. rng = np.random.RandomState(seed=utt.fetch_seed()) m = self.shared(rng.rand(4, 6).astype("float16")) o = tt.Split(2)(m, 0, [2, 2]) assert o[0].dtype == "float16" f = theano.function([], o, mode=self.mode) assert any( [ isinstance(node.op, self.split_op_class) for node in f.maker.fgraph.toposort() ] ) o1, o2 = f() assert np.allclose(o1, m.get_value(borrow=True)[:2]) assert np.allclose(o2, m.get_value(borrow=True)[2:]) def test_gpujoin_gpualloc(): a = tt.fmatrix("a") a_val = np.asarray(np.random.rand(4, 5), dtype="float32") b = tt.fmatrix("b") b_val = np.asarray(np.random.rand(3, 5), dtype="float32") f = theano.function( [a, b], tt.join(0, tt.zeros_like(a), tt.ones_like(b)) + 4, mode=mode_without_gpu ) f_gpu = theano.function( [a, b], tt.join(0, tt.zeros_like(a), tt.ones_like(b)), mode=mode_with_gpu ) f_gpu2 = theano.function( [a, b], tt.join(0, tt.zeros_like(a), tt.ones_like(b)) + 4, mode=mode_with_gpu ) assert sum([node.op == tt.alloc for node in f.maker.fgraph.toposort()]) == 2 assert sum([node.op == tt.join_ for node in f.maker.fgraph.toposort()]) == 1 assert ( sum([isinstance(node.op, GpuAlloc) for node in f_gpu.maker.fgraph.toposort()]) == 2 ) assert sum([node.op == gpu_join for node in f_gpu.maker.fgraph.toposort()]) == 1 assert ( sum([isinstance(node.op, GpuAlloc) for node in f_gpu2.maker.fgraph.toposort()]) == 2 ) assert sum([node.op == gpu_join for node in f_gpu2.maker.fgraph.toposort()]) == 1 assert np.allclose(f(a_val, b_val), f_gpu2(a_val, b_val)) def test_gpueye(): def check(dtype, N, M_=None, k=0): # Theano does not accept None as a tensor. # So we must use a real value. M = M_ # Currently DebugMode does not support None as inputs even if this is # allowed. if M is None: M = N N_symb = tt.iscalar() M_symb = tt.iscalar() k_symb = tt.iscalar() out = tt.eye(N_symb, M_symb, k_symb, dtype=dtype) + np.array(1).astype(dtype) f = theano.function([N_symb, M_symb, k_symb], out, mode=mode_with_gpu) result = np.asarray(f(N, M, k)) - np.array(1).astype(dtype) assert np.allclose(result, np.eye(N, M_, k, dtype=dtype)) assert result.dtype == np.dtype(dtype) assert any([isinstance(node.op, GpuEye) for node in f.maker.fgraph.toposort()]) for dtype in ["float32", "int32", "float16"]: check(dtype, 3) # M != N, k = 0 check(dtype, 3, 5) check(dtype, 5, 3) # N == M, k != 0 check(dtype, 3, 3, 1) check(dtype, 3, 3, -1) # N < M, k != 0 check(dtype, 3, 5, 1) check(dtype, 3, 5, -1) # N > M, k != 0 check(dtype, 5, 3, 1) check(dtype, 5, 3, -1) # k > M, -k > N, k > M, k > N check(dtype, 5, 3, 3) check(dtype, 3, 5, 3) check(dtype, 5, 3, -3) check(dtype, 3, 5, -3) check(dtype, 5, 3, 6) check(dtype, 3, 5, -6) def test_hostfromgpu_shape_i(): # Test that the shape is lifted over hostfromgpu m = mode_with_gpu.including( "local_dot_to_dot22", "local_dot22_to_dot22scalar", "specialize" ) a = tt.fmatrix("a") ca = theano.gpuarray.type.GpuArrayType("float32", (False, False))() av = np.asarray(np.random.rand(5, 4), dtype="float32") cv = gpuarray.asarray( np.random.rand(5, 4), dtype="float32", context=get_context(test_ctx_name) ) f = theano.function([a], GpuFromHost(test_ctx_name)(a), mode=m) assert any(isinstance(x.op, GpuFromHost) for x in f.maker.fgraph.toposort()) f = theano.function([a], GpuFromHost(test_ctx_name)(a).shape, mode=m) topo = f.maker.fgraph.toposort() assert isinstance(topo[0].op, tt.opt.Shape_i) assert isinstance(topo[1].op, tt.opt.Shape_i) assert isinstance(topo[2].op, tt.opt.MakeVector) assert tuple(f(av)) == (5, 4) f = theano.function([ca], host_from_gpu(ca), mode=m) assert host_from_gpu in [x.op for x in f.maker.fgraph.toposort()] f = theano.function([ca], host_from_gpu(ca).shape, mode=m) topo = f.maker.fgraph.toposort() assert isinstance(topo[0].op, theano.compile.Shape_i) assert isinstance(topo[1].op, theano.compile.Shape_i) assert isinstance(topo[2].op, tt.opt.MakeVector) assert tuple(f(cv)) == (5, 4) def test_Gpujoin_inplace(): # Test Gpujoin to work inplace. # # This function tests the case when several elements are passed to the # Gpujoin function but all except one of them are empty. In this case # Gpujoin should work inplace and the output should be the view of the # non-empty element. s = tt.lscalar() data = np.array([3, 4, 5], dtype=theano.config.floatX) x = gpuarray_shared_constructor(data, borrow=True) z = tt.zeros((s,)) join = GpuJoin(view=0) c = join(0, x, z) f = theano.function([s], theano.Out(c, borrow=True)) if not isinstance(mode_with_gpu, theano.compile.DebugMode): assert x.get_value(borrow=True, return_internal_type=True) is f(0) assert np.allclose(f(0), [3, 4, 5]) def test_gpu_tril_triu(): def check_l(m, k=0): m_symb = tt.matrix(dtype=m.dtype) k_symb = tt.iscalar() f = theano.function( [m_symb, k_symb], tt.tril(m_symb, k_symb), mode=mode_with_gpu ) result = f(m, k) assert np.allclose(result,

np.tril(m, k)

numpy.tril

from abc import ABCMeta, abstractmethod import os from vmaf.tools.misc import make_absolute_path, run_process from vmaf.tools.stats import ListStats __copyright__ = "Copyright 2016-2018, Netflix, Inc." __license__ = "Apache, Version 2.0" import re import numpy as np import ast from vmaf import ExternalProgramCaller, to_list from vmaf.config import VmafConfig, VmafExternalConfig from vmaf.core.executor import Executor from vmaf.core.result import Result from vmaf.tools.reader import YuvReader class FeatureExtractor(Executor): """ FeatureExtractor takes in a list of assets, and run feature extraction on them, and return a list of corresponding results. A FeatureExtractor must specify a unique type and version combination (by the TYPE and VERSION attribute), so that the Result generated by it can be identified. A derived class of FeatureExtractor must: 1) Override TYPE and VERSION 2) Override _generate_result(self, asset), which call a command-line executable and generate feature scores in a log file. 3) Override _get_feature_scores(self, asset), which read the feature scores from the log file, and return the scores in a dictionary format. For an example, follow VmafFeatureExtractor. """ __metaclass__ = ABCMeta @property @abstractmethod def ATOM_FEATURES(self): raise NotImplementedError def _read_result(self, asset): result = {} result.update(self._get_feature_scores(asset)) executor_id = self.executor_id return Result(asset, executor_id, result) @classmethod def get_scores_key(cls, atom_feature): return "{type}_{atom_feature}_scores".format( type=cls.TYPE, atom_feature=atom_feature) @classmethod def get_score_key(cls, atom_feature): return "{type}_{atom_feature}_score".format( type=cls.TYPE, atom_feature=atom_feature) def _get_feature_scores(self, asset): # routine to read the feature scores from the log file, and return # the scores in a dictionary format. log_file_path = self._get_log_file_path(asset) atom_feature_scores_dict = {} atom_feature_idx_dict = {} for atom_feature in self.ATOM_FEATURES: atom_feature_scores_dict[atom_feature] = [] atom_feature_idx_dict[atom_feature] = 0 with open(log_file_path, 'rt') as log_file: for line in log_file.readlines(): for atom_feature in self.ATOM_FEATURES: re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature) mo = re.match(re_template, line) if mo: cur_idx = int(mo.group(1)) assert cur_idx == atom_feature_idx_dict[atom_feature] # parse value, allowing NaN and inf val = float(mo.group(2)) if np.isnan(val) or np.isinf(val): val = None atom_feature_scores_dict[atom_feature].append(val) atom_feature_idx_dict[atom_feature] += 1 continue len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]]) assert len_score != 0 for atom_feature in self.ATOM_FEATURES[1:]: assert len_score == len(atom_feature_scores_dict[atom_feature]), \ "Feature data possibly corrupt. Run cleanup script and try again." feature_result = {} for atom_feature in self.ATOM_FEATURES: scores_key = self.get_scores_key(atom_feature) feature_result[scores_key] = atom_feature_scores_dict[atom_feature] return feature_result class VmafFeatureExtractor(FeatureExtractor): TYPE = "VMAF_feature" # VERSION = '0.1' # vmaf_study; Anush's VIF fix # VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr # VERSION = '0.2.1' # expose vif num/den of each scale # VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case # VERSION = '0.2.2b' # expose adm_den/num_scalex # VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef # VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step # VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2 VERSION = '0.2.4c' # Modify by moving motion2 to c code ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2', 'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr', 'vif_num_scale0', 'vif_den_scale0', 'vif_num_scale1', 'vif_den_scale1', 'vif_num_scale2', 'vif_den_scale2', 'vif_num_scale3', 'vif_den_scale3', 'adm_num_scale0', 'adm_den_scale0', 'adm_num_scale1', 'adm_den_scale1', 'adm_num_scale2', 'adm_den_scale2', 'adm_num_scale3', 'adm_den_scale3', ] DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3', 'vif2', 'adm2', 'adm3', 'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3', ] ADM2_CONSTANT = 0 ADM_SCALE_CONSTANT = 0 def _generate_result(self, asset): # routine to call the command-line executable and generate feature # scores in the log file. quality_width, quality_height = asset.quality_width_height log_file_path = self._get_log_file_path(asset) yuv_type=self._get_workfile_yuv_type(asset) ref_path=asset.ref_workfile_path dis_path=asset.dis_workfile_path w=quality_width h=quality_height logger = self.logger ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger) @classmethod def _post_process_result(cls, result): # override Executor._post_process_result result = super(VmafFeatureExtractor, cls)._post_process_result(result) # adm2 = # (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT) adm2_scores_key = cls.get_scores_key('adm2') adm_num_scores_key = cls.get_scores_key('adm_num') adm_den_scores_key = cls.get_scores_key('adm_den') result.result_dict[adm2_scores_key] = list( (np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) / (np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT) ) # vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3 vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0') vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0') vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1') vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1') vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2') vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2') vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3') vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3') vif_scale0_scores_key = cls.get_scores_key('vif_scale0') vif_scale1_scores_key = cls.get_scores_key('vif_scale1') vif_scale2_scores_key = cls.get_scores_key('vif_scale2') vif_scale3_scores_key = cls.get_scores_key('vif_scale3') result.result_dict[vif_scale0_scores_key] = list( (np.array(result.result_dict[vif_num_scale0_scores_key]) / np.array(result.result_dict[vif_den_scale0_scores_key])) ) result.result_dict[vif_scale1_scores_key] = list( (np.array(result.result_dict[vif_num_scale1_scores_key]) / np.array(result.result_dict[vif_den_scale1_scores_key])) ) result.result_dict[vif_scale2_scores_key] = list( (np.array(result.result_dict[vif_num_scale2_scores_key]) / np.array(result.result_dict[vif_den_scale2_scores_key])) ) result.result_dict[vif_scale3_scores_key] = list( (np.array(result.result_dict[vif_num_scale3_scores_key]) / np.array(result.result_dict[vif_den_scale3_scores_key])) ) # vif2 = # ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) + # (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0 vif_scores_key = cls.get_scores_key('vif2') result.result_dict[vif_scores_key] = list( ( (np.array(result.result_dict[vif_num_scale0_scores_key]) / np.array(result.result_dict[vif_den_scale0_scores_key])) + (np.array(result.result_dict[vif_num_scale1_scores_key]) / np.array(result.result_dict[vif_den_scale1_scores_key])) + (np.array(result.result_dict[vif_num_scale2_scores_key]) / np.array(result.result_dict[vif_den_scale2_scores_key])) + (np.array(result.result_dict[vif_num_scale3_scores_key]) / np.array(result.result_dict[vif_den_scale3_scores_key])) ) / 4.0 ) # adm_scalei = adm_num_scalei / adm_den_scalei, i = 0, 1, 2, 3 adm_num_scale0_scores_key = cls.get_scores_key('adm_num_scale0') adm_den_scale0_scores_key = cls.get_scores_key('adm_den_scale0') adm_num_scale1_scores_key = cls.get_scores_key('adm_num_scale1') adm_den_scale1_scores_key = cls.get_scores_key('adm_den_scale1') adm_num_scale2_scores_key = cls.get_scores_key('adm_num_scale2') adm_den_scale2_scores_key = cls.get_scores_key('adm_den_scale2') adm_num_scale3_scores_key = cls.get_scores_key('adm_num_scale3') adm_den_scale3_scores_key = cls.get_scores_key('adm_den_scale3') adm_scale0_scores_key = cls.get_scores_key('adm_scale0') adm_scale1_scores_key = cls.get_scores_key('adm_scale1') adm_scale2_scores_key = cls.get_scores_key('adm_scale2') adm_scale3_scores_key = cls.get_scores_key('adm_scale3') result.result_dict[adm_scale0_scores_key] = list( (np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale1_scores_key] = list( (np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale2_scores_key] = list( (np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) ) result.result_dict[adm_scale3_scores_key] = list( (np.array(result.result_dict[adm_num_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT) ) # adm3 = \ # (((adm_num_scale0 + ADM_SCALE_CONSTANT) / (adm_den_scale0 + ADM_SCALE_CONSTANT)) # + ((adm_num_scale1 + ADM_SCALE_CONSTANT) / (adm_den_scale1 + ADM_SCALE_CONSTANT)) # + ((adm_num_scale2 + ADM_SCALE_CONSTANT) / (adm_den_scale2 + ADM_SCALE_CONSTANT)) # + ((adm_num_scale3 + ADM_SCALE_CONSTANT) / (adm_den_scale3 + ADM_SCALE_CONSTANT))) / 4.0 adm3_scores_key = cls.get_scores_key('adm3') result.result_dict[adm3_scores_key] = list( ( ((np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)) + ((np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)) + ((np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)) + ((np.array(result.result_dict[adm_num_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT) / (np.array(result.result_dict[adm_den_scale3_scores_key]) + cls.ADM_SCALE_CONSTANT)) ) / 4.0 ) # validate for feature in cls.DERIVED_ATOM_FEATURES: assert cls.get_scores_key(feature) in result.result_dict return result class VifFrameDifferenceFeatureExtractor(FeatureExtractor): TYPE = "VifDiff_feature" VERSION = '0.1' ATOM_FEATURES = ['vifdiff', 'vifdiff_num', 'vifdiff_den', 'vifdiff_num_scale0', 'vifdiff_den_scale0', 'vifdiff_num_scale1', 'vifdiff_den_scale1', 'vifdiff_num_scale2', 'vifdiff_den_scale2', 'vifdiff_num_scale3', 'vifdiff_den_scale3', ] DERIVED_ATOM_FEATURES = ['vifdiff_scale0', 'vifdiff_scale1', 'vifdiff_scale2', 'vifdiff_scale3', ] ADM2_CONSTANT = 0 ADM_SCALE_CONSTANT = 0 def _generate_result(self, asset): # routine to call the command-line executable and generate feature # scores in the log file. quality_width, quality_height = asset.quality_width_height log_file_path = self._get_log_file_path(asset) yuv_type=self._get_workfile_yuv_type(asset) ref_path=asset.ref_workfile_path dis_path=asset.dis_workfile_path w=quality_width h=quality_height logger = self.logger ExternalProgramCaller.call_vifdiff_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger) @classmethod def _post_process_result(cls, result): # override Executor._post_process_result result = super(VifFrameDifferenceFeatureExtractor, cls)._post_process_result(result) # vifdiff_scalei = vifdiff_num_scalei / vifdiff_den_scalei, i = 0, 1, 2, 3 vifdiff_num_scale0_scores_key = cls.get_scores_key('vifdiff_num_scale0') vifdiff_den_scale0_scores_key = cls.get_scores_key('vifdiff_den_scale0') vifdiff_num_scale1_scores_key = cls.get_scores_key('vifdiff_num_scale1') vifdiff_den_scale1_scores_key = cls.get_scores_key('vifdiff_den_scale1') vifdiff_num_scale2_scores_key = cls.get_scores_key('vifdiff_num_scale2') vifdiff_den_scale2_scores_key = cls.get_scores_key('vifdiff_den_scale2') vifdiff_num_scale3_scores_key = cls.get_scores_key('vifdiff_num_scale3') vifdiff_den_scale3_scores_key = cls.get_scores_key('vifdiff_den_scale3') vifdiff_scale0_scores_key = cls.get_scores_key('vifdiff_scale0') vifdiff_scale1_scores_key = cls.get_scores_key('vifdiff_scale1') vifdiff_scale2_scores_key = cls.get_scores_key('vifdiff_scale2') vifdiff_scale3_scores_key = cls.get_scores_key('vifdiff_scale3') result.result_dict[vifdiff_scale0_scores_key] = list( (np.array(result.result_dict[vifdiff_num_scale0_scores_key]) / np.array(result.result_dict[vifdiff_den_scale0_scores_key])) ) result.result_dict[vifdiff_scale1_scores_key] = list( (np.array(result.result_dict[vifdiff_num_scale1_scores_key]) / np.array(result.result_dict[vifdiff_den_scale1_scores_key])) ) result.result_dict[vifdiff_scale2_scores_key] = list( (np.array(result.result_dict[vifdiff_num_scale2_scores_key]) / np.array(result.result_dict[vifdiff_den_scale2_scores_key])) ) result.result_dict[vifdiff_scale3_scores_key] = list( (np.array(result.result_dict[vifdiff_num_scale3_scores_key]) /

np.array(result.result_dict[vifdiff_den_scale3_scores_key])

numpy.array

# pvtrace is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation; either version 3 of the License, or # (at your option) any later version. # # pvtrace is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # # You should have received a copy of the GNU General Public License # along with this program. If not, see <http://www.gnu.org/licenses/>. import numpy as np from external.transformations import translation_matrix, rotation_matrix import external.transformations as tf from Trace import Photon from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm from Materials import Spectrum def random_spherecial_vector(): # This method of calculating isotropic vectors is taken from GNU Scientific Library LOOP = True while LOOP: x = -1. + 2. * np.random.uniform() y = -1. + 2. * np.random.uniform() s = x**2 + y**2 if s <= 1.0: LOOP = False z = -1. + 2. * s a = 2 * np.sqrt(1 - s) x = a * x y = a * y return np.array([x,y,z]) class SimpleSource(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False): super(SimpleSource, self).__init__() self.position = position self.direction = direction self.wavelength = wavelength self.use_random_polarisation = use_random_polarisation self.throw = 0 self.source_id = "SimpleSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength # If use_polarisation is set generate a random polarisation vector of the photon if self.use_random_polarisation: # Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon vec = random_spherecial_vector() vec[2] = 0. vec = norm(vec) R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1]) photon.polarisation = transform_direction(vec, R) else: photon.polarisation = None photon.id = self.throw self.throw = self.throw + 1 return photon class Laser(object): """A light source that will generate photons of a single colour, direction and position.""" def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None): super(Laser, self).__init__() self.position = np.array(position) self.direction = np.array(direction) self.wavelength = wavelength assert polarisation != None, "Polarisation of the Laser is not set." self.polarisation = np.array(polarisation) self.throw = 0 self.source_id = "LaserSource_" + str(id(self)) def photon(self): photon = Photon() photon.source = self.source_id photon.position = np.array(self.position) photon.direction = np.array(self.direction) photon.active = True photon.wavelength = self.wavelength photon.polarisation = self.polarisation photon.id = self.throw self.throw = self.throw + 1 return photon class PlanarSource(object): """A box that emits photons from the top surface (normal), sampled from the spectrum.""" def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05): super(PlanarSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.plane = FinitePlane(length=length, width=width) self.length = length self.width = width # direction is the direction that photons are fired out of the plane in the GLOBAL FRAME. # i.e. this is passed directly to the photon to set is's direction self.direction = direction self.throw = 0 self.source_id = "PlanarSource_" + str(id(self)) def translate(self, translation): self.plane.append_transform(tf.translation_matrix(translation)) def rotate(self, angle, axis): self.plane.append_transform(tf.rotation_matrix(angle, axis)) def photon(self): photon = Photon() photon.source = self.source_id photon.id = self.throw self.throw = self.throw + 1 # Create a point which is on the surface of the finite plane in it's local frame x = np.random.uniform(0., self.length) y = np.random.uniform(0., self.width) local_point = (x, y, 0.) # Transform the direciton photon.position = transform_point(local_point, self.plane.transform) photon.direction = self.direction photon.active = True if self.spectrum != None: photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform()) else: photon.wavelength = self.wavelength return photon class LensSource(object): """ A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize". The focus line should be perpendicular to the plane normal and aligned with the z-axis. """ def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)): super(LensSource, self).__init__() self.spectrum = spectrum self.wavelength = wavelength self.planeorigin = planeorigin self.planeextent = planeextent self.linepoint =

np.array(linepoint)

numpy.array

# ________ # / # \ / # \ / # \/ import random import textwrap import emd_mean import AdvEMDpy import emd_basis import emd_utils import numpy as np import pandas as pd import cvxpy as cvx import seaborn as sns import matplotlib.pyplot as plt from scipy.integrate import odeint from scipy.ndimage import gaussian_filter from emd_utils import time_extension, Utility from scipy.interpolate import CubicSpline from emd_hilbert import Hilbert, hilbert_spectrum from emd_preprocess import Preprocess from emd_mean import Fluctuation from AdvEMDpy import EMD # alternate packages from PyEMD import EMD as pyemd0215 import emd as emd040 sns.set(style='darkgrid') pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001) pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time) pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series) # plot 0 - addition fig = plt.figure(figsize=(9, 4)) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.title('First Iteration of Sifting Algorithm') plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1) plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()], c='r', label=r'$M(t_i)$', zorder=2) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4) plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()], pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()], c='c', label=r'$m(t_j)$', zorder=3) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5) plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5) plt.yticks(ticks=[-2, -1, 0, 1, 2]) plt.xticks(ticks=[0, np.pi, 2 * np.pi], labels=[r'0', r'$\pi$', r'$2\pi$']) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/pseudo_algorithm.png') plt.show() knots = np.arange(12) time = np.linspace(0, 11, 1101) basis = emd_basis.Basis(time=time, time_series=time) b_spline_basis = basis.cubic_b_spline(knots) chsi_basis = basis.chsi_basis(knots) # plot 1 plt.title('Non-Natural Cubic B-Spline Bases at Boundary') plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $') plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $') plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $') plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $') plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $') plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $']) plt.xlim(4.4, 6.6) plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') plt.legend(loc='upper left') plt.savefig('jss_figures/boundary_bases.png') plt.show() # plot 1a - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) knots_uniform = np.linspace(0, 2 * np.pi, 51) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0] fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Uniform Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Uniform Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Uniform Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots_uniform)): axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_uniform.png') plt.show() # plot 1b - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=1, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Statically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Statically Optimised Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Statically Optimised Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots)): axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_1.png') plt.show() # plot 1c - addition knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001) knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time) emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series) imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric', optimise_knots=2, verbose=False) fig, axs = plt.subplots(3, 1) fig.subplots_adjust(hspace=0.6) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Time Series and Dynamically Optimised Knots') axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100) axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].set_title('IMF 1 and Dynamically Knots') axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[2].set_title('IMF 2 and Dynamically Knots') axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100) axs[2].set_yticks(ticks=[-2, 0, 2]) axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[0].legend(loc='lower left') axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots') for i in range(3): for j in range(1, len(knots[i])): axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey') plt.savefig('jss_figures/knot_2.png') plt.show() # plot 1d - addition window = 81 fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Filtering Demonstration') axs[1].set_title('Zoomed Region') preprocess_time = pseudo_alg_time.copy() np.random.seed(1) random.seed(1) preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time)) for i in random.sample(range(1000), 500): preprocess_time_series[i] += np.random.normal(0, 1) preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series) axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12)) axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13)) axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12)) axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize interpolation filter', 14)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey', label=textwrap.fill('Quantile window', 12)) axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey') axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_filter.png') plt.show() # plot 1e - addition fig, axs = plt.subplots(2, 1) fig.subplots_adjust(hspace=0.4) figure_size = plt.gcf().get_size_inches() factor = 0.8 plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1])) plt.gcf().subplots_adjust(bottom=0.10) axs[0].set_title('Preprocess Smoothing Demonstration') axs[1].set_title('Zoomed Region') axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[0].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[0].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) downsampled_and_decimated = preprocess.downsample() axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 11)) downsampled = preprocess.downsample(decimate=False) axs[0].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black', label=textwrap.fill('Zoomed region', 10)) axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black') axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black') axs[0].set_yticks(ticks=[-2, 0, 2]) axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi]) axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$']) axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)') axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12)) axs[1].plot(preprocess_time, preprocess.hp()[1], label=textwrap.fill('Hodrick-Prescott smoothing', 12)) axs[1].plot(preprocess_time, preprocess.hw(order=51)[1], label=textwrap.fill('Henderson-Whittaker smoothing', 13)) axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1], label=textwrap.fill('Downsampled & decimated', 13)) axs[1].plot(downsampled[0], downsampled[1], label=textwrap.fill('Downsampled', 13)) axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi) axs[1].set_ylim(-3, 3) axs[1].set_yticks(ticks=[-2, 0, 2]) axs[1].set_xticks(ticks=[np.pi]) axs[1].set_xticklabels(labels=[r'$\pi$']) box_0 = axs[0].get_position() axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height]) axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15)) box_1 = axs[1].get_position() axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height]) plt.savefig('jss_figures/preprocess_smooth.png') plt.show() # plot 2 fig, axs = plt.subplots(1, 2, sharey=True) axs[0].set_title('Cubic B-Spline Bases') axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1') axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2') axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3') axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4') axs[0].legend(loc='upper left') axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-') axs[0].set_xticks([5, 6]) axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[0].set_xlim(4.5, 6.5) axs[1].set_title('Cubic Hermite Spline Bases') axs[1].plot(time, chsi_basis[10, :].T, '--') axs[1].plot(time, chsi_basis[11, :].T, '--') axs[1].plot(time, chsi_basis[12, :].T, '--') axs[1].plot(time, chsi_basis[13, :].T, '--') axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-') axs[1].set_xticks([5, 6]) axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $']) axs[1].set_xlim(4.5, 6.5) plt.savefig('jss_figures/comparing_bases.png') plt.show() # plot 3 a = 0.25 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101) max_dash = maxima_y[-1] * np.ones_like(max_dash_time) min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) min_dash = minima_y[-1] * np.ones_like(min_dash_time) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) max_discard = maxima_y[-1] max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1] max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101) max_discard_dash = max_discard * np.ones_like(max_discard_dash_time) dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101) dash_2 = np.linspace(minima_y[-1], max_discard, 101) end_point_time = time[-1] end_point = time_series[-1] time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101) time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi, (5 - a) * np.pi, 101))) time_series_anti_reflect = time_series_reflect[0] - time_series_reflect utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect) anti_max_bool = utils.max_bool_func_1st_order_fd() anti_max_point_time = time_reflect[anti_max_bool] anti_max_point = time_series_anti_reflect[anti_max_bool] utils = emd_utils.Utility(time=time, time_series=time_series_reflect) no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()] no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()] point_1 = 5.4 length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101) length_distance_time = point_1 * np.pi * np.ones_like(length_distance) length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101) length_top = maxima_y[-1] * np.ones_like(length_time) length_bottom = minima_y[-1] * np.ones_like(length_time) point_2 = 5.2 length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101) length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2) length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101) length_top_2 = time_series[-1] * np.ones_like(length_time_2) length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2) symmetry_axis_1_time = minima_x[-1] * np.ones(101) symmetry_axis_2_time = time[-1] * np.ones(101) symmetry_axis = np.linspace(-2, 2, 101) end_time = np.linspace(time[-1] - width, time[-1] + width, 101) end_signal = time_series[-1] * np.ones_like(end_time) anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101) anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time) ax = plt.subplot(111) plt.gcf().subplots_adjust(bottom=0.10) plt.plot(time, time_series, LineWidth=2, label='Signal') plt.title('Symmetry Edge Effects Example') plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10)) plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2, label=textwrap.fill('Anti-symmetric signal', 10)) plt.plot(max_dash_time, max_dash, 'k-') plt.plot(min_dash_time, min_dash, 'k-') plt.plot(dash_1_time, dash_1, 'k--') plt.plot(dash_2_time, dash_2, 'k--') plt.plot(length_distance_time, length_distance, 'k--') plt.plot(length_distance_time_2, length_distance_2, 'k--') plt.plot(length_time, length_top, 'k-') plt.plot(length_time, length_bottom, 'k-') plt.plot(length_time_2, length_top_2, 'k-') plt.plot(length_time_2, length_bottom_2, 'k-') plt.plot(end_time, end_signal, 'k-') plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1) plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1) plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1) plt.text(5.1 * np.pi, -0.7, r'$\beta$L') plt.text(5.34 * np.pi, -0.05, 'L') plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima') plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima') plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10)) plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10)) plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10)) plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10)) plt.xlim(3.9 * np.pi, 5.5 * np.pi) plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$')) plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2')) box_0 = ax.get_position() ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height]) ax.legend(loc='center left', bbox_to_anchor=(1, 0.5)) plt.savefig('jss_figures/edge_effects_symmetry_anti.png') plt.show() # plot 4 a = 0.21 width = 0.2 time = np.linspace(0, (5 - a) * np.pi, 1001) time_series = np.cos(time) + np.cos(5 * time) utils = emd_utils.Utility(time=time, time_series=time_series) max_bool = utils.max_bool_func_1st_order_fd() maxima_x = time[max_bool] maxima_y = time_series[max_bool] min_bool = utils.min_bool_func_1st_order_fd() minima_x = time[min_bool] minima_y = time_series[min_bool] max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101) max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101) max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1) max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1) min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101) min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101) min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1) min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1) dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101) dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101) dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101) dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101) s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1]) slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2]) slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1 max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1) max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101) dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101) dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101) s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1]) slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2]) slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2 min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1) min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101) dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time) dash_4 = np.linspace(slope_based_maximum, slope_based_minimum) maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101) maxima_dash_time_1 = maxima_x[-2] *

np.ones_like(maxima_dash)

numpy.ones_like

# coding: utf-8 # Licensed under a 3-clause BSD style license - see LICENSE.rst """ Test the Logarithmic Units and Quantities """ from __future__ import (absolute_import, unicode_literals, division, print_function) from ...extern import six from ...extern.six.moves import zip import pickle import itertools import pytest import numpy as np from numpy.testing.utils import assert_allclose from ...tests.helper import assert_quantity_allclose from ... import units as u, constants as c lu_units = [u.dex, u.mag, u.decibel] lu_subclasses = [u.DexUnit, u.MagUnit, u.DecibelUnit] lq_subclasses = [u.Dex, u.Magnitude, u.Decibel] pu_sample = (u.dimensionless_unscaled, u.m, u.g/u.s**2, u.Jy) class TestLogUnitCreation(object): def test_logarithmic_units(self): """Check logarithmic units are set up correctly.""" assert u.dB.to(u.dex) == 0.1 assert u.dex.to(u.mag) == -2.5 assert u.mag.to(u.dB) == -4 @pytest.mark.parametrize('lu_unit, lu_cls', zip(lu_units, lu_subclasses)) def test_callable_units(self, lu_unit, lu_cls): assert isinstance(lu_unit, u.UnitBase) assert callable(lu_unit) assert lu_unit._function_unit_class is lu_cls @pytest.mark.parametrize('lu_unit', lu_units) def test_equality_to_normal_unit_for_dimensionless(self, lu_unit): lu = lu_unit() assert lu == lu._default_function_unit # eg, MagUnit() == u.mag assert lu._default_function_unit == lu # and u.mag == MagUnit() @pytest.mark.parametrize('lu_unit, physical_unit', itertools.product(lu_units, pu_sample)) def test_call_units(self, lu_unit, physical_unit): """Create a LogUnit subclass using the callable unit and physical unit, and do basic check that output is right.""" lu1 = lu_unit(physical_unit) assert lu1.physical_unit == physical_unit assert lu1.function_unit == lu1._default_function_unit def test_call_invalid_unit(self): with pytest.raises(TypeError): u.mag([]) with pytest.raises(ValueError): u.mag(u.mag()) @pytest.mark.parametrize('lu_cls, physical_unit', itertools.product( lu_subclasses + [u.LogUnit], pu_sample)) def test_subclass_creation(self, lu_cls, physical_unit): """Create a LogUnit subclass object for given physical unit, and do basic check that output is right.""" lu1 = lu_cls(physical_unit) assert lu1.physical_unit == physical_unit assert lu1.function_unit == lu1._default_function_unit lu2 = lu_cls(physical_unit, function_unit=2*lu1._default_function_unit) assert lu2.physical_unit == physical_unit assert lu2.function_unit == u.Unit(2*lu2._default_function_unit) with pytest.raises(ValueError): lu_cls(physical_unit, u.m) def test_predefined_magnitudes(): assert_quantity_allclose((-21.1*u.STmag).physical, 1.*u.erg/u.cm**2/u.s/u.AA) assert_quantity_allclose((-48.6*u.ABmag).physical, 1.*u.erg/u.cm**2/u.s/u.Hz) assert_quantity_allclose((0*u.M_bol).physical, c.L_bol0) assert_quantity_allclose((0*u.m_bol).physical, c.L_bol0/(4.*np.pi*(10.*c.pc)**2)) def test_predefined_reinitialisation(): assert u.mag('ST') == u.STmag assert u.mag('AB') == u.ABmag assert u.mag('Bol') == u.M_bol assert u.mag('bol') == u.m_bol def test_predefined_string_roundtrip(): """Ensure roundtripping; see #5015""" with u.magnitude_zero_points.enable(): assert u.Unit(u.STmag.to_string()) == u.STmag assert u.Unit(u.ABmag.to_string()) == u.ABmag assert u.Unit(u.M_bol.to_string()) == u.M_bol assert u.Unit(u.m_bol.to_string()) == u.m_bol def test_inequality(): """Check __ne__ works (regresssion for #5342).""" lu1 = u.mag(u.Jy) lu2 = u.dex(u.Jy) lu3 = u.mag(u.Jy**2) lu4 = lu3 - lu1 assert lu1 != lu2 assert lu1 != lu3 assert lu1 == lu4 class TestLogUnitStrings(object): def test_str(self): """Do some spot checks that str, repr, etc. work as expected.""" lu1 = u.mag(u.Jy) assert str(lu1) == 'mag(Jy)' assert repr(lu1) == 'Unit("mag(Jy)")' assert lu1.to_string('generic') == 'mag(Jy)' with pytest.raises(ValueError): lu1.to_string('fits') lu2 = u.dex() assert str(lu2) == 'dex' assert repr(lu2) == 'Unit("dex(1)")' assert lu2.to_string() == 'dex(1)' lu3 = u.MagUnit(u.Jy, function_unit=2*u.mag) assert str(lu3) == '2 mag(Jy)' assert repr(lu3) == 'MagUnit("Jy", unit="2 mag")' assert lu3.to_string() == '2 mag(Jy)' lu4 = u.mag(u.ct) assert lu4.to_string('generic') == 'mag(ct)' assert lu4.to_string('latex') == ('$\\mathrm{mag}$$\\mathrm{\\left( ' '\\mathrm{ct} \\right)}$') assert lu4._repr_latex_() == lu4.to_string('latex') class TestLogUnitConversion(object): @pytest.mark.parametrize('lu_unit, physical_unit', itertools.product(lu_units, pu_sample)) def test_physical_unit_conversion(self, lu_unit, physical_unit): """Check various LogUnit subclasses are equivalent and convertible to their non-log counterparts.""" lu1 = lu_unit(physical_unit) assert lu1.is_equivalent(physical_unit) assert lu1.to(physical_unit, 0.) == 1. assert physical_unit.is_equivalent(lu1) assert physical_unit.to(lu1, 1.) == 0. pu = u.Unit(8.*physical_unit) assert lu1.is_equivalent(physical_unit) assert lu1.to(pu, 0.) == 0.125 assert pu.is_equivalent(lu1) assert_allclose(pu.to(lu1, 0.125), 0., atol=1.e-15) # Check we round-trip. value = np.linspace(0., 10., 6) assert_allclose(pu.to(lu1, lu1.to(pu, value)), value, atol=1.e-15) # And that we're not just returning True all the time. pu2 = u.g assert not lu1.is_equivalent(pu2) with pytest.raises(u.UnitsError): lu1.to(pu2) assert not pu2.is_equivalent(lu1) with pytest.raises(u.UnitsError): pu2.to(lu1) @pytest.mark.parametrize('lu_unit', lu_units) def test_container_unit_conversion(self, lu_unit): """Check that conversion to logarithmic units (u.mag, u.dB, u.dex) is only possible when the physical unit is dimensionless.""" values = np.linspace(0., 10., 6) lu1 = lu_unit(u.dimensionless_unscaled) assert lu1.is_equivalent(lu1.function_unit) assert_allclose(lu1.to(lu1.function_unit, values), values) lu2 = lu_unit(u.Jy) assert not lu2.is_equivalent(lu2.function_unit) with pytest.raises(u.UnitsError): lu2.to(lu2.function_unit, values) @pytest.mark.parametrize( 'flu_unit, tlu_unit, physical_unit', itertools.product(lu_units, lu_units, pu_sample)) def test_subclass_conversion(self, flu_unit, tlu_unit, physical_unit): """Check various LogUnit subclasses are equivalent and convertible to each other if they correspond to equivalent physical units.""" values = np.linspace(0., 10., 6) flu = flu_unit(physical_unit) tlu = tlu_unit(physical_unit) assert flu.is_equivalent(tlu) assert_allclose(flu.to(tlu), flu.function_unit.to(tlu.function_unit)) assert_allclose(flu.to(tlu, values), values * flu.function_unit.to(tlu.function_unit)) tlu2 = tlu_unit(u.Unit(100.*physical_unit)) assert flu.is_equivalent(tlu2) # Check that we round-trip. assert_allclose(flu.to(tlu2, tlu2.to(flu, values)), values, atol=1.e-15) tlu3 = tlu_unit(physical_unit.to_system(u.si)[0]) assert flu.is_equivalent(tlu3) assert_allclose(flu.to(tlu3, tlu3.to(flu, values)), values, atol=1.e-15) tlu4 = tlu_unit(u.g) assert not flu.is_equivalent(tlu4) with pytest.raises(u.UnitsError): flu.to(tlu4, values) def test_unit_decomposition(self): lu = u.mag(u.Jy) assert lu.decompose() == u.mag(u.Jy.decompose()) assert lu.decompose().physical_unit.bases == [u.kg, u.s] assert lu.si == u.mag(u.Jy.si) assert lu.si.physical_unit.bases == [u.kg, u.s] assert lu.cgs == u.mag(u.Jy.cgs) assert lu.cgs.physical_unit.bases == [u.g, u.s] def test_unit_multiple_possible_equivalencies(self): lu = u.mag(u.Jy) assert lu.is_equivalent(pu_sample) class TestLogUnitArithmetic(object): def test_multiplication_division(self): """Check that multiplication/division with other units is only possible when the physical unit is dimensionless, and that this turns the unit into a normal one.""" lu1 = u.mag(u.Jy) with pytest.raises(u.UnitsError): lu1 * u.m with pytest.raises(u.UnitsError): u.m * lu1 with pytest.raises(u.UnitsError): lu1 / lu1 for unit in (u.dimensionless_unscaled, u.m, u.mag, u.dex): with pytest.raises(u.UnitsError): lu1 / unit lu2 = u.mag(u.dimensionless_unscaled) with pytest.raises(u.UnitsError): lu2 * lu1 with pytest.raises(u.UnitsError): lu2 / lu1 # But dimensionless_unscaled can be cancelled. assert lu2 / lu2 == u.dimensionless_unscaled # With dimensionless, normal units are OK, but we return a plain unit. tf = lu2 * u.m tr = u.m * lu2 for t in (tf, tr): assert not isinstance(t, type(lu2)) assert t == lu2.function_unit * u.m with u.set_enabled_equivalencies(u.logarithmic()): with pytest.raises(u.UnitsError): t.to(lu2.physical_unit) # Now we essentially have a LogUnit with a prefactor of 100, # so should be equivalent again. t = tf / u.cm with u.set_enabled_equivalencies(u.logarithmic()): assert t.is_equivalent(lu2.function_unit) assert_allclose(t.to(u.dimensionless_unscaled, np.arange(3.)/100.), lu2.to(lu2.physical_unit, np.arange(3.))) # If we effectively remove lu1, a normal unit should be returned. t2 = tf / lu2 assert not isinstance(t2, type(lu2)) assert t2 == u.m t3 = tf / lu2.function_unit assert not isinstance(t3, type(lu2)) assert t3 == u.m # For completeness, also ensure non-sensical operations fail with pytest.raises(TypeError): lu1 * object() with pytest.raises(TypeError): slice(None) * lu1 with pytest.raises(TypeError): lu1 / [] with pytest.raises(TypeError): 1 / lu1 @pytest.mark.parametrize('power', (2, 0.5, 1, 0)) def test_raise_to_power(self, power): """Check that raising LogUnits to some power is only possible when the physical unit is dimensionless, and that conversion is turned off when the resulting logarithmic unit (such as mag**2) is incompatible.""" lu1 = u.mag(u.Jy) if power == 0: assert lu1 ** power == u.dimensionless_unscaled elif power == 1: assert lu1 ** power == lu1 else: with pytest.raises(u.UnitsError): lu1 ** power # With dimensionless, though, it works, but returns a normal unit. lu2 = u.mag(u.dimensionless_unscaled) t = lu2**power if power == 0: assert t == u.dimensionless_unscaled elif power == 1: assert t == lu2 else: assert not isinstance(t, type(lu2)) assert t == lu2.function_unit**power # also check we roundtrip t2 = t**(1./power) assert t2 == lu2.function_unit with u.set_enabled_equivalencies(u.logarithmic()): assert_allclose(t2.to(u.dimensionless_unscaled, np.arange(3.)), lu2.to(lu2.physical_unit, np.arange(3.))) @pytest.mark.parametrize('other', pu_sample) def test_addition_subtraction_to_normal_units_fails(self, other): lu1 = u.mag(u.Jy) with pytest.raises(u.UnitsError): lu1 + other with pytest.raises(u.UnitsError): lu1 - other with pytest.raises(u.UnitsError): other - lu1 def test_addition_subtraction_to_non_units_fails(self): lu1 = u.mag(u.Jy) with pytest.raises(TypeError): lu1 + 1. with pytest.raises(TypeError): lu1 - [1., 2., 3.] @pytest.mark.parametrize( 'other', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m), u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag))) def test_addition_subtraction(self, other): """Check physical units are changed appropriately""" lu1 = u.mag(u.Jy) other_pu = getattr(other, 'physical_unit', u.dimensionless_unscaled) lu_sf = lu1 + other assert lu_sf.is_equivalent(lu1.physical_unit * other_pu) lu_sr = other + lu1 assert lu_sr.is_equivalent(lu1.physical_unit * other_pu) lu_df = lu1 - other assert lu_df.is_equivalent(lu1.physical_unit / other_pu) lu_dr = other - lu1 assert lu_dr.is_equivalent(other_pu / lu1.physical_unit) def test_complicated_addition_subtraction(self): """for fun, a more complicated example of addition and subtraction""" dm0 = u.Unit('DM', 1./(4.*np.pi*(10.*u.pc)**2)) lu_dm = u.mag(dm0) lu_absST = u.STmag - lu_dm assert lu_absST.is_equivalent(u.erg/u.s/u.AA) def test_neg_pos(self): lu1 = u.mag(u.Jy) neg_lu = -lu1 assert neg_lu != lu1 assert neg_lu.physical_unit == u.Jy**-1 assert -neg_lu == lu1 pos_lu = +lu1 assert pos_lu is not lu1 assert pos_lu == lu1 def test_pickle(): lu1 = u.dex(u.cm/u.s**2) s = pickle.dumps(lu1) lu2 = pickle.loads(s) assert lu1 == lu2 def test_hashable(): lu1 = u.dB(u.mW) lu2 = u.dB(u.m) lu3 = u.dB(u.mW) assert hash(lu1) != hash(lu2) assert hash(lu1) == hash(lu3) luset = {lu1, lu2, lu3} assert len(luset) == 2 class TestLogQuantityCreation(object): @pytest.mark.parametrize('lq, lu', zip(lq_subclasses + [u.LogQuantity], lu_subclasses + [u.LogUnit])) def test_logarithmic_quantities(self, lq, lu): """Check logarithmic quantities are all set up correctly""" assert lq._unit_class == lu assert type(lu()._quantity_class(1.)) is lq @pytest.mark.parametrize('lq_cls, physical_unit', itertools.product(lq_subclasses, pu_sample)) def test_subclass_creation(self, lq_cls, physical_unit): """Create LogQuantity subclass objects for some physical units, and basic check on transformations""" value = np.arange(1., 10.) log_q = lq_cls(value * physical_unit) assert log_q.unit.physical_unit == physical_unit assert log_q.unit.function_unit == log_q.unit._default_function_unit assert_allclose(log_q.physical.value, value) with pytest.raises(ValueError): lq_cls(value, physical_unit) @pytest.mark.parametrize( 'unit', (u.mag, u.mag(), u.mag(u.Jy), u.mag(u.m), u.Unit(2*u.mag), u.MagUnit('', 2.*u.mag), u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag))) def test_different_units(self, unit): q = u.Magnitude(1.23, unit) assert q.unit.function_unit == getattr(unit, 'function_unit', unit) assert q.unit.physical_unit is getattr(unit, 'physical_unit', u.dimensionless_unscaled) @pytest.mark.parametrize('value, unit', ( (1.*u.mag(u.Jy), None), (1.*u.dex(u.Jy), None), (1.*u.mag(u.W/u.m**2/u.Hz), u.mag(u.Jy)), (1.*u.dex(u.W/u.m**2/u.Hz), u.mag(u.Jy)))) def test_function_values(self, value, unit): lq = u.Magnitude(value, unit) assert lq == value assert lq.unit.function_unit == u.mag assert lq.unit.physical_unit == getattr(unit, 'physical_unit', value.unit.physical_unit) @pytest.mark.parametrize( 'unit', (u.mag(), u.mag(u.Jy), u.mag(u.m), u.MagUnit('', 2.*u.mag), u.MagUnit(u.Jy, -1*u.mag), u.MagUnit(u.m, -2.*u.mag))) def test_indirect_creation(self, unit): q1 = 2.5 * unit assert isinstance(q1, u.Magnitude) assert q1.value == 2.5 assert q1.unit == unit pv = 100. * unit.physical_unit q2 = unit * pv assert q2.unit == unit assert q2.unit.physical_unit == pv.unit assert q2.to_value(unit.physical_unit) == 100. assert (q2._function_view / u.mag).to_value(1) == -5. q3 = unit / 0.4 assert q3 == q1 def test_from_view(self): # Cannot view a physical quantity as a function quantity, since the # values would change. q = [100., 1000.] * u.cm/u.s**2 with pytest.raises(TypeError): q.view(u.Dex) # But fine if we have the right magnitude. q = [2., 3.] * u.dex lq = q.view(u.Dex) assert isinstance(lq, u.Dex) assert lq.unit.physical_unit == u.dimensionless_unscaled assert np.all(q == lq) def test_using_quantity_class(self): """Check that we can use Quantity if we have subok=True""" # following issue #5851 lu = u.dex(u.AA) with pytest.raises(u.UnitTypeError): u.Quantity(1., lu) q = u.Quantity(1., lu, subok=True) assert type(q) is lu._quantity_class def test_conversion_to_and_from_physical_quantities(): """Ensures we can convert from regular quantities.""" mst = [10., 12., 14.] * u.STmag flux_lambda = mst.physical mst_roundtrip = flux_lambda.to(u.STmag) # check we return a logquantity; see #5178. assert isinstance(mst_roundtrip, u.Magnitude) assert mst_roundtrip.unit == mst.unit assert_allclose(mst_roundtrip.value, mst.value) wave = [4956.8, 4959.55, 4962.3] * u.AA flux_nu = mst.to(u.Jy, equivalencies=u.spectral_density(wave)) mst_roundtrip2 = flux_nu.to(u.STmag, u.spectral_density(wave)) assert isinstance(mst_roundtrip2, u.Magnitude) assert mst_roundtrip2.unit == mst.unit assert_allclose(mst_roundtrip2.value, mst.value) def test_quantity_decomposition(): lq = 10.*u.mag(u.Jy) assert lq.decompose() == lq assert lq.decompose().unit.physical_unit.bases == [u.kg, u.s] assert lq.si == lq assert lq.si.unit.physical_unit.bases == [u.kg, u.s] assert lq.cgs == lq assert lq.cgs.unit.physical_unit.bases == [u.g, u.s] class TestLogQuantityViews(object): def setup(self): self.lq = u.Magnitude(np.arange(10.) * u.Jy) self.lq2 = u.Magnitude(np.arange(5.)) def test_value_view(self): lq_value = self.lq.value assert type(lq_value) is np.ndarray lq_value[2] = -1. assert np.all(self.lq.value == lq_value) def test_function_view(self): lq_fv = self.lq._function_view assert type(lq_fv) is u.Quantity assert lq_fv.unit is self.lq.unit.function_unit lq_fv[3] = -2. * lq_fv.unit assert np.all(self.lq.value == lq_fv.value) def test_quantity_view(self): # Cannot view as Quantity, since the unit cannot be represented. with pytest.raises(TypeError): self.lq.view(u.Quantity) # But a dimensionless one is fine. q2 = self.lq2.view(u.Quantity) assert q2.unit is u.mag assert np.all(q2.value == self.lq2.value) lq3 = q2.view(u.Magnitude) assert type(lq3.unit) is u.MagUnit assert lq3.unit.physical_unit == u.dimensionless_unscaled assert np.all(lq3 == self.lq2) class TestLogQuantitySlicing(object): def test_item_get_and_set(self): lq1 = u.Magnitude(np.arange(1., 11.)*u.Jy) assert lq1[9] == u.Magnitude(10.*u.Jy) lq1[2] = 100.*u.Jy assert lq1[2] == u.Magnitude(100.*u.Jy) with pytest.raises(u.UnitsError): lq1[2] = 100.*u.m with pytest.raises(u.UnitsError): lq1[2] = 100.*u.mag with pytest.raises(u.UnitsError): lq1[2] = u.Magnitude(100.*u.m) assert lq1[2] == u.Magnitude(100.*u.Jy) def test_slice_get_and_set(self): lq1 = u.Magnitude(np.arange(1., 10.)*u.Jy) lq1[2:4] = 100.*u.Jy assert np.all(lq1[2:4] == u.Magnitude(100.*u.Jy)) with pytest.raises(u.UnitsError): lq1[2:4] = 100.*u.m with pytest.raises(u.UnitsError): lq1[2:4] = 100.*u.mag with pytest.raises(u.UnitsError): lq1[2:4] = u.Magnitude(100.*u.m) assert np.all(lq1[2] == u.Magnitude(100.*u.Jy)) class TestLogQuantityArithmetic(object): def test_multiplication_division(self): """Check that multiplication/division with other quantities is only possible when the physical unit is dimensionless, and that this turns the result into a normal quantity.""" lq = u.Magnitude(np.arange(1., 11.)*u.Jy) with pytest.raises(u.UnitsError): lq * (1.*u.m) with pytest.raises(u.UnitsError): (1.*u.m) * lq with pytest.raises(u.UnitsError): lq / lq for unit in (u.m, u.mag, u.dex): with pytest.raises(u.UnitsError): lq / unit lq2 = u.Magnitude(np.arange(1, 11.)) with pytest.raises(u.UnitsError): lq2 * lq with pytest.raises(u.UnitsError): lq2 / lq with pytest.raises(u.UnitsError): lq / lq2 # but dimensionless_unscaled can be cancelled r = lq2 / u.Magnitude(2.) assert r.unit == u.dimensionless_unscaled assert np.all(r.value == lq2.value/2.) # with dimensionless, normal units OK, but return normal quantities tf = lq2 * u.m tr = u.m * lq2 for t in (tf, tr): assert not isinstance(t, type(lq2)) assert t.unit == lq2.unit.function_unit * u.m with u.set_enabled_equivalencies(u.logarithmic()): with pytest.raises(u.UnitsError): t.to(lq2.unit.physical_unit) t = tf / (50.*u.cm) # now we essentially have the same quantity but with a prefactor of 2 assert t.unit.is_equivalent(lq2.unit.function_unit) assert_allclose(t.to(lq2.unit.function_unit), lq2._function_view*2) @pytest.mark.parametrize('power', (2, 0.5, 1, 0)) def test_raise_to_power(self, power): """Check that raising LogQuantities to some power is only possible when the physical unit is dimensionless, and that conversion is turned off when the resulting logarithmic unit (say, mag**2) is incompatible.""" lq = u.Magnitude(

np.arange(1., 4.)

numpy.arange

import argparse import json import numpy as np import pandas as pd import os from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split from sklearn.metrics import classification_report,f1_score from keras.models import Sequential from keras.layers import Dense, Dropout from keras import backend as K from keras.utils.vis_utils import plot_model from sklearn.externals import joblib import time def f1(y_true, y_pred): def recall(y_true, y_pred): """Recall metric. Only computes a batch-wise average of recall. Computes the recall, a metric for multi-label classification of how many relevant items are selected. """ true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1))) possible_positives = K.sum(K.round(K.clip(y_true, 0, 1))) recall = true_positives / (possible_positives + K.epsilon()) return recall def precision(y_true, y_pred): """Precision metric. Only computes a batch-wise average of precision. Computes the precision, a metric for multi-label classification of how many selected items are relevant. """ true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1))) predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1))) precision = true_positives / (predicted_positives + K.epsilon()) return precision precision = precision(y_true, y_pred) recall = recall(y_true, y_pred) return 2*((precision*recall)/(precision+recall+K.epsilon())) def get_embeddings(sentences_list,layer_json): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :return: Dictionary with key each sentence of the sentences_list and as value the embedding ''' sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence embeddings = dict()##dict with key the index of each sentence and as value the its embedding sentence_emb = dict()#key:sentence,value:its embedding with open(sentences_list,'r') as file: for index,line in enumerate(file): sentences[index] = line.strip() with open(layer_json, 'r',encoding='utf-8') as f: for line in f: embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features']) for key,value in sentences.items(): sentence_emb[value] = embeddings[key] return sentence_emb def train_classifier(sentences_list,layer_json,dataset_csv,filename): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :param dataset_csv: the path of the dataset :param filename: The path of the pickle file that the model will be stored :return: ''' dataset = pd.read_csv(dataset_csv) bert_dict = get_embeddings(sentences_list,layer_json) length = list() sentence_emb = list() previous_emb = list() next_list = list() section_list = list() label = list() errors = 0 for row in dataset.iterrows(): sentence = row[1][0].strip() previous = row[1][1].strip() nexts = row[1][2].strip() section = row[1][3].strip() if sentence in bert_dict: sentence_emb.append(bert_dict[sentence]) else: sentence_emb.append(np.zeros(768)) print(sentence) errors += 1 if previous in bert_dict: previous_emb.append(bert_dict[previous]) else: previous_emb.append(np.zeros(768)) if nexts in bert_dict: next_list.append(bert_dict[nexts]) else: next_list.append(np.zeros(768)) if section in bert_dict: section_list.append(bert_dict[section]) else: section_list.append(np.zeros(768)) length.append(row[1][4]) label.append(row[1][5]) sentence_emb = np.asarray(sentence_emb) print(sentence_emb.shape) next_emb = np.asarray(next_list) print(next_emb.shape) previous_emb = np.asarray(previous_emb) print(previous_emb.shape) section_emb = np.asarray(section_list) print(sentence_emb.shape) length = np.asarray(length) print(length.shape) label = np.asarray(label) print(errors) features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1) features = np.column_stack([features, length]) # np.append(features,length,axis=1) print(features.shape) X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42) log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1) log.fit(X_train, y_train) #save the model _ = joblib.dump(log, filename, compress=9) predictions = log.predict(X_val) print("###########################################") print("Results using embeddings from the",layer_json,"file") print(classification_report(y_val, predictions)) print("F1 score using Logistic Regression:",f1_score(y_val, predictions)) print("###########################################") #train a DNN f1_results = list() for i in range(3): model = Sequential() model.add(Dense(64, activation='relu', trainable=True)) model.add(Dense(128, activation='relu', trainable=True)) model.add(Dropout(0.30)) model.add(Dense(64, activation='relu', trainable=True)) model.add(Dropout(0.25)) model.add(Dense(64, activation='relu', trainable=True)) model.add(Dropout(0.35)) model.add(Dense(1, activation='sigmoid')) # compile network model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1]) # fit network model.fit(X_train, y_train, epochs=100, batch_size=64) loss, f_1 = model.evaluate(X_val, y_val, verbose=1) print('\nTest F1: %f' % (f_1 * 100)) f1_results.append(f_1) model = None print("###########################################") print("Results using embeddings from the", layer_json, "file") # evaluate print(np.mean(f1_results)) print("###########################################") def parameter_tuning_LR(sentences_list,layer_json,dataset_csv): ''' :param sentences_list: the path o the sentences.txt :param layer_json: the path of the json file that contains the embeddings of the sentences :param dataset_csv: the path of the dataset :return: ''' dataset = pd.read_csv(dataset_csv) bert_dict = get_embeddings(sentences_list,layer_json) length = list() sentence_emb = list() previous_emb = list() next_list = list() section_list = list() label = list() errors = 0 for row in dataset.iterrows(): sentence = row[1][0].strip() previous = row[1][1].strip() nexts = row[1][2].strip() section = row[1][3].strip() if sentence in bert_dict: sentence_emb.append(bert_dict[sentence]) else: sentence_emb.append(np.zeros(768)) print(sentence) errors += 1 if previous in bert_dict: previous_emb.append(bert_dict[previous]) else: previous_emb.append(np.zeros(768)) if nexts in bert_dict: next_list.append(bert_dict[nexts]) else: next_list.append(np.zeros(768)) if section in bert_dict: section_list.append(bert_dict[section]) else: section_list.append(np.zeros(768)) length.append(row[1][4]) label.append(row[1][5]) sentence_emb = np.asarray(sentence_emb) print(sentence_emb.shape) next_emb = np.asarray(next_list) print(next_emb.shape) previous_emb = np.asarray(previous_emb) print(previous_emb.shape) section_emb = np.asarray(section_list) print(sentence_emb.shape) length = np.asarray(length) print(length.shape) label = np.asarray(label) print(errors) features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1) features =

np.column_stack([features, length])

numpy.column_stack

# pylint: disable=protected-access """ Test the wrappers for the C API. """ import os from contextlib import contextmanager import numpy as np import numpy.testing as npt import pandas as pd import pytest import xarray as xr from packaging.version import Version from pygmt import Figure, clib from pygmt.clib.conversion import dataarray_to_matrix from pygmt.clib.session import FAMILIES, VIAS from pygmt.exceptions import ( GMTCLibError, GMTCLibNoSessionError, GMTInvalidInput, GMTVersionError, ) from pygmt.helpers import GMTTempFile TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data") with clib.Session() as _lib: gmt_version = Version(_lib.info["version"]) @contextmanager def mock(session, func, returns=None, mock_func=None): """ Mock a GMT C API function to make it always return a given value. Used to test that exceptions are raised when API functions fail by producing a NULL pointer as output or non-zero status codes. Needed because it's not easy to get some API functions to fail without inducing a Segmentation Fault (which is a good thing because libgmt usually only fails with errors). """ if mock_func is None: def mock_api_function(*args): # pylint: disable=unused-argument """ A mock GMT API function that always returns a given value. """ return returns mock_func = mock_api_function get_libgmt_func = session.get_libgmt_func def mock_get_libgmt_func(name, argtypes=None, restype=None): """ Return our mock function. """ if name == func: return mock_func return get_libgmt_func(name, argtypes, restype) setattr(session, "get_libgmt_func", mock_get_libgmt_func) yield setattr(session, "get_libgmt_func", get_libgmt_func) def test_getitem(): """ Test that I can get correct constants from the C lib. """ ses = clib.Session() assert ses["GMT_SESSION_EXTERNAL"] != -99999 assert ses["GMT_MODULE_CMD"] != -99999 assert ses["GMT_PAD_DEFAULT"] != -99999 assert ses["GMT_DOUBLE"] != -99999 with pytest.raises(GMTCLibError): ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement def test_create_destroy_session(): """ Test that create and destroy session are called without errors. """ # Create two session and make sure they are not pointing to the same memory session1 = clib.Session() session1.create(name="test_session1") assert session1.session_pointer is not None session2 = clib.Session() session2.create(name="test_session2") assert session2.session_pointer is not None assert session2.session_pointer != session1.session_pointer session1.destroy() session2.destroy() # Create and destroy a session twice ses = clib.Session() for __ in range(2): with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement ses.create("session1") assert ses.session_pointer is not None ses.destroy() with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement def test_create_session_fails(): """ Check that an exception is raised when failing to create a session. """ ses = clib.Session() with mock(ses, "GMT_Create_Session", returns=None): with pytest.raises(GMTCLibError): ses.create("test-session-name") # Should fail if trying to create a session before destroying the old one. ses.create("test1") with pytest.raises(GMTCLibError): ses.create("test2") def test_destroy_session_fails(): """ Fail to destroy session when given bad input. """ ses = clib.Session() with pytest.raises(GMTCLibNoSessionError): ses.destroy() ses.create("test-session") with mock(ses, "GMT_Destroy_Session", returns=1): with pytest.raises(GMTCLibError): ses.destroy() ses.destroy() def test_call_module(): """ Run a command to see if call_module works. """ data_fname = os.path.join(TEST_DATA_DIR, "points.txt") out_fname = "test_call_module.txt" with clib.Session() as lib: with GMTTempFile() as out_fname: lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name)) assert os.path.exists(out_fname.name) output = out_fname.read().strip() assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338" def test_call_module_invalid_arguments(): """ Fails for invalid module arguments. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("info", "bogus-data.bla") def test_call_module_invalid_name(): """ Fails when given bad input. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("meh", "") def test_call_module_error_message(): """ Check is the GMT error message was captured. """ with clib.Session() as lib: try: lib.call_module("info", "bogus-data.bla") except GMTCLibError as error: assert "Module 'info' failed with status code" in str(error) assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error) def test_method_no_session(): """ Fails when not in a session. """ # Create an instance of Session without "with" so no session is created. lib = clib.Session() with pytest.raises(GMTCLibNoSessionError): lib.call_module("gmtdefaults", "") with pytest.raises(GMTCLibNoSessionError): lib.session_pointer # pylint: disable=pointless-statement def test_parse_constant_single(): """ Parsing a single family argument correctly. """ lib = clib.Session() for family in FAMILIES: parsed = lib._parse_constant(family, valid=FAMILIES) assert parsed == lib[family] def test_parse_constant_composite(): """ Parsing a composite constant argument (separated by |) correctly. """ lib = clib.Session() test_cases = ((family, via) for family in FAMILIES for via in VIAS) for family, via in test_cases: composite = "|".join([family, via]) expected = lib[family] + lib[via] parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS) assert parsed == expected def test_parse_constant_fails(): """ Check if the function fails when given bad input. """ lib = clib.Session() test_cases = [ "SOME_random_STRING", "GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR", "GMT_IS_DATASET|NOT_A_PROPER_VIA", "NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX", "NOT_A_PROPER_FAMILY|ALSO_INVALID", ] for test_case in test_cases: with pytest.raises(GMTInvalidInput): lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS) # Should also fail if not given valid modifiers but is using them anyway. # This should work... lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS ) # But this shouldn't. with pytest.raises(GMTInvalidInput): lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None ) def test_create_data_dataset(): """ Run the function to make sure it doesn't fail badly. """ with clib.Session() as lib: # Dataset from vectors data_vector = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_VECTOR", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], # columns, rows, layers, dtype ) # Dataset from matrices data_matrix = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_MATRIX", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) assert data_vector != data_matrix def test_create_data_grid_dim(): """ Create a grid ignoring range and inc. """ with clib.Session() as lib: # Grids from matrices using dim lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) def test_create_data_grid_range(): """ Create a grid specifying range and inc instead of dim. """ with clib.Session() as lib: # Grids from matrices using range and int lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) def test_create_data_fails(): """ Check that create_data raises exceptions for invalid input and output. """ # Passing in invalid mode with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="Not_a_valid_mode", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # Passing in invalid geometry with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_GRID", geometry="Not_a_valid_geometry", mode="GMT_CONTAINER_ONLY", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # If the data pointer returned is None (NULL pointer) with pytest.raises(GMTCLibError): with clib.Session() as lib: with mock(lib, "GMT_Create_Data", returns=None): lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[11, 10, 2, 0], ) def test_virtual_file(): """ Test passing in data via a virtual file with a Dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (5, 3) for dtype in dtypes: with clib.Session() as lib: family = "GMT_IS_DATASET|GMT_VIA_MATRIX" geometry = "GMT_IS_POINT" dataset = lib.create_data( family=family, geometry=geometry, mode="GMT_CONTAINER_ONLY", dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype ) data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) lib.put_matrix(dataset, matrix=data) # Add the dataset to a virtual file and pass it along to gmt info vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset) with lib.open_virtual_file(*vfargs) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtual_file_fails(): """ Check that opening and closing virtual files raises an exception for non- zero return codes. """ vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IN|GMT_IS_REFERENCE", None, ) # Mock Open_VirtualFile to test the status check when entering the context. # If the exception is raised, the code won't get to the closing of the # virtual file. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): print("Should not get to this code") # Test the status check when closing the virtual file # Mock the opening to return 0 (success) so that we don't open a file that # we won't close later. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock( lib, "GMT_Close_VirtualFile", returns=1 ): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): pass print("Shouldn't get to this code either") def test_virtual_file_bad_direction(): """ Test passing an invalid direction argument. """ with clib.Session() as lib: vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IS_GRID", # The invalid direction argument 0, ) with pytest.raises(GMTInvalidInput): with lib.open_virtual_file(*vfargs): print("This should have failed") def test_virtualfile_from_vectors(): """ Test the automation for transforming vectors to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 10 for dtype in dtypes: x = np.arange(size, dtype=dtype) y = np.arange(size, size * 2, 1, dtype=dtype) z = np.arange(size * 2, size * 3, 1, dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected @pytest.mark.parametrize("dtype", [str, object]) def test_virtualfile_from_vectors_one_string_or_object_column(dtype): """ Test passing in one column with string or object dtype into virtual file dataset. """ size = 5 x = np.arange(size, dtype=np.int32) y = np.arange(size, size * 2, 1, dtype=np.int32) strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, strings) as vfile: with GMTTempFile() as outfile: lib.call_module("convert", f"{vfile} ->{outfile.name}") output = outfile.read(keep_tabs=True) expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings)) assert output == expected @pytest.mark.parametrize("dtype", [str, object]) def test_virtualfile_from_vectors_two_string_or_object_columns(dtype): """ Test passing in two columns of string or object dtype into virtual file dataset. """ size = 5 x = np.arange(size, dtype=np.int32) y = np.arange(size, size * 2, 1, dtype=np.int32) strings1 = np.array(["a", "bc", "def", "ghij", "klmno"], dtype=dtype) strings2 = np.array(["pqrst", "uvwx", "yz!", "@#", "$"], dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, strings1, strings2) as vfile: with GMTTempFile() as outfile: lib.call_module("convert", f"{vfile} ->{outfile.name}") output = outfile.read(keep_tabs=True) expected = "".join( f"{h}\t{i}\t{j} {k}\n" for h, i, j, k in zip(x, y, strings1, strings2) ) assert output == expected def test_virtualfile_from_vectors_transpose(): """ Test transforming matrix columns to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (7, 5) for dtype in dtypes: data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) with clib.Session() as lib: with lib.virtualfile_from_vectors(*data.T) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} -C ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["{:.0f}\t{:.0f}".format(col.min(), col.max()) for col in data.T] ) expected = "{}\n".format(bounds) assert output == expected def test_virtualfile_from_vectors_diff_size(): """ Test the function fails for arrays of different sizes. """ x = np.arange(5) y = np.arange(6) with clib.Session() as lib: with pytest.raises(GMTInvalidInput): with lib.virtualfile_from_vectors(x, y): print("This should have failed") def test_virtualfile_from_matrix(): """ Test transforming a matrix to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (7, 5) for dtype in dtypes: data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) with clib.Session() as lib: with lib.virtualfile_from_matrix(data) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtualfile_from_matrix_slice(): """ Test transforming a slice of a larger array to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (10, 6) for dtype in dtypes: full_data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) rows = 5 cols = 3 data = full_data[:rows, :cols] with clib.Session() as lib: with lib.virtualfile_from_matrix(data) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(rows, bounds) assert output == expected def test_virtualfile_from_vectors_pandas(): """ Pass vectors to a dataset using pandas Series. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 13 for dtype in dtypes: data = pd.DataFrame( data=dict( x=np.arange(size, dtype=dtype), y=np.arange(size, size * 2, 1, dtype=dtype), z=np.arange(size * 2, size * 3, 1, dtype=dtype), ) ) with clib.Session() as lib: with lib.virtualfile_from_vectors(data.x, data.y, data.z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( [ "<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (data.x, data.y, data.z) ] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected def test_virtualfile_from_vectors_arraylike(): """ Pass array-like vectors to a dataset. """ size = 13 x = list(range(0, size, 1)) y = tuple(range(size, size * 2, 1)) z = range(size * 2, size * 3, 1) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(min(i), max(i)) for i in (x, y, z)] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected def test_extract_region_fails(): """ Check that extract region fails if nothing has been plotted. """ Figure() with pytest.raises(GMTCLibError): with clib.Session() as lib: lib.extract_region() def test_extract_region_two_figures(): """ Extract region should handle multiple figures existing at the same time. """ # Make two figures before calling extract_region to make sure that it's # getting from the current figure, not the last figure. fig1 = Figure() region1 = np.array([0, 10, -20, -10]) fig1.coast(region=region1, projection="M6i", frame=True, land="black") fig2 = Figure() fig2.basemap(region="US.HI+r5", projection="M6i", frame=True) # Activate the first figure and extract the region from it # Use in a different session to avoid any memory problems. with clib.Session() as lib: lib.call_module("figure", "{} -".format(fig1._name)) with clib.Session() as lib: wesn1 = lib.extract_region() npt.assert_allclose(wesn1, region1) # Now try it with the second one with clib.Session() as lib: lib.call_module("figure", "{} -".format(fig2._name)) with clib.Session() as lib: wesn2 = lib.extract_region() npt.assert_allclose(wesn2, np.array([-165.0, -150.0, 15.0, 25.0])) def test_write_data_fails(): """ Check that write data raises an exception for non-zero return codes. """ # It's hard to make the C API function fail without causing a Segmentation # Fault. Can't test this if by giving a bad file name because if # output=='', GMT will just write to stdout and spaces are valid file # names. Use a mock instead just to exercise this part of the code. with clib.Session() as lib: with mock(lib, "GMT_Write_Data", returns=1): with pytest.raises(GMTCLibError): lib.write_data( "GMT_IS_VECTOR", "GMT_IS_POINT", "GMT_WRITE_SET", [1] * 6, "some-file-name", None, ) def test_dataarray_to_matrix_works(): """ Check that dataarray_to_matrix returns correct output. """ data = np.diag(v=

np.arange(3)

numpy.arange

# pylint: disable=protected-access """ Test the wrappers for the C API. """ import os from contextlib import contextmanager import numpy as np import numpy.testing as npt import pandas as pd import pytest import xarray as xr from packaging.version import Version from pygmt import Figure, clib from pygmt.clib.conversion import dataarray_to_matrix from pygmt.clib.session import FAMILIES, VIAS from pygmt.exceptions import ( GMTCLibError, GMTCLibNoSessionError, GMTInvalidInput, GMTVersionError, ) from pygmt.helpers import GMTTempFile TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data") with clib.Session() as _lib: gmt_version = Version(_lib.info["version"]) @contextmanager def mock(session, func, returns=None, mock_func=None): """ Mock a GMT C API function to make it always return a given value. Used to test that exceptions are raised when API functions fail by producing a NULL pointer as output or non-zero status codes. Needed because it's not easy to get some API functions to fail without inducing a Segmentation Fault (which is a good thing because libgmt usually only fails with errors). """ if mock_func is None: def mock_api_function(*args): # pylint: disable=unused-argument """ A mock GMT API function that always returns a given value. """ return returns mock_func = mock_api_function get_libgmt_func = session.get_libgmt_func def mock_get_libgmt_func(name, argtypes=None, restype=None): """ Return our mock function. """ if name == func: return mock_func return get_libgmt_func(name, argtypes, restype) setattr(session, "get_libgmt_func", mock_get_libgmt_func) yield setattr(session, "get_libgmt_func", get_libgmt_func) def test_getitem(): """ Test that I can get correct constants from the C lib. """ ses = clib.Session() assert ses["GMT_SESSION_EXTERNAL"] != -99999 assert ses["GMT_MODULE_CMD"] != -99999 assert ses["GMT_PAD_DEFAULT"] != -99999 assert ses["GMT_DOUBLE"] != -99999 with pytest.raises(GMTCLibError): ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement def test_create_destroy_session(): """ Test that create and destroy session are called without errors. """ # Create two session and make sure they are not pointing to the same memory session1 = clib.Session() session1.create(name="test_session1") assert session1.session_pointer is not None session2 = clib.Session() session2.create(name="test_session2") assert session2.session_pointer is not None assert session2.session_pointer != session1.session_pointer session1.destroy() session2.destroy() # Create and destroy a session twice ses = clib.Session() for __ in range(2): with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement ses.create("session1") assert ses.session_pointer is not None ses.destroy() with pytest.raises(GMTCLibNoSessionError): ses.session_pointer # pylint: disable=pointless-statement def test_create_session_fails(): """ Check that an exception is raised when failing to create a session. """ ses = clib.Session() with mock(ses, "GMT_Create_Session", returns=None): with pytest.raises(GMTCLibError): ses.create("test-session-name") # Should fail if trying to create a session before destroying the old one. ses.create("test1") with pytest.raises(GMTCLibError): ses.create("test2") def test_destroy_session_fails(): """ Fail to destroy session when given bad input. """ ses = clib.Session() with pytest.raises(GMTCLibNoSessionError): ses.destroy() ses.create("test-session") with mock(ses, "GMT_Destroy_Session", returns=1): with pytest.raises(GMTCLibError): ses.destroy() ses.destroy() def test_call_module(): """ Run a command to see if call_module works. """ data_fname = os.path.join(TEST_DATA_DIR, "points.txt") out_fname = "test_call_module.txt" with clib.Session() as lib: with GMTTempFile() as out_fname: lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name)) assert os.path.exists(out_fname.name) output = out_fname.read().strip() assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338" def test_call_module_invalid_arguments(): """ Fails for invalid module arguments. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("info", "bogus-data.bla") def test_call_module_invalid_name(): """ Fails when given bad input. """ with clib.Session() as lib: with pytest.raises(GMTCLibError): lib.call_module("meh", "") def test_call_module_error_message(): """ Check is the GMT error message was captured. """ with clib.Session() as lib: try: lib.call_module("info", "bogus-data.bla") except GMTCLibError as error: assert "Module 'info' failed with status code" in str(error) assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error) def test_method_no_session(): """ Fails when not in a session. """ # Create an instance of Session without "with" so no session is created. lib = clib.Session() with pytest.raises(GMTCLibNoSessionError): lib.call_module("gmtdefaults", "") with pytest.raises(GMTCLibNoSessionError): lib.session_pointer # pylint: disable=pointless-statement def test_parse_constant_single(): """ Parsing a single family argument correctly. """ lib = clib.Session() for family in FAMILIES: parsed = lib._parse_constant(family, valid=FAMILIES) assert parsed == lib[family] def test_parse_constant_composite(): """ Parsing a composite constant argument (separated by |) correctly. """ lib = clib.Session() test_cases = ((family, via) for family in FAMILIES for via in VIAS) for family, via in test_cases: composite = "|".join([family, via]) expected = lib[family] + lib[via] parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS) assert parsed == expected def test_parse_constant_fails(): """ Check if the function fails when given bad input. """ lib = clib.Session() test_cases = [ "SOME_random_STRING", "GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR", "GMT_IS_DATASET|NOT_A_PROPER_VIA", "NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX", "NOT_A_PROPER_FAMILY|ALSO_INVALID", ] for test_case in test_cases: with pytest.raises(GMTInvalidInput): lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS) # Should also fail if not given valid modifiers but is using them anyway. # This should work... lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS ) # But this shouldn't. with pytest.raises(GMTInvalidInput): lib._parse_constant( "GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None ) def test_create_data_dataset(): """ Run the function to make sure it doesn't fail badly. """ with clib.Session() as lib: # Dataset from vectors data_vector = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_VECTOR", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], # columns, rows, layers, dtype ) # Dataset from matrices data_matrix = lib.create_data( family="GMT_IS_DATASET|GMT_VIA_MATRIX", geometry="GMT_IS_POINT", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) assert data_vector != data_matrix def test_create_data_grid_dim(): """ Create a grid ignoring range and inc. """ with clib.Session() as lib: # Grids from matrices using dim lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[10, 20, 1, 0], ) def test_create_data_grid_range(): """ Create a grid specifying range and inc instead of dim. """ with clib.Session() as lib: # Grids from matrices using range and int lib.create_data( family="GMT_IS_GRID|GMT_VIA_MATRIX", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) def test_create_data_fails(): """ Check that create_data raises exceptions for invalid input and output. """ # Passing in invalid mode with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="Not_a_valid_mode", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # Passing in invalid geometry with pytest.raises(GMTInvalidInput): with clib.Session() as lib: lib.create_data( family="GMT_IS_GRID", geometry="Not_a_valid_geometry", mode="GMT_CONTAINER_ONLY", dim=[0, 0, 1, 0], ranges=[150.0, 250.0, -20.0, 20.0], inc=[0.1, 0.2], ) # If the data pointer returned is None (NULL pointer) with pytest.raises(GMTCLibError): with clib.Session() as lib: with mock(lib, "GMT_Create_Data", returns=None): lib.create_data( family="GMT_IS_DATASET", geometry="GMT_IS_SURFACE", mode="GMT_CONTAINER_ONLY", dim=[11, 10, 2, 0], ) def test_virtual_file(): """ Test passing in data via a virtual file with a Dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (5, 3) for dtype in dtypes: with clib.Session() as lib: family = "GMT_IS_DATASET|GMT_VIA_MATRIX" geometry = "GMT_IS_POINT" dataset = lib.create_data( family=family, geometry=geometry, mode="GMT_CONTAINER_ONLY", dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype ) data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) lib.put_matrix(dataset, matrix=data) # Add the dataset to a virtual file and pass it along to gmt info vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset) with lib.open_virtual_file(*vfargs) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtual_file_fails(): """ Check that opening and closing virtual files raises an exception for non- zero return codes. """ vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IN|GMT_IS_REFERENCE", None, ) # Mock Open_VirtualFile to test the status check when entering the context. # If the exception is raised, the code won't get to the closing of the # virtual file. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): print("Should not get to this code") # Test the status check when closing the virtual file # Mock the opening to return 0 (success) so that we don't open a file that # we won't close later. with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock( lib, "GMT_Close_VirtualFile", returns=1 ): with pytest.raises(GMTCLibError): with lib.open_virtual_file(*vfargs): pass print("Shouldn't get to this code either") def test_virtual_file_bad_direction(): """ Test passing an invalid direction argument. """ with clib.Session() as lib: vfargs = ( "GMT_IS_DATASET|GMT_VIA_MATRIX", "GMT_IS_POINT", "GMT_IS_GRID", # The invalid direction argument 0, ) with pytest.raises(GMTInvalidInput): with lib.open_virtual_file(*vfargs): print("This should have failed") def test_virtualfile_from_vectors(): """ Test the automation for transforming vectors to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 10 for dtype in dtypes: x = np.arange(size, dtype=dtype) y = np.arange(size, size * 2, 1, dtype=dtype) z = np.arange(size * 2, size * 3, 1, dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected @pytest.mark.parametrize("dtype", [str, object]) def test_virtualfile_from_vectors_one_string_or_object_column(dtype): """ Test passing in one column with string or object dtype into virtual file dataset. """ size = 5 x = np.arange(size, dtype=np.int32) y = np.arange(size, size * 2, 1, dtype=np.int32) strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, strings) as vfile: with GMTTempFile() as outfile: lib.call_module("convert", f"{vfile} ->{outfile.name}") output = outfile.read(keep_tabs=True) expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings)) assert output == expected @pytest.mark.parametrize("dtype", [str, object]) def test_virtualfile_from_vectors_two_string_or_object_columns(dtype): """ Test passing in two columns of string or object dtype into virtual file dataset. """ size = 5 x = np.arange(size, dtype=np.int32) y = np.arange(size, size * 2, 1, dtype=np.int32) strings1 = np.array(["a", "bc", "def", "ghij", "klmno"], dtype=dtype) strings2 = np.array(["pqrst", "uvwx", "yz!", "@#", "$"], dtype=dtype) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, strings1, strings2) as vfile: with GMTTempFile() as outfile: lib.call_module("convert", f"{vfile} ->{outfile.name}") output = outfile.read(keep_tabs=True) expected = "".join( f"{h}\t{i}\t{j} {k}\n" for h, i, j, k in zip(x, y, strings1, strings2) ) assert output == expected def test_virtualfile_from_vectors_transpose(): """ Test transforming matrix columns to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (7, 5) for dtype in dtypes: data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) with clib.Session() as lib: with lib.virtualfile_from_vectors(*data.T) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} -C ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["{:.0f}\t{:.0f}".format(col.min(), col.max()) for col in data.T] ) expected = "{}\n".format(bounds) assert output == expected def test_virtualfile_from_vectors_diff_size(): """ Test the function fails for arrays of different sizes. """ x = np.arange(5) y = np.arange(6) with clib.Session() as lib: with pytest.raises(GMTInvalidInput): with lib.virtualfile_from_vectors(x, y): print("This should have failed") def test_virtualfile_from_matrix(): """ Test transforming a matrix to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (7, 5) for dtype in dtypes: data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) with clib.Session() as lib: with lib.virtualfile_from_matrix(data) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds) assert output == expected def test_virtualfile_from_matrix_slice(): """ Test transforming a slice of a larger array to virtual file dataset. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() shape = (10, 6) for dtype in dtypes: full_data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape) rows = 5 cols = 3 data = full_data[:rows, :cols] with clib.Session() as lib: with lib.virtualfile_from_matrix(data) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T] ) expected = "<matrix memory>: N = {}\t{}\n".format(rows, bounds) assert output == expected def test_virtualfile_from_vectors_pandas(): """ Pass vectors to a dataset using pandas Series. """ dtypes = "float32 float64 int32 int64 uint32 uint64".split() size = 13 for dtype in dtypes: data = pd.DataFrame( data=dict( x=np.arange(size, dtype=dtype), y=np.arange(size, size * 2, 1, dtype=dtype), z=np.arange(size * 2, size * 3, 1, dtype=dtype), ) ) with clib.Session() as lib: with lib.virtualfile_from_vectors(data.x, data.y, data.z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( [ "<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (data.x, data.y, data.z) ] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected def test_virtualfile_from_vectors_arraylike(): """ Pass array-like vectors to a dataset. """ size = 13 x = list(range(0, size, 1)) y = tuple(range(size, size * 2, 1)) z = range(size * 2, size * 3, 1) with clib.Session() as lib: with lib.virtualfile_from_vectors(x, y, z) as vfile: with GMTTempFile() as outfile: lib.call_module("info", "{} ->{}".format(vfile, outfile.name)) output = outfile.read(keep_tabs=True) bounds = "\t".join( ["<{:.0f}/{:.0f}>".format(min(i), max(i)) for i in (x, y, z)] ) expected = "<vector memory>: N = {}\t{}\n".format(size, bounds) assert output == expected def test_extract_region_fails(): """ Check that extract region fails if nothing has been plotted. """ Figure() with pytest.raises(GMTCLibError): with clib.Session() as lib: lib.extract_region() def test_extract_region_two_figures(): """ Extract region should handle multiple figures existing at the same time. """ # Make two figures before calling extract_region to make sure that it's # getting from the current figure, not the last figure. fig1 = Figure() region1 = np.array([0, 10, -20, -10]) fig1.coast(region=region1, projection="M6i", frame=True, land="black") fig2 = Figure() fig2.basemap(region="US.HI+r5", projection="M6i", frame=True) # Activate the first figure and extract the region from it # Use in a different session to avoid any memory problems. with clib.Session() as lib: lib.call_module("figure", "{} -".format(fig1._name)) with clib.Session() as lib: wesn1 = lib.extract_region() npt.assert_allclose(wesn1, region1) # Now try it with the second one with clib.Session() as lib: lib.call_module("figure", "{} -".format(fig2._name)) with clib.Session() as lib: wesn2 = lib.extract_region() npt.assert_allclose(wesn2, np.array([-165.0, -150.0, 15.0, 25.0])) def test_write_data_fails(): """ Check that write data raises an exception for non-zero return codes. """ # It's hard to make the C API function fail without causing a Segmentation # Fault. Can't test this if by giving a bad file name because if # output=='', GMT will just write to stdout and spaces are valid file # names. Use a mock instead just to exercise this part of the code. with clib.Session() as lib: with mock(lib, "GMT_Write_Data", returns=1): with pytest.raises(GMTCLibError): lib.write_data( "GMT_IS_VECTOR", "GMT_IS_POINT", "GMT_WRITE_SET", [1] * 6, "some-file-name", None, ) def test_dataarray_to_matrix_works(): """ Check that dataarray_to_matrix returns correct output. """ data = np.diag(v=np.arange(3)) x = np.linspace(start=0, stop=4, num=3) y = np.linspace(start=5, stop=9, num=3) grid = xr.DataArray(data, coords=[("y", y), ("x", x)]) matrix, region, inc = dataarray_to_matrix(grid) npt.assert_allclose(actual=matrix, desired=np.flipud(data)) npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])

npt.assert_allclose(actual=inc, desired=[x[1] - x[0], y[1] - y[0]])

numpy.testing.assert_allclose