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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]) | numpy.array |
"""
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])) | numpy.dtype |
#
# 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) | numpy.random.randn |
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""
iris dataset
"""
import numpy as np
from sklearn import datasets
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler, MinMaxScaler
from sklearn.decomposition import PCA
from qiskit.aqua import MissingOptionalLibraryError
def iris(training_size, test_size, n, plot_data=False):
""" returns iris dataset """
class_labels = [r'A', r'B', r'C']
data, target = datasets.load_iris(return_X_y=True)
sample_train, sample_test, label_train, label_test = \
train_test_split(data, target, test_size=1, random_state=42)
# Now we standardize for gaussian around 0 with unit variance
std_scale = StandardScaler().fit(sample_train)
sample_train = std_scale.transform(sample_train)
sample_test = std_scale.transform(sample_test)
# Now reduce number of features to number of qubits
pca = PCA(n_components=n).fit(sample_train)
sample_train = pca.transform(sample_train)
sample_test = pca.transform(sample_test)
# Scale to the range (-1,+1)
samples = | np.append(sample_train, sample_test, axis=0) | numpy.append |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones |
'''
<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)) | numpy.zeros |
'''
-------------------------------------------------------------------------------------------------
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))
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] == 4:
veh_ca = np.arctan(veh_cgf[1] / veh_cgs[1])
veh_a1 = np.abs(veh_cgf[0] - veh_striking[3])
veh_a2 = np.abs( | np.sqrt(veh_cgf[1] ** 2 + veh_cgs[1] ** 2) | numpy.sqrt |
"""
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) | 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)):
raise ValueError("`x0` violates bound constraints.")
if as_linear_operator:
if rel_step is None:
rel_step = relative_step[method]
return _linear_operator_difference(fun_wrapped, x0,
f0, rel_step, method)
else:
h = _compute_absolute_step(rel_step, x0, method)
if method == '2-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '1-sided', lb, ub)
elif method == '3-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '2-sided', lb, ub)
elif method == 'cs':
use_one_sided = False
if sparsity is None:
return _dense_difference(fun_wrapped, x0, f0, h,
use_one_sided, method)
else:
if not issparse(sparsity) and len(sparsity) == 2:
structure, groups = sparsity
else:
structure = sparsity
groups = group_columns(sparsity)
if issparse(structure):
structure = csc_matrix(structure)
else:
structure = np.atleast_2d(structure)
groups = np.atleast_1d(groups)
return _sparse_difference(fun_wrapped, x0, f0, h,
use_one_sided, structure,
groups, method)
def _linear_operator_difference(fun, x0, f0, h, method):
m = f0.size
n = x0.size
if method == '2-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / | norm(p) | numpy.linalg.norm |
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import os
import matplotlib.pyplot as plt
import CurveFit
import shutil
#find all DIRECTORIES containing non-hidden files ending in FILENAME
def getDataDirectories(DIRECTORY, FILENAME="valLoss.txt"):
directories=[]
for directory in os.scandir(DIRECTORY):
for item in os.scandir(directory):
if item.name.endswith(FILENAME) and not item.name.startswith("."):
directories.append(directory.path)
return directories
#get all non-hidden data files in DIRECTORY with extension EXT
def getDataFiles(DIRECTORY, EXT='txt'):
datafiles=[]
for item in os.scandir(DIRECTORY):
if item.name.endswith("."+EXT) and not item.name.startswith("."):
datafiles.append(item.path)
return datafiles
#checking if loss ever doesn't decrease for numEpochs epochs in a row.
def stopsDecreasing(loss, epoch, numEpochs):
minLoss=np.inf
epochMin=0
for i in range(0,loss.size):
if loss[i] < minLoss:
minLoss=loss[i]
epochMin=epoch[i]
elif (epoch[i]-epochMin) >= numEpochs:
return i, minLoss
return i, minLoss
#dirpath is where the accuracy and loss files are stored. want to move the files into the same format expected by grabNNData.
def createFolders(SEARCHDIR, SAVEDIR):
for item in os.scandir(SEARCHDIR):
name=str(item.name)
files=name.split('-')
SAVEFULLDIR=SAVEDIR+str(files[0])
if not os.path.exists(SAVEFULLDIR):
try:
os.makedirs(SAVEFULLDIR)
except FileExistsError:
#directory already exists--must have been created between the if statement & our attempt at making directory
pass
shutil.move(item.path, SAVEFULLDIR+"/"+str(files[1]))
#a function to read in information (e.g. accuracy, loss) stored at FILENAME
def grabNNData(FILENAME, header='infer', sep=' '):
data = pd.read_csv(FILENAME, sep, header=header)
if ('epochs' in data.columns) and ('trainLoss' in data.columns) and ('valLoss' in data.columns) and ('valAcc' in data.columns) and ('batch_size' in data.columns) and ('learning_rate' in data.columns):
sortedData=data.sort_values(by="epochs", axis=0, ascending=True)
epoch=np.array(sortedData['epochs'])
trainLoss=np.array(sortedData['trainLoss'])
valLoss=np.array(sortedData['valLoss'])
valAcc=np.array(sortedData['valAcc'])
batch_size=np.array(sortedData['batch_size'])
learning_rate=np.array(sortedData['learning_rate'])
convKers=np.array(sortedData['convKernels'])
return(epoch, trainLoss, valLoss, valAcc, batch_size, learning_rate, convKers)
elif ('epochs' in data.columns) and ('trainLoss' in data.columns) and ('valLoss' in data.columns) and ('valAcc' in data.columns):
sortedData=data.sort_values(by="epochs", axis=0, ascending=True)
epoch=np.array(sortedData['epochs'])
trainLoss=np.array(sortedData['trainLoss'])
valLoss=np.array(sortedData['valLoss'])
valAcc= | np.array(sortedData['valAcc']) | numpy.array |
# 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.)*u.Jy)
q = 1.23 * other
with pytest.raises(u.UnitsError):
lq + q
with pytest.raises(u.UnitsError):
lq - q
with pytest.raises(u.UnitsError):
q - lq
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check that addition/subtraction with quantities with magnitude or
MagUnit units works, and that it changes the physical units
appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq + other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_sr = other + lq
assert_allclose(lq_sr.physical, lq.physical * other_physical)
lq_df = lq - other
assert_allclose(lq_df.physical, lq.physical / other_physical)
lq_dr = other - lq
assert_allclose(lq_dr.physical, other_physical / lq.physical)
@pytest.mark.parametrize('other', pu_sample)
def test_inplace_addition_subtraction_unit_checks(self, other):
lu1 = u.mag(u.Jy)
lq1 = u.Magnitude(np.arange(1., 10.), lu1)
with pytest.raises(u.UnitsError):
lq1 += other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
with pytest.raises(u.UnitsError):
lq1 -= other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_inplace_addition_subtraction(self, other):
"""Check that inplace addition/subtraction with quantities with
magnitude or MagUnit units works, and that it changes the physical
units appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq.copy()
lq_sf += other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_df = lq.copy()
lq_df -= other
assert_allclose(lq_df.physical, lq.physical / other_physical)
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))
DMmag = u.mag(dm0)
m_st = 10. * u.STmag
dm = 5. * DMmag
M_st = m_st - dm
assert M_st.unit.is_equivalent(u.erg/u.s/u.AA)
assert np.abs(M_st.physical /
(m_st.physical*4.*np.pi*(100.*u.pc)**2) - 1.) < 1.e-15
class TestLogQuantityComparisons(object):
def test_comparison_to_non_quantities_fails(self):
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
# On python2, ordering operations always succeed, given essentially
# meaningless results.
if not six.PY2:
with pytest.raises(TypeError):
lq > 'a'
assert not (lq == 'a')
assert lq != 'a'
def test_comparison(self):
lq1 = u.Magnitude(np.arange(1., 4.)*u.Jy)
lq2 = u.Magnitude(2.*u.Jy)
assert np.all((lq1 > lq2) == np.array([True, False, False]))
assert np.all((lq1 == lq2) == np.array([False, True, False]))
lq3 = u.Dex(2.*u.Jy)
assert np.all((lq1 > lq3) == np.array([True, False, False]))
assert np.all((lq1 == lq3) == np.array([False, True, False]))
lq4 = u.Magnitude(2.*u.m)
assert not (lq1 == lq4)
assert lq1 != lq4
with pytest.raises(u.UnitsError):
lq1 < lq4
q5 = 1.5 * u.Jy
assert np.all((lq1 > q5) == np.array([True, False, False]))
assert np.all((q5 < lq1) == np.array([True, False, False]))
with pytest.raises(u.UnitsError):
lq1 >= 2.*u.m
with pytest.raises(u.UnitsError):
lq1 <= lq1.value * u.mag
# For physically dimensionless, we can compare with the function unit.
lq6 = u.Magnitude(np.arange(1., 4.))
fv6 = lq6.value * u.mag
assert np.all(lq6 == fv6)
# but not some arbitrary unit, of course.
with pytest.raises(u.UnitsError):
lq6 < 2.*u.m
class TestLogQuantityMethods(object):
def setup(self):
self.mJy = np.arange(1., 5.).reshape(2, 2) * u.mag(u.Jy)
self.m1 = np.arange(1., 5.5, 0.5).reshape(3, 3) * u.mag()
self.mags = (self.mJy, self.m1)
@pytest.mark.parametrize('method', ('mean', 'min', 'max', 'round', 'trace',
'std', 'var', 'ptp', 'diff', 'ediff1d'))
def test_always_ok(self, method):
for mag in self.mags:
res = getattr(mag, method)()
assert np.all(res.value ==
getattr(mag._function_view, method)().value)
if method in ('std', 'ptp', 'diff', 'ediff1d'):
assert res.unit == u.mag()
elif method == 'var':
assert res.unit == u.mag**2
else:
assert res.unit == mag.unit
def test_clip(self):
for mag in self.mags:
assert np.all(mag.clip(2. * mag.unit, 4. * mag.unit).value ==
mag.value.clip(2., 4.))
@pytest.mark.parametrize('method', ('sum', 'cumsum', 'nansum'))
def test_only_ok_if_dimensionless(self, method):
res = getattr(self.m1, method)()
assert np.all(res.value ==
getattr(self.m1._function_view, method)().value)
assert res.unit == self.m1.unit
with pytest.raises(TypeError):
getattr(self.mJy, method)()
def test_dot(self):
assert np.all(self.m1.dot(self.m1).value ==
self.m1.value.dot(self.m1.value))
@pytest.mark.parametrize('method', ('prod', 'cumprod'))
def test_never_ok(self, method):
with pytest.raises(ValueError):
getattr(self.mJy, method)()
with pytest.raises(ValueError):
getattr(self.m1, method)()
class TestLogQuantityUfuncs(object):
"""Spot checks on ufuncs."""
def setup(self):
self.mJy = np.arange(1., 5.).reshape(2, 2) * u.mag(u.Jy)
self.m1 = np.arange(1., 5.5, 0.5).reshape(3, 3) * u.mag()
self.mags = (self.mJy, self.m1)
def test_power(self):
assert np.all(np.power(self.mJy, 0.) == 1.)
assert np.all(np.power(self.m1, 1.) == self.m1)
assert np.all( | np.power(self.mJy, 1.) | numpy.power |
# ________
# /
# \ /
# \ /
# \/
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) | 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) | numpy.ones_like |
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]) | numpy.array |
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) | numpy.argmax |
# 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)*np.sin(theta)
z = np.cos(theta)
direction = (x,y,z)
transform = tf.translation_matrix((0,0,0))
point = transform_point(self.center, transform)
photon.direction = direction
photon.position = point
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
photon.active = True
return photon
class RadialSource(object):
"""
A point source that emits at discrete angles theta(i) and phi(i)
"""
def __init__(self, spectrum = None, wavelength = 555, center = (0.,0.,0.), phimin = 0, phimax = 2*np.pi, thetamin = 0, thetamax = np.pi, spacing=20):
super(RadialSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.center = center
self.phimin = phimin
self.phimax = phimax
self.thetamin = thetamin
self.thetamax = thetamax
self.spacing = spacing
self.throw = 0
self.source_id = "RadialSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
intphi = np.random.randint(1, self.spacing+1)
inttheta = np.random.randint(1, self.spacing+1)
phi = intphi*(self.phimax-self.phimin)/self.spacing
if self.thetamin == self.thetamax:
theta = self.thetamin
else:
theta = inttheta*(self.thetamax-self.thetamin)/self.spacing
x = np.cos(phi)*np.sin(theta)
y = | np.sin(phi) | numpy.sin |
'''
<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) | numpy.zeros_like |
import os
import random
from typing import Any, Dict, List, Union
import numpy as np
import torch
from colorama import Fore, Style
from sklearn.metrics import f1_score
from sklearn.metrics import precision_recall_fscore_support as score
from sklearn.metrics import precision_score, recall_score
def highlight(input_: Any) -> str:
input_ = str(input_)
return str(Fore.YELLOW + str(input_) + Style.RESET_ALL)
def get_intent_labels(args: Any) -> List[str]:
return [
label.strip()
for label in open(
os.path.join(args.data_dir, args.intent_label_file), "r", encoding="utf-8"
)
]
def get_slot_labels(args: Any) -> List[str]:
return [
label.strip()
for label in open(
os.path.join(args.data_dir, args.slot_label_file), "r", encoding="utf-8"
)
]
def get_pos_labels(args: Any) -> List[str]:
return [
label.strip()
for label in open(
os.path.join(args.data_dir, args.pos_label_file), "r", encoding="utf-8"
)
]
def set_torch_seed(seed: Any, no_cuda: bool) -> None:
random.seed(seed)
np.random.seed(seed)
torch.manual_seed(seed) # type: ignore
if not no_cuda and torch.cuda.is_available():
torch.cuda.manual_seed_all(seed) # type: ignore
def compute_metrics(
intent_preds: List[str],
intent_labels: List[str],
slot_preds: List[List[str]],
slot_labels: List[List[str]],
) -> Dict[Any, Any]:
assert (
len(intent_preds) == len(intent_labels) == len(slot_preds) == len(slot_labels)
)
results: Dict[Any, Any] = {}
intent_result = get_intent_acc(intent_preds, intent_labels)
slot_result = get_slot_metrics(slot_preds, slot_labels)
sementic_result = get_sentence_frame_acc(
intent_preds, intent_labels, slot_preds, slot_labels
)
# New metrics added following Dan's request.
slot_simple_result = get_slot_simple_metrics(slot_preds, slot_labels)
partial_match_result = get_partial_match_metrics(slot_preds, slot_labels)
results.update(intent_result)
results.update(slot_result)
results.update(sementic_result)
results.update(slot_simple_result)
results.update(partial_match_result)
return results
def simplify_tokens(preds: List[str]) -> List[str]:
simple_preds = []
for p in preds:
if p.endswith("TERM"):
simple_preds.append("TERM")
elif p.endswith("DEF"):
simple_preds.append("DEF")
else:
simple_preds.append(p)
return simple_preds
def get_partial_match_metrics(
preds: List[List[str]], labels: List[List[str]]
) -> Dict[Any, Any]:
"""
Suppose there are N such pairs in the gold data and the system predicts M such pairs. Say a ‘partial match’ happens when the system predicts a pair <term,defn> and there is some overlap (at least one token) between the predicted and gold term spans AND there is some overlap between the predicted and gold definition spans. Let X be the number of partial matches. What are
Partial match precision = P/M
Partial match recall = P/N
"""
assert len(preds) == len(labels)
both_in_preds, both_in_labels = [], []
partial_matches, exact_matches = [], []
for pred_sent, label_sent in zip(preds, labels):
simple_pred_sent = simplify_tokens(pred_sent)
simple_label_sent = simplify_tokens(label_sent)
# check whether term/def exist together
both_in_pred = "TERM" in simple_pred_sent and "DEF" in simple_pred_sent
both_in_label = "TERM" in simple_label_sent and "DEF" in simple_label_sent
both_in_preds.append(both_in_pred)
both_in_labels.append(both_in_label)
partial_match = False
exact_match = False
match: List[Union[str, bool]] = []
if both_in_pred and both_in_label:
for p, l in zip(simple_pred_sent, simple_label_sent):
if p == l:
match.append(p)
else:
match.append(False)
if "TERM" in match and "DEF" in match:
partial_match = True
if False not in match:
exact_match = True
partial_matches.append(partial_match)
exact_matches.append(exact_match)
count_both_in_preds = sum(both_in_preds) # N
count_both_in_labels = sum(both_in_labels) # M
count_partial_matches = sum(partial_matches) # P
count_exact_matches = sum(exact_matches) # E
partial_precision = count_partial_matches / count_both_in_preds
partial_recall = count_partial_matches / count_both_in_labels
partial_fscore = (
2 * partial_precision * partial_recall / (partial_precision + partial_recall)
)
exact_precision = count_exact_matches / count_both_in_preds
exact_recall = count_exact_matches / count_both_in_labels
exact_fscore = 2 * exact_precision * exact_recall / (exact_precision + exact_recall)
return {
"partial_match_precision": partial_precision,
"partial_match_recall": partial_recall,
"partial_match_f1": partial_fscore,
"exact_match_precision": exact_precision,
"excat_match_recall": exact_recall,
"excat_match_f1": exact_fscore,
}
def get_slot_simple_metrics(
preds: List[List[str]], labels: List[List[str]]
) -> Dict[Any, Any]:
"""
Conceptually, define the following new types of ‘virtual tags’
TERM = B-term OR I-Term (ie the union of those two tags)
DEF = B-Def OR I-Def
Now, what are the P,R & F1 numbers for TERM and DEF? (I think these matter because users may just care about accuracy of term and defn matching and the macro averaged scores conflate other things like recall on these metrics and precision on O. Likewise the current macro average treats missing the first word in a definition differently from skipping the last word.
"""
assert len(preds) == len(labels)
# flatten
preds_flattened = [p for ps in preds for p in ps]
labels_flattened = [l for ls in labels for l in ls]
# simplify by replacing {B,I}-TERM to TERM and {B,I}-DEF to DEF
simple_preds = simplify_tokens(preds_flattened)
simple_labels = simplify_tokens(labels_flattened)
assert len(simple_preds) == len(simple_labels)
label_names = ["O", "TERM", "DEF"]
p, r, f, s = score(simple_labels, simple_preds, average=None, labels=label_names)
s = [int(si) for si in s]
p = [round(float(pi), 3) for pi in p]
r = [round(float(pi), 3) for pi in r]
f = [round(float(pi), 3) for pi in f]
per_class = {"p": list(p), "r": list(r), "f": list(f), "s": list(s)}
# pprint(per_class)
return {
"slot_merged_TERM_precision": per_class["p"][1],
"slot_merged_TERM_recall": per_class["r"][1],
"slot_merged_TERM_f1": per_class["f"][1],
"slot_merged_DEFINITION_precision": per_class["p"][2],
"slot_merged_DEFINITION_recall": per_class["r"][2],
"slot_merged_DEFINITION_f1": per_class["f"][2],
}
def get_slot_metrics(preds: List[List[str]], labels: List[List[str]]) -> Dict[Any, Any]:
assert len(preds) == len(labels)
# flatten
preds_flattened = [p for ps in preds for p in ps]
labels_flattened = [l for ls in labels for l in ls]
macro_f1 = f1_score(labels_flattened, preds_flattened, average="macro")
micro_f1 = f1_score(labels_flattened, preds_flattened, average="micro")
macro_p = precision_score(labels_flattened, preds_flattened, average="macro")
micro_p = precision_score(labels_flattened, preds_flattened, average="micro")
macro_r = recall_score(labels_flattened, preds_flattened, average="macro")
micro_r = recall_score(labels_flattened, preds_flattened, average="micro")
label_names = ["O", "B-TERM", "I-TERM", "B-DEF", "I-DEF"]
p, r, f, s = score(
labels_flattened, preds_flattened, average=None, labels=label_names
)
s = [int(si) for si in s]
p = [round(float(pi), 3) for pi in p]
r = [round(float(pi), 3) for pi in r]
f = [round(float(pi), 3) for pi in f]
per_class = {"p": list(p), "r": list(r), "f": list(f), "s": list(s)}
# print(per_class)
return {
"slot_precision_macro": macro_p,
"slot_recall_macro": macro_r,
"slot_f1_macro": macro_f1,
"slot_precision_micro": micro_p,
"slot_recall_micro": micro_r,
"slot_f1_micro": micro_f1,
"slot_precision_per_label": per_class["p"],
"slot_recal_per_label": per_class["r"],
"slot_f1_per_label": per_class["f"],
"slot_num_per_label": per_class["s"],
}
def get_intent_acc(preds: List[str], labels: List[str]) -> Dict[Any, Any]:
acc = (preds == labels).mean()
return {"intent_acc": acc}
def read_prediction_text(args: Any) -> List[str]:
return [
text.strip()
for text in open(
os.path.join(args.pred_dir, args.pred_input_file), "r", encoding="utf-8"
)
]
def get_sentence_frame_acc(
intent_preds: List[str],
intent_labels: List[str],
slot_preds: List[List[str]],
slot_labels: List[List[str]],
) -> Dict[Any, Any]:
"""For the cases that intent and all the slots are correct (in one sentence)"""
# Get the intent comparison result
intent_result = intent_preds == intent_labels
# Get the slot comparision result
slot_result = []
for preds, labels in zip(slot_preds, slot_labels):
assert len(preds) == len(labels)
one_sent_result = True
for p, l in zip(preds, labels):
if p != l:
one_sent_result = False
break
slot_result.append(one_sent_result)
slot_result = | np.array(slot_result) | numpy.array |
# Copyright 2021 Huawei Technologies Co., Ltd
#
# 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.
# ============================================================================
"""
postprocess.
"""
import os
import argparse
import numpy as np
from src.ms_utils import calculate_auc
from mindspore import context, load_checkpoint
def softmax(x):
t_max = np.max(x, axis=1, keepdims=True) # returns max of each row and keeps same dims
e_x = | np.exp(x - t_max) | numpy.exp |
#!/usr/bin/env python
# encoding: utf-8
import numbers
import os
import re
import sys
from itertools import chain
import numpy as np
import scipy.sparse as sp
import six
import pickle
from .model import get_convo_nn2
from .stop_words import THAI_STOP_WORDS
from .utils import CHAR_TYPES_MAP, CHARS_MAP, create_feature_array
MODULE_PATH = os.path.dirname(__file__)
WEIGHT_PATH = os.path.join(MODULE_PATH, 'weight', 'cnn_without_ne_ab.h5')
TOKENIZER = None
def tokenize(text, custom_dict=None):
"""
Tokenize given Thai text string
Input
=====
text: str, Thai text string
custom_dict: str (or list), path to customized dictionary file
It allows the function not to tokenize given dictionary wrongly.
The file should contain custom words separated by line.
Alternatively, you can provide list of custom words too.
Output
======
tokens: list, list of tokenized words
Example
=======
>> deepcut.tokenize('ตัดคำได้ดีมาก')
>> ['ตัดคำ','ได้','ดี','มาก']
"""
global TOKENIZER
if not TOKENIZER:
TOKENIZER = DeepcutTokenizer()
return TOKENIZER.tokenize(text, custom_dict=custom_dict)
def _custom_dict(word, text, word_end):
word_length = len(word)
initial_loc = 0
while True:
try:
start_char = re.search(word, text).start()
first_char = start_char + initial_loc
last_char = first_char + word_length - 1
initial_loc += start_char + word_length
text = text[start_char + word_length:]
word_end[first_char:last_char] = (word_length - 1) * [0]
word_end[last_char] = 1
except:
break
return word_end
def _document_frequency(X):
"""
Count the number of non-zero values for each feature in sparse X.
"""
if sp.isspmatrix_csr(X):
return np.bincount(X.indices, minlength=X.shape[1])
return np.diff(sp.csc_matrix(X, copy=False).indptr)
def _check_stop_list(stop):
"""
Check stop words list
ref: https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/feature_extraction/text.py#L87-L95
"""
if stop == "thai":
return THAI_STOP_WORDS
elif isinstance(stop, six.string_types):
raise ValueError("not a built-in stop list: %s" % stop)
elif stop is None:
return None
# assume it's a collection
return frozenset(stop)
def load_model(file_path):
"""
Load saved pickle file of DeepcutTokenizer
Parameters
==========
file_path: str, path to saved model from ``save_model`` method in DeepcutTokenizer
"""
tokenizer = pickle.load(open(file_path, 'rb'))
tokenizer.model = get_convo_nn2()
tokenizer.model = tokenizer.model.load_weights(WEIGHT_PATH)
return tokenizer
class DeepcutTokenizer(object):
"""
Class for tokenizing given Thai text documents using deepcut library
Parameters
==========
ngram_range : tuple, tuple for ngram range for vocabulary, (1, 1) for unigram
and (1, 2) for bigram
stop_words : list or set, list or set of stop words to be removed
if None, max_df can be set to value [0.7, 1.0) to automatically remove
vocabulary. If using "thai", this will use list of pre-populated stop words
max_features : int or None, if provided, only consider number of vocabulary
ordered by term frequencies
max_df : float in range [0.0, 1.0] or int, default=1.0
ignore terms that have a document frequency higher than the given threshold
min_df : float in range [0.0, 1.0] or int, default=1
ignore terms that have a document frequency lower than the given threshold
dtype : type, optional
Example
=======
raw_documents = ['ฉันอยากกินข้าวของฉัน',
'ฉันอยากกินไก่',
'อยากนอนอย่างสงบ']
tokenizer = DeepcutTokenizer(ngram_range=(1, 1))
X = tokenizer.fit_tranform(raw_documents) # document-term matrix in sparse CSR format
>> X.todense()
>> [[0, 0, 1, 0, 1, 0, 2, 1],
[0, 1, 1, 0, 1, 0, 1, 0],
[1, 0, 0, 1, 1, 1, 0, 0]]
>> tokenizer.vocabulary_
>> {'นอน': 0, 'ไก่': 1, 'กิน': 2, 'อย่าง': 3, 'อยาก': 4, 'สงบ': 5, 'ฉัน': 6, 'ข้าว': 7}
"""
def __init__(self, ngram_range=(1, 1), stop_words=None,
max_df=1.0, min_df=1, max_features=None, dtype= | np.dtype('float64') | numpy.dtype |
#!/usr/bin/env python
# encoding: utf-8
import numbers
import os
import re
import sys
from itertools import chain
import numpy as np
import scipy.sparse as sp
import six
import pickle
from .model import get_convo_nn2
from .stop_words import THAI_STOP_WORDS
from .utils import CHAR_TYPES_MAP, CHARS_MAP, create_feature_array
MODULE_PATH = os.path.dirname(__file__)
WEIGHT_PATH = os.path.join(MODULE_PATH, 'weight', 'cnn_without_ne_ab.h5')
TOKENIZER = None
def tokenize(text, custom_dict=None):
"""
Tokenize given Thai text string
Input
=====
text: str, Thai text string
custom_dict: str (or list), path to customized dictionary file
It allows the function not to tokenize given dictionary wrongly.
The file should contain custom words separated by line.
Alternatively, you can provide list of custom words too.
Output
======
tokens: list, list of tokenized words
Example
=======
>> deepcut.tokenize('ตัดคำได้ดีมาก')
>> ['ตัดคำ','ได้','ดี','มาก']
"""
global TOKENIZER
if not TOKENIZER:
TOKENIZER = DeepcutTokenizer()
return TOKENIZER.tokenize(text, custom_dict=custom_dict)
def _custom_dict(word, text, word_end):
word_length = len(word)
initial_loc = 0
while True:
try:
start_char = re.search(word, text).start()
first_char = start_char + initial_loc
last_char = first_char + word_length - 1
initial_loc += start_char + word_length
text = text[start_char + word_length:]
word_end[first_char:last_char] = (word_length - 1) * [0]
word_end[last_char] = 1
except:
break
return word_end
def _document_frequency(X):
"""
Count the number of non-zero values for each feature in sparse X.
"""
if sp.isspmatrix_csr(X):
return np.bincount(X.indices, minlength=X.shape[1])
return np.diff(sp.csc_matrix(X, copy=False).indptr)
def _check_stop_list(stop):
"""
Check stop words list
ref: https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/feature_extraction/text.py#L87-L95
"""
if stop == "thai":
return THAI_STOP_WORDS
elif isinstance(stop, six.string_types):
raise ValueError("not a built-in stop list: %s" % stop)
elif stop is None:
return None
# assume it's a collection
return frozenset(stop)
def load_model(file_path):
"""
Load saved pickle file of DeepcutTokenizer
Parameters
==========
file_path: str, path to saved model from ``save_model`` method in DeepcutTokenizer
"""
tokenizer = pickle.load(open(file_path, 'rb'))
tokenizer.model = get_convo_nn2()
tokenizer.model = tokenizer.model.load_weights(WEIGHT_PATH)
return tokenizer
class DeepcutTokenizer(object):
"""
Class for tokenizing given Thai text documents using deepcut library
Parameters
==========
ngram_range : tuple, tuple for ngram range for vocabulary, (1, 1) for unigram
and (1, 2) for bigram
stop_words : list or set, list or set of stop words to be removed
if None, max_df can be set to value [0.7, 1.0) to automatically remove
vocabulary. If using "thai", this will use list of pre-populated stop words
max_features : int or None, if provided, only consider number of vocabulary
ordered by term frequencies
max_df : float in range [0.0, 1.0] or int, default=1.0
ignore terms that have a document frequency higher than the given threshold
min_df : float in range [0.0, 1.0] or int, default=1
ignore terms that have a document frequency lower than the given threshold
dtype : type, optional
Example
=======
raw_documents = ['ฉันอยากกินข้าวของฉัน',
'ฉันอยากกินไก่',
'อยากนอนอย่างสงบ']
tokenizer = DeepcutTokenizer(ngram_range=(1, 1))
X = tokenizer.fit_tranform(raw_documents) # document-term matrix in sparse CSR format
>> X.todense()
>> [[0, 0, 1, 0, 1, 0, 2, 1],
[0, 1, 1, 0, 1, 0, 1, 0],
[1, 0, 0, 1, 1, 1, 0, 0]]
>> tokenizer.vocabulary_
>> {'นอน': 0, 'ไก่': 1, 'กิน': 2, 'อย่าง': 3, 'อยาก': 4, 'สงบ': 5, 'ฉัน': 6, 'ข้าว': 7}
"""
def __init__(self, ngram_range=(1, 1), stop_words=None,
max_df=1.0, min_df=1, max_features=None, dtype=np.dtype('float64')):
self.model = get_convo_nn2()
self.model.load_weights(WEIGHT_PATH)
self.vocabulary_ = {}
self.ngram_range = ngram_range
self.dtype = dtype
self.max_df = max_df
self.min_df = min_df
if max_df < 0 or min_df < 0:
raise ValueError("negative value for max_df or min_df")
self.max_features = max_features
self.stop_words = _check_stop_list(stop_words)
def _word_ngrams(self, tokens):
"""
Turn tokens into a tokens of n-grams
ref: https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/feature_extraction/text.py#L124-L153
"""
# handle stop words
if self.stop_words is not None:
tokens = [w for w in tokens if w not in self.stop_words]
# handle token n-grams
min_n, max_n = self.ngram_range
if max_n != 1:
original_tokens = tokens
if min_n == 1:
# no need to do any slicing for unigrams
# just iterate through the original tokens
tokens = list(original_tokens)
min_n += 1
else:
tokens = []
n_original_tokens = len(original_tokens)
# bind method outside of loop to reduce overhead
tokens_append = tokens.append
space_join = " ".join
for n in range(min_n,
min(max_n + 1, n_original_tokens + 1)):
for i in range(n_original_tokens - n + 1):
tokens_append(space_join(original_tokens[i: i + n]))
return tokens
def _limit_features(self, X, vocabulary,
high=None, low=None, limit=None):
"""Remove too rare or too common features.
ref: https://github.com/scikit-learn/scikit-learn/blob/ef5cb84a/sklearn/feature_extraction/text.py#L734-L773
"""
if high is None and low is None and limit is None:
return X, set()
# Calculate a mask based on document frequencies
dfs = _document_frequency(X)
mask = np.ones(len(dfs), dtype=bool)
if high is not None:
mask &= dfs <= high
if low is not None:
mask &= dfs >= low
if limit is not None and mask.sum() > limit:
tfs = np.asarray(X.sum(axis=0)).ravel()
mask_inds = (-tfs[mask]).argsort()[:limit]
new_mask = np.zeros(len(dfs), dtype=bool)
new_mask[np.where(mask)[0][mask_inds]] = True
mask = new_mask
new_indices = | np.cumsum(mask) | numpy.cumsum |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones |
'''
-------------------------------------------------------------------------------------------------
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]) | numpy.arctan |
# 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) | numpy.arange |
# -*- encoding:utf-8 -*-
# @Time : 2021/1/3 15:15
# @Author : gfjiang
import os.path as osp
import mmcv
import numpy as np
import cvtools
import matplotlib.pyplot as plt
import cv2.cv2 as cv
from functools import partial
import torch
import math
from cvtools.utils.path import add_prefix_filename_suffix
from mmdet.ops import nms
from mmdet.apis import init_detector, inference_detector
def draw_features(module, input, output, work_dir='./'):
x = output.cpu().numpy()
out_channels = list(output.shape)[1]
height = int(math.sqrt(out_channels))
width = height
if list(output.shape)[2] < 128:
return
fig = plt.figure(figsize=(32, 32))
fig.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95, wspace=0.05, hspace=0.05)
for i in range(height * width):
plt.subplot(height, width, i + 1)
plt.axis('off')
img = x[0, i, :, :]
pmin = np.min(img)
pmax = np.max(img)
img = ((img - pmin) / (pmax - pmin + 0.000001))*255 # float在[0，1]之间，转换成0-255
img = img.astype(np.uint8) # 转成unit8
img = cv.applyColorMap(img, cv.COLORMAP_JET) # 生成heat map
img = img[:, :, ::-1] # 注意cv2（BGR）和matplotlib(RGB)通道是相反的
plt.imshow(img)
# print("{}/{}".format(i,width*height))
savename = get_image_name_for_hook(module, work_dir)
fig.savefig(savename, dpi=100)
fig.clf()
plt.close()
def get_image_name_for_hook(module, work_dir='./'):
"""
Generate image filename for hook function
Parameters:
-----------
module: module of neural network
"""
# os.makedirs(work_dir, exist_ok=True)
module_name = str(module)
base_name = module_name.split('(')[0]
index = 0
image_name = '.' # '.' is surely exist, to make first loop condition True
while osp.exists(image_name):
index += 1
image_name = osp.join(
work_dir, 'feats', '%s_%d.png' % (base_name, index))
return image_name
class AerialDetectionOBB(object):
def __init__(self, config, pth):
self.imgs = []
self.cfg = mmcv.Config.fromfile(config)
self.pth = pth
print('loading model {} ...'.format(pth))
self.model = init_detector(self.cfg, self.pth, device='cuda:0')
self.results = []
self.img_detected = []
# self.vis_feats((torch.nn.Conv2d, torch.nn.MaxPool2d))
def __call__(self,
imgs_or_path,
det_thrs=0.5,
vis=False,
vis_thr=0.5,
save_root=''):
if isinstance(imgs_or_path, str):
self.imgs += cvtools.get_files_list(imgs_or_path)
else:
self.imgs += imgs_or_path
prog_bar = mmcv.ProgressBar(len(self.imgs))
for _, img in enumerate(self.imgs):
self.detect(img, det_thrs=det_thrs, vis=vis,
vis_thr=vis_thr, save_root=save_root)
prog_bar.update()
def detect(self,
img,
det_thrs=0.5,
vis=False,
vis_thr=0.5,
save_root=''):
result = inference_detector(self.model, img)
# result = self.nms(result)
if isinstance(det_thrs, float):
det_thrs = [det_thrs] * len(result)
if vis:
to_file = osp.join(save_root, osp.basename(img))
to_file = add_prefix_filename_suffix(to_file, suffix='_obb')
self.vis(img, result, vis_thr=vis_thr, to_file=to_file)
result = [det[det[..., -1] > det_thr] for det, det_thr
in zip(result, det_thrs)]
if len(result) == 0:
print('detect: image {} has no object.'.format(img))
self.img_detected.append(img)
self.results.append(result)
return result
def nms(self, result, nms_th=0.3):
dets_num = [len(det_cls) for det_cls in result]
result = np.vstack(result)
_, ids = nms(result, nms_th)
total_num = 0
nms_result = []
for num in dets_num:
ids_cls = ids[np.where((total_num <= ids) & (ids < num))[0]]
nms_result.append(result[ids_cls])
total_num += num
return nms_result
def vis(self, img, bbox_result, vis_thr=0.5,
to_file='vis.jpg'):
bboxes = | np.vstack(bbox_result) | numpy.vstack |
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]])
left = np.array([[0, 0], [0.5, 0.5], [0,1]])
right = | np.array([[1, 0], [0.5, 0.5], [1,1]]) | numpy.array |
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) | 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)
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) | numpy.linspace |
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])),
)
)
for pixel_index in range(grid.shape[0]):
if grid_radii[pixel_index] > border_min_radii:
closest_pixel_index = np.argmin(
np.square(grid[pixel_index, 0] - border_grid[:, 0])
+ np.square(grid[pixel_index, 1] - border_grid[:, 1])
)
move_factor = (
border_grid_radii[closest_pixel_index] / grid_radii[pixel_index]
)
if move_factor < 1.0:
grid_relocated[pixel_index, :] = (
move_factor * (grid[pixel_index, :] - border_origin[:])
+ border_origin[:]
)
return grid_relocated
@numba_util.jit()
def furthest_grid_2d_slim_index_from(
grid_2d_slim: np.ndarray, slim_indexes: np.ndarray, coordinate: Tuple[float, float]
) -> int:
distance_to_centre = 0.0
for slim_index in slim_indexes:
y = grid_2d_slim[slim_index, 0]
x = grid_2d_slim[slim_index, 1]
distance_to_centre_new = (x - coordinate[1]) ** 2 + (y - coordinate[0]) ** 2
if distance_to_centre_new >= distance_to_centre:
distance_to_centre = distance_to_centre_new
furthest_grid_2d_slim_index = slim_index
return furthest_grid_2d_slim_index
def grid_2d_slim_from(
grid_2d_native: np.ndarray, mask: np.ndarray, sub_size: int
) -> np.ndarray:
"""
For a native 2D grid and mask of shape [total_y_pixels, total_x_pixels, 2], map the values of all unmasked
pixels to a slimmed grid of shape [total_unmasked_pixels, 2].
The pixel coordinate origin is at the top left corner of the native grid and goes right-wards and downwards, such
that for an grid of shape (3,3) where all pixels are unmasked:
- pixel [0,0] of the 2D grid will correspond to index 0 of the 1D grid.
- pixel [0,1] of the 2D grid will correspond to index 1 of the 1D grid.
- pixel [1,0] of the 2D grid will correspond to index 4 of the 1D grid.
Parameters
----------
grid_2d_native : ndarray
The native grid of (y,x) values which are mapped to the slimmed grid.
mask_2d
A 2D array of bools, where `False` values mean unmasked and are included in the mapping.
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-array.
Returns
-------
ndarray
A 1D grid of values mapped from the 2D grid with dimensions (total_unmasked_pixels).
"""
grid_1d_slim_y = array_2d_util.array_2d_slim_from(
array_2d_native=grid_2d_native[:, :, 0], mask_2d=mask, sub_size=sub_size
)
grid_1d_slim_x = array_2d_util.array_2d_slim_from(
array_2d_native=grid_2d_native[:, :, 1], mask_2d=mask, sub_size=sub_size
)
return np.stack((grid_1d_slim_y, grid_1d_slim_x), axis=-1)
def grid_2d_native_from(
grid_2d_slim: np.ndarray, mask_2d: np.ndarray, sub_size: int
) -> np.ndarray:
"""
For a slimmed 2D grid of shape [total_unmasked_pixels, 2], that was computed by extracting the unmasked values
from a native 2D grid of shape [total_y_pixels, total_x_pixels, 2], map the slimmed grid's coordinates back to the
native 2D grid where masked values are set to zero.
This uses a 1D array 'slim_to_native' where each index gives the 2D pixel indexes of the grid's native unmasked
pixels, for example:
- If slim_to_native[0] = [0,0], the first value of the 1D array maps to the pixels [0,0,:] of the native 2D grid.
- If slim_to_native[1] = [0,1], the second value of the 1D array maps to the pixels [0,1,:] of the native 2D grid.
- If slim_to_native[4] = [1,1], the fifth value of the 1D array maps to the pixels [1,1,:] of the native 2D grid.
Parameters
----------
grid_2d_slim
The (y,x) values of the slimmed 2D grid which are mapped to the native 2D grid.
mask_2d
A 2D array of bools, where `False` values mean unmasked and are included in the mapping.
sub_size
The size (sub_size x sub_size) of each unmasked pixels sub-array.
Returns
-------
ndarray
A NumPy array of shape [total_y_pixels, total_x_pixels, 2] corresponding to the (y,x) values of the native 2D
mapped from the slimmed grid.
"""
grid_2d_native_y = array_2d_util.array_2d_native_from(
array_2d_slim=grid_2d_slim[:, 0], mask_2d=mask_2d, sub_size=sub_size
)
grid_2d_native_x = array_2d_util.array_2d_native_from(
array_2d_slim=grid_2d_slim[:, 1], mask_2d=mask_2d, sub_size=sub_size
)
return np.stack((grid_2d_native_y, grid_2d_native_x), axis=-1)
@numba_util.jit()
def grid_2d_slim_upscaled_from(
grid_slim: np.ndarray,
upscale_factor: int,
pixel_scales: Union[float, Tuple[float, float]],
) -> np.ndarray:
"""
From an input slimmed 2D grid, return an upscaled slimmed 2D grid where (y,x) coordinates are added at an
upscaled resolution to each grid coordinate, analogous to a sub-grid.
Parameters
----------
grid_slim
The slimmed grid of (y,x) coordinates over which a square uniform grid is overlaid.
upscale_factor
The upscaled resolution at which the new grid coordinates are computed.
pixel_scales
The pixel scale of the uniform grid that laid over the irregular grid of (y,x) coordinates.
"""
grid_2d_slim_upscaled = np.zeros(
shape=(grid_slim.shape[0] * upscale_factor ** 2, 2)
)
upscale_index = 0
y_upscale_half = pixel_scales[0] / 2
y_upscale_step = pixel_scales[0] / upscale_factor
x_upscale_half = pixel_scales[1] / 2
x_upscale_step = pixel_scales[1] / upscale_factor
for slim_index in range(grid_slim.shape[0]):
y_grid = grid_slim[slim_index, 0]
x_grid = grid_slim[slim_index, 1]
for y in range(upscale_factor):
for x in range(upscale_factor):
grid_2d_slim_upscaled[upscale_index, 0] = (
y_grid
+ y_upscale_half
- y * y_upscale_step
- (y_upscale_step / 2.0)
)
grid_2d_slim_upscaled[upscale_index, 1] = (
x_grid
- x_upscale_half
+ x * x_upscale_step
+ (x_upscale_step / 2.0)
)
upscale_index += 1
return grid_2d_slim_upscaled
def grid_2d_of_points_within_radius(
radius: float, centre: Tuple[float, float], grid_2d: np.ndarray
):
y_inside = []
x_inside = []
for i in range(len(grid_2d[:, 0])):
if (grid_2d[i, 0] - centre[0]) ** 2 + (
grid_2d[i, 1] - centre[1]
) ** 2 > radius ** 2:
y_inside.append(grid_2d[i, 0])
x_inside.append(grid_2d[i, 1])
return np.asarray(y_inside, x_inside)
def compute_polygon_area(points):
x = points[:, 1]
y = points[:, 0]
return 0.5 * np.abs(np.dot(x, np.roll(y, 1)) - np.dot(y, | np.roll(x, 1) | numpy.roll |
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]))
)
# validate
for feature in cls.DERIVED_ATOM_FEATURES:
assert cls.get_scores_key(feature) in result.result_dict
return result
class PsnrFeatureExtractor(FeatureExtractor):
TYPE = "PSNR_feature"
VERSION = "1.0"
ATOM_FEATURES = ['psnr']
def _generate_result(self, asset):
# routine to call the command-line executable and generate quality
# 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_psnr(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
class MomentFeatureExtractor(FeatureExtractor):
TYPE = "Moment_feature"
# VERSION = "1.0" # call executable
VERSION = "1.1" # python only
ATOM_FEATURES = ['ref1st', 'ref2nd', 'dis1st', 'dis2nd', ]
DERIVED_ATOM_FEATURES = ['refvar', 'disvar', ]
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_w, quality_h = asset.quality_width_height
ref_scores_mtx = None
with YuvReader(filepath=asset.ref_workfile_path, width=quality_w, height=quality_h,
yuv_type=self._get_workfile_yuv_type(asset)) as ref_yuv_reader:
scores_mtx_list = []
i = 0
for ref_yuv in ref_yuv_reader:
ref_y = ref_yuv[0]
firstm = ref_y.mean()
secondm = ref_y.var() + firstm**2
scores_mtx_list.append( | np.hstack(([firstm], [secondm])) | numpy.hstack |
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) | numpy.zeros |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.sin |
# ________
# /
# \ /
# \ /
# \/
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$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = | np.linspace(0, (5 - a) * np.pi, 1001) | numpy.linspace |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$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) | numpy.random.normal |
# -*- 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) | numpy.array |
from gtrain import Model
import numpy as np
import tensorflow as tf
class NetForHypinv(Model):
"""
Implementaion of the crutial function for the HypINV algorithm.
Warning: Do not use this class but implement its subclass, for example see FCNetForHypinv
"""
def __init__(self, weights):
self.eval_session = None
self.grad_session = None
self.initial_x = None
self.center = None
self.weights = weights
self.out_for_eval = None #(going to be filled in build_for_eval method)
self.boundary_out_for_eval = None
self.trained_x = None
self.training_class_index = None
self.x = None # tf variable for inversion (going to be filled in build method)
self.x_for_eval = None
self.out = None
self.boundary_out = None # list of tf tensorf for each class of softmax class vs others output
self.loss = None
self.boundary_loss = None
self.t = None #target
self.boundary_t = None
self.x1 = None # this attribute is used of purposes of modified loss function
def __del__(self):
# close arr sessions
if self.eval_session:
self.eval_session.close()
if self.grad_session:
self.grad_session.close()
def set_initial_x(self, initial_x):
# sets starting point for the search of the closest point
self.initial_x = initial_x
def set_center(self, center):
# sets center point
self.center = center / np.linalg.norm(center)
def set_x1(self, x1):
# sets x1 to which we want to found the cosest point x0
self.x1 = x1
def has_modified_loss(self):
pass # if uses modified loss then it returns true
def set_initial_x_in_session(self, x, session=None):
# sets initial x in certain session
if session is None:
self.set_initial_x(x)
else:
pass # overide this method
def eval(self, x):
if len(x.shape) == 1:
x = x.reshape((1,len(x)))
if not self.eval_session:
self.eval_session = tf.Session()
with self.eval_session.as_default():
self.build_for_eval()
self.eval_session.run(tf.global_variables_initializer())
return self.eval_session.run(self.out_for_eval, {self.x_for_eval: x})
def boundary_eval(self, x, class_index):
# evaluates binary classificaitons class_index and other classes
if not self.eval_session:
self.eval_session = tf.Session()
with self.eval_session.as_default():
self.build_for_eval()
self.eval_session.run(tf.global_variables_initializer())
return self.eval_session.run(self.boundary_out_for_eval[class_index], {self.x_for_eval: x})
def get_boundary_gradient(self, x, class_index):
# computes gradient of the boundary for specified class_index
if not self.grad_session:
self.grad_session = tf.Session()
with self.grad_session.as_default():
self.build_for_eval()
self.grad = list()
for i in range(len(self.weights[0][-1][0])):
self.grad.append(tf.gradients(self.boundary_out_for_eval[i], [self.x_for_eval])[0])
self.grad_x = self.x_for_eval
return self.grad_session.run(self.grad[class_index], {self.grad_x: x})
def build_for_eval(self):
# build model for evaluation
pass #override this method (fill self.out_for_eval)
def train_ended(self, session):
self.trained_x = session.run(self.x)
def build(self):
# build model for training
pass #override this method (fill self.x, self.out)
def set_train_class(self, class_index):
# sets class of the x1
self.training_class_index = class_index
# overided methods from gtrain.Model
def get_loss(self):
if self.training_class_index is None:
return self.loss
else:
return self.boundary_loss[self.training_class_index]
def get_hits(self):
return self.get_loss()
def get_count(self):
return self.get_loss()
def get_train_summaries(self):
return []
def get_dev_summaries(self):
return []
def get_placeholders(self):
if self.training_class_index is None:
return [self.t]
else:
return [self.boundary_t]
#________________________________________EXAMPLES_OF_NetForHypinv_CLASS_____________________________________________
class FCNetForHypinv(NetForHypinv):
"""
Implementation of multi layer perceptron to by used in HypINV rule extraction algorithm
"""
def __init__(self, weights, function=tf.sigmoid, use_modified_loss=False, mu = 0.01):
"""
:param weights: saved as [list of weights for layers][0 weight, 1 bias]
:param function: tf function for propagation. For example tf.nn.sigmoid, tf.atan
:param use_modified_loss: weather the modified loss should be used
:param mu: factor of the penalty terms that specified the distance between x0 and x1 and
the distance x1 from the boundary
"""
super(FCNetForHypinv, self).__init__(weights)
self.function = function
self.layer_sizes = [len(self.weights[0][0])]
for bias in weights[1]:
self.layer_sizes.append(len(bias))
self.num_classes = self.layer_sizes[-1]
self.initial_x = np.zeros([1, self.layer_sizes[0]])
self.use_modified_loss = use_modified_loss
self.mu = mu
def build(self):
with tf.name_scope("Input"):
if self.center is not None:
self.point_weights = tf.Variable(self.center.reshape((1, len(self.center))),
dtype=tf.float64, trainable=False, name="Boundary_point")
init_factor = self.center
init_factor[init_factor!=0] = self.initial_x[init_factor!=0] / self.center[init_factor!=0]
self.factor = tf.Variable(init_factor.reshape((1, len(self.center))),
dtype=tf.float64, name="factor")
else:
self.point_weights = tf.Variable(self.initial_x.reshape((1, len(self.initial_x))),
dtype=tf.float64, trainable=False, name="Boundary_point")
self.factor = tf.Variable(np.ones((1, len(self.center))),
dtype=tf.float64, name="factor")
self.x = self.point_weights * self.factor
with tf.name_scope("Target"):
if self.use_modified_loss:
x1_constant = tf.constant(self.x1.reshape((1, len(self.x1))), dtype=tf.float64)
self.t = tf.placeholder(tf.float64, shape=[None, self.num_classes], name="Target_output")
self.boundary_t = tf.placeholder(tf.float64, shape=[None, 2], name="Target_boundary_output")
with tf.name_scope("FC_net"):
flowing_x = self.x
for i, _ in enumerate(self.weights[0]):
with tf.name_scope("layer_{}".format(i)):
W = tf.constant(self.weights[0][i], name="Weight_{}".format(i), dtype=tf.float64)
b = tf.constant(self.weights[1][i], name="Bias_{}".format(i), dtype=tf.float64)
flowing_x = self.function(tf.nn.xw_plus_b(flowing_x, W, b))
y = flowing_x
self.out = tf.nn.softmax(y)
with tf.name_scope("Binary_class_output"):
self.boundary_out = list()
for i in range(self.num_classes):
mask = True+np.zeros(self.num_classes, dtype=np.bool)
mask[i] = False
x0 = self.out[:,i]
x1 = tf.reduce_max(tf.boolean_mask(self.out, mask, axis=1), axis=1)
s = x0+x1
out = tf.stack([x0/s, x1/s], axis=1)
self.boundary_out.append(out)
with tf.name_scope("Loss_functions"):
self.loss = tf.reduce_mean(
tf.nn.l2_loss(self.out-self.t),
name="loss")
with tf.name_scope("Binary_class_loss"):
self.boundary_loss = list()
if self.use_modified_loss:
for i in range(self.num_classes):
self.boundary_loss.append(
tf.reduce_mean(tf.nn.l2_loss(self.boundary_out[i]-self.boundary_t)) +
self.mu * tf.reduce_mean(tf.nn.l2_loss(self.x - x1_constant))
)
else:
for i in range(self.num_classes):
self.boundary_loss.append(
tf.reduce_mean(tf.nn.l2_loss(self.boundary_out[i] - self.boundary_t))
)
def set_initial_x_in_session(self, x, session=None):
if session is None:
self.set_initial_x(x)
else:
if self.center is None:
session.run([
self.point_weights.assign(x.reshape((1, len(x)))),
self.factor.assign(np.ones((1, len(x))))
])
else:
init_factor = self.center
init_factor[init_factor!=0] = x[init_factor!=0] / self.center[init_factor!=0]
session.run(self.factor.assign(init_factor.reshape((1,len(init_factor)))))
def build_for_eval(self):
with tf.name_scope("eInput"):
self.x_for_eval = tf.placeholder(tf.float32, shape=[None, len(self.weights[0][0])])#tf.Variable(tf.constant(self.initial_x), name="Boundary_point")
with tf.name_scope("eFC_net"):
flowing_x = self.x_for_eval
for i, _ in enumerate(self.weights[0]):
W = tf.constant(self.weights[0][i], name="eWeight_{}".format(i))
b = tf.constant(self.weights[1][i], name="eBias_{}".format(i))
flowing_x = self.function(tf.nn.xw_plus_b(flowing_x, W, b), name="elayer_{}".format(i))
y = flowing_x
self.out_for_eval = tf.nn.softmax(y)
with tf.name_scope("Binary_class_output"):
self.boundary_out_for_eval = list()
for i in range(self.num_classes):
mask = True+np.zeros(self.num_classes, dtype=np.bool)
mask[i] = False
x0 = self.out_for_eval[:, i]
x1 = tf.reduce_max(tf.boolean_mask(self.out_for_eval, mask, axis=1), axis=1)
s = x0+x1
out = tf.stack([x0/s, x1/s], axis=1)
self.boundary_out_for_eval.append(out)
def has_modified_loss(self):
return self.use_modified_loss
def name(self):
return "Hypinv_FC_net_{}".format("-".join([str(ls) for ls in self.layer_sizes]))
class FCNetForHypinvBinary(FCNetForHypinv):
"""
Implementation of multi layer perceptron to by used in HypINV rule extraction algorithm
The task is simplified to the binary classificaiton base_class_index against the other classes
"""
def __init__(self, weights, base_class_index, function=tf.sigmoid, use_modified_loss=False, mu = 0.01):
"""
:param weights: saved as [list of weights for layers][0 weight, 1 bias]
:param base_class_index: an index of the class which is used as the base class
:param function: tf function for propagation. For example tf.nn.sigmoid, tf.atan
:param use_modified_loss: weather the modified loss should be used
:param mu: factor of the penalty terms that specified the distance between x0 and x1 and
the distance x1 from the boundary
"""
super(FCNetForHypinvBinary, self).__init__(weights)
self.base_class_index = base_class_index
self.function = function
self.layer_sizes = [len(self.weights[0][0])]
for bias in weights[1]:
self.layer_sizes.append(len(bias))
self.num_classes = self.layer_sizes[-1]
self.initial_x = np.zeros([1, self.layer_sizes[0]])
self.use_modified_loss = use_modified_loss
self.mu = mu
def build(self):
with tf.name_scope("Input"):
self.init_point = tf.Variable(self.initial_x.reshape((1, len(self.initial_x))),
dtype=tf.float64, trainable=False, name="Boundary_point")
self.factor = tf.Variable(np.ones((1, len(self.initial_x))),
dtype=tf.float64, name="factor")
self.x = self.init_point * self.factor
with tf.name_scope("Target"):
if self.use_modified_loss:
x1_constant = tf.constant(self.x1.reshape((1, len(self.x1))), dtype=tf.float64)
self.t = tf.placeholder(tf.float64, shape=[None, 2], name="Target_output")
self.boundary_t = tf.placeholder(tf.float64, shape=[None, 2], name="Target_boundary_output")
with tf.name_scope("FC_net"):
flowing_x = self.x
for i, _ in enumerate(self.weights[0]):
with tf.name_scope("layer_{}".format(i)):
W = tf.constant(self.weights[0][i], name="Weight_{}".format(i), dtype=tf.float64)
b = tf.constant(self.weights[1][i], name="Bias_{}".format(i), dtype=tf.float64)
flowing_x = self.function(tf.nn.xw_plus_b(flowing_x, W, b))
y = flowing_x
full_out = tf.nn.softmax(y)
with tf.name_scope("Binary_class_output"):
self.boundary_out = list()
mask = True+np.zeros(self.num_classes, dtype=np.bool)
mask[self.base_class_index] = False
x0 = full_out[:,self.base_class_index]
x1 = tf.reduce_max(tf.boolean_mask(full_out, mask, axis=1), axis=1)
s = x0+x1
self.out = tf.stack([x0/s, x1/s], axis=1)
self.boundary_out.append(self.out)
self.boundary_out.append(tf.stack([x1/s, x0/s], axis=1))
with tf.name_scope("Loss_functions"):
self.loss = tf.reduce_mean(
tf.nn.l2_loss(self.out-self.t),
name="loss")
with tf.name_scope("Binary_class_loss"):
self.boundary_loss = list()
if self.use_modified_loss:
for i in range(2):
self.boundary_loss.append(
tf.reduce_mean(tf.nn.l2_loss(self.boundary_out[i]-self.boundary_t)) +
self.mu * tf.reduce_mean(tf.nn.l2_loss(self.x - x1_constant))
)
else:
for i in range(2):
self.boundary_loss.append(
tf.reduce_mean(tf.nn.l2_loss(self.boundary_out[i] - self.boundary_t))
)
def build_for_eval(self):
with tf.name_scope("eInput"):
self.x_for_eval = tf.placeholder(tf.float32, shape=[None, len(self.weights[0][0])])#tf.Variable(tf.constant(self.initial_x), name="Boundary_point")
with tf.name_scope("eFC_net"):
flowing_x = self.x_for_eval
for i, _ in enumerate(self.weights[0]):
W = tf.constant(self.weights[0][i], name="eWeight_{}".format(i))
b = tf.constant(self.weights[1][i], name="eBias_{}".format(i))
flowing_x = self.function(tf.nn.xw_plus_b(flowing_x, W, b), name="elayer_{}".format(i))
y = flowing_x
full_out = tf.nn.softmax(y)
with tf.name_scope("Binary_class_output"):
self.boundary_out_for_eval = list()
mask = True+ | np.zeros(self.num_classes, dtype=np.bool) | numpy.zeros |
import numpy as np
import pytest
from astropy import convolution
from scipy.signal import medfilt
import astropy.units as u
from ..spectra.spectrum1d import Spectrum1D
from ..tests.spectral_examples import simulated_spectra
from ..manipulation.smoothing import (convolution_smooth, box_smooth,
gaussian_smooth, trapezoid_smooth,
median_smooth)
def compare_flux(flux_smooth1, flux_smooth2, flux_original, rtol=0.01):
"""
There are two things to compare for each set of smoothing:
1. Compare the smoothed flux from the astropy machinery vs
the smoothed flux from specutils. This is done by
comparing flux_smooth1 and flux_smooth2.
2. Next we want to compare the smoothed flux to the original
flux. This is a little more difficult as smoothing will
make a difference for median filter, but less so for
convolution based smoothing if the kernel is normalized
(area under the kernel = 1).
In this second case the rtol (relative tolerance) is used
judiciously.
"""
# Compare, element by element, the two smoothed fluxes.
assert np.allclose(flux_smooth1, flux_smooth2)
# Compare the total spectral flux of the smoothed to the original.
assert np.allclose(sum(flux_smooth1), sum(flux_original), rtol=rtol)
def test_smooth_custom_kernel(simulated_spectra):
"""
Test CustomKernel smoothing with correct parmaeters.
"""
# Create the original spectrum
spec1 = simulated_spectra.s1_um_mJy_e1
flux_original = spec1.flux
# Create a custom kernel (some weird asymmetric-ness)
numpy_kernel = np.array([0.5, 1, 2, 0.5, 0.2])
numpy_kernel = numpy_kernel / | np.sum(numpy_kernel) | numpy.sum |
# Copyright 2021 Huawei Technologies Co., Ltd
#
# 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.
# ============================================================================
"""
postprocess.
"""
import os
import argparse
import numpy as np
from src.ms_utils import calculate_auc
from mindspore import context, load_checkpoint
def softmax(x):
t_max = | np.max(x, axis=1, keepdims=True) | numpy.max |
"""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)):
raise ValueError("`x0` violates bound constraints.")
if as_linear_operator:
if rel_step is None:
rel_step = relative_step[method]
return _linear_operator_difference(fun_wrapped, x0,
f0, rel_step, method)
else:
h = _compute_absolute_step(rel_step, x0, method)
if method == '2-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '1-sided', lb, ub)
elif method == '3-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '2-sided', lb, ub)
elif method == 'cs':
use_one_sided = False
if sparsity is None:
return _dense_difference(fun_wrapped, x0, f0, h,
use_one_sided, method)
else:
if not issparse(sparsity) and len(sparsity) == 2:
structure, groups = sparsity
else:
structure = sparsity
groups = group_columns(sparsity)
if issparse(structure):
structure = csc_matrix(structure)
else:
structure = np.atleast_2d(structure)
groups = np.atleast_1d(groups)
return _sparse_difference(fun_wrapped, x0, f0, h,
use_one_sided, structure,
groups, method)
def _linear_operator_difference(fun, x0, f0, h, method):
m = f0.size
n = x0.size
if method == '2-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p
df = fun(x) - f0
return df / dx
elif method == '3-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = 2*h / norm(p)
x1 = x0 - (dx/2)*p
x2 = x0 + (dx/2)*p
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
return df / dx
elif method == 'cs':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p*1.j
f1 = fun(x)
df = f1.imag
return df / dx
else:
raise RuntimeError("Never be here.")
return LinearOperator((m, n), matvec)
def _dense_difference(fun, x0, f0, h, use_one_sided, method):
m = f0.size
n = x0.size
J_transposed = np.empty((n, m))
h_vecs = np.diag(h)
for i in range(h.size):
if method == '2-point':
x = x0 + h_vecs[i]
dx = x[i] - x0[i] # Recompute dx as exactly representable number.
df = fun(x) - f0
elif method == '3-point' and use_one_sided[i]:
x1 = x0 + h_vecs[i]
x2 = x0 + 2 * h_vecs[i]
dx = x2[i] - x0[i]
f1 = fun(x1)
f2 = fun(x2)
df = -3.0 * f0 + 4 * f1 - f2
elif method == '3-point' and not use_one_sided[i]:
x1 = x0 - h_vecs[i]
x2 = x0 + h_vecs[i]
dx = x2[i] - x1[i]
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
elif method == 'cs':
f1 = fun(x0 + h_vecs[i]*1.j)
df = f1.imag
dx = h_vecs[i, i]
else:
raise RuntimeError("Never be here.")
J_transposed[i] = df / dx
if m == 1:
J_transposed = np.ravel(J_transposed)
return J_transposed.T
def _sparse_difference(fun, x0, f0, h, use_one_sided,
structure, groups, method):
m = f0.size
n = x0.size
row_indices = []
col_indices = []
fractions = []
n_groups = | np.max(groups) | numpy.max |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones |
from data.data_loader_dad import (
NASA_Anomaly,
WADI
)
from exp.exp_basic import Exp_Basic
from models.model import Informer
from utils.tools import EarlyStopping, adjust_learning_rate
from utils.metrics import metric
from sklearn.metrics import classification_report
import numpy as np
import torch
import torch.nn as nn
from torch import optim
from torch.utils.data import DataLoader
import os
import time
import warnings
warnings.filterwarnings('ignore')
class Exp_Informer_DAD(Exp_Basic):
def __init__(self, args):
super(Exp_Informer_DAD, self).__init__(args)
def _build_model(self):
model_dict = {
'informer':Informer,
}
if self.args.model=='informer':
model = model_dict[self.args.model](
self.args.enc_in,
self.args.dec_in,
self.args.c_out,
self.args.seq_len,
self.args.label_len,
self.args.pred_len,
self.args.factor,
self.args.d_model,
self.args.n_heads,
self.args.e_layers,
self.args.d_layers,
self.args.d_ff,
self.args.dropout,
self.args.attn,
self.args.embed,
self.args.data[:-1],
self.args.activation,
self.device
)
return model.double()
def _get_data(self, flag):
args = self.args
data_dict = {
'SMAP':NASA_Anomaly,
'MSL':NASA_Anomaly,
'WADI':WADI,
}
Data = data_dict[self.args.data]
if flag == 'test':
shuffle_flag = False; drop_last = True; batch_size = args.batch_size
else:
shuffle_flag = True; drop_last = True; batch_size = args.batch_size
data_set = Data(
root_path=args.root_path,
data_path=args.data_path,
flag=flag,
size=[args.seq_len, args.label_len, args.pred_len],
features=args.features,
target=args.target
)
print(flag, len(data_set))
data_loader = DataLoader(
data_set,
batch_size=batch_size,
shuffle=shuffle_flag,
num_workers=args.num_workers,
drop_last=drop_last)
return data_set, data_loader
def _select_optimizer(self):
model_optim = optim.Adam(self.model.parameters(), lr=self.args.learning_rate)
return model_optim
def _select_criterion(self):
criterion = nn.MSELoss()
return criterion
def vali(self, vali_data, vali_loader, criterion):
self.model.eval()
total_loss = []
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark,batch_label) in enumerate(vali_loader):
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
pred = outputs.detach().cpu()
true = batch_y.detach().cpu()
loss = criterion(pred, true)
total_loss.append(loss)
total_loss = np.average(total_loss)
self.model.train()
return total_loss
def train(self, setting):
train_data, train_loader = self._get_data(flag = 'train')
vali_data, vali_loader = self._get_data(flag = 'val')
test_data, test_loader = self._get_data(flag = 'test')
path = './checkpoints/'+setting
if not os.path.exists(path):
os.makedirs(path)
time_now = time.time()
train_steps = len(train_loader)
early_stopping = EarlyStopping(patience=self.args.patience, verbose=True)
model_optim = self._select_optimizer()
criterion = self._select_criterion()
for epoch in range(self.args.train_epochs):
iter_count = 0
train_loss = []
self.model.train()
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark) in enumerate(train_loader):
iter_count += 1
model_optim.zero_grad()
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
loss = criterion(outputs, batch_y)
train_loss.append(loss.item())
if (i+1) % 100==0:
print("\titers: {0}, epoch: {1} | loss: {2:.7f}".format(i + 1, epoch + 1, loss.item()))
speed = (time.time()-time_now)/iter_count
left_time = speed*((self.args.train_epochs - epoch)*train_steps - i)
print('\tspeed: {:.4f}s/iter; left time: {:.4f}s'.format(speed, left_time))
iter_count = 0
time_now = time.time()
loss.backward()
model_optim.step()
train_loss = np.average(train_loss)
vali_loss = self.vali(vali_data, vali_loader, criterion)
test_loss = self.vali(test_data, test_loader, criterion)
print("Epoch: {0}, Steps: {1} | Train Loss: {2:.7f} Vali Loss: {3:.7f} Test Loss: {4:.7f}".format(
epoch + 1, train_steps, train_loss, vali_loss, test_loss))
early_stopping(vali_loss, self.model, path)
if early_stopping.early_stop:
print("Early stopping")
break
adjust_learning_rate(model_optim, epoch+1, self.args)
best_model_path = path+'/'+'checkpoint.pth'
self.model.load_state_dict(torch.load(best_model_path))
return self.model
def test(self, setting):
test_data, test_loader = self._get_data(flag='test')
self.model.eval()
preds = []
trues = []
labels = []
with torch.no_grad():
for i, (batch_x,batch_y,batch_x_mark,batch_y_mark,batch_label) in enumerate(test_loader):
batch_x = batch_x.double().to(self.device)
batch_y = batch_y.double()
batch_x_mark = batch_x_mark.double().to(self.device)
batch_y_mark = batch_y_mark.double().to(self.device)
# decoder input
dec_inp = torch.zeros_like(batch_y[:,-self.args.pred_len:,:]).double()
dec_inp = torch.cat([batch_y[:,:self.args.label_len,:], dec_inp], dim=1).double().to(self.device)
# encoder - decoder
outputs = self.model(batch_x, batch_x_mark, dec_inp, batch_y_mark)
batch_y = batch_y[:,-self.args.pred_len:,:].to(self.device)
pred = outputs.detach().cpu().numpy()#.squeeze()
true = batch_y.detach().cpu().numpy()#.squeeze()
batch_label = batch_label.long().detach().numpy()
preds.append(pred)
trues.append(true)
labels.append(batch_label)
preds = np.array(preds)
trues = np.array(trues)
labels = np.array(labels)
print('test shape:', preds.shape, trues.shape)
preds = preds.reshape(-1, preds.shape[-2], preds.shape[-1])
trues = trues.reshape(-1, trues.shape[-2], trues.shape[-1])
labels = labels.reshape(-1, labels.shape[-1])
print('test shape:', preds.shape, trues.shape)
# result save
folder_path = './results/' + setting +'/'
if not os.path.exists(folder_path):
os.makedirs(folder_path)
mae, mse, rmse, mape, mspe = metric(preds, trues)
print('mse:{}, mae:{}'.format(mse, mae))
np.save(folder_path+'metrics.npy', | np.array([mae, mse, rmse, mape, mspe]) | 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]) | 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).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]])
def test_dataarray_to_matrix_negative_x_increment():
"""
Check if dataarray_to_matrix returns correct output with flipped x.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=4, stop=0, 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.flip(data, axis=(0, 1)))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_negative_y_increment():
"""
Check that dataarray_to_matrix returns correct output with flipped y.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=0, stop=4, num=3)
y = np.linspace(start=9, stop=5, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
npt.assert_allclose(actual=matrix, desired=data)
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_negative_x_and_y_increment():
"""
Check that dataarray_to_matrix returns correct output with flipped x/y.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=4, stop=0, num=3)
y = np.linspace(start=9, stop=5, 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.fliplr(data))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_dims_fails():
"""
Check that it fails for > 2 dims.
"""
# Make a 3D regular grid
data = np.ones((10, 12, 11), dtype="float32")
x = np.arange(11)
y = | np.arange(12) | 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) | numpy.ones_like |
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) | numpy.random.rand |
import sys
import numpy as np
from matplotlib import pyplot as pl
from rw import WriteGTiff
fn = '../pozo-steep-vegetated-pcl.npy'
pts = | np.load(fn) | numpy.load |
#
# 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) ** 2,
)
posteriors = tfp.distributions.MultivariateNormalDiag(
loc=np.random.randn(*posteriors_shape),
scale_diag= | np.random.randn(*posteriors_shape) | numpy.random.randn |
"""
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) | 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) | 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) | numpy.linspace |
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) | numpy.int32 |
#
# 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) ** 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(prior=prior, encoder=encoder)
tf.random.set_seed(seed)
sample_prior = lv(inputs, seed=seed2)
tf.random.set_seed(seed)
prior_expected = np.concatenate([inputs, prior.sample(num_data, seed=seed2)], axis=-1)
| np.testing.assert_array_equal(sample_prior, prior_expected) | numpy.testing.assert_array_equal |
import sys
import numpy as np
from matplotlib import pyplot as pl
from rw import WriteGTiff
fn = '../pozo-steep-vegetated-pcl.npy'
pts = np.load(fn)
x, y, z, c = pts[:, 0], pts[:, 1], pts[:, 2], pts[:, 5]
ix = (0.2 * (x - x.min())).astype('int')
iy = (0.2 * (y - y.min())).astype('int')
shape = (100, 100)
xb = np.arange(shape[1]+1)
yb = np.arange(shape[0]+1)
fg, ax = pl.subplots(ncols = 2, nrows = 2,
figsize = (10.24, 10.24),
sharex = True, sharey = True)
uc = (2, 5)
for j in range(len(uc)):
print('Class %i' % uc[j])
b = c == uc[j]
cx, cy, cz = ix[b], iy[b], z[b]
mean = np.zeros(shape)
stdr = np.zeros(shape)
for i in range(shape[0]):
print('% 3d%%' % i)
for k in range(shape[1]):
b = (cy == i) * (cx == k)
mean[i, k] = cz[b].mean()
stdr[i, k] = cz[b].std()
fname = 'pozo_5m_dem_mean_cl%i.tif' % uc[j]
WriteGTiff(fname, mean, x.min(), y.min()+500, step = 5)
| np.save('pozo_5m_dem_mean_cl%i.npy' % uc[j], mean) | numpy.save |
"""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) | numpy.std |
'''
<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]) | numpy.linalg.norm |
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) | numpy.nonzero |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones_like |
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
Test for the piezo tensor class
"""
__author__ = "<NAME>"
__version__ = "0.1"
__maintainer__ = "<NAME>"
__email__ = "<EMAIL>"
__status__ = "Development"
__date__ = "4/1/16"
import os
import unittest
import numpy as np
from pymatgen.analysis.piezo import PiezoTensor
from pymatgen.util.testing import PymatgenTest
class PiezoTest(PymatgenTest):
def setUp(self):
self.piezo_struc = self.get_structure("BaNiO3")
self.voigt_matrix = np.array(
[
[0.0, 0.0, 0.0, 0.0, 0.03839, 0.0],
[0.0, 0.0, 0.0, 0.03839, 0.0, 0.0],
[6.89822, 6.89822, 27.46280, 0.0, 0.0, 0.0],
]
)
self.vasp_matrix = np.array(
[
[0.0, 0.0, 0.0, 0.0, 0.0, 0.03839],
[0.0, 0.0, 0.0, 0.0, 0.03839, 0.0, 0.0],
[6.89822, 6.89822, 27.46280, 0.0, 0.0, 0.0],
]
)
self.full_tensor_array = [
[[0.0, 0.0, 0.03839], [0.0, 0.0, 0.0], [0.03839, 0.0, 0.0]],
[[0.0, 0.0, 0.0], [0.0, 0.0, 0.03839], [0.0, 0.03839, 0.0]],
[[6.89822, 0.0, 0.0], [0.0, 6.89822, 0.0], [0.0, 0.0, 27.4628]],
]
def test_new(self):
pt = PiezoTensor(self.full_tensor_array)
self.assertArrayAlmostEqual(pt, self.full_tensor_array)
bad_dim_array = | np.zeros((3, 3)) | numpy.zeros |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones |
from __future__ import division
from timeit import default_timer as timer
import csv
import numpy as np
import itertools
from munkres import Munkres, print_matrix, make_cost_matrix
import sys
from classes import *
from functions import *
from math import sqrt
import Tkinter as tk
import tkFileDialog as filedialog
root = tk.Tk()
root.withdraw()
p_file = filedialog.askopenfilename(title='Please select the posting file')
c_file = filedialog.askopenfilename(title='Please select the candidate file')
"""for use with /users/java_jonathan/postings_lge.csv and
/Users/java_jonathan/candidates_lge.csv"""
# p_file = raw_input("Please enter the path for the postings file: ")
# p_file = p_file.strip()
# c_file = raw_input("Please enter the path for the candidate file: ")
# c_file = c_file.strip()
start = timer()
with open(p_file,'r') as f:
#with open('/Users/Jonathan/Google Drive/CPD/Python/postings.csv','r') as f:
reader = csv.reader(f)
postingsAll = list(reader)
with open(c_file,'r') as f:
reader = csv.reader(f)
candidatesAll = list(reader)
"""create empty lists to fill with lists of lists output by iterating function
below"""
names = []
totalMatrix = []
for list in candidatesAll:
candidate = Candidate(*list)
names.append(candidate.name)
n = 0
for list in postingsAll:
posting = Posting(*list)
totalMatrix.append(matchDept(posting,candidate) + matchAnchor(posting,candidate)
+matchLocation(posting,candidate) + matchCompetency(posting,candidate) +
matchSkill(posting,candidate)+matchCohort(posting,candidate))
n += 1
l = len(names)
names.extend([0] * (n-l))
totalMatrix.extend([0] * (n**2 - len(totalMatrix)))
totalMatrix = np.asarray(totalMatrix)
totalMatrix = np.reshape(totalMatrix,(n,-1))
#at this point the matrix is structured as candidates down and jobs across
totalMatrix = np.transpose(totalMatrix)
#now it's switched!
totalMatrix = np.subtract( | np.amax(totalMatrix) | numpy.amax |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
__all__ = ['imread', 'imsave']
import numpy as np
from PIL import Image
from ...util import img_as_ubyte, img_as_uint
def imread(fname, dtype=None, img_num=None, **kwargs):
"""Load an image from file.
Parameters
----------
fname : str or file
File name or file-like-object.
dtype : numpy dtype object or string specifier
Specifies data type of array elements.
img_num : int, optional
Specifies which image to read in a file with multiple images
(zero-indexed).
kwargs : keyword pairs, optional
Addition keyword arguments to pass through.
Notes
-----
Files are read using the Python Imaging Library.
See PIL docs [1]_ for a list of supported formats.
References
----------
.. [1] http://pillow.readthedocs.org/en/latest/handbook/image-file-formats.html
"""
if isinstance(fname, str):
with open(fname, 'rb') as f:
im = Image.open(f)
return pil_to_ndarray(im, dtype=dtype, img_num=img_num)
else:
im = Image.open(fname)
return pil_to_ndarray(im, dtype=dtype, img_num=img_num)
def pil_to_ndarray(image, dtype=None, img_num=None):
"""Import a PIL Image object to an ndarray, in memory.
Parameters
----------
Refer to ``imread``.
"""
try:
# this will raise an IOError if the file is not readable
image.getdata()[0]
except IOError as e:
site = "http://pillow.readthedocs.org/en/latest/installation.html#external-libraries"
pillow_error_message = str(e)
error_message = ('Could not load "%s" \n'
'Reason: "%s"\n'
'Please see documentation at: %s'
% (image.filename, pillow_error_message, site))
raise ValueError(error_message)
frames = []
grayscale = None
i = 0
while 1:
try:
image.seek(i)
except EOFError:
break
frame = image
if img_num is not None and img_num != i:
image.getdata()[0]
i += 1
continue
if image.format == 'PNG' and image.mode == 'I' and dtype is None:
dtype = 'uint16'
if image.mode == 'P':
if grayscale is None:
grayscale = _palette_is_grayscale(image)
if grayscale:
frame = image.convert('L')
else:
if image.format == 'PNG' and 'transparency' in image.info:
frame = image.convert('RGBA')
else:
frame = image.convert('RGB')
elif image.mode == '1':
frame = image.convert('L')
elif 'A' in image.mode:
frame = image.convert('RGBA')
elif image.mode == 'CMYK':
frame = image.convert('RGB')
if image.mode.startswith('I;16'):
shape = image.size
dtype = '>u2' if image.mode.endswith('B') else '<u2'
if 'S' in image.mode:
dtype = dtype.replace('u', 'i')
frame = np.fromstring(frame.tobytes(), dtype)
frame.shape = shape[::-1]
else:
frame = np.array(frame, dtype=dtype)
frames.append(frame)
i += 1
if img_num is not None:
break
if hasattr(image, 'fp') and image.fp:
image.fp.close()
if img_num is None and len(frames) > 1:
return | np.array(frames) | numpy.array |
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))
labels = torch.from_numpy( | np.array(labels) | numpy.array |
"""
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) | numpy.multiply |
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
import os
import contorno
from constantes import INTERVALOS, PASSOS, TAMANHO_BARRA, DELTA_T, DELTA_X
z_temp = contorno.p_3
TAMANHO_BARRA = 2
x = np.linspace(0.0, TAMANHO_BARRA, INTERVALOS+1)
y = np.linspace(0.0, DELTA_T, PASSOS+1)
z = []
for k in range(PASSOS+1):
z_k = np.copy(z_temp)
z.append(z_k)
for i in range(1, INTERVALOS):
z_temp[i] = z_k[i] + (DELTA_T/(DELTA_X**2)) * (z_k[i+1]-2*z_k[i]+z_k[i-1])
z = np.asarray(z)
x, y = | np.meshgrid(x, y) | numpy.meshgrid |
from __future__ import annotations
from datetime import timedelta
import operator
from sys import getsizeof
from typing import (
TYPE_CHECKING,
Any,
Callable,
Hashable,
List,
cast,
)
import warnings
import numpy as np
from pandas._libs import index as libindex
from pandas._libs.lib import no_default
from pandas._typing import Dtype
from pandas.compat.numpy import function as nv
from pandas.util._decorators import (
cache_readonly,
doc,
)
from pandas.util._exceptions import rewrite_exception
from pandas.core.dtypes.common import (
ensure_platform_int,
ensure_python_int,
is_float,
is_integer,
is_scalar,
is_signed_integer_dtype,
is_timedelta64_dtype,
)
from pandas.core.dtypes.generic import ABCTimedeltaIndex
from pandas.core import ops
import pandas.core.common as com
from pandas.core.construction import extract_array
import pandas.core.indexes.base as ibase
from pandas.core.indexes.base import maybe_extract_name
from pandas.core.indexes.numeric import (
Float64Index,
Int64Index,
NumericIndex,
)
from pandas.core.ops.common import unpack_zerodim_and_defer
if TYPE_CHECKING:
from pandas import Index
_empty_range = range(0)
class RangeIndex(NumericIndex):
"""
Immutable Index implementing a monotonic integer range.
RangeIndex is a memory-saving special case of Int64Index limited to
representing monotonic ranges. Using RangeIndex may in some instances
improve computing speed.
This is the default index type used
by DataFrame and Series when no explicit index is provided by the user.
Parameters
----------
start : int (default: 0), range, or other RangeIndex instance
If int and "stop" is not given, interpreted as "stop" instead.
stop : int (default: 0)
step : int (default: 1)
dtype : np.int64
Unused, accepted for homogeneity with other index types.
copy : bool, default False
Unused, accepted for homogeneity with other index types.
name : object, optional
Name to be stored in the index.
Attributes
----------
start
stop
step
Methods
-------
from_range
See Also
--------
Index : The base pandas Index type.
Int64Index : Index of int64 data.
"""
_typ = "rangeindex"
_engine_type = libindex.Int64Engine
_dtype_validation_metadata = (is_signed_integer_dtype, "signed integer")
_can_hold_na = False
_range: range
# --------------------------------------------------------------------
# Constructors
def __new__(
cls,
start=None,
stop=None,
step=None,
dtype: Dtype | None = None,
copy: bool = False,
name: Hashable = None,
) -> RangeIndex:
cls._validate_dtype(dtype)
name = maybe_extract_name(name, start, cls)
# RangeIndex
if isinstance(start, RangeIndex):
return start.copy(name=name)
elif isinstance(start, range):
return cls._simple_new(start, name=name)
# validate the arguments
if com.all_none(start, stop, step):
raise TypeError("RangeIndex(...) must be called with integers")
start = ensure_python_int(start) if start is not None else 0
if stop is None:
start, stop = 0, start
else:
stop = ensure_python_int(stop)
step = ensure_python_int(step) if step is not None else 1
if step == 0:
raise ValueError("Step must not be zero")
rng = range(start, stop, step)
return cls._simple_new(rng, name=name)
@classmethod
def from_range(
cls, data: range, name=None, dtype: Dtype | None = None
) -> RangeIndex:
"""
Create RangeIndex from a range object.
Returns
-------
RangeIndex
"""
if not isinstance(data, range):
raise TypeError(
f"{cls.__name__}(...) must be called with object coercible to a "
f"range, {repr(data)} was passed"
)
cls._validate_dtype(dtype)
return cls._simple_new(data, name=name)
@classmethod
def _simple_new(cls, values: range, name: Hashable = None) -> RangeIndex:
result = object.__new__(cls)
assert isinstance(values, range)
result._range = values
result._name = name
result._cache = {}
result._reset_identity()
return result
# --------------------------------------------------------------------
@cache_readonly
def _constructor(self) -> type[Int64Index]:
""" return the class to use for construction """
return Int64Index
@cache_readonly
def _data(self) -> np.ndarray:
"""
An int array that for performance reasons is created only when needed.
The constructed array is saved in ``_cache``.
"""
return | np.arange(self.start, self.stop, self.step, dtype=np.int64) | 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)
# 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) | numpy.linspace |
# 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) | numpy.arange |
# 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)*np.sin(theta)
z = np.cos(theta)
direction = (x,y,z)
transform = tf.translation_matrix((0,0,0))
point = transform_point(self.center, transform)
photon.direction = direction
photon.position = point
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
photon.active = True
return photon
class RadialSource(object):
"""
A point source that emits at discrete angles theta(i) and phi(i)
"""
def __init__(self, spectrum = None, wavelength = 555, center = (0.,0.,0.), phimin = 0, phimax = 2*np.pi, thetamin = 0, thetamax = np.pi, spacing=20):
super(RadialSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.center = center
self.phimin = phimin
self.phimax = phimax
self.thetamin = thetamin
self.thetamax = thetamax
self.spacing = spacing
self.throw = 0
self.source_id = "RadialSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
intphi = np.random.randint(1, self.spacing+1)
inttheta = np.random.randint(1, self.spacing+1)
phi = intphi*(self.phimax-self.phimin)/self.spacing
if self.thetamin == self.thetamax:
theta = self.thetamin
else:
theta = inttheta*(self.thetamax-self.thetamin)/self.spacing
x = np.cos(phi)* | np.sin(theta) | numpy.sin |
'''
<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) | numpy.ones |
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) | numpy.around |
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import numpy as np
import os
import contorno
from constantes import INTERVALOS, PASSOS, TAMANHO_BARRA, DELTA_T, DELTA_X
z_temp = contorno.p_3
TAMANHO_BARRA = 2
x = np.linspace(0.0, TAMANHO_BARRA, INTERVALOS+1)
y = | np.linspace(0.0, DELTA_T, PASSOS+1) | numpy.linspace |
"""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)):
raise ValueError("`x0` violates bound constraints.")
if as_linear_operator:
if rel_step is None:
rel_step = relative_step[method]
return _linear_operator_difference(fun_wrapped, x0,
f0, rel_step, method)
else:
h = _compute_absolute_step(rel_step, x0, method)
if method == '2-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '1-sided', lb, ub)
elif method == '3-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '2-sided', lb, ub)
elif method == 'cs':
use_one_sided = False
if sparsity is None:
return _dense_difference(fun_wrapped, x0, f0, h,
use_one_sided, method)
else:
if not issparse(sparsity) and len(sparsity) == 2:
structure, groups = sparsity
else:
structure = sparsity
groups = group_columns(sparsity)
if issparse(structure):
structure = csc_matrix(structure)
else:
structure = np.atleast_2d(structure)
groups = np.atleast_1d(groups)
return _sparse_difference(fun_wrapped, x0, f0, h,
use_one_sided, structure,
groups, method)
def _linear_operator_difference(fun, x0, f0, h, method):
m = f0.size
n = x0.size
if method == '2-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p
df = fun(x) - f0
return df / dx
elif method == '3-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = 2*h / norm(p)
x1 = x0 - (dx/2)*p
x2 = x0 + (dx/2)*p
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
return df / dx
elif method == 'cs':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p*1.j
f1 = fun(x)
df = f1.imag
return df / dx
else:
raise RuntimeError("Never be here.")
return LinearOperator((m, n), matvec)
def _dense_difference(fun, x0, f0, h, use_one_sided, method):
m = f0.size
n = x0.size
J_transposed = np.empty((n, m))
h_vecs = np.diag(h)
for i in range(h.size):
if method == '2-point':
x = x0 + h_vecs[i]
dx = x[i] - x0[i] # Recompute dx as exactly representable number.
df = fun(x) - f0
elif method == '3-point' and use_one_sided[i]:
x1 = x0 + h_vecs[i]
x2 = x0 + 2 * h_vecs[i]
dx = x2[i] - x0[i]
f1 = fun(x1)
f2 = fun(x2)
df = -3.0 * f0 + 4 * f1 - f2
elif method == '3-point' and not use_one_sided[i]:
x1 = x0 - h_vecs[i]
x2 = x0 + h_vecs[i]
dx = x2[i] - x1[i]
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
elif method == 'cs':
f1 = fun(x0 + h_vecs[i]*1.j)
df = f1.imag
dx = h_vecs[i, i]
else:
raise RuntimeError("Never be here.")
J_transposed[i] = df / dx
if m == 1:
J_transposed = np.ravel(J_transposed)
return J_transposed.T
def _sparse_difference(fun, x0, f0, h, use_one_sided,
structure, groups, method):
m = f0.size
n = x0.size
row_indices = []
col_indices = []
fractions = []
n_groups = np.max(groups) + 1
for group in range(n_groups):
# Perturb variables which are in the same group simultaneously.
e = np.equal(group, groups)
h_vec = h * e
if method == '2-point':
x = x0 + h_vec
dx = x - x0
df = fun(x) - f0
# The result is written to columns which correspond to perturbed
# variables.
cols, = np.nonzero(e)
# Find all non-zero elements in selected columns of Jacobian.
i, j, _ = find(structure[:, cols])
# Restore column indices in the full array.
j = cols[j]
elif method == '3-point':
# Here we do conceptually the same but separate one-sided
# and two-sided schemes.
x1 = x0.copy()
x2 = x0.copy()
mask_1 = use_one_sided & e
x1[mask_1] += h_vec[mask_1]
x2[mask_1] += 2 * h_vec[mask_1]
mask_2 = ~use_one_sided & e
x1[mask_2] -= h_vec[mask_2]
x2[mask_2] += h_vec[mask_2]
dx = np.zeros(n)
dx[mask_1] = x2[mask_1] - x0[mask_1]
dx[mask_2] = x2[mask_2] - x1[mask_2]
f1 = fun(x1)
f2 = fun(x2)
cols, = np.nonzero(e)
i, j, _ = find(structure[:, cols])
j = cols[j]
mask = use_one_sided[j]
df = np.empty(m)
rows = i[mask]
df[rows] = -3 * f0[rows] + 4 * f1[rows] - f2[rows]
rows = i[~mask]
df[rows] = f2[rows] - f1[rows]
elif method == 'cs':
f1 = fun(x0 + h_vec*1.j)
df = f1.imag
dx = h_vec
cols, = np.nonzero(e)
i, j, _ = find(structure[:, cols])
j = cols[j]
else:
raise ValueError("Never be here.")
# All that's left is to compute the fraction. We store i, j and
# fractions as separate arrays and later construct coo_matrix.
row_indices.append(i)
col_indices.append(j)
fractions.append(df[i] / dx[j])
row_indices = np.hstack(row_indices)
col_indices = | np.hstack(col_indices) | numpy.hstack |
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]) | numpy.mean |
# 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.)*u.Jy)
q = 1.23 * other
with pytest.raises(u.UnitsError):
lq + q
with pytest.raises(u.UnitsError):
lq - q
with pytest.raises(u.UnitsError):
q - lq
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_addition_subtraction(self, other):
"""Check that addition/subtraction with quantities with magnitude or
MagUnit units works, and that it changes the physical units
appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq + other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_sr = other + lq
assert_allclose(lq_sr.physical, lq.physical * other_physical)
lq_df = lq - other
assert_allclose(lq_df.physical, lq.physical / other_physical)
lq_dr = other - lq
assert_allclose(lq_dr.physical, other_physical / lq.physical)
@pytest.mark.parametrize('other', pu_sample)
def test_inplace_addition_subtraction_unit_checks(self, other):
lu1 = u.mag(u.Jy)
lq1 = u.Magnitude(np.arange(1., 10.), lu1)
with pytest.raises(u.UnitsError):
lq1 += other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
with pytest.raises(u.UnitsError):
lq1 -= other
assert np.all(lq1.value == np.arange(1., 10.))
assert lq1.unit == lu1
@pytest.mark.parametrize(
'other', (1.23 * u.mag, 2.34 * u.mag(),
u.Magnitude(3.45 * u.Jy), u.Magnitude(4.56 * u.m),
5.67 * u.Unit(2*u.mag), u.Magnitude(6.78, 2.*u.mag)))
def test_inplace_addition_subtraction(self, other):
"""Check that inplace addition/subtraction with quantities with
magnitude or MagUnit units works, and that it changes the physical
units appropriately."""
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
other_physical = other.to(getattr(other.unit, 'physical_unit',
u.dimensionless_unscaled),
equivalencies=u.logarithmic())
lq_sf = lq.copy()
lq_sf += other
assert_allclose(lq_sf.physical, lq.physical * other_physical)
lq_df = lq.copy()
lq_df -= other
assert_allclose(lq_df.physical, lq.physical / other_physical)
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))
DMmag = u.mag(dm0)
m_st = 10. * u.STmag
dm = 5. * DMmag
M_st = m_st - dm
assert M_st.unit.is_equivalent(u.erg/u.s/u.AA)
assert np.abs(M_st.physical /
(m_st.physical*4.*np.pi*(100.*u.pc)**2) - 1.) < 1.e-15
class TestLogQuantityComparisons(object):
def test_comparison_to_non_quantities_fails(self):
lq = u.Magnitude(np.arange(1., 10.)*u.Jy)
# On python2, ordering operations always succeed, given essentially
# meaningless results.
if not six.PY2:
with pytest.raises(TypeError):
lq > 'a'
assert not (lq == 'a')
assert lq != 'a'
def test_comparison(self):
lq1 = u.Magnitude( | np.arange(1., 4.) | numpy.arange |
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]])
left = np.array([[0, 0], [0.5, 0.5], [0,1]])
right = np.array([[1, 0], [0.5, 0.5], [1,1]])
tri = [left, down, right, up]
pos = [[0.2, 0.5], [0.5, 0.2], [0.8, 0.5], [0.5, 0.8]]
cmap = plt.cm.RdYlGn
norm = colors.Normalize(vmin=.0,vmax=.6)
ax.imshow( | np.zeros(dims) | numpy.zeros |
try:
import importlib.resources as pkg_resources
except ImportError:
# Try backported to PY<37 `importlib_resources`.
import importlib_resources as pkg_resources
from . import images
from gym import Env, spaces
from time import time
import numpy as np
from copy import copy
import colorsys
import pygame
from pygame.transform import scale
class MinesweeperEnv(Env):
def __init__(self, grid_shape=(10, 15), bombs_density=0.1, n_bombs=None, impact_size=3, max_time=999, chicken=False):
self.grid_shape = grid_shape
self.grid_size = np.prod(grid_shape)
self.n_bombs = max(1, int(bombs_density * self.grid_size)) if n_bombs is None else n_bombs
self.n_bombs = min(self.grid_size - 1, self.n_bombs)
self.flaged_bombs = 0
self.flaged_empty = 0
self.max_time = max_time
if impact_size % 2 == 0:
raise ValueError('Impact_size must be an odd number !')
self.impact_size = impact_size
# Define constants
self.HIDDEN = 0
self.REVEAL = 1
self.FLAG = 2
self.BOMB = self.impact_size ** 2
# Setting up gym Env conventions
nvec_observation = (self.BOMB + 2) * np.ones(self.grid_shape)
self.observation_space = spaces.MultiDiscrete(nvec_observation)
nvec_action = np.array(self.grid_shape + (2,))
self.action_space = spaces.MultiDiscrete(nvec_action)
# Initalize state
self.state = | np.zeros(self.grid_shape + (2,), dtype=np.uint8) | numpy.zeros |
# ________
# /
# \ /
# \ /
# \/
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) | 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]), 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]) | 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) | numpy.dot |
"""
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):
raise ValueError(
f"The {name} of the random variable does not have the correct "
f"dtype. Expected {dtype.name} but got {value.dtype.name}."
)
@classmethod
def _ensure_numpy_float(
cls, name: str, value: Any, force_scalar: bool = False
) -> Union[np.float_, np.ndarray]:
if np.isscalar(value):
if not isinstance(value, np.float_):
try:
value = _utils.as_numpy_scalar(value, dtype=np.float_)
except TypeError as err:
raise TypeError(
f"The function `{name}` specified via the constructor of "
f"`{cls.__name__}` must return a scalar value that can be "
f"converted to a `np.float_`, which is not possible for "
f"{value} of type {type(value)}."
) from err
elif not force_scalar:
try:
value = | np.asarray(value, dtype=np.float_) | numpy.asarray |
###############################################################################
# @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) | 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), 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) | numpy.array |
"""
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)
except UnicodeError as err:
# Friendlier error message
raise UnicodeError("Unpickling a python object failed: %r\n"
"You may need to pass the encoding= option "
"to numpy.load" % (err,)) from err
else:
if isfileobj(fp):
# We can use the fast fromfile() function.
array = | numpy.fromfile(fp, dtype=dtype, count=count) | numpy.fromfile |
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]) | 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]) | numpy.abs |
import time
import h5py
import hdbscan
import numpy as np
import torch
from sklearn.cluster import MeanShift
from pytorch3dunet.datasets.hdf5 import SliceBuilder
from pytorch3dunet.unet3d.utils import get_logger
from pytorch3dunet.unet3d.utils import unpad
logger = get_logger('UNet3DPredictor')
class _AbstractPredictor:
def __init__(self, model, loader, output_file, config, **kwargs):
self.model = model
self.loader = loader
self.output_file = output_file
self.config = config
self.predictor_config = kwargs
@staticmethod
def _volume_shape(dataset):
# TODO: support multiple internal datasets
raw = dataset.raws[0]
if raw.ndim == 3:
return raw.shape
else:
return raw.shape[1:]
@staticmethod
def _get_output_dataset_names(number_of_datasets, prefix='predictions'):
if number_of_datasets == 1:
return [prefix]
else:
return [f'{prefix}{i}' for i in range(number_of_datasets)]
def predict(self):
raise NotImplementedError
class StandardPredictor(_AbstractPredictor):
"""
Applies the model on the given dataset and saves the result in the `output_file` in the H5 format.
Predictions from the network are kept in memory. If the results from the network don't fit in into RAM
use `LazyPredictor` instead.
The output dataset names inside the H5 is given by `des_dataset_name` config argument. If the argument is
not present in the config 'predictions{n}' is used as a default dataset name, where `n` denotes the number
of the output head from the network.
Args:
model (Unet3D): trained 3D UNet model used for prediction
data_loader (torch.utils.data.DataLoader): input data loader
output_file (str): path to the output H5 file
config (dict): global config dict
"""
def __init__(self, model, loader, output_file, config, **kwargs):
super().__init__(model, loader, output_file, config, **kwargs)
def predict(self):
out_channels = self.config['model'].get('out_channels')
if out_channels is None:
out_channels = self.config['model']['dt_out_channels']
prediction_channel = self.config.get('prediction_channel', None)
if prediction_channel is not None:
logger.info(f"Using only channel '{prediction_channel}' from the network output")
device = self.config['device']
output_heads = self.config['model'].get('output_heads', 1)
logger.info(f'Running prediction on {len(self.loader)} batches...')
# dimensionality of the the output predictions
volume_shape = self._volume_shape(self.loader.dataset)
if prediction_channel is None:
prediction_maps_shape = (out_channels,) + volume_shape
else:
# single channel prediction map
prediction_maps_shape = (1,) + volume_shape
logger.info(f'The shape of the output prediction maps (CDHW): {prediction_maps_shape}')
avoid_block_artifacts = self.predictor_config.get('avoid_block_artifacts', True)
logger.info(f'Avoid block artifacts: {avoid_block_artifacts}')
# create destination H5 file
h5_output_file = h5py.File(self.output_file, 'w')
# allocate prediction and normalization arrays
logger.info('Allocating prediction and normalization arrays...')
prediction_maps, normalization_masks = self._allocate_prediction_maps(prediction_maps_shape,
output_heads, h5_output_file)
# Sets the module in evaluation mode explicitly (necessary for batchnorm/dropout layers if present)
self.model.eval()
# Set the `testing=true` flag otherwise the final Softmax/Sigmoid won't be applied!
self.model.testing = True
# Run predictions on the entire input dataset
with torch.no_grad():
for batch, indices in self.loader:
# send batch to device
batch = batch.to(device)
# forward pass
predictions = self.model(batch)
# wrap predictions into a list if there is only one output head from the network
if output_heads == 1:
predictions = [predictions]
# for each output head
for prediction, prediction_map, normalization_mask in zip(predictions, prediction_maps,
normalization_masks):
# convert to numpy array
prediction = prediction.cpu().numpy()
# for each batch sample
for pred, index in zip(prediction, indices):
# save patch index: (C,D,H,W)
if prediction_channel is None:
channel_slice = slice(0, out_channels)
else:
channel_slice = slice(0, 1)
index = (channel_slice,) + index
if prediction_channel is not None:
# use only the 'prediction_channel'
logger.info(f"Using channel '{prediction_channel}'...")
pred = np.expand_dims(pred[prediction_channel], axis=0)
logger.info(f'Saving predictions for slice:{index}...')
if avoid_block_artifacts:
# unpad in order to avoid block artifacts in the output probability maps
u_prediction, u_index = unpad(pred, index, volume_shape)
# accumulate probabilities into the output prediction array
prediction_map[u_index] += u_prediction
# count voxel visits for normalization
normalization_mask[u_index] += 1
else:
# accumulate probabilities into the output prediction array
prediction_map[index] += pred
# count voxel visits for normalization
normalization_mask[index] += 1
# save results to
self._save_results(prediction_maps, normalization_masks, output_heads, h5_output_file, self.loader.dataset)
# close the output H5 file
h5_output_file.close()
def _allocate_prediction_maps(self, output_shape, output_heads, output_file):
# initialize the output prediction arrays
prediction_maps = [np.zeros(output_shape, dtype='float32') for _ in range(output_heads)]
# initialize normalization mask in order to average out probabilities of overlapping patches
normalization_masks = [np.zeros(output_shape, dtype='uint8') for _ in range(output_heads)]
return prediction_maps, normalization_masks
def _save_results(self, prediction_maps, normalization_masks, output_heads, output_file, dataset):
# save probability maps
prediction_datasets = self._get_output_dataset_names(output_heads, prefix='predictions')
for prediction_map, normalization_mask, prediction_dataset in zip(prediction_maps, normalization_masks,
prediction_datasets):
prediction_map = prediction_map / normalization_mask
if dataset.mirror_padding:
pad_width = dataset.pad_width
logger.info(f'Dataset loaded with mirror padding, pad_width: {pad_width}. Cropping before saving...')
prediction_map = prediction_map[:, pad_width:-pad_width, pad_width:-pad_width, pad_width:-pad_width]
logger.info(f'Saving predictions to: {output_file}/{prediction_dataset}...')
output_file.create_dataset(prediction_dataset, data=prediction_map, compression="gzip")
class LazyPredictor(StandardPredictor):
"""
Applies the model on the given dataset and saves the result in the `output_file` in the H5 format.
Predicted patches are directly saved into the H5 and they won't be stored in memory. Since this predictor
is slower than the `StandardPredictor` it should only be used when the predicted volume does not fit into RAM.
The output dataset names inside the H5 is given by `des_dataset_name` config argument. If the argument is
not present in the config 'predictions{n}' is used as a default dataset name, where `n` denotes the number
of the output head from the network.
Args:
model (Unet3D): trained 3D UNet model used for prediction
data_loader (torch.utils.data.DataLoader): input data loader
output_file (str): path to the output H5 file
config (dict): global config dict
"""
def __init__(self, model, loader, output_file, config, **kwargs):
super().__init__(model, loader, output_file, config, **kwargs)
def _allocate_prediction_maps(self, output_shape, output_heads, output_file):
# allocate datasets for probability maps
prediction_datasets = self._get_output_dataset_names(output_heads, prefix='predictions')
prediction_maps = [
output_file.create_dataset(dataset_name, shape=output_shape, dtype='float32', chunks=True,
compression='gzip')
for dataset_name in prediction_datasets]
# allocate datasets for normalization masks
normalization_datasets = self._get_output_dataset_names(output_heads, prefix='normalization')
normalization_masks = [
output_file.create_dataset(dataset_name, shape=output_shape, dtype='uint8', chunks=True,
compression='gzip')
for dataset_name in normalization_datasets]
return prediction_maps, normalization_masks
def _save_results(self, prediction_maps, normalization_masks, output_heads, output_file, dataset):
if dataset.mirror_padding:
logger.warn(
f'Mirror padding unsupported in LazyPredictor. Output predictions will be padded with pad_width: {dataset.pad_width}')
prediction_datasets = self._get_output_dataset_names(output_heads, prefix='predictions')
normalization_datasets = self._get_output_dataset_names(output_heads, prefix='normalization')
# normalize the prediction_maps inside the H5
for prediction_map, normalization_mask, prediction_dataset, normalization_dataset in zip(prediction_maps,
normalization_masks,
prediction_datasets,
normalization_datasets):
# split the volume into 4 parts and load each into the memory separately
logger.info(f'Normalizing {prediction_dataset}...')
z, y, x = prediction_map.shape[1:]
# take slices which are 1/27 of the original volume
patch_shape = (z // 3, y // 3, x // 3)
for index in SliceBuilder._build_slices(prediction_map, patch_shape=patch_shape, stride_shape=patch_shape):
logger.info(f'Normalizing slice: {index}')
prediction_map[index] /= normalization_mask[index]
# make sure to reset the slice that has been visited already in order to avoid 'double' normalization
# when the patches overlap with each other
normalization_mask[index] = 1
logger.info(f'Deleting {normalization_dataset}...')
del output_file[normalization_dataset]
class EmbeddingsPredictor(_AbstractPredictor):
"""
Applies the embedding model on the given dataset and saves the result in the `output_file` in the H5 format.
The resulting volume is the segmentation itself (not the embedding vectors) obtained by clustering embeddings
with HDBSCAN or MeanShift algorithm patch by patch and then stitching the patches together.
"""
def __init__(self, model, loader, output_file, config, clustering, iou_threshold=0.7, noise_label=-1, **kwargs):
super().__init__(model, loader, output_file, config, **kwargs)
self.iou_threshold = iou_threshold
self.noise_label = noise_label
self.clustering = clustering
assert clustering in ['hdbscan', 'meanshift'], 'Only HDBSCAN and MeanShift are supported'
logger.info(f'IoU threshold: {iou_threshold}')
self.clustering_name = clustering
self.clustering = self._get_clustering(clustering, kwargs)
def predict(self):
device = self.config['device']
output_heads = self.config['model'].get('output_heads', 1)
logger.info(f'Running prediction on {len(self.loader)} patches...')
# dimensionality of the the output segmentation
volume_shape = self._volume_shape(self.loader.dataset)
logger.info(f'The shape of the output segmentation (DHW): {volume_shape}')
logger.info('Allocating segmentation array...')
# initialize the output prediction arrays
output_segmentations = [np.zeros(volume_shape, dtype='int32') for _ in range(output_heads)]
# initialize visited_voxels arrays
visited_voxels_arrays = [np.zeros(volume_shape, dtype='uint8') for _ in range(output_heads)]
# Sets the module in evaluation mode explicitly
self.model.eval()
self.model.testing = True
# Run predictions on the entire input dataset
with torch.no_grad():
for batch, indices in self.loader:
# logger.info(f'Predicting embeddings for slice:{index}')
# send batch to device
batch = batch.to(device)
# forward pass
embeddings = self.model(batch)
# wrap predictions into a list if there is only one output head from the network
if output_heads == 1:
embeddings = [embeddings]
for prediction, output_segmentation, visited_voxels_array in zip(embeddings, output_segmentations,
visited_voxels_arrays):
# convert to numpy array
prediction = prediction.cpu().numpy()
# iterate sequentially because of the current simple stitching that we're using
for pred, index in zip(prediction, indices):
# convert embeddings to segmentation with hdbscan clustering
segmentation = self._embeddings_to_segmentation(pred)
# stitch patches
self._merge_segmentation(segmentation, index, output_segmentation, visited_voxels_array)
# save results
with h5py.File(self.output_file, 'w') as output_file:
prediction_datasets = self._get_output_dataset_names(output_heads,
prefix=f'segmentation/{self.clustering_name}')
for output_segmentation, prediction_dataset in zip(output_segmentations, prediction_datasets):
logger.info(f'Saving predictions to: {output_file}/{prediction_dataset}...')
output_file.create_dataset(prediction_dataset, data=output_segmentation, compression="gzip")
def _embeddings_to_segmentation(self, embeddings):
"""
Cluster embeddings vectors with HDBSCAN and return the segmented volume.
Args:
embeddings (ndarray): 4D (CDHW) embeddings tensor
Returns:
3D (DHW) segmentation
"""
# shape of the output segmentation
output_shape = embeddings.shape[1:]
# reshape (C, D, H, W) -> (C, D * H * W) and transpose -> (D * H * W, C)
flattened_embeddings = embeddings.reshape(embeddings.shape[0], -1).transpose()
logger.info('Clustering embeddings...')
# perform clustering and reshape in order to get the segmentation volume
start = time.time()
clusters = self.clustering.fit_predict(flattened_embeddings).reshape(output_shape)
logger.info(
f'Number of clusters found by {self.clustering}: {np.max(clusters)}. Duration: {time.time() - start} sec.')
return clusters
def _merge_segmentation(self, segmentation, index, output_segmentation, visited_voxels_array):
"""
Given the `segmentation` patch, its `index` in the `output_segmentation` array and the array visited voxels
merge the segmented patch (`segmentation`) into the `output_segmentation`
Args:
segmentation (ndarray): segmented patch
index (tuple): position of the patch inside `output_segmentation` volume
output_segmentation (ndarray): current state of the output segmentation
visited_voxels_array (ndarray): array of voxels visited so far (same size as `output_segmentation`); visited
voxels will be marked by a number greater than 0
"""
index = tuple(index)
# get new unassigned label
max_label = np.max(output_segmentation) + 1
# make sure there are no clashes between current segmentation patch and the output_segmentation
# but keep the noise label
noise_mask = segmentation == self.noise_label
segmentation += int(max_label)
segmentation[noise_mask] = self.noise_label
# get the overlap mask in the current patch
overlap_mask = visited_voxels_array[index] > 0
# get the new labels inside the overlap_mask
new_labels = np.unique(segmentation[overlap_mask])
merged_labels = self._merge_labels(output_segmentation[index], new_labels, segmentation)
# relabel new segmentation with the merged labels
for current_label, new_label in merged_labels:
segmentation[segmentation == new_label] = current_label
# update the output_segmentation
output_segmentation[index] = segmentation
# visit the patch
visited_voxels_array[index] += 1
def _merge_labels(self, current_segmentation, new_labels, new_segmentation):
def _most_frequent_label(labels):
unique, counts = np.unique(labels, return_counts=True)
ind = np.argmax(counts)
return unique[ind]
result = []
# iterate over new_labels and merge regions if the IoU exceeds a given threshold
for new_label in new_labels:
# skip 'noise' label assigned by hdbscan
if new_label == self.noise_label:
continue
new_label_mask = new_segmentation == new_label
# get only the most frequent overlapping label
most_frequent_label = _most_frequent_label(current_segmentation[new_label_mask])
# skip 'noise' label
if most_frequent_label == self.noise_label:
continue
current_label_mask = current_segmentation == most_frequent_label
# compute Jaccard index
iou = | np.bitwise_and(new_label_mask, current_label_mask) | numpy.bitwise_and |
# 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() | numpy.random.uniform |
"""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)):
raise ValueError("`x0` violates bound constraints.")
if as_linear_operator:
if rel_step is None:
rel_step = relative_step[method]
return _linear_operator_difference(fun_wrapped, x0,
f0, rel_step, method)
else:
h = _compute_absolute_step(rel_step, x0, method)
if method == '2-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '1-sided', lb, ub)
elif method == '3-point':
h, use_one_sided = _adjust_scheme_to_bounds(
x0, h, 1, '2-sided', lb, ub)
elif method == 'cs':
use_one_sided = False
if sparsity is None:
return _dense_difference(fun_wrapped, x0, f0, h,
use_one_sided, method)
else:
if not issparse(sparsity) and len(sparsity) == 2:
structure, groups = sparsity
else:
structure = sparsity
groups = group_columns(sparsity)
if issparse(structure):
structure = csc_matrix(structure)
else:
structure = np.atleast_2d(structure)
groups = np.atleast_1d(groups)
return _sparse_difference(fun_wrapped, x0, f0, h,
use_one_sided, structure,
groups, method)
def _linear_operator_difference(fun, x0, f0, h, method):
m = f0.size
n = x0.size
if method == '2-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p
df = fun(x) - f0
return df / dx
elif method == '3-point':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = 2*h / norm(p)
x1 = x0 - (dx/2)*p
x2 = x0 + (dx/2)*p
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
return df / dx
elif method == 'cs':
def matvec(p):
if np.array_equal(p, np.zeros_like(p)):
return np.zeros(m)
dx = h / norm(p)
x = x0 + dx*p*1.j
f1 = fun(x)
df = f1.imag
return df / dx
else:
raise RuntimeError("Never be here.")
return LinearOperator((m, n), matvec)
def _dense_difference(fun, x0, f0, h, use_one_sided, method):
m = f0.size
n = x0.size
J_transposed = np.empty((n, m))
h_vecs = np.diag(h)
for i in range(h.size):
if method == '2-point':
x = x0 + h_vecs[i]
dx = x[i] - x0[i] # Recompute dx as exactly representable number.
df = fun(x) - f0
elif method == '3-point' and use_one_sided[i]:
x1 = x0 + h_vecs[i]
x2 = x0 + 2 * h_vecs[i]
dx = x2[i] - x0[i]
f1 = fun(x1)
f2 = fun(x2)
df = -3.0 * f0 + 4 * f1 - f2
elif method == '3-point' and not use_one_sided[i]:
x1 = x0 - h_vecs[i]
x2 = x0 + h_vecs[i]
dx = x2[i] - x1[i]
f1 = fun(x1)
f2 = fun(x2)
df = f2 - f1
elif method == 'cs':
f1 = fun(x0 + h_vecs[i]*1.j)
df = f1.imag
dx = h_vecs[i, i]
else:
raise RuntimeError("Never be here.")
J_transposed[i] = df / dx
if m == 1:
J_transposed = np.ravel(J_transposed)
return J_transposed.T
def _sparse_difference(fun, x0, f0, h, use_one_sided,
structure, groups, method):
m = f0.size
n = x0.size
row_indices = []
col_indices = []
fractions = []
n_groups = np.max(groups) + 1
for group in range(n_groups):
# Perturb variables which are in the same group simultaneously.
e = np.equal(group, groups)
h_vec = h * e
if method == '2-point':
x = x0 + h_vec
dx = x - x0
df = fun(x) - f0
# The result is written to columns which correspond to perturbed
# variables.
cols, = np.nonzero(e)
# Find all non-zero elements in selected columns of Jacobian.
i, j, _ = find(structure[:, cols])
# Restore column indices in the full array.
j = cols[j]
elif method == '3-point':
# Here we do conceptually the same but separate one-sided
# and two-sided schemes.
x1 = x0.copy()
x2 = x0.copy()
mask_1 = use_one_sided & e
x1[mask_1] += h_vec[mask_1]
x2[mask_1] += 2 * h_vec[mask_1]
mask_2 = ~use_one_sided & e
x1[mask_2] -= h_vec[mask_2]
x2[mask_2] += h_vec[mask_2]
dx = | np.zeros(n) | numpy.zeros |
#!/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)
P = 1e5
for T in Tlist:
korig = original_kinetics.getRateCoefficient(T, P)
krevrev = reversereverseKinetics.getRateCoefficient(T, P)
self.assertAlmostEqual(korig / krevrev, 1.0, 0)
@work_in_progress
def testGenerateReverseRateCoefficientArrheniusEP(self):
"""
Test the Reaction.generateReverseRateCoefficient() method works for the ArrheniusEP format.
"""
from rmgpy.kinetics import ArrheniusEP
original_kinetics = ArrheniusEP(
A = (2.65e12, 'cm^3/(mol*s)'),
n = 0.0,
alpha = 0.5,
E0 = (41.84, 'kJ/mol'),
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, original_kinetics.Tmax, 200.0, numpy.float64)
P = 1e5
for T in Tlist:
korig = original_kinetics.getRateCoefficient(T, P)
krevrev = reversereverseKinetics.getRateCoefficient(T, P)
self.assertAlmostEqual(korig / krevrev, 1.0, 0)
def testGenerateReverseRateCoefficientPDepArrhenius(self):
"""
Test the Reaction.generateReverseRateCoefficient() method works for the PDepArrhenius format.
"""
from rmgpy.kinetics import PDepArrhenius
arrhenius0 = Arrhenius(
A = (1.0e6,"s^-1"),
n = 1.0,
Ea = (10.0,"kJ/mol"),
T0 = (300.0,"K"),
Tmin = (300.0,"K"),
Tmax = (2000.0,"K"),
comment = """This data is completely made up""",
)
arrhenius1 = Arrhenius(
A = (1.0e12,"s^-1"),
n = 1.0,
Ea = (20.0,"kJ/mol"),
T0 = (300.0,"K"),
Tmin = (300.0,"K"),
Tmax = (2000.0,"K"),
comment = """This data is completely made up""",
)
pressures = numpy.array([0.1, 10.0])
arrhenius = [arrhenius0, arrhenius1]
Tmin = 300.0
Tmax = 2000.0
Pmin = 0.1
Pmax = 10.0
comment = """This data is completely made up"""
original_kinetics = PDepArrhenius(
pressures = (pressures,"bar"),
arrhenius = arrhenius,
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
Pmin = (Pmin,"bar"),
Pmax = (Pmax,"bar"),
comment = comment,
)
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(Tmin, Tmax, 200.0, numpy.float64)
P = 1e5
for T in Tlist:
korig = original_kinetics.getRateCoefficient(T, P)
krevrev = reversereverseKinetics.getRateCoefficient(T, P)
self.assertAlmostEqual(korig / krevrev, 1.0, 0)
def testGenerateReverseRateCoefficientMultiArrhenius(self):
"""
Test the Reaction.generateReverseRateCoefficient() method works for the MultiArrhenius format.
"""
from rmgpy.kinetics import MultiArrhenius
pressures = numpy.array([0.1, 10.0])
Tmin = 300.0
Tmax = 2000.0
Pmin = 0.1
Pmax = 10.0
comment = """This data is completely made up"""
arrhenius = [
Arrhenius(
A = (9.3e-14,"cm^3/(molecule*s)"),
n = 0.0,
Ea = (4740*constants.R*0.001,"kJ/mol"),
T0 = (1,"K"),
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
),
Arrhenius(
A = (1.4e-9,"cm^3/(molecule*s)"),
n = 0.0,
Ea = (11200*constants.R*0.001,"kJ/mol"),
T0 = (1,"K"),
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
),
]
original_kinetics = MultiArrhenius(
arrhenius = arrhenius,
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
)
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(Tmin, Tmax, 200.0, numpy.float64)
P = 1e5
for T in Tlist:
korig = original_kinetics.getRateCoefficient(T, P)
krevrev = reversereverseKinetics.getRateCoefficient(T, P)
self.assertAlmostEqual(korig / krevrev, 1.0, 0)
def testGenerateReverseRateCoefficientMultiPDepArrhenius(self):
"""
Test the Reaction.generateReverseRateCoefficient() method works for the MultiPDepArrhenius format.
"""
from rmgpy.kinetics import PDepArrhenius, MultiPDepArrhenius
Tmin = 350.
Tmax = 1500.
Pmin = 1e-1
Pmax = 1e1
pressures = numpy.array([1e-1,1e1])
comment = 'CH3 + C2H6 <=> CH4 + C2H5 (Baulch 2005)'
arrhenius = [
PDepArrhenius(
pressures = (pressures,"bar"),
arrhenius = [
Arrhenius(
A = (9.3e-16,"cm^3/(molecule*s)"),
n = 0.0,
Ea = (4740*constants.R*0.001,"kJ/mol"),
T0 = (1,"K"),
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
),
Arrhenius(
A = (9.3e-14,"cm^3/(molecule*s)"),
n = 0.0,
Ea = (4740*constants.R*0.001,"kJ/mol"),
T0 = (1,"K"),
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
),
],
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
Pmin = (Pmin,"bar"),
Pmax = (Pmax,"bar"),
comment = comment,
),
PDepArrhenius(
pressures = (pressures,"bar"),
arrhenius = [
Arrhenius(
A = (1.4e-11,"cm^3/(molecule*s)"),
n = 0.0,
Ea = (11200*constants.R*0.001,"kJ/mol"),
T0 = (1,"K"),
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
),
Arrhenius(
A = (1.4e-9,"cm^3/(molecule*s)"),
n = 0.0,
Ea = (11200*constants.R*0.001,"kJ/mol"),
T0 = (1,"K"),
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
comment = comment,
),
],
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
Pmin = (Pmin,"bar"),
Pmax = (Pmax,"bar"),
comment = comment,
),
]
original_kinetics = MultiPDepArrhenius(
arrhenius = arrhenius,
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
Pmin = (Pmin,"bar"),
Pmax = (Pmax,"bar"),
comment = comment,
)
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(Tmin, Tmax, 200.0, numpy.float64)
P = 1e5
for T in Tlist:
korig = original_kinetics.getRateCoefficient(T, P)
krevrev = reversereverseKinetics.getRateCoefficient(T, P)
self.assertAlmostEqual(korig / krevrev, 1.0, 0)
def testGenerateReverseRateCoefficientThirdBody(self):
"""
Test the Reaction.generateReverseRateCoefficient() method works for the ThirdBody format.
"""
from rmgpy.kinetics import ThirdBody
arrheniusLow = Arrhenius(
A = (2.62e+33,"cm^6/(mol^2*s)"),
n = -4.76,
Ea = (10.21,"kJ/mol"),
T0 = (1,"K"),
)
efficiencies = {"C": 3, "C(=O)=O": 2, "CC": 3, "O": 6, "[Ar]": 0.7, "[C]=O": 1.5, "[H][H]": 2}
Tmin = 300.
Tmax = 2000.
Pmin = 0.01
Pmax = 100.
comment = """H + CH3 -> CH4"""
thirdBody = ThirdBody(
arrheniusLow = arrheniusLow,
Tmin = (Tmin,"K"),
Tmax = (Tmax,"K"),
Pmin = (Pmin,"bar"),
Pmax = (Pmax,"bar"),
efficiencies = efficiencies,
comment = comment,
)
original_kinetics = thirdBody
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(Tmin, Tmax, 200.0, numpy.float64) | numpy.arange |
"""
This script will modulate the blinky lights using the following algorithm:
1) uses user-provided location to obtain row of pixel data from bathy image
2) samples a 'number of LEDs' number of pixels from that row
3) shifts the sampled row data to center it at the location specified by user
4) displays resulting pixels on Blinky Tape
5) shifts next row by a given latitude, also specified by user
6) sleeps for user-specified period of time
Uses the following arguments:
-l/--location: tuple
Location of the user in tuple(lat, lon). This represents the center of the LED strip. Defaults to (0, 0)
-u/--update-interval: int
Update interval of the script, in minutes. Defaults to 10.
-p/--port: str
Serial port of the BlinkyLight (e.g., 'ttyAMA0', 'COM3'). Defaults to 'COM5'.
-d/--delta_latitude: int
Vertical change in latitude every update rate. May be 0, but this will result in a never-changing LEDs.
-i/--image: str
Name of the PNG image that contains the color coded pathymetric data.
The file current named mapserv.png was obtained using the following API:
https://www.gebco.net/data_and_products/gebco_web_services/web_map_service/mapserv?request=getmap&service=wms&BBOX=-90,-180,90,180&format=image/png&height=600&width=1200&crs=EPSG:4326&layers=GEBCO_LATEST_SUB_ICE_TOPO&version=1.3.0
In lieu of providing command line arguments, you may alternatively edit the defaults in bath_config.json.
NOTE: runs via:
runfile('/BlinkyTape_Python/bathymetry_blink/bathymetry_blink.py', wdir='/BlinkyTape_Python/')
(C) 2021 <NAME> (https://joeycodes.dev)
MIT Licensed
"""
import optparse
import json
from blinkytape import BlinkyTape
from time import sleep
from PIL import Image
import numpy as np
import sys
MAX_ERRORS = 3
num_errors = 0
# Obtain default parameters
with open("./bathymetry_blink/bathy_config.json") as f:
config = json.load(f)
# Default Blinky Tape port on Raspberry Pi is /dev/ttyACM0
parser = optparse.OptionParser()
parser.add_option("-p", "--port", dest="portname",
help="serial port (ex: /dev/ttyACM0)", default=config["port"])
parser.add_option("-l", "--location", dest="location",
help="Location of the center of the LED strip (ex: 70,-110)", default=config["location"])
parser.add_option("-u", "--update-rate", dest="update_rate",
help="How often to update elevation profile (mins) (ex: 5)", default=config["update_rate"])
parser.add_option("-d", "--delta-latitude", dest="delta_latitude",
help="Change in latitude during update (ex: 5)", default=config["delta_latitude"])
parser.add_option("-n", "--num-leds", dest="num_leds",
help="Number of LEDs in strip (ex: 60)", default=config["num_leds"])
parser.add_option("-i", "--image", dest="image_name",
help="Name of the map/bathymetry image (ex: ./mapserv.png)", default=config["image"])
(options, args) = parser.parse_args()
if args:
print("Unknown parameters: " + args)
# grab the values provided by user (or defaults)
port = options.portname
loc = options.location
rate = options.update_rate
delta = options.delta_latitude
n_leds = options.num_leds
i_name = options.image_name
# Some visual indication that it works, for headless setups (green tape)
bt = BlinkyTape(port, n_leds)
bt.displayColor(0, 100, 0)
bt.show()
sleep(2)
while True:
try:
# first, load image
im = Image.open(i_name) # Can be many different formats.
cols, rows = im.size
a = np.asarray(im) # of shape (rows, cols, channels)
# map loc latitude to 0-based index
latitude_index = min(rows - 1, max(0, (int)(((loc[0] - -90) / (90 - -90)) * (rows - 0) + 0)))
longitude_index = min(cols - 1, max(0, (int)(((loc[1] - -180) / (180 - -180)) * (cols - 0) + 0)))
# update the location of the next row of elevation data to take
loc[0] += delta
loc[0] = ((loc[0] + 90) % 180) - 90 # wraps to next pole if overflow
print("Lat index: " + str(latitude_index))
print("Lon index: " + str(longitude_index))
print("Next latitude: " + str(loc[0]))
# grab the applicable pixel indices
indices = [(int)(x*(cols/n_leds)) for x in range(n_leds)]
# sample that row of pixel data
output_pixels = np.take(a[latitude_index], indices, axis=0)
# rotate the row to center around the specified longitude
output_pixels = | np.roll(output_pixels, longitude_index, axis=0) | numpy.roll |
# ________
# /
# \ /
# \ /
# \/
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) | 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) | 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) | numpy.cos |
# 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]])
def test_dataarray_to_matrix_negative_x_increment():
"""
Check if dataarray_to_matrix returns correct output with flipped x.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=4, stop=0, 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.flip(data, axis=(0, 1)))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_negative_y_increment():
"""
Check that dataarray_to_matrix returns correct output with flipped y.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=0, stop=4, num=3)
y = np.linspace(start=9, stop=5, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
| npt.assert_allclose(actual=matrix, desired=data) | numpy.testing.assert_allclose |
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]) | numpy.zeros |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
import io
import logging
import json
import numpy
import torch
import numpy as np
from tqdm import tqdm
from clie.inputters import constant
from clie.objects import Sentence
from torch.utils.data import Dataset
from torch.utils.data.sampler import Sampler
logger = logging.getLogger(__name__)
def load_word_embeddings(file):
embeddings_index = {}
fin = io.open(file, 'r', encoding='utf-8', newline='\n', errors='ignore')
n, d = map(int, fin.readline().split())
for i, line in tqdm(enumerate(fin), total=n):
tokens = line.rstrip().split(' ')
v = | numpy.array(tokens[1:], dtype=float) | numpy.array |
import torch
import torchvision
import matplotlib
import matplotlib.pyplot as plt
from PIL import Image
from captum.attr import GuidedGradCam, GuidedBackprop
from captum.attr import LayerActivation, LayerConductance, LayerGradCam
from data_utils import *
from image_utils import *
from captum_utils import *
import numpy as np
from visualizers import GradCam
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
X, y, class_names = load_imagenet_val(num=5)
# FOR THIS SECTION ONLY, we need to use gradients. We introduce a new model we will use explicitly for GradCAM for this.
gc_model = torchvision.models.squeezenet1_1(pretrained=True)
gc = GradCam()
X_tensor = torch.cat([preprocess(Image.fromarray(x)) for x in X], dim=0).requires_grad_(True)
y_tensor = torch.LongTensor(y)
# Guided Back-Propagation
gbp_result = gc.guided_backprop(X_tensor,y_tensor, gc_model)
plt.figure(figsize=(24, 24))
for i in range(gbp_result.shape[0]):
plt.subplot(1, 5, i + 1)
img = gbp_result[i]
img = rescale(img)
plt.imshow(img)
plt.title(class_names[y[i]])
plt.axis('off')
plt.gcf().tight_layout()
plt.savefig('visualization/guided_backprop.png')
# GradCam
# GradCAM. We have given you which module(=layer) that we need to capture gradients from, which you can see in conv_module variable below
gc_model = torchvision.models.squeezenet1_1(pretrained=True)
for param in gc_model.parameters():
param.requires_grad = True
X_tensor = torch.cat([preprocess(Image.fromarray(x)) for x in X], dim=0).requires_grad_(True)
y_tensor = torch.LongTensor(y)
gradcam_result = gc.grad_cam(X_tensor, y_tensor, gc_model)
plt.figure(figsize=(24, 24))
for i in range(gradcam_result.shape[0]):
gradcam_val = gradcam_result[i]
img = X[i] + (matplotlib.cm.jet(gradcam_val)[:,:,:3]*255)
img = img / np.max(img)
plt.subplot(1, 5, i + 1)
plt.imshow(img)
plt.title(class_names[y[i]])
plt.axis('off')
plt.gcf().tight_layout()
plt.savefig('visualization/gradcam.png')
# As a final step, we can combine GradCam and Guided Backprop to get Guided GradCam.
X_tensor = torch.cat([preprocess(Image.fromarray(x)) for x in X], dim=0).requires_grad_(True)
y_tensor = torch.LongTensor(y)
gradcam_result = gc.grad_cam(X_tensor, y_tensor, gc_model)
gbp_result = gc.guided_backprop(X_tensor, y_tensor, gc_model)
plt.figure(figsize=(24, 24))
for i in range(gradcam_result.shape[0]):
gbp_val = gbp_result[i]
gradcam_val = np.expand_dims(gradcam_result[i], axis=2)
# Pointwise multiplication and normalization of the gradcam and guided backprop results (2 lines)
img = gradcam_val * gbp_val
img = np.expand_dims(img.transpose(2, 0, 1), axis=0)
img = | np.float32(img) | numpy.float32 |
# 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]])
def test_dataarray_to_matrix_negative_x_increment():
"""
Check if dataarray_to_matrix returns correct output with flipped x.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=4, stop=0, 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.flip(data, axis=(0, 1)))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[abs(x[1] - x[0]), abs(y[1] - y[0])])
def test_dataarray_to_matrix_negative_y_increment():
"""
Check that dataarray_to_matrix returns correct output with flipped y.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=0, stop=4, num=3)
y = | np.linspace(start=9, stop=5, num=3) | numpy.linspace |