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# 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) | numpy.random.uniform |
# ________
# /
# \ /
# \ /
# \/
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) | 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) | numpy.full |
# Created by <NAME> on 8/28/19
import gym
import numpy as np
import torch
from interpretable_ddts.agents.ddt_agent import DDTAgent
from interpretable_ddts.agents.mlp_agent import MLPAgent
from interpretable_ddts.opt_helpers.replay_buffer import discount_reward
import torch.multiprocessing as mp
import argparse
import copy
import random
def run_episode(q, agent_in, ENV_NAME, seed=0):
agent = agent_in.duplicate()
if ENV_NAME == 'lunar':
env = gym.make('LunarLander-v2')
elif ENV_NAME == 'cart':
env = gym.make('CartPole-v1')
else:
raise Exception('No valid environment selected')
done = False
torch.manual_seed(seed)
env.seed(seed)
np.random.seed(seed)
env.action_space.seed(seed)
random.seed(seed)
state = env.reset() # Reset environment and record the starting state
while not done:
action = agent.get_action(state)
# Step through environment using chosen action
state, reward, done, _ = env.step(action)
# env.render()
# Save reward
agent.save_reward(reward)
if done:
break
reward_sum = | np.sum(agent.replay_buffer.rewards_list) | numpy.sum |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = | np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1) | numpy.concatenate |
# sys
import os
import sys
import numpy as np
import random
import pickle
import json
# torch
import torch
import torch.nn as nn
from torchvision import datasets, transforms
# operation
from . import tools
class Feeder_UCF(torch.utils.data.Dataset):
""" Feeder for skeleton-based action recognition in kinetics-skeleton dataset
Arguments:
data_path: the path to '.npy' data, the shape of data should be (N, C, T, V, M)
label_path: the path to label
random_choose: If true, randomly choose a portion of the input sequence
random_shift: If true, randomly pad zeros at the begining or end of sequence
random_move: If true, perform randomly but continuously changed transformation to input sequence
window_size: The length of the output sequence
pose_matching: If ture, match the pose between two frames
num_person_in: The number of people the feeder can observe in the input sequence
num_person_out: The number of people the feeder in the output sequence
debug: If true, only use the first 100 samples
"""
def __init__(self,
data_path,
label_path,
ignore_empty_sample=True,
random_choose=False,
random_shift=False,
random_move=False,
window_size=-1,
pose_matching=False,
num_person_in=5,
num_person_out=2,
debug=False):
self.debug = debug
self.data_path = data_path
self.label_path = label_path
self.random_choose = random_choose
self.random_shift = random_shift
self.random_move = random_move
self.window_size = window_size
self.num_person_in = num_person_in
self.num_person_out = num_person_out
self.pose_matching = pose_matching
self.ignore_empty_sample = ignore_empty_sample
self.load_data()
def load_data(self):
# load file list
self.sample_name = os.listdir(self.data_path)
if self.debug:
self.sample_name = self.sample_name[0:2]
# load label
label_path = self.label_path
with open(label_path) as f:
label_info = json.load(f)
sample_id = [name.split('.')[0] for name in self.sample_name]
self.label = np.array(
[label_info[id]['label_index'] for id in sample_id])
has_skeleton = np.array(
[label_info[id]['has_skeleton'] for id in sample_id])
# ignore the samples which does not has skeleton sequence
if self.ignore_empty_sample:
self.sample_name = [
s for h, s in zip(has_skeleton, self.sample_name) if h
]
self.label = self.label[has_skeleton]
# output data shape (N, C, T, V, M)
self.N = len(self.sample_name) #sample
self.C = 3 #channel
self.T = 90000 #frame
self.V = 18 #joint
self.M = self.num_person_out #person
def __len__(self):
return len(self.sample_name)
def __iter__(self):
return self
def __getitem__(self, index):
# output shape (C, T, V, M)
# get data
sample_name = self.sample_name[index]
sample_path = os.path.join(self.data_path, sample_name)
with open(sample_path, 'r') as f:
video_info = json.load(f)
# fill data_numpy
data_numpy = | np.zeros((self.C, self.T, self.V, self.num_person_in)) | numpy.zeros |
# 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.) | 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) | numpy.ones_like |
# coding=utf-8
# Copyright (c) 2019 NVIDIA CORPORATION. All rights reserved.
# Copyright 2018 The Google AI Language Team Authors.
#
# 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.
"""BERT finetuning runner."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import collections
import csv
import os
import modeling
import optimization
import tokenization
import tensorflow as tf
import horovod.tensorflow as hvd
import time
from utils.utils import LogEvalRunHook, LogTrainRunHook, setup_xla_flags
from utils.gpu_affinity import set_affinity
import utils.dllogger_class
from dllogger import Verbosity
from utils.create_glue_data import *
import numpy as np
import tf_metrics
flags = tf.flags
FLAGS = flags.FLAGS
## Required parameters
flags.DEFINE_string(
"data_dir", None,
"The input data dir. Should contain the .tsv files (or other data files) "
"for the task.")
flags.DEFINE_string(
"bert_config_file", None,
"The config json file corresponding to the pre-trained BERT model. "
"This specifies the model architecture.")
flags.DEFINE_string("task_name", None, "The name of the task to train.")
flags.DEFINE_string("vocab_file", None,
"The vocabulary file that the BERT model was trained on.")
flags.DEFINE_string(
"output_dir", None,
"The output directory where the model checkpoints will be written.")
## Other parameters
flags.DEFINE_string(
"dllog_path", "/results/bert_dllog.json",
"filename where dllogger writes to")
flags.DEFINE_string(
"optimizer_type", "lamb",
"Optimizer type : adam or lamb")
flags.DEFINE_string(
"init_checkpoint", None,
"Initial checkpoint (usually from a pre-trained BERT model).")
flags.DEFINE_bool(
"do_lower_case", True,
"Whether to lower case the input text. Should be True for uncased "
"models and False for cased models.")
flags.DEFINE_integer(
"max_seq_length", 128,
"The maximum total input sequence length after WordPiece tokenization. "
"Sequences longer than this will be truncated, and sequences shorter "
"than this will be padded.")
flags.DEFINE_bool("do_train", False, "Whether to run training.")
flags.DEFINE_bool("do_eval", False, "Whether to run eval on the dev set.")
flags.DEFINE_bool(
"do_predict", False,
"Whether to run the model in inference mode on the test set.")
flags.DEFINE_integer("train_batch_size", 32, "Total batch size for training.")
flags.DEFINE_integer("eval_batch_size", 8, "Total batch size for eval.")
flags.DEFINE_integer("predict_batch_size", 8, "Total batch size for predict.")
flags.DEFINE_float("learning_rate", 5e-5, "The initial learning rate for Adam.")
flags.DEFINE_bool("use_trt", False, "Whether to use TF-TRT")
flags.DEFINE_float("num_train_epochs", 3.0,
"Total number of training epochs to perform.")
flags.DEFINE_float(
"warmup_proportion", 0.1,
"Proportion of training to perform linear learning rate warmup for. "
"E.g., 0.1 = 10% of training.")
flags.DEFINE_integer("save_checkpoints_steps", 1000,
"How often to save the model checkpoint.")
flags.DEFINE_integer("display_loss_steps", 10,
"How often to print loss from estimator")
flags.DEFINE_integer("iterations_per_loop", 1000,
"How many steps to make in each estimator call.")
flags.DEFINE_integer("num_accumulation_steps", 1,
"Number of accumulation steps before gradient update"
"Global batch size = num_accumulation_steps * train_batch_size")
flags.DEFINE_bool("amp", True, "Whether to enable AMP ops. When false, uses TF32 on A100 and FP32 on V100 GPUS.")
flags.DEFINE_bool("use_xla", True, "Whether to enable XLA JIT compilation.")
flags.DEFINE_bool("horovod", False, "Whether to use Horovod for multi-gpu runs")
flags.DEFINE_bool(
"verbose_logging", False,
"If true, all of the warnings related to data processing will be printed. "
"A number of warnings are expected for a normal SQuAD evaluation.")
def file_based_input_fn_builder(input_file, batch_size, seq_length, is_training,
drop_remainder, hvd=None):
"""Creates an `input_fn` closure to be passed to Estimator."""
name_to_features = {
"input_ids": tf.io.FixedLenFeature([seq_length], tf.int64),
"input_mask": tf.io.FixedLenFeature([seq_length], tf.int64),
"segment_ids": tf.io.FixedLenFeature([seq_length], tf.int64),
"label_ids": tf.io.FixedLenFeature([], tf.int64),
}
def _decode_record(record, name_to_features):
"""Decodes a record to a TensorFlow example."""
example = tf.parse_single_example(record, name_to_features)
# tf.Example only supports tf.int64, but the TPU only supports tf.int32.
# So cast all int64 to int32.
for name in list(example.keys()):
t = example[name]
if t.dtype == tf.int64:
t = tf.to_int32(t)
example[name] = t
return example
def input_fn():
"""The actual input function."""
# For training, we want a lot of parallel reading and shuffling.
# For eval, we want no shuffling and parallel reading doesn't matter.
d = tf.data.TFRecordDataset(input_file)
if is_training:
if hvd is not None: d = d.shard(hvd.size(), hvd.rank())
d = d.repeat()
d = d.shuffle(buffer_size=100)
d = d.apply(
tf.contrib.data.map_and_batch(
lambda record: _decode_record(record, name_to_features),
batch_size=batch_size,
drop_remainder=drop_remainder))
return d
return input_fn
def create_model(bert_config, is_training, input_ids, input_mask, segment_ids,
labels, num_labels, use_one_hot_embeddings):
"""Creates a classification model."""
model = modeling.BertModel(
config=bert_config,
is_training=is_training,
input_ids=input_ids,
input_mask=input_mask,
token_type_ids=segment_ids,
use_one_hot_embeddings=use_one_hot_embeddings,
compute_type=tf.float32)
# In the demo, we are doing a simple classification task on the entire
# segment.
#
# If you want to use the token-level output, use model.get_sequence_output()
# instead.
output_layer = model.get_pooled_output()
hidden_size = output_layer.shape[-1].value
output_weights = tf.get_variable(
"output_weights", [num_labels, hidden_size],
initializer=tf.truncated_normal_initializer(stddev=0.02))
output_bias = tf.get_variable(
"output_bias", [num_labels], initializer=tf.zeros_initializer())
with tf.variable_scope("loss"):
if is_training:
# I.e., 0.1 dropout
output_layer = tf.nn.dropout(output_layer, keep_prob=0.9)
logits = tf.matmul(output_layer, output_weights, transpose_b=True)
logits = tf.nn.bias_add(logits, output_bias, name='cls_logits')
probabilities = tf.nn.softmax(logits, axis=-1, name='cls_probabilities')
log_probs = tf.nn.log_softmax(logits, axis=-1)
one_hot_labels = tf.one_hot(labels, depth=num_labels, dtype=tf.float32)
per_example_loss = -tf.reduce_sum(one_hot_labels * log_probs, axis=-1, name='cls_per_example_loss')
loss = tf.reduce_mean(per_example_loss, name='cls_loss')
return (loss, per_example_loss, logits, probabilities)
def get_frozen_tftrt_model(bert_config, shape, num_labels, use_one_hot_embeddings, init_checkpoint):
tf_config = tf.compat.v1.ConfigProto()
tf_config.gpu_options.allow_growth = True
output_node_names = ['loss/cls_loss', 'loss/cls_per_example_loss', 'loss/cls_logits', 'loss/cls_probabilities']
with tf.Session(config=tf_config) as tf_sess:
input_ids = tf.placeholder(tf.int32, shape, 'input_ids')
input_mask = tf.placeholder(tf.int32, shape, 'input_mask')
segment_ids = tf.placeholder(tf.int32, shape, 'segment_ids')
label_ids = tf.placeholder(tf.int32, (None), 'label_ids')
create_model(bert_config, False, input_ids, input_mask, segment_ids, label_ids,
num_labels, use_one_hot_embeddings)
tvars = tf.trainable_variables()
(assignment_map, initialized_variable_names) = modeling.get_assignment_map_from_checkpoint(tvars, init_checkpoint)
tf.train.init_from_checkpoint(init_checkpoint, assignment_map)
tf_sess.run(tf.global_variables_initializer())
print("LOADED!")
tf.compat.v1.logging.info("**** Trainable Variables ****")
for var in tvars:
init_string = ""
if var.name in initialized_variable_names:
init_string = ", *INIT_FROM_CKPT*"
else:
init_string = ", *NOTTTTTTTTTTTTTTTTTTTTT"
tf.compat.v1.logging.info(" name = %s, shape = %s%s", var.name, var.shape, init_string)
frozen_graph = tf.graph_util.convert_variables_to_constants(tf_sess,
tf_sess.graph.as_graph_def(), output_node_names)
num_nodes = len(frozen_graph.node)
print('Converting graph using TensorFlow-TensorRT...')
from tensorflow.python.compiler.tensorrt import trt_convert as trt
converter = trt.TrtGraphConverter(
input_graph_def=frozen_graph,
nodes_blacklist=output_node_names,
max_workspace_size_bytes=(4096 << 20) - 1000,
precision_mode = "FP16" if FLAGS.amp else "FP32",
minimum_segment_size=4,
is_dynamic_op=True,
maximum_cached_engines=1000
)
frozen_graph = converter.convert()
print('Total node count before and after TF-TRT conversion:',
num_nodes, '->', len(frozen_graph.node))
print('TRT node count:',
len([1 for n in frozen_graph.node if str(n.op) == 'TRTEngineOp']))
with tf.io.gfile.GFile("frozen_modelTRT.pb", "wb") as f:
f.write(frozen_graph.SerializeToString())
return frozen_graph
def model_fn_builder(task_name, bert_config, num_labels, init_checkpoint, learning_rate,
num_train_steps, num_warmup_steps,
use_one_hot_embeddings, hvd=None):
"""Returns `model_fn` closure for Estimator."""
def model_fn(features, labels, mode, params): # pylint: disable=unused-argument
"""The `model_fn` for Estimator."""
def metric_fn(per_example_loss, label_ids, logits):
predictions = tf.argmax(logits, axis=-1, output_type=tf.int32)
if task_name == "cola":
FN, FN_op = tf.metrics.false_negatives(labels=label_ids, predictions=predictions)
FP, FP_op = tf.metrics.false_positives(labels=label_ids, predictions=predictions)
TP, TP_op = tf.metrics.true_positives(labels=label_ids, predictions=predictions)
TN, TN_op = tf.metrics.true_negatives(labels=label_ids, predictions=predictions)
MCC = (TP * TN - FP * FN) / ((TP + FP) * (TP + FN) * (TN + FP) * (TN + FN)) ** 0.5
MCC_op = tf.group(FN_op, TN_op, TP_op, FP_op, tf.identity(MCC, name="MCC"))
return {"MCC": (MCC, MCC_op)}
elif task_name == "mrpc":
accuracy = tf.metrics.accuracy(
labels=label_ids, predictions=predictions)
loss = tf.metrics.mean(values=per_example_loss)
f1 = tf_metrics.f1(labels=label_ids, predictions=predictions, num_classes=2, pos_indices=[1])
return {
"eval_accuracy": accuracy,
"eval_f1": f1,
"eval_loss": loss,
}
else:
accuracy = tf.metrics.accuracy(
labels=label_ids, predictions=predictions)
loss = tf.metrics.mean(values=per_example_loss)
return {
"eval_accuracy": accuracy,
"eval_loss": loss,
}
tf.compat.v1.logging.info("*** Features ***")
tf.compat.v1.logging.info("*** Features ***")
for name in sorted(features.keys()):
tf.compat.v1.logging.info(" name = %s, shape = %s" % (name, features[name].shape))
input_ids = features["input_ids"]
input_mask = features["input_mask"]
segment_ids = features["segment_ids"]
label_ids = features["label_ids"]
is_training = (mode == tf.estimator.ModeKeys.TRAIN)
if not is_training and FLAGS.use_trt:
trt_graph = get_frozen_tftrt_model(bert_config, input_ids.shape, num_labels, use_one_hot_embeddings, init_checkpoint)
(total_loss, per_example_loss, logits, probabilities) = tf.import_graph_def(trt_graph,
input_map={'input_ids':input_ids, 'input_mask':input_mask, 'segment_ids':segment_ids, 'label_ids':label_ids},
return_elements=['loss/cls_loss:0', 'loss/cls_per_example_loss:0', 'loss/cls_logits:0', 'loss/cls_probabilities:0'],
name='')
if mode == tf.estimator.ModeKeys.PREDICT:
predictions = {"probabilities": probabilities}
output_spec = tf.estimator.EstimatorSpec(
mode=mode, predictions=predictions)
elif mode == tf.estimator.ModeKeys.EVAL:
eval_metric_ops = metric_fn(per_example_loss, label_ids, logits)
output_spec = tf.estimator.EstimatorSpec(
mode=mode,
loss=total_loss,
eval_metric_ops=eval_metric_ops)
return output_spec
(total_loss, per_example_loss, logits, probabilities) = create_model(
bert_config, is_training, input_ids, input_mask, segment_ids, label_ids,
num_labels, use_one_hot_embeddings)
tvars = tf.trainable_variables()
initialized_variable_names = {}
if init_checkpoint and (hvd is None or hvd.rank() == 0):
(assignment_map, initialized_variable_names
) = modeling.get_assignment_map_from_checkpoint(tvars, init_checkpoint)
tf.train.init_from_checkpoint(init_checkpoint, assignment_map)
if FLAGS.verbose_logging:
tf.compat.v1.logging.info("**** Trainable Variables ****")
for var in tvars:
init_string = ""
if var.name in initialized_variable_names:
init_string = ", *INIT_FROM_CKPT*"
tf.compat.v1.logging.info(" name = %s, shape = %s%s", var.name, var.shape,
init_string)
output_spec = None
if mode == tf.estimator.ModeKeys.TRAIN:
train_op = optimization.create_optimizer(
total_loss, learning_rate, num_train_steps, num_warmup_steps,
hvd, False, FLAGS.amp, FLAGS.num_accumulation_steps, FLAGS.optimizer_type)
output_spec = tf.estimator.EstimatorSpec(
mode=mode,
loss=total_loss,
train_op=train_op)
elif mode == tf.estimator.ModeKeys.EVAL:
dummy_op = tf.no_op()
# Need to call mixed precision graph rewrite if fp16 to enable graph rewrite
if FLAGS.amp:
loss_scaler = tf.train.experimental.FixedLossScale(1)
dummy_op = tf.train.experimental.enable_mixed_precision_graph_rewrite(
optimization.LAMBOptimizer(learning_rate=0.0), loss_scaler)
eval_metric_ops = metric_fn(per_example_loss, label_ids, logits)
output_spec = tf.estimator.EstimatorSpec(
mode=mode,
loss=total_loss,
eval_metric_ops=eval_metric_ops)
else:
dummy_op = tf.no_op()
# Need to call mixed precision graph rewrite if fp16 to enable graph rewrite
if FLAGS.amp:
dummy_op = tf.train.experimental.enable_mixed_precision_graph_rewrite(
optimization.LAMBOptimizer(learning_rate=0.0))
output_spec = tf.estimator.EstimatorSpec(
mode=mode, predictions=probabilities)
return output_spec
return model_fn
# This function is not used by this file but is still used by the Colab and
# people who depend on it.
def input_fn_builder(features, batch_size, seq_length, is_training, drop_remainder, hvd=None):
"""Creates an `input_fn` closure to be passed to Estimator."""
all_input_ids = []
all_input_mask = []
all_segment_ids = []
all_label_ids = []
for feature in features:
all_input_ids.append(feature.input_ids)
all_input_mask.append(feature.input_mask)
all_segment_ids.append(feature.segment_ids)
all_label_ids.append(feature.label_id)
def input_fn():
"""The actual input function."""
num_examples = len(features)
# This is for demo purposes and does NOT scale to large data sets. We do
# not use Dataset.from_generator() because that uses tf.py_func which is
# not TPU compatible. The right way to load data is with TFRecordReader.
d = tf.data.Dataset.from_tensor_slices({
"input_ids":
tf.constant(
all_input_ids, shape=[num_examples, seq_length],
dtype=tf.int32),
"input_mask":
tf.constant(
all_input_mask,
shape=[num_examples, seq_length],
dtype=tf.int32),
"segment_ids":
tf.constant(
all_segment_ids,
shape=[num_examples, seq_length],
dtype=tf.int32),
"label_ids":
tf.constant(all_label_ids, shape=[num_examples], dtype=tf.int32),
})
if is_training:
if hvd is not None: d = d.shard(hvd.size(), hvd.rank())
d = d.repeat()
d = d.shuffle(buffer_size=100)
d = d.batch(batch_size=batch_size, drop_remainder=drop_remainder)
return d
return input_fn
def main(_):
setup_xla_flags()
tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.INFO)
dllogging = utils.dllogger_class.dllogger_class(FLAGS.dllog_path)
if FLAGS.horovod:
hvd.init()
processors = {
"cola": ColaProcessor,
"mnli": MnliProcessor,
"mrpc": MrpcProcessor,
"xnli": XnliProcessor,
}
if not FLAGS.do_train and not FLAGS.do_eval and not FLAGS.do_predict:
raise ValueError(
"At least one of `do_train`, `do_eval` or `do_predict' must be True.")
bert_config = modeling.BertConfig.from_json_file(FLAGS.bert_config_file)
if FLAGS.max_seq_length > bert_config.max_position_embeddings:
raise ValueError(
"Cannot use sequence length %d because the BERT model "
"was only trained up to sequence length %d" %
(FLAGS.max_seq_length, bert_config.max_position_embeddings))
tf.io.gfile.makedirs(FLAGS.output_dir)
task_name = FLAGS.task_name.lower()
if task_name not in processors:
raise ValueError("Task not found: %s" % (task_name))
processor = processors[task_name]()
label_list = processor.get_labels()
tokenizer = tokenization.FullTokenizer(
vocab_file=FLAGS.vocab_file, do_lower_case=FLAGS.do_lower_case)
master_process = True
training_hooks = []
global_batch_size = FLAGS.train_batch_size * FLAGS.num_accumulation_steps
hvd_rank = 0
config = tf.compat.v1.ConfigProto()
if FLAGS.horovod:
tf.compat.v1.logging.info("Multi-GPU training with TF Horovod")
tf.compat.v1.logging.info("hvd.size() = %d hvd.rank() = %d", hvd.size(), hvd.rank())
global_batch_size = FLAGS.train_batch_size * FLAGS.num_accumulation_steps * hvd.size()
master_process = (hvd.rank() == 0)
hvd_rank = hvd.rank()
config.gpu_options.visible_device_list = str(hvd.local_rank())
set_affinity(hvd.local_rank())
if hvd.size() > 1:
training_hooks.append(hvd.BroadcastGlobalVariablesHook(0))
if FLAGS.use_xla:
config.graph_options.optimizer_options.global_jit_level = tf.compat.v1.OptimizerOptions.ON_1
if FLAGS.amp:
tf.enable_resource_variables()
run_config = tf.estimator.RunConfig(
model_dir=FLAGS.output_dir if master_process else None,
session_config=config,
save_checkpoints_steps=FLAGS.save_checkpoints_steps if master_process else None,
save_summary_steps=FLAGS.save_checkpoints_steps if master_process else None,
log_step_count_steps=FLAGS.display_loss_steps,
keep_checkpoint_max=1)
if master_process:
tf.compat.v1.logging.info("***** Configuaration *****")
for key in FLAGS.__flags.keys():
tf.compat.v1.logging.info(' {}: {}'.format(key, getattr(FLAGS, key)))
tf.compat.v1.logging.info("**************************")
train_examples = None
num_train_steps = None
num_warmup_steps = None
training_hooks.append(LogTrainRunHook(global_batch_size, hvd_rank, FLAGS.save_checkpoints_steps, num_steps_ignore_xla=25))
if FLAGS.do_train:
train_examples = processor.get_train_examples(FLAGS.data_dir)
num_train_steps = int(
len(train_examples) / global_batch_size * FLAGS.num_train_epochs)
num_warmup_steps = int(num_train_steps * FLAGS.warmup_proportion)
start_index = 0
end_index = len(train_examples)
tmp_filenames = [os.path.join(FLAGS.output_dir, "train.tf_record")]
if FLAGS.horovod:
tmp_filenames = [os.path.join(FLAGS.output_dir, "train.tf_record{}".format(i)) for i in range(hvd.size())]
num_examples_per_rank = len(train_examples) // hvd.size()
remainder = len(train_examples) % hvd.size()
if hvd.rank() < remainder:
start_index = hvd.rank() * (num_examples_per_rank+1)
end_index = start_index + num_examples_per_rank + 1
else:
start_index = hvd.rank() * num_examples_per_rank + remainder
end_index = start_index + (num_examples_per_rank)
model_fn = model_fn_builder(
task_name=task_name,
bert_config=bert_config,
num_labels=len(label_list),
init_checkpoint=FLAGS.init_checkpoint,
learning_rate=FLAGS.learning_rate if not FLAGS.horovod else FLAGS.learning_rate * hvd.size(),
num_train_steps=num_train_steps,
num_warmup_steps=num_warmup_steps,
use_one_hot_embeddings=False,
hvd=None if not FLAGS.horovod else hvd)
estimator = tf.estimator.Estimator(
model_fn=model_fn,
config=run_config)
if FLAGS.do_train:
file_based_convert_examples_to_features(
train_examples[start_index:end_index], label_list, FLAGS.max_seq_length, tokenizer, tmp_filenames[hvd_rank])
tf.compat.v1.logging.info("***** Running training *****")
tf.compat.v1.logging.info(" Num examples = %d", len(train_examples))
tf.compat.v1.logging.info(" Batch size = %d", FLAGS.train_batch_size)
tf.compat.v1.logging.info(" Num steps = %d", num_train_steps)
train_input_fn = file_based_input_fn_builder(
input_file=tmp_filenames,
batch_size=FLAGS.train_batch_size,
seq_length=FLAGS.max_seq_length,
is_training=True,
drop_remainder=True,
hvd=None if not FLAGS.horovod else hvd)
train_start_time = time.time()
estimator.train(input_fn=train_input_fn, max_steps=num_train_steps, hooks=training_hooks)
train_time_elapsed = time.time() - train_start_time
train_time_wo_overhead = training_hooks[-1].total_time
avg_sentences_per_second = num_train_steps * global_batch_size * 1.0 / train_time_elapsed
ss_sentences_per_second = (training_hooks[-1].count - training_hooks[-1].skipped) * global_batch_size * 1.0 / train_time_wo_overhead
if master_process:
tf.compat.v1.logging.info("-----------------------------")
tf.compat.v1.logging.info("Total Training Time = %0.2f for Sentences = %d", train_time_elapsed,
num_train_steps * global_batch_size)
tf.compat.v1.logging.info("Total Training Time W/O Overhead = %0.2f for Sentences = %d", train_time_wo_overhead,
(training_hooks[-1].count - training_hooks[-1].skipped) * global_batch_size)
tf.compat.v1.logging.info("Throughput Average (sentences/sec) with overhead = %0.2f", avg_sentences_per_second)
tf.compat.v1.logging.info("Throughput Average (sentences/sec) = %0.2f", ss_sentences_per_second)
tf.compat.v1.logging.info("-----------------------------")
if FLAGS.do_eval and master_process:
eval_examples = processor.get_dev_examples(FLAGS.data_dir)
eval_file = os.path.join(FLAGS.output_dir, "eval.tf_record")
file_based_convert_examples_to_features(
eval_examples, label_list, FLAGS.max_seq_length, tokenizer, eval_file)
tf.compat.v1.logging.info("***** Running evaluation *****")
tf.compat.v1.logging.info(" Num examples = %d", len(eval_examples))
tf.compat.v1.logging.info(" Batch size = %d", FLAGS.eval_batch_size)
eval_drop_remainder = False
eval_input_fn = file_based_input_fn_builder(
input_file=eval_file,
batch_size=FLAGS.eval_batch_size,
seq_length=FLAGS.max_seq_length,
is_training=False,
drop_remainder=eval_drop_remainder)
eval_hooks = [LogEvalRunHook(FLAGS.eval_batch_size)]
eval_start_time = time.time()
result = estimator.evaluate(input_fn=eval_input_fn, hooks=eval_hooks)
eval_time_elapsed = time.time() - eval_start_time
time_list = eval_hooks[-1].time_list
time_list.sort()
# Removing outliers (init/warmup) in throughput computation.
eval_time_wo_overhead = sum(time_list[:int(len(time_list) * 0.8)])
num_sentences = (int(len(time_list) * 0.8)) * FLAGS.eval_batch_size
avg = np.mean(time_list)
cf_50 = max(time_list[:int(len(time_list) * 0.50)])
cf_90 = max(time_list[:int(len(time_list) * 0.90)])
cf_95 = max(time_list[:int(len(time_list) * 0.95)])
cf_99 = max(time_list[:int(len(time_list) * 0.99)])
cf_100 = max(time_list[:int(len(time_list) * 1)])
ss_sentences_per_second = num_sentences * 1.0 / eval_time_wo_overhead
tf.compat.v1.logging.info("-----------------------------")
tf.compat.v1.logging.info("Total Inference Time = %0.2f for Sentences = %d", eval_time_elapsed,
eval_hooks[-1].count * FLAGS.eval_batch_size)
tf.compat.v1.logging.info("Total Inference Time W/O Overhead = %0.2f for Sentences = %d", eval_time_wo_overhead,
num_sentences)
tf.compat.v1.logging.info("Summary Inference Statistics on EVAL set")
tf.compat.v1.logging.info("Batch size = %d", FLAGS.eval_batch_size)
tf.compat.v1.logging.info("Sequence Length = %d", FLAGS.max_seq_length)
tf.compat.v1.logging.info("Precision = %s", "fp16" if FLAGS.amp else "fp32")
tf.compat.v1.logging.info("Latency Confidence Level 50 (ms) = %0.2f", cf_50 * 1000)
tf.compat.v1.logging.info("Latency Confidence Level 90 (ms) = %0.2f", cf_90 * 1000)
tf.compat.v1.logging.info("Latency Confidence Level 95 (ms) = %0.2f", cf_95 * 1000)
tf.compat.v1.logging.info("Latency Confidence Level 99 (ms) = %0.2f", cf_99 * 1000)
tf.compat.v1.logging.info("Latency Confidence Level 100 (ms) = %0.2f", cf_100 * 1000)
tf.compat.v1.logging.info("Latency Average (ms) = %0.2f", avg * 1000)
tf.compat.v1.logging.info("Throughput Average (sentences/sec) = %0.2f", ss_sentences_per_second)
dllogging.logger.log(step=(), data={"throughput_val": ss_sentences_per_second}, verbosity=Verbosity.DEFAULT)
tf.compat.v1.logging.info("-----------------------------")
output_eval_file = os.path.join(FLAGS.output_dir, "eval_results.txt")
with tf.io.gfile.GFile(output_eval_file, "w") as writer:
tf.compat.v1.logging.info("***** Eval results *****")
for key in sorted(result.keys()):
dllogging.logger.log(step=(), data={key: float(result[key])}, verbosity=Verbosity.DEFAULT)
tf.compat.v1.logging.info(" %s = %s", key, str(result[key]))
writer.write("%s = %s\n" % (key, str(result[key])))
if FLAGS.do_predict and master_process:
predict_examples = processor.get_test_examples(FLAGS.data_dir)
predict_file = os.path.join(FLAGS.output_dir, "predict.tf_record")
file_based_convert_examples_to_features(predict_examples, label_list,
FLAGS.max_seq_length, tokenizer,
predict_file)
tf.compat.v1.logging.info("***** Running prediction*****")
tf.compat.v1.logging.info(" Num examples = %d", len(predict_examples))
tf.compat.v1.logging.info(" Batch size = %d", FLAGS.predict_batch_size)
predict_drop_remainder = False
predict_input_fn = file_based_input_fn_builder(
input_file=predict_file,
batch_size=FLAGS.predict_batch_size,
seq_length=FLAGS.max_seq_length,
is_training=False,
drop_remainder=predict_drop_remainder)
predict_hooks = [LogEvalRunHook(FLAGS.predict_batch_size)]
predict_start_time = time.time()
output_predict_file = os.path.join(FLAGS.output_dir, "test_results.tsv")
with tf.io.gfile.GFile(output_predict_file, "w") as writer:
tf.compat.v1.logging.info("***** Predict results *****")
for prediction in estimator.predict(input_fn=predict_input_fn, hooks=predict_hooks,
yield_single_examples=False):
output_line = "\t".join(
str(class_probability) for class_probability in prediction) + "\n"
writer.write(output_line)
predict_time_elapsed = time.time() - predict_start_time
time_list = predict_hooks[-1].time_list
time_list.sort()
# Removing outliers (init/warmup) in throughput computation.
predict_time_wo_overhead = sum(time_list[:int(len(time_list) * 0.8)])
num_sentences = (int(len(time_list) * 0.8)) * FLAGS.predict_batch_size
avg = | np.mean(time_list) | numpy.mean |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = | np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101) | 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])
else:
out = None
if len(inputs) == 1:
_, inp, u = get_inp_u_unary(ufunc, inputs)
out_arr = func(np.asarray(inp), out=out, **kwargs)
if ufunc in (multiply, divide) and method == 'reduce':
power_sign = POWER_SIGN_MAPPING[ufunc]
if 'axis' in kwargs and kwargs['axis'] is not None:
unit = u**(power_sign*inp.shape[kwargs['axis']])
else:
unit = u**(power_sign*inp.size)
else:
unit = self._ufunc_registry[ufunc](u)
ret_class = type(self)
elif len(inputs) == 2:
unit_operator = self._ufunc_registry[ufunc]
inps, units, ret_class = get_inp_u_binary(ufunc, inputs)
if unit_operator in (comparison_unit, arctan2_unit):
inps, units = handle_comparison_units(
inps, units, ufunc, ret_class)
elif unit_operator is preserve_units:
inps, units = handle_preserve_units(
inps, units, ufunc, ret_class)
unit = unit_operator(*units)
out_arr = func(np.asarray(inps[0]), np.asarray(inps[1]),
out=out, **kwargs)
if unit_operator in (multiply_units, divide_units):
out, out_arr, unit = handle_multiply_divide_units(
unit, units, out, out_arr)
else:
raise RuntimeError(
"Support for the %s ufunc with %i inputs has not been"
"added to YTArray." % (str(ufunc), len(inputs)))
if unit is None:
out_arr = np.array(out_arr, copy=False)
elif ufunc in (modf, divmod_):
out_arr = tuple((ret_class(o, unit) for o in out_arr))
elif out_arr.size == 1:
out_arr = YTQuantity(np.asarray(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
out_arr = YTArray(np.asarray(out_arr), unit)
else:
out_arr = ret_class(np.asarray(out_arr), unit)
if out is not None:
out_orig[0].flat[:] = out.flat[:]
if isinstance(out_orig[0], YTArray):
out_orig[0].units = unit
return out_arr
def copy(self, order='C'):
return type(self)(np.copy(np.asarray(self)), self.units)
def __array_finalize__(self, obj):
if obj is None and hasattr(self, 'units'):
return
self.units = getattr(obj, 'units', NULL_UNIT)
def __pos__(self):
""" Posify the data. """
# this needs to be defined for all numpy versions, see
# numpy issue #9081
return type(self)(super(YTArray, self).__pos__(), self.units)
@return_arr
def dot(self, b, out=None):
return super(YTArray, self).dot(b), self.units*b.units
def __reduce__(self):
"""Pickle reduction method
See the documentation for the standard library pickle module:
http://docs.python.org/2/library/pickle.html
Unit metadata is encoded in the zeroth element of third element of the
returned tuple, itself a tuple used to restore the state of the ndarray.
This is always defined for numpy arrays.
"""
np_ret = super(YTArray, self).__reduce__()
obj_state = np_ret[2]
unit_state = (((str(self.units), self.units.registry.lut),) + obj_state[:],)
new_ret = np_ret[:2] + unit_state + np_ret[3:]
return new_ret
def __setstate__(self, state):
"""Pickle setstate method
This is called inside pickle.read() and restores the unit data from the
metadata extracted in __reduce__ and then serialized by pickle.
"""
super(YTArray, self).__setstate__(state[1:])
try:
unit, lut = state[0]
except TypeError:
# this case happens when we try to load an old pickle file
# created before we serialized the unit symbol lookup table
# into the pickle file
unit, lut = str(state[0]), default_unit_symbol_lut.copy()
# need to fix up the lut if the pickle was saved prior to PR #1728
# when the pickle format changed
if len(lut['m']) == 2:
lut.update(default_unit_symbol_lut)
for k, v in [(k, v) for k, v in lut.items() if len(v) == 2]:
lut[k] = v + (0.0, r'\rm{' + k.replace('_', '\ ') + '}')
registry = UnitRegistry(lut=lut, add_default_symbols=False)
self.units = Unit(unit, registry=registry)
def __deepcopy__(self, memodict=None):
"""copy.deepcopy implementation
This is necessary for stdlib deepcopy of arrays and quantities.
"""
if memodict is None:
memodict = {}
ret = super(YTArray, self).__deepcopy__(memodict)
return type(self)(ret, copy.deepcopy(self.units))
class YTQuantity(YTArray):
"""
A scalar associated with a unit.
Parameters
----------
input_scalar : an integer or floating point scalar
The scalar to attach units to
input_units : String unit specification, unit symbol object, or astropy units
The units of the quantity. Powers must be specified using python syntax
(cm**3, not cm^3).
registry : A UnitRegistry object
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.
Examples
--------
>>> from yt import YTQuantity
>>> a = YTQuantity(1, 'cm')
>>> b = YTQuantity(2, 'm')
>>> a + b
201.0 cm
>>> b + a
2.01 m
NumPy ufuncs will pass through units where appropriate.
>>> import numpy as np
>>> a = YTQuantity(12, 'g/cm**3')
>>> np.abs(a)
12 g/cm**3
and strip them when it would be annoying to deal with them.
>>> print(np.log10(a))
1.07918124605
YTQuantity is tightly integrated with yt datasets:
>>> import yt
>>> ds = yt.load('IsolatedGalaxy/galaxy0030/galaxy0030')
>>> a = ds.quan(5, 'code_length')
>>> a.in_cgs()
1.543e+25 cm
This is equivalent to:
>>> b = YTQuantity(5, 'code_length', registry=ds.unit_registry)
>>> np.all(a == b)
True
"""
def __new__(cls, input_scalar, input_units=None, registry=None,
dtype=np.float64, bypass_validation=False):
if not isinstance(input_scalar, (numeric_type, np.number, np.ndarray)):
raise RuntimeError("YTQuantity values must be numeric")
ret = YTArray.__new__(cls, input_scalar, input_units, registry,
dtype=dtype, bypass_validation=bypass_validation)
if ret.size > 1:
raise RuntimeError("YTQuantity instances must be scalars")
return ret
def __repr__(self):
return str(self)
def validate_numpy_wrapper_units(v, arrs):
if not any(isinstance(a, YTArray) for a in arrs):
return v
if not all(isinstance(a, YTArray) for a in arrs):
raise RuntimeError("Not all of your arrays are YTArrays.")
a1 = arrs[0]
if not all(a.units == a1.units for a in arrs[1:]):
raise RuntimeError("Your arrays must have identical units.")
v.units = a1.units
return v
def uconcatenate(arrs, axis=0):
"""Concatenate a sequence of arrays.
This wrapper around numpy.concatenate preserves units. All input arrays must
have the same units. See the documentation of numpy.concatenate for full
details.
Examples
--------
>>> A = yt.YTArray([1, 2, 3], 'cm')
>>> B = yt.YTArray([2, 3, 4], 'cm')
>>> uconcatenate((A, B))
YTArray([ 1., 2., 3., 2., 3., 4.]) cm
"""
v = np.concatenate(arrs, axis=axis)
v = validate_numpy_wrapper_units(v, arrs)
return v
def ucross(arr1, arr2, registry=None, axisa=-1, axisb=-1, axisc=-1, axis=None):
"""Applies the cross product to two YT arrays.
This wrapper around numpy.cross preserves units.
See the documentation of numpy.cross for full
details.
"""
v = np.cross(arr1, arr2, axisa=axisa, axisb=axisb, axisc=axisc, axis=axis)
units = arr1.units * arr2.units
arr = YTArray(v, units, registry=registry)
return arr
def uintersect1d(arr1, arr2, assume_unique=False):
"""Find the sorted unique elements of the two input arrays.
A wrapper around numpy.intersect1d that preserves units. All input arrays
must have the same units. See the documentation of numpy.intersect1d for
full details.
Examples
--------
>>> A = yt.YTArray([1, 2, 3], 'cm')
>>> B = yt.YTArray([2, 3, 4], 'cm')
>>> uintersect1d(A, B)
YTArray([ 2., 3.]) cm
"""
v = np.intersect1d(arr1, arr2, assume_unique=assume_unique)
v = validate_numpy_wrapper_units(v, [arr1, arr2])
return v
def uunion1d(arr1, arr2):
"""Find the union of two arrays.
A wrapper around numpy.intersect1d that preserves units. All input arrays
must have the same units. See the documentation of numpy.intersect1d for
full details.
Examples
--------
>>> A = yt.YTArray([1, 2, 3], 'cm')
>>> B = yt.YTArray([2, 3, 4], 'cm')
>>> uunion1d(A, B)
YTArray([ 1., 2., 3., 4.]) cm
"""
v = np.union1d(arr1, arr2)
v = validate_numpy_wrapper_units(v, [arr1, arr2])
return v
def unorm(data, ord=None, axis=None, keepdims=False):
"""Matrix or vector norm that preserves units
This is a wrapper around np.linalg.norm that preserves units. See
the documentation for that function for descriptions of the keyword
arguments.
The keepdims argument is ignored if the version of numpy installed is
older than numpy 1.10.0.
"""
if LooseVersion(np.__version__) < LooseVersion('1.10.0'):
norm = np.linalg.norm(data, ord=ord, axis=axis)
else:
norm = np.linalg.norm(data, ord=ord, axis=axis, keepdims=keepdims)
if norm.shape == ():
return YTQuantity(norm, data.units)
return YTArray(norm, data.units)
def udot(op1, op2):
"""Matrix or vector dot product that preserves units
This is a wrapper around np.dot that preserves units.
"""
dot = np.dot(op1.d, op2.d)
units = op1.units*op2.units
if dot.shape == ():
return YTQuantity(dot, units)
return YTArray(dot, units)
def uvstack(arrs):
"""Stack arrays in sequence vertically (row wise) while preserving units
This is a wrapper around np.vstack that preserves units.
"""
v = np.vstack(arrs)
v = validate_numpy_wrapper_units(v, arrs)
return v
def uhstack(arrs):
"""Stack arrays in sequence horizontally (column wise) while preserving units
This is a wrapper around np.hstack that preserves units.
"""
v = np.hstack(arrs)
v = validate_numpy_wrapper_units(v, arrs)
return v
def ustack(arrs, axis=0):
"""Join a sequence of arrays along a new axis while preserving units
The axis parameter specifies the index of the new axis in the
dimensions of the result. For example, if ``axis=0`` it will be the
first dimension and if ``axis=-1`` it will be the last dimension.
This is a wrapper around np.stack that preserves units.
"""
v = | np.stack(arrs) | numpy.stack |
# ________
# /
# \ /
# \ /
# \/
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 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = | np.linspace(0, 2 * np.pi, 51) | numpy.linspace |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = | np.linspace(minima_y[-1], maxima_y[-1], 101) | 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)
fractions = np.hstack(fractions)
J = coo_matrix((fractions, (row_indices, col_indices)), shape=(m, n))
return csr_matrix(J)
def check_derivative(fun, jac, x0, bounds=(-np.inf, np.inf), args=(),
kwargs={}):
"""Check correctness of a function computing derivatives (Jacobian or
gradient) by comparison with a finite difference approximation.
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.
jac : callable
Function which computes Jacobian matrix of `fun`. It must work with
argument x the same way as `fun`. The return value must be array_like
or sparse matrix with an appropriate shape.
x0 : array_like of shape (n,) or float
Point at which to estimate the derivatives. Float will be converted
to 1-D array.
bounds : 2-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.
args, kwargs : tuple and dict, optional
Additional arguments passed to `fun` and `jac`. Both empty by default.
The calling signature is ``fun(x, *args, **kwargs)`` and the same
for `jac`.
Returns
-------
accuracy : float
The maximum among all relative errors for elements with absolute values
higher than 1 and absolute errors for elements with absolute values
less or equal than 1. If `accuracy` is on the order of 1e-6 or lower,
then it is likely that your `jac` implementation is correct.
See Also
--------
approx_derivative : Compute finite difference approximation of derivative.
Examples
--------
>>> import numpy as np
>>> from scipy.optimize import check_derivative
>>>
>>>
>>> def f(x, c1, c2):
... return np.array([x[0] * np.sin(c1 * x[1]),
... x[0] * np.cos(c2 * x[1])])
...
>>> def jac(x, c1, c2):
... return np.array([
... [np.sin(c1 * x[1]), c1 * x[0] * np.cos(c1 * x[1])],
... [np.cos(c2 * x[1]), -c2 * x[0] * np.sin(c2 * x[1])]
... ])
...
>>>
>>> x0 = np.array([1.0, 0.5 * np.pi])
>>> check_derivative(f, jac, x0, args=(1, 2))
2.4492935982947064e-16
"""
J_to_test = jac(x0, *args, **kwargs)
if issparse(J_to_test):
J_diff = approx_derivative(fun, x0, bounds=bounds, sparsity=J_to_test,
args=args, kwargs=kwargs)
J_to_test = csr_matrix(J_to_test)
abs_err = J_to_test - J_diff
i, j, abs_err_data = find(abs_err)
J_diff_data = np.asarray(J_diff[i, j]).ravel()
return np.max(np.abs(abs_err_data) /
np.maximum(1, np.abs(J_diff_data)))
else:
J_diff = approx_derivative(fun, x0, bounds=bounds,
args=args, kwargs=kwargs)
abs_err = np.abs(J_to_test - J_diff)
return np.max(abs_err / np.maximum(1, | np.abs(J_diff) | numpy.abs |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length]) # np.append(features,length,axis=1)
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1)
log.fit(X_train, y_train)
#save the model
_ = joblib.dump(log, filename, compress=9)
predictions = log.predict(X_val)
print("###########################################")
print("Results using embeddings from the",layer_json,"file")
print(classification_report(y_val, predictions))
print("F1 score using Logistic Regression:",f1_score(y_val, predictions))
print("###########################################")
#train a DNN
f1_results = list()
for i in range(3):
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
# compile network
model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1])
# fit network
model.fit(X_train, y_train, epochs=100, batch_size=64)
loss, f_1 = model.evaluate(X_val, y_val, verbose=1)
print('\nTest F1: %f' % (f_1 * 100))
f1_results.append(f_1)
model = None
print("###########################################")
print("Results using embeddings from the", layer_json, "file")
# evaluate
print(np.mean(f1_results))
print("###########################################")
def parameter_tuning_LR(sentences_list,layer_json,dataset_csv):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length])
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
C = [0.1,1,2,5,10]
solver = ['newton-cg','saga','sag']
best_params = dict()
best_score = 0.0
for c in C:
for s in solver:
start = time.time()
log = LogisticRegression(random_state=0, solver=s, max_iter=1000, C=c)
log.fit(X_train, y_train)
predictions = log.predict(X_val)
print("###########################################")
print("LR with C =",c,'and solver = ',s)
print("Results using embeddings from the", layer_json, "file")
print(classification_report(y_val, predictions))
f1 = f1_score(y_val, predictions)
if f1 > best_score:
best_score = f1
best_params['c'] = c
best_params['solver'] = s
print("F1 score using Logistic Regression:",f1)
print("###########################################")
end = time.time()
running_time = end - start
print("Running time:"+str(running_time))
def visualize_DNN(file_to_save):
'''
Save the DNN architecture to a png file. Better use the Visulize_DNN.ipynd
:param file_to_save: the png file that the architecture of the DNN will be saved.
:return: None
'''
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
plot_model(model, to_file=file_to_save, show_shapes=True)
def save_model(sentences_list,layer_json,dataset_csv,pkl):
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list, layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = | np.asarray(previous_emb) | numpy.asarray |
import numpy as np
from stumpff import C, S
from CelestialBody import BODIES
from numerical import newton, laguerre
from lagrange import calc_f, calc_fd, calc_g, calc_gd
def kepler_chi(chi, alpha, r0, vr0, mu, dt):
''' Kepler's Equation of the universal anomaly, modified
for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \
(1 - alpha*r0)*chi**3*S(z) + \
r0*chi - np.sqrt(mu)*dt
def dkepler_dchi(chi, alpha, r0, vr0, mu, dt):
''' Derivative of Kepler's Equation of the universal anomaly,
modified for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/ | np.sqrt(mu) | 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) | 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) | 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) | numpy.ones_like |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), 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) | 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)
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) | 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() | numpy.random.uniform |
import os
from PIL import Image
import cv2
from os import listdir
from os.path import join
import matplotlib.pyplot as plt
import matplotlib
from matplotlib.colors import LogNorm
from io_utils.io_common import create_folder
from viz_utils.constants import PlotMode, BackgroundType
import pylab
import numpy as np
import cmocean
import shapely
import cartopy.crs as ccrs
import cartopy.feature as cfeature
import cartopy
def select_colormap(field_name):
'''
Based on the name if the field it chooses a colormap from cmocean
Args:
field_name:
Returns:
'''
if np.any([field_name.find(x) != -1 for x in ('ssh', 'srfhgt', 'adt','surf_el')]):
# cmaps_fields.append(cmocean.cm.deep_r)
return cmocean.cm.curl
elif np.any([field_name.find(x) != -1 for x in ('temp', 'sst', 'temperature')]):
return cmocean.cm.thermal
elif np.any([field_name.find(x) != -1 for x in ('vorticity', 'vort')]):
return cmocean.cm.curl
elif np.any([field_name.find(x) != -1 for x in ('salin', 'sss', 'sal')]):
return cmocean.cm.haline
elif field_name.find('error') != -1:
return cmocean.cm.diff
elif field_name.find('binary') != -1:
return cmocean.cm.oxy
elif np.any([field_name.find(x) != -1 for x in ('u_', 'v_', 'u-vel.', 'v-vel.','velocity')]):
return cmocean.cm.speed
class EOAImageVisualizer:
"""This class makes plenty of plots assuming we are plotting Geospatial data (maps).
It is made to read xarrays, numpy arrays, and numpy arrays in dictionaries
vizobj = new EOAImageVisualizer(disp_images=True, output_folder='output',
lats=[lats],lons=[lons])
"""
_COLORS = ['y', 'r', 'c', 'b', 'g', 'w', 'k', 'y', 'r', 'c', 'b', 'g', 'w', 'k']
_figsize = 8
_font_size = 30
_units = ''
_max_imgs_per_row = 4
_mincbar = np.nan # User can set a min and max colorbar values to 'force' same color bar to all plots
_maxcbar = np.nan
_flip_data = True
_eoas_pyutils_path = './eoas_pyutils'# This is the path where the eoas_utils folder is stored with respect to the main project
_contourf = False # When plotting non-regular grids and need precision
_background = BackgroundType.BLUE_MARBLE_LR # Select the background to use
_auto_colormap = True # Selects the colormap based on the name of the field
_show_var_names = False # Includes the name of the field name in the titles
_additional_polygons = [] # MUST BE SHAPELY GEOMETRIES In case we want to include additional polygons in the plots (all of them)
# If you want to add a streamplot of a vector field. It must be a dictionary with keys x,y,u,v
# and optional density, color, cmap, arrowsize, arrowstyle, minlength
_vector_field = None
_norm = None # Use to normalize the colormap. For example with LogNorm
# vizobj = EOAImageVisualizer(disp_images=True, output_folder='output',
# lats=[lats],lons=[lons])
def __init__(self, disp_images=True, output_folder='output',
lats=[-90,90], lons =[-180,180],
projection=ccrs.PlateCarree(), **kwargs):
# All the arguments that are passed to the constructor of the class MUST have its name on it.
self._disp_images = disp_images
self._output_folder = output_folder
self._projection = projection
bbox = self.getExtent(lats, lons)
self._extent = bbox
self._lats = lats
self._lons = lons
self._fig_prop = (bbox[1]-bbox[0])/(bbox[3]-bbox[2])
self._contour_labels = False
for arg_name, arg_value in kwargs.items():
self.__dict__["_" + arg_name] = arg_value
print(self.__dict__["_" + arg_name])
def __getattr__(self, attr):
'''Generic getter for all the properties of the class'''
return self.__dict__["_" + attr]
def __setattr__(self, attr, value):
'''Generic setter for all the properties of the class'''
self.__dict__["_" + attr] = value
def add_colorbar(self, fig, im, ax, show_color_bar, label=""):
# https://matplotlib.org/api/_as_gen/matplotlib.pyplot.colorbar.html
if show_color_bar:
font_size_cbar = self._font_size * .5
# TODO how to make this automatic and works always
cbar = fig.colorbar(im, ax=ax, shrink=.7)
cbar.ax.tick_params(labelsize=font_size_cbar)
if label != "":
cbar.set_label(label, fontsize=font_size_cbar*1.2)
else:
cbar.set_label(self._units, fontsize=font_size_cbar*1.2)
def plot_slice_eoa(self, c_img, ax, cmap='gray', mode=PlotMode.RASTER, mincbar=np.nan, maxcbar=np.nan) -> None:
"""
Plots a 2D img for EOA data.
:param c_img: 2D array
:param ax: geoaxes
:return:
"""
c_ax = ax
if self._flip_data:
origin = 'lower'
else:
origin = 'upper'
if self._background == BackgroundType.CARTO_DEF:
c_ax.stock_img()
else:
if self._background == BackgroundType.BLUE_MARBLE_LR:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/bluemarble.png'))
if self._background == BackgroundType.BLUE_MARBLE_HR:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/bluemarble_5400x2700.jpg'))
if self._background == BackgroundType.TOPO:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/etopo.png'))
if self._background == BackgroundType.BATHYMETRY:
img = plt.imread(join(self._eoas_pyutils_path,'viz_utils/imgs/bathymetry_3600x1800.jpg'))
c_ax.imshow(img, origin='upper', extent=(-180,180,-90,90), transform=ccrs.PlateCarree())
if mode == PlotMode.RASTER or mode == PlotMode.MERGED:
if self._contourf:
im = c_ax.contourf(self._lons, self._lats, c_img, num_colors=255, cmap='inferno', extent=self._extent)
else:
if np.isnan(mincbar):
im = c_ax.imshow(c_img, extent=self._extent, origin=origin, cmap=cmap, transform=self._projection, norm=self._norm)
else:
im = c_ax.imshow(c_img, extent=self._extent, origin=origin, cmap=cmap, vmin=mincbar, vmax=maxcbar, transform=self._projection, norm=self._norm)
if mode == PlotMode.CONTOUR or mode == PlotMode.MERGED:
c_ax.set_extent(self.getExtent(list(self._lats), list(self._lons)))
if mode == PlotMode.CONTOUR:
im = c_ax.contour(c_img, extent=self._extent, transform=self._projection)
if mode == PlotMode.MERGED:
if self._contour_labels:
c_ax.contour(c_img, self._contour_labels, colors='r', extent=self._extent, transform=self._projection)
else:
c_ax.contour(c_img, extent=self._extent, transform=self._projection)
if len(self._additional_polygons) > 0:
pol_lats = []
pol_lons = []
for c_polygon in self._additional_polygons:
if isinstance(c_polygon, shapely.geometry.linestring.LineString):
x,y = c_polygon.xy
elif isinstance(c_polygon, shapely.geometry.polygon.Polygon):
x, y = c_polygon.exterior.xy
pol_lats += y
pol_lons += x
c_ax.plot(x,y, transform=self._projection, c='r')
# Adds a threshold to the plot to see the polygons
c_ax.set_extent(self.getExtent(list(self._lats) + pol_lats, list(self._lons) + pol_lons, 0.5))
if self._vector_field != None:
try:
u = self._vector_field['u']
v = self._vector_field['v']
x = self._vector_field['x']
y = self._vector_field['y']
vec_keys = self._vector_field.keys()
c = 'r'
density = 1
linewidth = 3
vec_cmap = cmocean.cm.solar
if 'color' in vec_keys:
c = self._vector_field['color']
if 'density' in vec_keys:
density = self._vector_field['density']
if 'linewidth' in vec_keys:
linewidth = self._vector_field['linewidth']
if 'cmap' in vec_keys:
vec_cmap = self._vector_field['cmap']
c_ax.set_extent(self.getExtent(list(self._lats), list(self._lons)))
c_ax.streamplot(x, y, u, v, transform=self._projection, density=density, color=c,
cmap=vec_cmap, linewidth=linewidth)
except Exception as e:
print(F"Couldn't add vector field e:{e}")
gl = c_ax.gridlines(draw_labels=True, color='grey', alpha=0.5, linestyle='--')
# gl.xlabel_style = {'size': self._font_size/2, 'color': '#aaaaaa', 'weight':'bold'}
font_coords = {'size': self._font_size*.6}
gl.xlabel_style = font_coords
gl.ylabel_style = font_coords
gl.top_labels = False
gl.right_labels = False
return im
def get_proper_size(self, rows, cols):
"""
Obtains the proper size for a figure.
:param rows: how many rows will the figure have
:param cols: how many colswill the figure have
:param prop: Proportion is the proportion to use w/h
:return:
"""
if rows == 1:
return self._figsize * cols * self._fig_prop, self._figsize
else:
return self._figsize * cols * self._fig_prop, self._figsize * rows
def _close_figure(self):
"""Depending on what is disp_images, the figures are displayed or just closed"""
if self._disp_images:
plt.show()
else:
plt.close()
def getExtent(self, lats, lons, expand_ext=0.0):
'''
Obtains the bbox of the coordinates. If included threshold then increases the bbox in all directions with that thres
Args:
lats:
lons:
inc_threshold:
Returns:
'''
minLat = np.amin(lats) - expand_ext
maxLat = | np.amax(lats) | 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 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\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) | numpy.ones_like |
#!/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) | 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) | numpy.ones_like |
# -*- coding: utf-8 -*-
import argparse
import os
import shutil
import time
import numpy as np
import random
from collections import OrderedDict
import torch
import torch.backends.cudnn as cudnn
from callbacks import AverageMeter
from data_utils.causal_data_loader_frames import VideoFolder
from utils import save_results
from tqdm import tqdm
parser = argparse.ArgumentParser(description='Counterfactual CAR')
# Path, dataset and log related arguments
parser.add_argument('--root_frames', type=str, default='/mnt/data1/home/sunpengzhan/sth-sth-v2/',
help='path to the folder with frames')
parser.add_argument('--json_data_train', type=str, default='../data/dataset_splits/compositional/train.json',
help='path to the json file with train video meta data')
parser.add_argument('--json_data_val', type=str, default='../data/dataset_splits/compositional/validation.json',
help='path to the json file with validation video meta data')
parser.add_argument('--json_file_labels', type=str, default='../data/dataset_splits/compositional/labels.json',
help='path to the json file with ground truth labels')
parser.add_argument('--dataset', default='smth_smth',
help='which dataset to train')
parser.add_argument('--logname', default='my_method',
help='name of the experiment for checkpoints and logs')
parser.add_argument('--print_freq', '-p', default=20, type=int,
metavar='N', help='print frequency (default: 20)')
parser.add_argument('--ckpt', default='./ckpt',
help='folder to output checkpoints')
parser.add_argument('--resume_vision', default='', type=str, metavar='PATH',
help='path to latest checkpoint (default: none)')
parser.add_argument('--resume_coord', default='', type=str, metavar='PATH',
help='path to latest checkpoint (default: none)')
parser.add_argument('--resume_fusion', default='', type=str, metavar='PATH',
help='path to latest checkpoint (default: none)')
# model, image&feature dim and training related arguments
parser.add_argument('--model_vision', default='rgb_roi')
parser.add_argument('--model_coord', default='interaction')
parser.add_argument('--model_fusion', default='concat_fusion')
parser.add_argument('--fusion_function', default='fused_sum', type=str,
help='function for fusing activations from each branch')
parser.add_argument('--img_feature_dim', default=512, type=int, metavar='N',
help='intermediate feature dimension for image-based features')
parser.add_argument('--coord_feature_dim', default=512, type=int, metavar='N',
help='intermediate feature dimension for coord-based features')
parser.add_argument('--size', default=224, type=int, metavar='N',
help='primary image input size')
parser.add_argument('--num_boxes', default=4, type=int,
help='num of boxes for each image')
parser.add_argument('--num_frames', default=16, type=int,
help='num of frames for the model')
parser.add_argument('--num_classes', default=174, type=int,
help='num of class in the model')
parser.add_argument('--epochs', default=30, type=int, metavar='N',
help='number of total epochs to run')
parser.add_argument('--start_epoch', default=None, type=int, metavar='N',
help='manual epoch number (useful on restarts)')
parser.add_argument('--batch_size', '-b', default=16, type=int,
metavar='N', help='mini-batch size')
parser.add_argument('--lr', '--learning-rate', default=0.01, type=float,
metavar='LR', help='initial learning rate')
parser.add_argument('--lr_steps', default=[24, 35, 45], type=float, nargs="+",
metavar='LRSteps', help='epochs to decay learning rate by 10')
parser.add_argument('--momentum', default=0.9, type=float, metavar='M',
help='momentum')
parser.add_argument('--weight_decay', '--wd', default=0.0001, type=float,
metavar='W', help='weight decay (default: 1e-4)')
parser.add_argument('--clip_gradient', '-cg', default=5, type=float,
metavar='W', help='gradient norm clipping (default: 5)')
parser.add_argument('--search_stride', type=int, default=5, help='test performance every n strides')
# train mode, hardware setting and others related arguments
parser.add_argument('-j', '--workers', default=4, type=int, metavar='N',
help='number of data loading workers (default: 4)')
parser.add_argument('-e', '--evaluate', dest='evaluate', action='store_true',
help='evaluate model on validation set')
parser.add_argument('--cf_inference_group', action='store_true', help='counterfactual inference model on validation set')
parser.add_argument('--parallel', default=True, type=bool,
help='whether or not train with multi GPUs')
parser.add_argument('--gpu_index', type=str, default='0, 1, 2, 3', help='the index of gpu you want to use')
best_loss = 1000000
def main():
global args, best_loss
args = parser.parse_args()
os.environ['CUDA_VISIBLE_DEVICES'] = args.gpu_index
print(args)
# create vision model
if args.model_vision == 'global_i3d':
from model.model_lib import VideoGlobalModel as RGBModel
print('global_i3d loaded!!')
elif args.model_vision == 'rgb_roi':
from model.model_lib import BboxVisualModel as RGBModel
print('rgb_roi loaded!!')
else:
print("no such a vision model!")
# create coord model
if args.model_coord == 'interaction':
from model.model_lib import BboxInteractionLatentModel as BboxModel
print('interaction loaded!!')
else:
print("no such a coordinate model!")
# create fusion model
if args.model_fusion == 'concat_fusion':
from model.model_lib import ConcatFusionModel as FusionModel
print('concat_fusion loaded!!')
else:
print('no such a fusion model!')
# load model branch
vision_model = RGBModel(args)
coord_model = BboxModel(args)
fusion_model = FusionModel(args)
# create the fusion function for the activation of three branches
if args.fusion_function == 'fused_sum':
from fusion_function import logsigsum as fusion_func
print('fused_sum loaded!!')
elif args.fusion_function == 'naive_sum':
from fusion_function import naivesum as fusion_func
print('naive_sum loaded!!')
else:
print('no such a fusion function!')
fusion_function = fusion_func()
if args.parallel:
vision_model = torch.nn.DataParallel(vision_model).cuda()
coord_model = torch.nn.DataParallel(coord_model).cuda()
fusion_model = torch.nn.DataParallel(fusion_model).cuda()
else:
vision_model = vision_model.cuda()
coord_model = coord_model.cuda()
fusion_model = fusion_model.cuda()
# optionally resume vision model from a checkpoint
if args.resume_vision:
assert os.path.isfile(args.resume_vision), "No checkpoint found at '{}'".format(args.resume_vision)
print("=> loading checkpoint '{}'".format(args.resume_vision))
checkpoint = torch.load(args.resume_vision)
if args.start_epoch is None:
args.start_epoch = checkpoint['epoch']
best_loss = checkpoint['best_loss']
vision_model.load_state_dict(checkpoint['state_dict'])
print("=> loaded checkpoint '{}' (epoch {})"
.format(args.resume_vision, checkpoint['epoch']))
# optionally resume coord model from a checkpoint
if args.resume_coord:
assert os.path.isfile(args.resume_coord), "No checkpoint found at '{}'".format(args.resume_coord)
print("=> loading checkpoint '{}'".format(args.resume_coord))
checkpoint = torch.load(args.resume_coord)
if args.start_epoch is None:
args.start_epoch = checkpoint['epoch']
best_loss = checkpoint['best_loss']
coord_model.load_state_dict(checkpoint['state_dict'])
print("=> loaded checkpoint '{}' (epoch {})"
.format(args.resume_coord, checkpoint['epoch']))
if args.resume_fusion:
assert os.path.isfile(args.resume_fusion), "No checkpoint found at '{}'".format(args.resume_fusion)
print("=> loading checkpoint '{}'".format(args.resume_fusion))
checkpoint = torch.load(args.resume_fusion)
if args.start_epoch is None:
args.start_epoch = checkpoint['epoch']
best_loss = checkpoint['best_loss']
fusion_model.load_state_dict(checkpoint['state_dict'])
print("=> loaded checkpoint '{}' (epoch {})"
.format(args.resume_fusion, checkpoint['epoch']))
if args.start_epoch is None:
args.start_epoch = 0
cudnn.benchmark = True
# create training and validation dataset
dataset_train = VideoFolder(root=args.root_frames,
num_boxes=args.num_boxes,
file_input=args.json_data_train,
file_labels=args.json_file_labels,
frames_duration=args.num_frames,
args=args,
is_val=False,
if_augment=True,
)
dataset_val = VideoFolder(root=args.root_frames,
num_boxes=args.num_boxes,
file_input=args.json_data_val,
file_labels=args.json_file_labels,
frames_duration=args.num_frames,
args=args,
is_val=True,
if_augment=True,
)
# create training and validation loader
train_loader = torch.utils.data.DataLoader(
dataset_train,
batch_size=args.batch_size, shuffle=True,
num_workers=args.workers, drop_last=True,
pin_memory=True
)
val_loader = torch.utils.data.DataLoader(
dataset_val, drop_last=True,
batch_size=args.batch_size, shuffle=False,
num_workers=args.workers, pin_memory=False
)
model_list = [vision_model, coord_model, fusion_model]
optimizer_vision = torch.optim.SGD(filter(lambda p: p.requires_grad, vision_model.parameters()),
momentum=args.momentum, lr=args.lr, weight_decay=args.weight_decay)
optimizer_coord = torch.optim.SGD(filter(lambda p: p.requires_grad, coord_model.parameters()),
momentum=args.momentum, lr=args.lr, weight_decay=args.weight_decay)
optimizer_fusion = torch.optim.SGD(filter(lambda p: p.requires_grad, fusion_model.parameters()),
momentum=args.momentum, lr=args.lr, weight_decay=args.weight_decay)
optimizer_list = [optimizer_vision, optimizer_coord, optimizer_fusion]
criterion = torch.nn.CrossEntropyLoss()
search_list = | np.linspace(0.0, 1.0, 11) | numpy.linspace |
import numpy as np
from skimage.transform import resize
from skimage import measure
from skimage.measure import regionprops
class OCROnObjects():
def __init__(self, license_plate):
character_objects = self.identify_boundary_objects(license_plate)
self.get_regions(character_objects, license_plate)
def identify_boundary_objects(self, a_license_plate):
labelImage = measure.label(a_license_plate)
character_dimensions = (0.4*a_license_plate.shape[0], 0.85*a_license_plate.shape[0], 0.04*a_license_plate.shape[1], 0.15*a_license_plate.shape[1])
minHeight, maxHeight, minWidth, maxWidth = character_dimensions
regionLists = regionprops(labelImage)
return regionLists
def get_regions(self, character_objects, a_license_plate):
"""
used to map out regions where the license plate charcters are
the principle of connected component analysis and labelling
were used
Parameters:
-----------
a_license_plate: 2D numpy binary image of the license plate
Returns:
--------
a dictionary containing the index
fullscale: 3D array containig 2D array of each character
columnsVal: 1D array the starting column of each character
coordinates:
"""
cord = []
counter=0
column_list = []
character_dimensions = (0.35*a_license_plate.shape[0], 0.60*a_license_plate.shape[0], 0.05*a_license_plate.shape[1], 0.15*a_license_plate.shape[1])
minHeight, maxHeight, minWidth, maxWidth = character_dimensions
for regions in character_objects:
minimumRow, minimumCol, maximumRow, maximumCol = regions.bbox
character_height = maximumRow - minimumRow
character_width = maximumCol - minimumCol
roi = a_license_plate[minimumRow:maximumRow, minimumCol:maximumCol]
if character_height > minHeight and character_height < maxHeight and character_width > minWidth and character_width < maxWidth:
if counter == 0:
samples = resize(roi, (20,20))
cord.append(regions.bbox)
counter += 1
elif counter == 1:
roismall = resize(roi, (20,20))
samples = | np.concatenate((samples[None,:,:], roismall[None,:,:]), axis=0) | numpy.concatenate |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = | np.asarray(previous_emb) | numpy.asarray |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
# coding=utf-8
import logging
import traceback
from os import makedirs
from os.path import exists, join
from textwrap import fill
import matplotlib.patheffects as PathEffects
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
from koino.plot import big_square, default_alpha
from matplotlib import cm
from ..utils.base import jaccard
def plot_silhouette(
X, figure_fp, n_clusters, silhouette_values, cluster_labels, silhouette_avg
):
# Create a subplot with 1 row and 2 columns
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(26, 10))
# The 1st subplot is the silhouette plot
# The silhouette coefficient can range from -1, 1 but here all
# lie within [-0.1, 1]
ax1.set_xlim([-0.1, 1])
# The (n_clusters+1)*10 is for inserting blank space between silhouette
# plots of individual clusters, to demarcate them clearly.
ax1.set_ylim([0, len(X) + (n_clusters + 1) * 10])
y_lower = 10
for k in range(n_clusters):
# Aggregate the silhouette scores for samples belonging to
# cluster i, and sort them
ith_cluster_silhouette_values = np.sort(silhouette_values[cluster_labels == k])
size_cluster_i = ith_cluster_silhouette_values.shape[0]
y_upper = y_lower + size_cluster_i
color = cm.spectral(float(k) / n_clusters)
ax1.fill_betweenx(
np.arange(y_lower, y_upper),
0,
ith_cluster_silhouette_values,
facecolor=color,
edgecolor=color,
alpha=default_alpha,
)
# Label the silhouette plots with their cluster numbers at the
# middle
ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(k))
# Compute the new y_lower for next plot
y_lower = y_upper + 10 # 10 for the 0 samples
ax1.set_title("The silhouette plot for the various clusters.")
ax1.set_xlabel("The silhouette coefficient values")
ax1.set_ylabel("Cluster label")
# The vertical line for average silhouette score of all the values
ax1.axvline(x=silhouette_avg, color="red", linestyle="--")
ax1.set_yticks([]) # Clear the yaxis labels / ticks
ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
# Construct cluster
# 2nd Plot showing the actual clusters formed
colors = cm.spectral(cluster_labels.astype(float) / n_clusters)
# colors = y
ax2.scatter(X[:, 0], X[:, 1], marker=".", s=20, lw=0, alpha=default_alpha, c=colors)
ax2.set_title("The visualization of the clustered data.")
ax2.set_xlabel("Feature space for the 1st feature")
ax2.set_ylabel("Feature space for the 2nd feature")
plt.suptitle(
("Silhouette analysis for KMeans " "with n_clusters = %d" % n_clusters),
fontsize=14,
fontweight="bold",
)
plt.savefig(figure_fp)
plt.close()
plt.clf()
def plot_cluster_assignments(
X, y, n_clusters, figures_dir, transparent=False, cluster_names=None, title=""
):
"""Clustering assignments scatter plot
Notes
-----
Can use mean or median to fix cluster centroid coordinates."""
if cluster_names is None:
cluster_names = ["Cluster {}".format(i + 1) for i in range(n_clusters)]
# We first reorder the data points according to the centroids labels
X = np.vstack([X[y == i] for i in range(n_clusters)])
y = np.hstack([y[y == i] for i in range(n_clusters)])
# Choose a color palette with seaborn.
palette = np.array(sns.color_palette("hls", n_clusters))
fig, ax = plt.subplots(figsize=big_square)
# for i in range(n_clusters):
# mask = y == i
# ax.scatter(X[mask, 0], X[mask, 1], lw=0, s=20, c=palette[i],
# label=cluster_names[i])
ax.set_title(title)
ax.scatter(X[:, 0], X[:, 1], lw=0, s=20, c=palette[y.astype(np.int)])
ax.axis("off")
# Add the labels for each cluster.
for i in range(n_clusters):
# Position of each label.
samples = | np.atleast_2d(X[y == i, :2]) | numpy.atleast_2d |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones |
"""Test the search module"""
from collections.abc import Iterable, Sized
from io import StringIO
from itertools import chain, product
from functools import partial
import pickle
import sys
from types import GeneratorType
import re
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.fixes import sp_version
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_warns_message
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._mocking import CheckingClassifier, MockDataFrame
from scipy.stats import bernoulli, expon, uniform
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.base import clone
from sklearn.exceptions import NotFittedError
from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_multilabel_classification
from sklearn.model_selection import fit_grid_point
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import LeaveOneGroupOut
from sklearn.model_selection import LeavePGroupsOut
from sklearn.model_selection import GroupKFold
from sklearn.model_selection import GroupShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.model_selection import ParameterGrid
from sklearn.model_selection import ParameterSampler
from sklearn.model_selection._search import BaseSearchCV
from sklearn.model_selection._validation import FitFailedWarning
from sklearn.svm import LinearSVC, SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.tree import DecisionTreeClassifier
from sklearn.cluster import KMeans
from sklearn.neighbors import KernelDensity
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import f1_score
from sklearn.metrics import recall_score
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.metrics import roc_auc_score
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression
from sklearn.experimental import enable_hist_gradient_boosting # noqa
from sklearn.ensemble import HistGradientBoostingClassifier
from sklearn.model_selection.tests.common import OneTimeSplitter
# Neither of the following two estimators inherit from BaseEstimator,
# to test hyperparameter search on user-defined classifiers.
class MockClassifier:
"""Dummy classifier to test the parameter search algorithms"""
def __init__(self, foo_param=0):
self.foo_param = foo_param
def fit(self, X, Y):
assert len(X) == len(Y)
self.classes_ = np.unique(Y)
return self
def predict(self, T):
return T.shape[0]
def transform(self, X):
return X + self.foo_param
def inverse_transform(self, X):
return X - self.foo_param
predict_proba = predict
predict_log_proba = predict
decision_function = predict
def score(self, X=None, Y=None):
if self.foo_param > 1:
score = 1.
else:
score = 0.
return score
def get_params(self, deep=False):
return {'foo_param': self.foo_param}
def set_params(self, **params):
self.foo_param = params['foo_param']
return self
class LinearSVCNoScore(LinearSVC):
"""An LinearSVC classifier that has no score method."""
@property
def score(self):
raise AttributeError
X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
y = np.array([1, 1, 2, 2])
def assert_grid_iter_equals_getitem(grid):
assert list(grid) == [grid[i] for i in range(len(grid))]
@pytest.mark.parametrize("klass", [ParameterGrid,
partial(ParameterSampler, n_iter=10)])
@pytest.mark.parametrize(
"input, error_type, error_message",
[(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'),
([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'),
({'foo': 0}, TypeError, "Parameter.* value is not iterable .*"
r"\(key='foo', value=0\)")]
)
def test_validate_parameter_input(klass, input, error_type, error_message):
with pytest.raises(error_type, match=error_message):
klass(input)
def test_parameter_grid():
# Test basic properties of ParameterGrid.
params1 = {"foo": [1, 2, 3]}
grid1 = ParameterGrid(params1)
assert isinstance(grid1, Iterable)
assert isinstance(grid1, Sized)
assert len(grid1) == 3
assert_grid_iter_equals_getitem(grid1)
params2 = {"foo": [4, 2],
"bar": ["ham", "spam", "eggs"]}
grid2 = ParameterGrid(params2)
assert len(grid2) == 6
# loop to assert we can iterate over the grid multiple times
for i in range(2):
# tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2)
points = set(tuple(chain(*(sorted(p.items())))) for p in grid2)
assert (points ==
set(("bar", x, "foo", y)
for x, y in product(params2["bar"], params2["foo"])))
assert_grid_iter_equals_getitem(grid2)
# Special case: empty grid (useful to get default estimator settings)
empty = ParameterGrid({})
assert len(empty) == 1
assert list(empty) == [{}]
assert_grid_iter_equals_getitem(empty)
assert_raises(IndexError, lambda: empty[1])
has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}])
assert len(has_empty) == 4
assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}]
assert_grid_iter_equals_getitem(has_empty)
def test_grid_search():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3)
# make sure it selects the smallest parameter in case of ties
old_stdout = sys.stdout
sys.stdout = StringIO()
grid_search.fit(X, y)
sys.stdout = old_stdout
assert grid_search.best_estimator_.foo_param == 2
assert_array_equal(grid_search.cv_results_["param_foo_param"].data,
[1, 2, 3])
# Smoke test the score etc:
grid_search.score(X, y)
grid_search.predict_proba(X)
grid_search.decision_function(X)
grid_search.transform(X)
# Test exception handling on scoring
grid_search.scoring = 'sklearn'
assert_raises(ValueError, grid_search.fit, X, y)
def test_grid_search_pipeline_steps():
# check that parameters that are estimators are cloned before fitting
pipe = Pipeline([('regressor', LinearRegression())])
param_grid = {'regressor': [LinearRegression(), Ridge()]}
grid_search = GridSearchCV(pipe, param_grid, cv=2)
grid_search.fit(X, y)
regressor_results = grid_search.cv_results_['param_regressor']
assert isinstance(regressor_results[0], LinearRegression)
assert isinstance(regressor_results[1], Ridge)
assert not hasattr(regressor_results[0], 'coef_')
assert not hasattr(regressor_results[1], 'coef_')
assert regressor_results[0] is not grid_search.best_estimator_
assert regressor_results[1] is not grid_search.best_estimator_
# check that we didn't modify the parameter grid that was passed
assert not hasattr(param_grid['regressor'][0], 'coef_')
assert not hasattr(param_grid['regressor'][1], 'coef_')
@pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV])
def test_SearchCV_with_fit_params(SearchCV):
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(expected_fit_params=['spam', 'eggs'])
searcher = SearchCV(
clf, {'foo_param': [1, 2, 3]}, cv=2, error_score="raise"
)
# The CheckingClassifier generates an assertion error if
# a parameter is missing or has length != len(X).
err_msg = r"Expected fit parameter\(s\) \['eggs'\] not seen."
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(10))
err_msg = "Fit parameter spam has length 1; expected"
with pytest.raises(AssertionError, match=err_msg):
searcher.fit(X, y, spam=np.ones(1), eggs=np.zeros(10))
searcher.fit(X, y, spam=np.ones(10), eggs=np.zeros(10))
@ignore_warnings
def test_grid_search_no_score():
# Test grid-search on classifier that has no score function.
clf = LinearSVC(random_state=0)
X, y = make_blobs(random_state=0, centers=2)
Cs = [.1, 1, 10]
clf_no_score = LinearSVCNoScore(random_state=0)
grid_search = GridSearchCV(clf, {'C': Cs}, scoring='accuracy')
grid_search.fit(X, y)
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs},
scoring='accuracy')
# smoketest grid search
grid_search_no_score.fit(X, y)
# check that best params are equal
assert grid_search_no_score.best_params_ == grid_search.best_params_
# check that we can call score and that it gives the correct result
assert grid_search.score(X, y) == grid_search_no_score.score(X, y)
# giving no scoring function raises an error
grid_search_no_score = GridSearchCV(clf_no_score, {'C': Cs})
assert_raise_message(TypeError, "no scoring", grid_search_no_score.fit,
[[1]])
def test_grid_search_score_method():
X, y = make_classification(n_samples=100, n_classes=2, flip_y=.2,
random_state=0)
clf = LinearSVC(random_state=0)
grid = {'C': [.1]}
search_no_scoring = GridSearchCV(clf, grid, scoring=None).fit(X, y)
search_accuracy = GridSearchCV(clf, grid, scoring='accuracy').fit(X, y)
search_no_score_method_auc = GridSearchCV(LinearSVCNoScore(), grid,
scoring='roc_auc'
).fit(X, y)
search_auc = GridSearchCV(clf, grid, scoring='roc_auc').fit(X, y)
# Check warning only occurs in situation where behavior changed:
# estimator requires score method to compete with scoring parameter
score_no_scoring = search_no_scoring.score(X, y)
score_accuracy = search_accuracy.score(X, y)
score_no_score_auc = search_no_score_method_auc.score(X, y)
score_auc = search_auc.score(X, y)
# ensure the test is sane
assert score_auc < 1.0
assert score_accuracy < 1.0
assert score_auc != score_accuracy
assert_almost_equal(score_accuracy, score_no_scoring)
assert_almost_equal(score_auc, score_no_score_auc)
def test_grid_search_groups():
# Check if ValueError (when groups is None) propagates to GridSearchCV
# And also check if groups is correctly passed to the cv object
rng = np.random.RandomState(0)
X, y = make_classification(n_samples=15, n_classes=2, random_state=0)
groups = rng.randint(0, 3, 15)
clf = LinearSVC(random_state=0)
grid = {'C': [1]}
group_cvs = [LeaveOneGroupOut(), LeavePGroupsOut(2),
GroupKFold(n_splits=3), GroupShuffleSplit()]
for cv in group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
assert_raise_message(ValueError,
"The 'groups' parameter should not be None.",
gs.fit, X, y)
gs.fit(X, y, groups=groups)
non_group_cvs = [StratifiedKFold(), StratifiedShuffleSplit()]
for cv in non_group_cvs:
gs = GridSearchCV(clf, grid, cv=cv)
# Should not raise an error
gs.fit(X, y)
def test_classes__property():
# Test that classes_ property matches best_estimator_.classes_
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
Cs = [.1, 1, 10]
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
grid_search.fit(X, y)
assert_array_equal(grid_search.best_estimator_.classes_,
grid_search.classes_)
# Test that regressors do not have a classes_ attribute
grid_search = GridSearchCV(Ridge(), {'alpha': [1.0, 2.0]})
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute before it's fit
grid_search = GridSearchCV(LinearSVC(random_state=0), {'C': Cs})
assert not hasattr(grid_search, 'classes_')
# Test that the grid searcher has no classes_ attribute without a refit
grid_search = GridSearchCV(LinearSVC(random_state=0),
{'C': Cs}, refit=False)
grid_search.fit(X, y)
assert not hasattr(grid_search, 'classes_')
def test_trivial_cv_results_attr():
# Test search over a "grid" with only one point.
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1]}, cv=3)
grid_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
random_search = RandomizedSearchCV(clf, {'foo_param': [0]}, n_iter=1, cv=3)
random_search.fit(X, y)
assert hasattr(grid_search, "cv_results_")
def test_no_refit():
# Test that GSCV can be used for model selection alone without refitting
clf = MockClassifier()
for scoring in [None, ['accuracy', 'precision']]:
grid_search = GridSearchCV(
clf, {'foo_param': [1, 2, 3]}, refit=False, cv=3
)
grid_search.fit(X, y)
assert not hasattr(grid_search, "best_estimator_") and \
hasattr(grid_search, "best_index_") and \
hasattr(grid_search, "best_params_")
# Make sure the functions predict/transform etc raise meaningful
# error messages
for fn_name in ('predict', 'predict_proba', 'predict_log_proba',
'transform', 'inverse_transform'):
assert_raise_message(NotFittedError,
('refit=False. %s is available only after '
'refitting on the best parameters'
% fn_name), getattr(grid_search, fn_name), X)
# Test that an invalid refit param raises appropriate error messages
for refit in ["", 5, True, 'recall', 'accuracy']:
assert_raise_message(ValueError, "For multi-metric scoring, the "
"parameter refit must be set to a scorer key",
GridSearchCV(clf, {}, refit=refit,
scoring={'acc': 'accuracy',
'prec': 'precision'}
).fit,
X, y)
def test_grid_search_error():
# Test that grid search will capture errors on data with different length
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, X_[:180], y_)
def test_grid_search_one_grid_point():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
param_dict = {"C": [1.0], "kernel": ["rbf"], "gamma": [0.1]}
clf = SVC(gamma='auto')
cv = GridSearchCV(clf, param_dict)
cv.fit(X_, y_)
clf = SVC(C=1.0, kernel="rbf", gamma=0.1)
clf.fit(X_, y_)
assert_array_equal(clf.dual_coef_, cv.best_estimator_.dual_coef_)
def test_grid_search_when_param_grid_includes_range():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = None
grid_search = GridSearchCV(clf, {'foo_param': range(1, 4)}, cv=3)
grid_search.fit(X, y)
assert grid_search.best_estimator_.foo_param == 2
def test_grid_search_bad_param_grid():
param_dict = {"C": 1}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'int'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": []}
clf = SVC()
assert_raise_message(
ValueError,
"Parameter values for parameter (C) need to be a non-empty sequence.",
GridSearchCV, clf, param_dict)
param_dict = {"C": "1,2,3"}
clf = SVC(gamma='auto')
assert_raise_message(
ValueError,
"Parameter grid for parameter (C) needs to"
" be a list or numpy array, but got (<class 'str'>)."
" Single values need to be wrapped in a list"
" with one element.",
GridSearchCV, clf, param_dict)
param_dict = {"C": np.ones((3, 2))}
clf = SVC()
assert_raises(ValueError, GridSearchCV, clf, param_dict)
def test_grid_search_sparse():
# Test that grid search works with both dense and sparse matrices
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(X_[:180].tocoo(), y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert np.mean(y_pred == y_pred2) >= .9
assert C == C2
def test_grid_search_sparse_scoring():
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred = cv.predict(X_[180:])
C = cv.best_estimator_.C
X_ = sp.csr_matrix(X_)
clf = LinearSVC()
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring="f1")
cv.fit(X_[:180], y_[:180])
y_pred2 = cv.predict(X_[180:])
C2 = cv.best_estimator_.C
assert_array_equal(y_pred, y_pred2)
assert C == C2
# Smoke test the score
# np.testing.assert_allclose(f1_score(cv.predict(X_[:180]), y[:180]),
# cv.score(X_[:180], y[:180]))
# test loss where greater is worse
def f1_loss(y_true_, y_pred_):
return -f1_score(y_true_, y_pred_)
F1Loss = make_scorer(f1_loss, greater_is_better=False)
cv = GridSearchCV(clf, {'C': [0.1, 1.0]}, scoring=F1Loss)
cv.fit(X_[:180], y_[:180])
y_pred3 = cv.predict(X_[180:])
C3 = cv.best_estimator_.C
assert C == C3
assert_array_equal(y_pred, y_pred3)
def test_grid_search_precomputed_kernel():
# Test that grid search works when the input features are given in the
# form of a precomputed kernel matrix
X_, y_ = make_classification(n_samples=200, n_features=100, random_state=0)
# compute the training kernel matrix corresponding to the linear kernel
K_train = np.dot(X_[:180], X_[:180].T)
y_train = y_[:180]
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
cv.fit(K_train, y_train)
assert cv.best_score_ >= 0
# compute the test kernel matrix
K_test = np.dot(X_[180:], X_[:180].T)
y_test = y_[180:]
y_pred = cv.predict(K_test)
assert np.mean(y_pred == y_test) >= 0
# test error is raised when the precomputed kernel is not array-like
# or sparse
assert_raises(ValueError, cv.fit, K_train.tolist(), y_train)
def test_grid_search_precomputed_kernel_error_nonsquare():
# Test that grid search returns an error with a non-square precomputed
# training kernel matrix
K_train = np.zeros((10, 20))
y_train = np.ones((10, ))
clf = SVC(kernel='precomputed')
cv = GridSearchCV(clf, {'C': [0.1, 1.0]})
assert_raises(ValueError, cv.fit, K_train, y_train)
class BrokenClassifier(BaseEstimator):
"""Broken classifier that cannot be fit twice"""
def __init__(self, parameter=None):
self.parameter = parameter
def fit(self, X, y):
assert not hasattr(self, 'has_been_fit_')
self.has_been_fit_ = True
def predict(self, X):
return np.zeros(X.shape[0])
@ignore_warnings
def test_refit():
# Regression test for bug in refitting
# Simulates re-fitting a broken estimator; this used to break with
# sparse SVMs.
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = GridSearchCV(BrokenClassifier(), [{'parameter': [0, 1]}],
scoring="precision", refit=True)
clf.fit(X, y)
def test_refit_callable():
"""
Test refit=callable, which adds flexibility in identifying the
"best" estimator.
"""
def refit_callable(cv_results):
"""
A dummy function tests `refit=callable` interface.
Return the index of a model that has the least
`mean_test_score`.
"""
# Fit a dummy clf with `refit=True` to get a list of keys in
# clf.cv_results_.
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring='precision', refit=True)
clf.fit(X, y)
# Ensure that `best_index_ != 0` for this dummy clf
assert clf.best_index_ != 0
# Assert every key matches those in `cv_results`
for key in clf.cv_results_.keys():
assert key in cv_results
return cv_results['mean_test_score'].argmin()
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring='precision', refit=refit_callable)
clf.fit(X, y)
assert clf.best_index_ == 0
# Ensure `best_score_` is disabled when using `refit=callable`
assert not hasattr(clf, 'best_score_')
def test_refit_callable_invalid_type():
"""
Test implementation catches the errors when 'best_index_' returns an
invalid result.
"""
def refit_callable_invalid_type(cv_results):
"""
A dummy function tests when returned 'best_index_' is not integer.
"""
return None
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.1, 1]},
scoring='precision', refit=refit_callable_invalid_type)
with pytest.raises(TypeError,
match='best_index_ returned is not an integer'):
clf.fit(X, y)
@pytest.mark.parametrize('out_bound_value', [-1, 2])
@pytest.mark.parametrize('search_cv', [RandomizedSearchCV, GridSearchCV])
def test_refit_callable_out_bound(out_bound_value, search_cv):
"""
Test implementation catches the errors when 'best_index_' returns an
out of bound result.
"""
def refit_callable_out_bound(cv_results):
"""
A dummy function tests when returned 'best_index_' is out of bounds.
"""
return out_bound_value
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
clf = search_cv(LinearSVC(random_state=42), {'C': [0.1, 1]},
scoring='precision', refit=refit_callable_out_bound)
with pytest.raises(IndexError, match='best_index_ index out of range'):
clf.fit(X, y)
def test_refit_callable_multi_metric():
"""
Test refit=callable in multiple metric evaluation setting
"""
def refit_callable(cv_results):
"""
A dummy function tests `refit=callable` interface.
Return the index of a model that has the least
`mean_test_prec`.
"""
assert 'mean_test_prec' in cv_results
return cv_results['mean_test_prec'].argmin()
X, y = make_classification(n_samples=100, n_features=4,
random_state=42)
scoring = {'Accuracy': make_scorer(accuracy_score), 'prec': 'precision'}
clf = GridSearchCV(LinearSVC(random_state=42), {'C': [0.01, 0.1, 1]},
scoring=scoring, refit=refit_callable)
clf.fit(X, y)
assert clf.best_index_ == 0
# Ensure `best_score_` is disabled when using `refit=callable`
assert not hasattr(clf, 'best_score_')
def test_gridsearch_nd():
# Pass X as list in GridSearchCV
X_4d = np.arange(10 * 5 * 3 * 2).reshape(10, 5, 3, 2)
y_3d = np.arange(10 * 7 * 11).reshape(10, 7, 11)
check_X = lambda x: x.shape[1:] == (5, 3, 2)
check_y = lambda x: x.shape[1:] == (7, 11)
clf = CheckingClassifier(
check_X=check_X, check_y=check_y, methods_to_check=["fit"],
)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]})
grid_search.fit(X_4d, y_3d).score(X, y)
assert hasattr(grid_search, "cv_results_")
def test_X_as_list():
# Pass X as list in GridSearchCV
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(
check_X=lambda x: isinstance(x, list), methods_to_check=["fit"],
)
cv = KFold(n_splits=3)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv)
grid_search.fit(X.tolist(), y).score(X, y)
assert hasattr(grid_search, "cv_results_")
def test_y_as_list():
# Pass y as list in GridSearchCV
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
clf = CheckingClassifier(
check_y=lambda x: isinstance(x, list), methods_to_check=["fit"],
)
cv = KFold(n_splits=3)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=cv)
grid_search.fit(X, y.tolist()).score(X, y)
assert hasattr(grid_search, "cv_results_")
@ignore_warnings
def test_pandas_input():
# check cross_val_score doesn't destroy pandas dataframe
types = [(MockDataFrame, MockDataFrame)]
try:
from pandas import Series, DataFrame
types.append((DataFrame, Series))
except ImportError:
pass
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
for InputFeatureType, TargetType in types:
# X dataframe, y series
X_df, y_ser = InputFeatureType(X), TargetType(y)
def check_df(x):
return isinstance(x, InputFeatureType)
def check_series(x):
return isinstance(x, TargetType)
clf = CheckingClassifier(check_X=check_df, check_y=check_series)
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]})
grid_search.fit(X_df, y_ser).score(X_df, y_ser)
grid_search.predict(X_df)
assert hasattr(grid_search, "cv_results_")
def test_unsupervised_grid_search():
# test grid-search with unsupervised estimator
X, y = make_blobs(n_samples=50, random_state=0)
km = KMeans(random_state=0, init="random", n_init=1)
# Multi-metric evaluation unsupervised
scoring = ['adjusted_rand_score', 'fowlkes_mallows_score']
for refit in ['adjusted_rand_score', 'fowlkes_mallows_score']:
grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]),
scoring=scoring, refit=refit)
grid_search.fit(X, y)
# Both ARI and FMS can find the right number :)
assert grid_search.best_params_["n_clusters"] == 3
# Single metric evaluation unsupervised
grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]),
scoring='fowlkes_mallows_score')
grid_search.fit(X, y)
assert grid_search.best_params_["n_clusters"] == 3
# Now without a score, and without y
grid_search = GridSearchCV(km, param_grid=dict(n_clusters=[2, 3, 4]))
grid_search.fit(X)
assert grid_search.best_params_["n_clusters"] == 4
def test_gridsearch_no_predict():
# test grid-search with an estimator without predict.
# slight duplication of a test from KDE
def custom_scoring(estimator, X):
return 42 if estimator.bandwidth == .1 else 0
X, _ = make_blobs(cluster_std=.1, random_state=1,
centers=[[0, 1], [1, 0], [0, 0]])
search = GridSearchCV(KernelDensity(),
param_grid=dict(bandwidth=[.01, .1, 1]),
scoring=custom_scoring)
search.fit(X)
assert search.best_params_['bandwidth'] == .1
assert search.best_score_ == 42
def test_param_sampler():
# test basic properties of param sampler
param_distributions = {"kernel": ["rbf", "linear"],
"C": uniform(0, 1)}
sampler = ParameterSampler(param_distributions=param_distributions,
n_iter=10, random_state=0)
samples = [x for x in sampler]
assert len(samples) == 10
for sample in samples:
assert sample["kernel"] in ["rbf", "linear"]
assert 0 <= sample["C"] <= 1
# test that repeated calls yield identical parameters
param_distributions = {"C": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]}
sampler = ParameterSampler(param_distributions=param_distributions,
n_iter=3, random_state=0)
assert [x for x in sampler] == [x for x in sampler]
if sp_version >= (0, 16):
param_distributions = {"C": uniform(0, 1)}
sampler = ParameterSampler(param_distributions=param_distributions,
n_iter=10, random_state=0)
assert [x for x in sampler] == [x for x in sampler]
def check_cv_results_array_types(search, param_keys, score_keys):
# Check if the search `cv_results`'s array are of correct types
cv_results = search.cv_results_
assert all(isinstance(cv_results[param], np.ma.MaskedArray)
for param in param_keys)
assert all(cv_results[key].dtype == object for key in param_keys)
assert not any(isinstance(cv_results[key], np.ma.MaskedArray)
for key in score_keys)
assert all(cv_results[key].dtype == np.float64
for key in score_keys if not key.startswith('rank'))
scorer_keys = search.scorer_.keys() if search.multimetric_ else ['score']
for key in scorer_keys:
assert cv_results['rank_test_%s' % key].dtype == np.int32
def check_cv_results_keys(cv_results, param_keys, score_keys, n_cand):
# Test the search.cv_results_ contains all the required results
assert_array_equal(sorted(cv_results.keys()),
sorted(param_keys + score_keys + ('params',)))
assert all(cv_results[key].shape == (n_cand,)
for key in param_keys + score_keys)
def test_grid_search_cv_results():
X, y = make_classification(n_samples=50, n_features=4,
random_state=42)
n_splits = 3
n_grid_points = 6
params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]),
dict(kernel=['poly', ], degree=[1, 2])]
param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel')
score_keys = ('mean_test_score', 'mean_train_score',
'rank_test_score',
'split0_test_score', 'split1_test_score',
'split2_test_score',
'split0_train_score', 'split1_train_score',
'split2_train_score',
'std_test_score', 'std_train_score',
'mean_fit_time', 'std_fit_time',
'mean_score_time', 'std_score_time')
n_candidates = n_grid_points
search = GridSearchCV(SVC(), cv=n_splits, param_grid=params,
return_train_score=True)
search.fit(X, y)
cv_results = search.cv_results_
# Check if score and timing are reasonable
assert all(cv_results['rank_test_score'] >= 1)
assert (all(cv_results[k] >= 0) for k in score_keys
if k != 'rank_test_score')
assert (all(cv_results[k] <= 1) for k in score_keys
if 'time' not in k and
k != 'rank_test_score')
# Check cv_results structure
check_cv_results_array_types(search, param_keys, score_keys)
check_cv_results_keys(cv_results, param_keys, score_keys, n_candidates)
# Check masking
cv_results = search.cv_results_
n_candidates = len(search.cv_results_['params'])
assert all((cv_results['param_C'].mask[i] and
cv_results['param_gamma'].mask[i] and
not cv_results['param_degree'].mask[i])
for i in range(n_candidates)
if cv_results['param_kernel'][i] == 'linear')
assert all((not cv_results['param_C'].mask[i] and
not cv_results['param_gamma'].mask[i] and
cv_results['param_degree'].mask[i])
for i in range(n_candidates)
if cv_results['param_kernel'][i] == 'rbf')
def test_random_search_cv_results():
X, y = make_classification(n_samples=50, n_features=4, random_state=42)
n_splits = 3
n_search_iter = 30
params = [{'kernel': ['rbf'], 'C': expon(scale=10),
'gamma': expon(scale=0.1)},
{'kernel': ['poly'], 'degree': [2, 3]}]
param_keys = ('param_C', 'param_degree', 'param_gamma', 'param_kernel')
score_keys = ('mean_test_score', 'mean_train_score',
'rank_test_score',
'split0_test_score', 'split1_test_score',
'split2_test_score',
'split0_train_score', 'split1_train_score',
'split2_train_score',
'std_test_score', 'std_train_score',
'mean_fit_time', 'std_fit_time',
'mean_score_time', 'std_score_time')
n_cand = n_search_iter
search = RandomizedSearchCV(SVC(), n_iter=n_search_iter,
cv=n_splits,
param_distributions=params,
return_train_score=True)
search.fit(X, y)
cv_results = search.cv_results_
# Check results structure
check_cv_results_array_types(search, param_keys, score_keys)
check_cv_results_keys(cv_results, param_keys, score_keys, n_cand)
n_candidates = len(search.cv_results_['params'])
assert all((cv_results['param_C'].mask[i] and
cv_results['param_gamma'].mask[i] and
not cv_results['param_degree'].mask[i])
for i in range(n_candidates)
if cv_results['param_kernel'][i] == 'linear')
assert all((not cv_results['param_C'].mask[i] and
not cv_results['param_gamma'].mask[i] and
cv_results['param_degree'].mask[i])
for i in range(n_candidates)
if cv_results['param_kernel'][i] == 'rbf')
@pytest.mark.parametrize(
"SearchCV, specialized_params",
[(GridSearchCV, {'param_grid': {'C': [1, 10]}}),
(RandomizedSearchCV,
{'param_distributions': {'C': [1, 10]}, 'n_iter': 2})]
)
def test_search_default_iid(SearchCV, specialized_params):
# Test the IID parameter TODO: Clearly this test does something else???
# noise-free simple 2d-data
X, y = make_blobs(centers=[[0, 0], [1, 0], [0, 1], [1, 1]], random_state=0,
cluster_std=0.1, shuffle=False, n_samples=80)
# split dataset into two folds that are not iid
# first one contains data of all 4 blobs, second only from two.
mask = np.ones(X.shape[0], dtype=np.bool)
mask[np.where(y == 1)[0][::2]] = 0
mask[np.where(y == 2)[0][::2]] = 0
# this leads to perfect classification on one fold and a score of 1/3 on
# the other
# create "cv" for splits
cv = [[mask, ~mask], [~mask, mask]]
common_params = {'estimator': SVC(), 'cv': cv,
'return_train_score': True}
search = SearchCV(**common_params, **specialized_params)
search.fit(X, y)
test_cv_scores = np.array(
[search.cv_results_['split%d_test_score' % s][0]
for s in range(search.n_splits_)]
)
test_mean = search.cv_results_['mean_test_score'][0]
test_std = search.cv_results_['std_test_score'][0]
train_cv_scores = np.array(
[search.cv_results_['split%d_train_score' % s][0]
for s in range(search.n_splits_)]
)
train_mean = search.cv_results_['mean_train_score'][0]
train_std = search.cv_results_['std_train_score'][0]
assert search.cv_results_['param_C'][0] == 1
# scores are the same as above
assert_allclose(test_cv_scores, [1, 1. / 3.])
assert_allclose(train_cv_scores, [1, 1])
# Unweighted mean/std is used
assert test_mean == pytest.approx(np.mean(test_cv_scores))
assert test_std == pytest.approx(np.std(test_cv_scores))
# For the train scores, we do not take a weighted mean irrespective of
# i.i.d. or not
assert train_mean == pytest.approx(1)
assert train_std == pytest.approx(0)
def test_grid_search_cv_results_multimetric():
X, y = make_classification(n_samples=50, n_features=4, random_state=42)
n_splits = 3
params = [dict(kernel=['rbf', ], C=[1, 10], gamma=[0.1, 1]),
dict(kernel=['poly', ], degree=[1, 2])]
grid_searches = []
for scoring in ({'accuracy': make_scorer(accuracy_score),
'recall': make_scorer(recall_score)},
'accuracy', 'recall'):
grid_search = GridSearchCV(SVC(), cv=n_splits,
param_grid=params,
scoring=scoring, refit=False)
grid_search.fit(X, y)
grid_searches.append(grid_search)
compare_cv_results_multimetric_with_single(*grid_searches)
def test_random_search_cv_results_multimetric():
X, y = make_classification(n_samples=50, n_features=4, random_state=42)
n_splits = 3
n_search_iter = 30
# Scipy 0.12's stats dists do not accept seed, hence we use param grid
params = dict(C=np.logspace(-4, 1, 3),
gamma=np.logspace(-5, 0, 3, base=0.1))
for refit in (True, False):
random_searches = []
for scoring in (('accuracy', 'recall'), 'accuracy', 'recall'):
# If True, for multi-metric pass refit='accuracy'
if refit:
probability = True
refit = 'accuracy' if isinstance(scoring, tuple) else refit
else:
probability = False
clf = SVC(probability=probability, random_state=42)
random_search = RandomizedSearchCV(clf, n_iter=n_search_iter,
cv=n_splits,
param_distributions=params,
scoring=scoring,
refit=refit, random_state=0)
random_search.fit(X, y)
random_searches.append(random_search)
compare_cv_results_multimetric_with_single(*random_searches)
compare_refit_methods_when_refit_with_acc(
random_searches[0], random_searches[1], refit)
def compare_cv_results_multimetric_with_single(
search_multi, search_acc, search_rec):
"""Compare multi-metric cv_results with the ensemble of multiple
single metric cv_results from single metric grid/random search"""
assert search_multi.multimetric_
assert_array_equal(sorted(search_multi.scorer_),
('accuracy', 'recall'))
cv_results_multi = search_multi.cv_results_
cv_results_acc_rec = {re.sub('_score$', '_accuracy', k): v
for k, v in search_acc.cv_results_.items()}
cv_results_acc_rec.update({re.sub('_score$', '_recall', k): v
for k, v in search_rec.cv_results_.items()})
# Check if score and timing are reasonable, also checks if the keys
# are present
assert all((np.all(cv_results_multi[k] <= 1) for k in (
'mean_score_time', 'std_score_time', 'mean_fit_time',
'std_fit_time')))
# Compare the keys, other than time keys, among multi-metric and
# single metric grid search results. np.testing.assert_equal performs a
# deep nested comparison of the two cv_results dicts
np.testing.assert_equal({k: v for k, v in cv_results_multi.items()
if not k.endswith('_time')},
{k: v for k, v in cv_results_acc_rec.items()
if not k.endswith('_time')})
def compare_refit_methods_when_refit_with_acc(search_multi, search_acc, refit):
"""Compare refit multi-metric search methods with single metric methods"""
assert search_acc.refit == refit
if refit:
assert search_multi.refit == 'accuracy'
else:
assert not search_multi.refit
return # search cannot predict/score without refit
X, y = make_blobs(n_samples=100, n_features=4, random_state=42)
for method in ('predict', 'predict_proba', 'predict_log_proba'):
assert_almost_equal(getattr(search_multi, method)(X),
getattr(search_acc, method)(X))
assert_almost_equal(search_multi.score(X, y), search_acc.score(X, y))
for key in ('best_index_', 'best_score_', 'best_params_'):
assert getattr(search_multi, key) == getattr(search_acc, key)
def test_search_cv_results_rank_tie_breaking():
X, y = make_blobs(n_samples=50, random_state=42)
# The two C values are close enough to give similar models
# which would result in a tie of their mean cv-scores
param_grid = {'C': [1, 1.001, 0.001]}
grid_search = GridSearchCV(SVC(), param_grid=param_grid,
return_train_score=True)
random_search = RandomizedSearchCV(SVC(), n_iter=3,
param_distributions=param_grid,
return_train_score=True)
for search in (grid_search, random_search):
search.fit(X, y)
cv_results = search.cv_results_
# Check tie breaking strategy -
# Check that there is a tie in the mean scores between
# candidates 1 and 2 alone
assert_almost_equal(cv_results['mean_test_score'][0],
cv_results['mean_test_score'][1])
assert_almost_equal(cv_results['mean_train_score'][0],
cv_results['mean_train_score'][1])
assert not np.allclose(cv_results['mean_test_score'][1],
cv_results['mean_test_score'][2])
assert not np.allclose(cv_results['mean_train_score'][1],
cv_results['mean_train_score'][2])
# 'min' rank should be assigned to the tied candidates
assert_almost_equal(search.cv_results_['rank_test_score'], [1, 1, 3])
def test_search_cv_results_none_param():
X, y = [[1], [2], [3], [4], [5]], [0, 0, 0, 0, 1]
estimators = (DecisionTreeRegressor(), DecisionTreeClassifier())
est_parameters = {"random_state": [0, None]}
cv = KFold()
for est in estimators:
grid_search = GridSearchCV(est, est_parameters, cv=cv,
).fit(X, y)
assert_array_equal(grid_search.cv_results_['param_random_state'],
[0, None])
@ignore_warnings()
def test_search_cv_timing():
svc = LinearSVC(random_state=0)
X = [[1, ], [2, ], [3, ], [4, ]]
y = [0, 1, 1, 0]
gs = GridSearchCV(svc, {'C': [0, 1]}, cv=2, error_score=0)
rs = RandomizedSearchCV(svc, {'C': [0, 1]}, cv=2, error_score=0, n_iter=2)
for search in (gs, rs):
search.fit(X, y)
for key in ['mean_fit_time', 'std_fit_time']:
# NOTE The precision of time.time in windows is not high
# enough for the fit/score times to be non-zero for trivial X and y
assert np.all(search.cv_results_[key] >= 0)
assert np.all(search.cv_results_[key] < 1)
for key in ['mean_score_time', 'std_score_time']:
assert search.cv_results_[key][1] >= 0
assert search.cv_results_[key][0] == 0.0
assert np.all(search.cv_results_[key] < 1)
assert hasattr(search, "refit_time_")
assert isinstance(search.refit_time_, float)
assert search.refit_time_ >= 0
def test_grid_search_correct_score_results():
# test that correct scores are used
n_splits = 3
clf = LinearSVC(random_state=0)
X, y = make_blobs(random_state=0, centers=2)
Cs = [.1, 1, 10]
for score in ['f1', 'roc_auc']:
grid_search = GridSearchCV(clf, {'C': Cs}, scoring=score, cv=n_splits)
cv_results = grid_search.fit(X, y).cv_results_
# Test scorer names
result_keys = list(cv_results.keys())
expected_keys = (("mean_test_score", "rank_test_score") +
tuple("split%d_test_score" % cv_i
for cv_i in range(n_splits)))
assert all(np.in1d(expected_keys, result_keys))
cv = StratifiedKFold(n_splits=n_splits)
n_splits = grid_search.n_splits_
for candidate_i, C in enumerate(Cs):
clf.set_params(C=C)
cv_scores = np.array(
list(grid_search.cv_results_['split%d_test_score'
% s][candidate_i]
for s in range(n_splits)))
for i, (train, test) in enumerate(cv.split(X, y)):
clf.fit(X[train], y[train])
if score == "f1":
correct_score = f1_score(y[test], clf.predict(X[test]))
elif score == "roc_auc":
dec = clf.decision_function(X[test])
correct_score = roc_auc_score(y[test], dec)
assert_almost_equal(correct_score, cv_scores[i])
# FIXME remove test_fit_grid_point as the function will be removed on 0.25
@ignore_warnings(category=FutureWarning)
def test_fit_grid_point():
X, y = make_classification(random_state=0)
cv = StratifiedKFold()
svc = LinearSVC(random_state=0)
scorer = make_scorer(accuracy_score)
for params in ({'C': 0.1}, {'C': 0.01}, {'C': 0.001}):
for train, test in cv.split(X, y):
this_scores, this_params, n_test_samples = fit_grid_point(
X, y, clone(svc), params, train, test,
scorer, verbose=False)
est = clone(svc).set_params(**params)
est.fit(X[train], y[train])
expected_score = scorer(est, X[test], y[test])
# Test the return values of fit_grid_point
assert_almost_equal(this_scores, expected_score)
assert params == this_params
assert n_test_samples == test.size
# Should raise an error upon multimetric scorer
assert_raise_message(ValueError, "For evaluating multiple scores, use "
"sklearn.model_selection.cross_validate instead.",
fit_grid_point, X, y, svc, params, train, test,
{'score': scorer}, verbose=True)
# FIXME remove test_fit_grid_point_deprecated as
# fit_grid_point will be removed on 0.25
def test_fit_grid_point_deprecated():
X, y = make_classification(random_state=0)
svc = LinearSVC(random_state=0)
scorer = make_scorer(accuracy_score)
msg = ("fit_grid_point is deprecated in version 0.23 "
"and will be removed in version 0.25")
params = {'C': 0.1}
train, test = next(StratifiedKFold().split(X, y))
with pytest.warns(FutureWarning, match=msg):
fit_grid_point(X, y, svc, params, train, test, scorer, verbose=False)
def test_pickle():
# Test that a fit search can be pickled
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, refit=True, cv=3)
grid_search.fit(X, y)
grid_search_pickled = pickle.loads(pickle.dumps(grid_search))
assert_array_almost_equal(grid_search.predict(X),
grid_search_pickled.predict(X))
random_search = RandomizedSearchCV(clf, {'foo_param': [1, 2, 3]},
refit=True, n_iter=3, cv=3)
random_search.fit(X, y)
random_search_pickled = pickle.loads(pickle.dumps(random_search))
assert_array_almost_equal(random_search.predict(X),
random_search_pickled.predict(X))
def test_grid_search_with_multioutput_data():
# Test search with multi-output estimator
X, y = make_multilabel_classification(return_indicator=True,
random_state=0)
est_parameters = {"max_depth": [1, 2, 3, 4]}
cv = KFold()
estimators = [DecisionTreeRegressor(random_state=0),
DecisionTreeClassifier(random_state=0)]
# Test with grid search cv
for est in estimators:
grid_search = GridSearchCV(est, est_parameters, cv=cv)
grid_search.fit(X, y)
res_params = grid_search.cv_results_['params']
for cand_i in range(len(res_params)):
est.set_params(**res_params[cand_i])
for i, (train, test) in enumerate(cv.split(X, y)):
est.fit(X[train], y[train])
correct_score = est.score(X[test], y[test])
assert_almost_equal(
correct_score,
grid_search.cv_results_['split%d_test_score' % i][cand_i])
# Test with a randomized search
for est in estimators:
random_search = RandomizedSearchCV(est, est_parameters,
cv=cv, n_iter=3)
random_search.fit(X, y)
res_params = random_search.cv_results_['params']
for cand_i in range(len(res_params)):
est.set_params(**res_params[cand_i])
for i, (train, test) in enumerate(cv.split(X, y)):
est.fit(X[train], y[train])
correct_score = est.score(X[test], y[test])
assert_almost_equal(
correct_score,
random_search.cv_results_['split%d_test_score'
% i][cand_i])
def test_predict_proba_disabled():
# Test predict_proba when disabled on estimator.
X = np.arange(20).reshape(5, -1)
y = [0, 0, 1, 1, 1]
clf = SVC(probability=False)
gs = GridSearchCV(clf, {}, cv=2).fit(X, y)
assert not hasattr(gs, "predict_proba")
def test_grid_search_allows_nans():
# Test GridSearchCV with SimpleImputer
X = np.arange(20, dtype=np.float64).reshape(5, -1)
X[2, :] = np.nan
y = [0, 0, 1, 1, 1]
p = Pipeline([
('imputer', SimpleImputer(strategy='mean', missing_values=np.nan)),
('classifier', MockClassifier()),
])
GridSearchCV(p, {'classifier__foo_param': [1, 2, 3]}, cv=2).fit(X, y)
class FailingClassifier(BaseEstimator):
"""Classifier that raises a ValueError on fit()"""
FAILING_PARAMETER = 2
def __init__(self, parameter=None):
self.parameter = parameter
def fit(self, X, y=None):
if self.parameter == FailingClassifier.FAILING_PARAMETER:
raise ValueError("Failing classifier failed as required")
def predict(self, X):
return | np.zeros(X.shape[0]) | 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.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) | numpy.ones_like |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = | np.matmul(weights, train_input) | numpy.matmul |
""" Unit tests for the system interface."""
import unittest
from six import assertRaisesRegex
from six.moves import cStringIO
import numpy as np
from openmdao.api import Problem, Group, IndepVarComp, ExecComp
from openmdao.test_suite.components.options_feature_vector import VectorDoublingComp
from openmdao.utils.assert_utils import assert_rel_error, assert_warning
class TestSystem(unittest.TestCase):
def test_vector_context_managers(self):
g1 = Group()
g1.add_subsystem('Indep', IndepVarComp('a', 5.0), promotes=['a'])
g2 = g1.add_subsystem('G2', Group(), promotes=['*'])
g2.add_subsystem('C1', ExecComp('b=2*a'), promotes=['a', 'b'])
model = Group()
model.add_subsystem('G1', g1, promotes=['b'])
model.add_subsystem('Sink', ExecComp('c=2*b'), promotes=['b'])
p = Problem(model=model)
p.set_solver_print(level=0)
# Test pre-setup errors
with self.assertRaises(Exception) as cm:
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(str(cm.exception),
"Group: Cannot get vectors because setup has not yet been called.")
with self.assertRaises(Exception) as cm:
d_inputs, d_outputs, d_residuals = model.get_linear_vectors('vec')
self.assertEqual(str(cm.exception),
"Group: Cannot get vectors because setup has not yet been called.")
p.setup()
p.run_model()
# Test inputs with original values
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(inputs['G1.G2.C1.a'], 5.)
inputs, outputs, residuals = g1.get_nonlinear_vectors()
self.assertEqual(inputs['G2.C1.a'], 5.)
# Test inputs after setting a new value
inputs, outputs, residuals = g2.get_nonlinear_vectors()
inputs['C1.a'] = -1.
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(inputs['G1.G2.C1.a'], -1.)
inputs, outputs, residuals = g1.get_nonlinear_vectors()
self.assertEqual(inputs['G2.C1.a'], -1.)
# Test outputs with original values
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(outputs['G1.G2.C1.b'], 10.)
inputs, outputs, residuals = g2.get_nonlinear_vectors()
# Test outputs after setting a new value
inputs, outputs, residuals = model.get_nonlinear_vectors()
outputs['G1.G2.C1.b'] = 123.
self.assertEqual(outputs['G1.G2.C1.b'], 123.)
inputs, outputs, residuals = g2.get_nonlinear_vectors()
outputs['C1.b'] = 789.
self.assertEqual(outputs['C1.b'], 789.)
# Test residuals
inputs, outputs, residuals = model.get_nonlinear_vectors()
residuals['G1.G2.C1.b'] = 99.0
self.assertEqual(residuals['G1.G2.C1.b'], 99.0)
# Test linear
d_inputs, d_outputs, d_residuals = model.get_linear_vectors('linear')
d_outputs['G1.G2.C1.b'] = 10.
self.assertEqual(d_outputs['G1.G2.C1.b'], 10.)
# Test linear with invalid vec_name
with self.assertRaises(Exception) as cm:
d_inputs, d_outputs, d_residuals = model.get_linear_vectors('bad_name')
self.assertEqual(str(cm.exception),
"Group (<model>): There is no linear vector named %s" % 'bad_name')
def test_set_checks_shape(self):
indep = IndepVarComp()
indep.add_output('a')
indep.add_output('x', shape=(5, 1))
g1 = Group()
g1.add_subsystem('Indep', indep, promotes=['a', 'x'])
g2 = g1.add_subsystem('G2', Group(), promotes=['*'])
g2.add_subsystem('C1', ExecComp('b=2*a'), promotes=['a', 'b'])
g2.add_subsystem('C2', ExecComp('y=2*x',
x= | np.zeros((5, 1)) | numpy.zeros |
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]) | numpy.array |
'''
<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) | 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) | numpy.linspace |
# pvtrace is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# pvtrace is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as np
from external.transformations import translation_matrix, rotation_matrix
import external.transformations as tf
from Trace import Photon
from Geometry import Box, Cylinder, FinitePlane, transform_point, transform_direction, rotation_matrix_from_vector_alignment, norm
from Materials import Spectrum
def random_spherecial_vector():
# This method of calculating isotropic vectors is taken from GNU Scientific Library
LOOP = True
while LOOP:
x = -1. + 2. * np.random.uniform()
y = -1. + 2. * np.random.uniform()
s = x**2 + y**2
if s <= 1.0:
LOOP = False
z = -1. + 2. * s
a = 2 * np.sqrt(1 - s)
x = a * x
y = a * y
return np.array([x,y,z])
class SimpleSource(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, use_random_polarisation=False):
super(SimpleSource, self).__init__()
self.position = position
self.direction = direction
self.wavelength = wavelength
self.use_random_polarisation = use_random_polarisation
self.throw = 0
self.source_id = "SimpleSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
# If use_polarisation is set generate a random polarisation vector of the photon
if self.use_random_polarisation:
# Randomise rotation angle around xy-plane, the transform from +z to the direction of the photon
vec = random_spherecial_vector()
vec[2] = 0.
vec = norm(vec)
R = rotation_matrix_from_vector_alignment(self.direction, [0,0,1])
photon.polarisation = transform_direction(vec, R)
else:
photon.polarisation = None
photon.id = self.throw
self.throw = self.throw + 1
return photon
class Laser(object):
"""A light source that will generate photons of a single colour, direction and position."""
def __init__(self, position=[0,0,0], direction=[0,0,1], wavelength=555, polarisation=None):
super(Laser, self).__init__()
self.position = np.array(position)
self.direction = np.array(direction)
self.wavelength = wavelength
assert polarisation != None, "Polarisation of the Laser is not set."
self.polarisation = np.array(polarisation)
self.throw = 0
self.source_id = "LaserSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.position = np.array(self.position)
photon.direction = np.array(self.direction)
photon.active = True
photon.wavelength = self.wavelength
photon.polarisation = self.polarisation
photon.id = self.throw
self.throw = self.throw + 1
return photon
class PlanarSource(object):
"""A box that emits photons from the top surface (normal), sampled from the spectrum."""
def __init__(self, spectrum=None, wavelength=555, direction=(0,0,1), length=0.05, width=0.05):
super(PlanarSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.plane = FinitePlane(length=length, width=width)
self.length = length
self.width = width
# direction is the direction that photons are fired out of the plane in the GLOBAL FRAME.
# i.e. this is passed directly to the photon to set is's direction
self.direction = direction
self.throw = 0
self.source_id = "PlanarSource_" + str(id(self))
def translate(self, translation):
self.plane.append_transform(tf.translation_matrix(translation))
def rotate(self, angle, axis):
self.plane.append_transform(tf.rotation_matrix(angle, axis))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Create a point which is on the surface of the finite plane in it's local frame
x = np.random.uniform(0., self.length)
y = np.random.uniform(0., self.width)
local_point = (x, y, 0.)
# Transform the direciton
photon.position = transform_point(local_point, self.plane.transform)
photon.direction = self.direction
photon.active = True
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSource(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSource, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.throw = 0
self.source_id = "LensSource_" + str(id(self))
def photon(self):
photon = Photon()
photon.source = self.source_id
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
z = np.random.uniform(self.planeorigin[2],self.planeextent[2])
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[1] = self.linepoint[1] + np.random.uniform(-self.focussize,self.focussize)
focuspoint[2] = photon.position[2]
direction = focuspoint - photon.position
modulus = (direction[0]**2+direction[1]**2+direction[2]**2)**0.5
photon.direction = direction/modulus
# Wavelength
if self.spectrum != None:
photon.wavelength = self.spectrum.wavelength_at_probability(np.random.uniform())
else:
photon.wavelength = self.wavelength
return photon
class LensSourceAngle(object):
"""
A source where photons generated in a plane are focused on a line with space tolerance given by variable "focussize".
The focus line should be perpendicular to the plane normal and aligned with the z-axis.
For this lense an additional z-boost is added (Angle of incidence in z-direction).
"""
def __init__(self, spectrum = None, wavelength = 555, linepoint=(0,0,0), linedirection=(0,0,1), angle = 0, focussize = 0, planeorigin = (-1,-1,-1), planeextent = (-1,1,1)):
super(LensSourceAngle, self).__init__()
self.spectrum = spectrum
self.wavelength = wavelength
self.planeorigin = planeorigin
self.planeextent = planeextent
self.linepoint = np.array(linepoint)
self.linedirection = np.array(linedirection)
self.focussize = focussize
self.angle = angle
self.throw = 0
self.source_id = "LensSourceAngle_" + str(id(self))
def photon(self):
photon = Photon()
photon.id = self.throw
self.throw = self.throw + 1
# Position
x = np.random.uniform(self.planeorigin[0],self.planeextent[0])
y = np.random.uniform(self.planeorigin[1],self.planeextent[1])
boost = y*np.tan(self.angle)
z = np.random.uniform(self.planeorigin[2],self.planeextent[2]) - boost
photon.position = np.array((x,y,z))
# Direction
focuspoint = np.array((0.,0.,0.))
focuspoint[0] = self.linepoint[0] + | np.random.uniform(-self.focussize,self.focussize) | numpy.random.uniform |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
import os
import numpy as np
import pandas as pd
import tensorflow as tf
from keras.preprocessing.image import ImageDataGenerator
from keras.preprocessing.image import img_to_array, load_img
from keras.utils.np_utils import to_categorical
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.preprocessing import LabelEncoder, StandardScaler
def load_numeric_training(standardize=True):
data = pd.read_csv('../train.csv')
ID = data.pop('id')
y = data.pop('species')
y = LabelEncoder().fit(y).transform(y)
X = StandardScaler().fit(data).transform(data) if standardize else data.values
return ID.values, X, y
def load_numeric_test(standardize=True):
data = pd.read_csv('../test.csv')
ID = data.pop('id')
test = StandardScaler().fit(data).transform(data) if standardize else data.values
return ID.values, test
def resize_img(img, max_dim=96):
max_axis = np.argmax(img.size)
scale = max_dim / img.size[max_axis]
return img.resize((int(img.size[0] * scale), int(img.size[1] * scale)))
def load_img_data(ids, max_dim=96, center=True):
X = np.empty((len(ids), max_dim, max_dim, 1))
for i, id in enumerate(ids):
img = load_img('../images/{}.jpg'.format(id), grayscale=True)
img = resize_img(img, max_dim=max_dim)
x = img_to_array(img)
h, w = x.shape[:2]
if center:
h1 = (max_dim - h) >> 1
h2 = h1 + h
w1 = (max_dim - w) >> 1
w2 = w1 + w
else:
h1, h2, w1, w2 = 0, h, 0, w
X[i][h1:h2, w1:w2][:] = x
return np.around(X / 255)
def load_train_data(split=0.9, random_state=7):
ID, X_num_train, y = load_numeric_training()
X_img_train = load_img_data(ID)
sss = StratifiedShuffleSplit(n_splits=1, train_size=split, test_size=1 - split, random_state=random_state)
train_idx, val_idx = next(sss.split(X_num_train, y))
ID_tr, X_num_tr, X_img_tr, y_tr = ID[train_idx], X_num_train[train_idx], X_img_train[train_idx], y[train_idx]
ID_val, X_num_val, X_img_val, y_val = ID[val_idx], X_num_train[val_idx], X_img_train[val_idx], y[val_idx]
return (ID_tr, X_num_tr, X_img_tr, y_tr), (ID_val, X_num_val, X_img_val, y_val)
def load_test_data():
ID, X_num_test = load_numeric_test()
X_img_test = load_img_data(ID)
return ID, X_num_test, X_img_test
print('Loading train data ...')
(ID_train, X_num_tr, X_img_tr, y_tr), (ID_val, X_num_val, X_img_val, y_val) = load_train_data()
# Prepare ID-to-label and ID-to-numerical dictionary
ID_y_dic, ID_num_dic = {}, {}
for i in range(len(ID_train)):
ID_y_dic[ID_train[i]] = y_tr[i]
ID_num_dic[ID_train[i]] = X_num_tr[i, :]
print('Loading test data ...')
ID_test, X_num_test, X_img_test = load_test_data()
# Convert label to categorical/one-hot
ID_train, y_tr, y_val = to_categorical(ID_train), to_categorical(y_tr), to_categorical((y_val))
def _bytes_feature(value):
return tf.train.Feature(bytes_list=tf.train.BytesList(value=[value]))
def _int64_feature(value):
return tf.train.Feature(int64_list=tf.train.Int64List(value=[value]))
def _float32_feature(value):
return tf.train.Feature(float_list=tf.train.FloatList(value=value))
def write_val_data():
val_data_path = '../tfrecords/val_data_1.tfrecords'
if os.path.exists(val_data_path):
print('Warning: old file exists, removed.')
os.remove(val_data_path)
val_image, val_num, val_label = X_img_val.astype(np.bool), X_num_val.astype(np.float64), y_val.astype(np.bool)
print(val_image.shape, val_num.shape, val_label.shape)
val_writer = tf.python_io.TFRecordWriter(val_data_path)
print('Writing data into tfrecord ...')
for i in range(len(val_image)):
image, num, label = val_image[i], val_num[i], val_label[i]
feature = {'image': _bytes_feature(image.tostring()),
'num': _bytes_feature(num.tostring()),
'label': _bytes_feature(label.tostring())}
example = tf.train.Example(features=tf.train.Features(feature=feature))
val_writer.write(example.SerializeToString())
print('Done!')
def write_train_data():
imgen = ImageDataGenerator(rotation_range=20, zoom_range=0.2, horizontal_flip=True,
vertical_flip=True, fill_mode='nearest')
imgen_train = imgen.flow(X_img_tr, ID_train, batch_size=32, seed=7)
print('Generating augmented images')
all_images = []
all_ID = []
p = True
for i in range(28 * 200):
print('Generating augmented images for epoch {}, batch {}'.format(i // 28, i % 28))
X, ID = imgen_train.next()
all_images.append(X)
all_ID.append(np.argmax(ID, axis=1))
all_images = | np.concatenate(all_images) | numpy.concatenate |
"""
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) | numpy.isscalar |
"""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) | numpy.abs |
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])))
i += 1
ref_scores_mtx = np.vstack(scores_mtx_list)
dis_scores_mtx = None
with YuvReader(filepath=asset.dis_workfile_path, width=quality_w, height=quality_h,
yuv_type=self._get_workfile_yuv_type(asset)) as dis_yuv_reader:
scores_mtx_list = []
i = 0
for dis_yuv in dis_yuv_reader:
dis_y = dis_yuv[0]
firstm = dis_y.mean()
secondm = dis_y.var() + firstm**2
scores_mtx_list.append( | np.hstack(([firstm], [secondm])) | numpy.hstack |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
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") | numpy.timedelta64 |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
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]]) | 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) | numpy.ones_like |
# 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) | numpy.array |
import numpy as np
import tensorflow as tf
H = 2
N = 2
M = 3
BS = 10
def my_softmax(arr):
max_elements = np.reshape(np.max(arr, axis = 2), (BS, N, 1))
arr = arr - max_elements
exp_array = np.exp(arr)
print (exp_array)
sum_array = np.reshape(np.sum(exp_array, axis=2), (BS, N, 1))
return exp_array /sum_array
def masked_softmax(logits, mask, dim):
"""
Takes masked softmax over given dimension of logits.
Inputs:
logits: Numpy array. We want to take softmax over dimension dim.
mask: Numpy array of same shape as logits.
Has 1s where there's real data in logits, 0 where there's padding
dim: int. dimension over which to take softmax
Returns:
masked_logits: Numpy array same shape as logits.
This is the same as logits, but with 1e30 subtracted
(i.e. very large negative number) in the padding locations.
prob_dist: Numpy array same shape as logits.
The result of taking softmax over masked_logits in given dimension.
Should be 0 in padding locations.
Should sum to 1 over given dimension.
"""
exp_mask = (1 - tf.cast(mask, 'float64')) * (-1e30) # -large where there's padding, 0 elsewhere
print (exp_mask)
masked_logits = tf.add(logits, exp_mask) # where there's padding, set logits to -large
prob_dist = tf.nn.softmax(masked_logits, dim)
return masked_logits, prob_dist
def test_build_similarity(contexts, questions):
w_sim_1 = tf.get_variable('w_sim_1',
initializer=w_1) # 2 * H
w_sim_2 = tf.get_variable('w_sim_2',
initializer=w_2) # 2 * self.hidden_size
w_sim_3 = tf.get_variable('w_sim_3',
initializer=w_3) # 2 * self.hidden_size
q_tile = tf.tile(tf.expand_dims(questions, 0), [N, 1, 1, 1]) # N x BS x M x 2H
q_tile = tf.transpose(q_tile, (1, 0, 3, 2)) # BS x N x 2H x M
contexts = tf.expand_dims(contexts, -1) # BS x N x 2H x 1
result = (contexts * q_tile) # BS x N x 2H x M
tf.assert_equal(tf.shape(result), [BS, N, 2 * H, M])
result = tf.transpose(result, (0, 1, 3, 2)) # BS x N x M x 2H
result = tf.reshape(result, (-1, N * M, 2 * H)) # BS x (NxM) x 2H
tf.assert_equal(tf.shape(result), [BS, N*M, 2*H])
# w_sim_1 = tf.tile(tf.expand_dims(w_sim_1, 0), [BS, 1])
# w_sim_2 = tf.tile(tf.expand_dims(w_sim_2, 0), [BS, 1])
# w_sim_3 = tf.tile(tf.expand_dims(w_sim_3, 0), [BS, 1])
term1 = tf.matmul(tf.reshape(contexts, (BS * N, 2*H)), tf.expand_dims(w_sim_1, -1)) # BS x N
term1 = tf.reshape(term1, (-1, N))
term2 = tf.matmul(tf.reshape(questions, (BS * M, 2*H)), tf.expand_dims(w_sim_2, -1)) # BS x M
term2 = tf.reshape(term2, (-1, M))
term3 = tf.matmul(tf.reshape(result, (BS * N * M, 2* H)), tf.expand_dims(w_sim_3, -1))
term3 = tf.reshape(term3, (-1, N, M)) # BS x N x M
S = tf.reshape(term1,(-1, N, 1)) + term3 + tf.reshape(term2, (-1, 1, M))
return S
def test_build_sim_mask():
context_mask = np.array([True, True]) # BS x N
question_mask = np.array([True, True, False]) # BS x M
context_mask = np.tile(context_mask, [BS, 1])
question_mask = np.tile(question_mask, [BS, 1])
context_mask = tf.get_variable('context_mask', initializer=context_mask)
question_mask = tf.get_variable('question_mask', initializer=question_mask)
context_mask = tf.expand_dims(context_mask, -1) # BS x N x 1
question_mask = tf.expand_dims(question_mask, -1) # BS x M x 1
question_mask = tf.transpose(question_mask, (0, 2, 1)) # BS x 1 x M
sim_mask = tf.matmul(tf.cast(context_mask, dtype=tf.int32),
tf.cast(question_mask, dtype=tf.int32)) # BS x N x M
return sim_mask
def test_build_c2q(S, S_mask, questions):
_, alpha = masked_softmax(S, mask, 2) # BS x N x M
return tf.matmul(alpha, questions)
def test_build_q2c(S, S_mask, contexts):
# S = BS x N x M
# contexts = BS x N x 2H
m = tf.reduce_max(S * tf.cast(S_mask, dtype=tf.float64), axis=2) # BS x N
beta = tf.expand_dims(tf.nn.softmax(m), -1) # BS x N x 1
beta = tf.transpose(beta, (0, 2, 1))
q2c = tf.matmul(beta, contexts)
return m, beta, q2c
def test_concatenation(c2q, q2c):
q2c = tf.tile(q2c, (1, N, 1))
output = tf.concat([c2q, q2c], axis=2)
tf.assert_equal(tf.shape(output), [BS, N, 4*H])
return output
if __name__== "__main__":
w_1 = np.array([1., 2., 3., 4.])
w_2 = np.array([5., 6., 7., 8.])
w_3 = np.array([13., 12., 11., 10.])
c = np.array([[[1., 2., 3., 4.], [5., 6., 7., 8.]]]) # BS x N x 2H
q = np.array([[[1., 2., 3., 0.], [5., 6., 7., 4.], [8., 9. , 10., 11.]]]) # BS x M x 2H
c = | np.tile(c, [BS, 1, 1]) | numpy.tile |
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) | numpy.zeros |
import numpy as np
from stumpff import C, S
from CelestialBody import BODIES
from numerical import newton, laguerre
from lagrange import calc_f, calc_fd, calc_g, calc_gd
def kepler_chi(chi, alpha, r0, vr0, mu, dt):
''' Kepler's Equation of the universal anomaly, modified
for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi**2*C(z) + \
(1 - alpha*r0)*chi**3*S(z) + \
r0*chi - np.sqrt(mu)*dt
def dkepler_dchi(chi, alpha, r0, vr0, mu, dt):
''' Derivative of Kepler's Equation of the universal anomaly,
modified for use in numerical solvers. '''
z = alpha*chi**2
return (r0*vr0/np.sqrt(mu))*chi*(1 - alpha*chi**2*S(z)) + \
(1 - alpha*r0)*chi**2*C(z) + r0
def d2kepler_dchi2(chi, alpha, r0, vr0, mu, dt):
''' Second derivative of Kepler's Equation of the universal
anomaly, modified for use in numerical solvers. '''
z = alpha*chi**2
S_ = S(z)
return (r0*vr0/np.sqrt(mu))*(1 - 3*z*S_ + z*(C(z) - 3*S_)) + \
chi*(1 - z*S_)*(1 - alpha*r0)
def solve_kepler_chi(r_0, v_0, dt, body=BODIES['Earth'], method='laguerre', tol=1e-7, max_iters=100):
''' Solve Kepler's Equation of the universal anomaly chi using the specified
numerical method. Applies Algorithm 3.4 from Orbital Mechanics for Engineering
Students, 4 ed, Curtis.
:param r_0: `iterable` (km) initial position 3-vector
:param v_0: `iterable` (km/s) initial velocity 3-vector
:param dt: `float` (s) time after initial state to solve for r, v as 3-vectors
:param body: `CelestialBody` (--) the celestial body to use for orbital parameters
:param method: `str` (--) which numerical method to use to solve Kepler's Equation
:param tol: `float` (--) decimal tolerance for numerical method (default 1e-7 is IEEE 745 single precision)
:param max_iters: `int` (--) maximum number of iterations in numerical method before breaking
:return: (km) final position 3-vector, (km/s) final velocity 3-vector
'''
VALID_METHODS = ('laguerre', 'newton')
mu = body.mu # (km**3/s**2) gravitational parameter of the specified primary body
r0 = np.linalg.norm(r_0) # (km) initial position magnitude
v0 = np.linalg.norm(v_0) # (km/s) initial velocity magnitude
vr0 = np.dot(v_0, r_0)/r0 # (km/s) initial radial velocity magnitude
alpha = 2/r0 - v0**2/mu # (1/km) inverse of semi-major axis
chi0 = np.sqrt(mu)*np.abs(alpha)*dt
if method not in VALID_METHODS:
print(f'Method \'{method}\' is not valid, must be one of {VALID_METHODS}.\nDefaulting to laguerre method.')
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
elif method == 'newton':
chi, _, _ = newton(chi0, kepler_chi, dkepler_dchi, alpha, r0, vr0, mu, dt)
else: # method == 'laguerre'
chi, _, _ = laguerre(chi0, kepler_chi, dkepler_dchi, d2kepler_dchi2, alpha, r0, vr0, mu, dt)
f = calc_f(chi, r0, alpha)
g = calc_g(dt, mu, chi, alpha)
r_1 = f*r_0 + g*v_0
r1 = np.linalg.norm(r_1)
fd = calc_fd(mu, r1, r0, alpha, chi)
gd = calc_gd(chi, r1, alpha)
v_1 = fd*r_0 + gd*v_0
return r_1, v_1
def solve_kepler_E(e, Me, tol=1e-7, max_iters=100):
''' Solve Kepler's Equation in the form containing Eccentric Anomaly (E),
eccentricity (e), and Mean Anomaly of Ellipse (Me). Uses Algorithm 3.1 from Orbital
Mechanics for Engineering Students, 4 ed, Curtis. '''
# TODO: have this function make use of one of the numerical methods in numerical.py
def f(E, e, Me):
return E - e*np.sin(E) - Me
def fp(E, e):
return 1 - e*np.cos(E)
E = Me + e/2 if Me < np.pi else Me - e/2
ratio = f(E, e, Me)/fp(E, e)
iters = 0
while abs(ratio) > tol and iters < max_iters:
E -= ratio
ratio = f(E, e, Me)/fp(E, e)
iters += 1
E -= ratio
converged = np.abs(ratio) <= tol
return E, iters, converged
def test():
''' Test the functionality of solve_kepler_chi
and solve_kepler_laguerre using Problem 3.20 from
Orbital Mechanics for Engineering Students, 4 ed, Curtis.
'''
# given starting information
Earth = BODIES['Earth'] # `CelestialBody` (--) Earth and all the Earth things
r_0 = np.array([20000, -105000, -19000]) # (km) initial position vector
v_0 = | np.array([0.9, -3.4, -1.5]) | numpy.array |
'''
<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]) | numpy.linalg.norm |
'''
-------------------------------------------------------------------------------------------------
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) | numpy.cos |
import os
import sys
import click
import pickle
import sncosmo
import numpy as np
from astropy.table import Table
DATA_PATH = '/home/samdixon/jla_light_curves/'
def modify_error(lc, error_floor=0.):
"""Add an error floor of `error_floor` times the maximum flux of the band
to each observation
"""
data = sncosmo.photdata.photometric_data(lc).normalized(zp=25., zpsys='ab')
new_lc = {'time': data.time,
'band': data.band,
'flux': data.flux,
'fluxerr': data.fluxerr,
'zp': data.zp,
'zpsys': data.zpsys}
for band in set(data.band):
band_cut = data.band==band
max_flux_in_band = np.max(data.flux[band_cut])
new_lc['fluxerr'][band_cut] = np.sqrt((error_floor*max_flux_in_band)**2+data.fluxerr[band_cut]**2)
new_lc = Table(new_lc, meta=lc.meta)
return new_lc
def fit_lc_and_save(lc, model_name, save_dir, no_mc):
name = lc.meta['SN']
model = sncosmo.Model(source=model_name,
effects=[sncosmo.CCM89Dust()],
effect_names=['mw'],
effect_frames=['obs'])
if type(name) is float:
name = int(name)
z = lc.meta['Z_HELIO']
mwebv = lc.meta['MWEBV']
bounds = {}
try:
t0 = float(lc.meta['DayMax'].split()[0])
bounds['t0'] = (t0-5, t0+5)
except KeyError:
try:
t0 = | np.mean(lc['Date']) | numpy.mean |
"""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) | numpy.finfo |
import numpy as np
from sklearn.linear_model import LogisticRegression
from .models import User
from .twitter import vectorize_tweet
def predict_user(user1_name, user2_name, tweet_text):
"""
Determine and return which user is more likely to say a given Tweet.
Example: predict_user('ausen', 'elonmusk', 'Lambda School Rocks!')
Returns 1 corresponding to 1st user passed in, or 0 for second.
"""
user1 = User.query.filter(User.name == user1_name).one()
user2 = User.query.filter(User.name == user2_name).one()
user1_vect = | np.array([tweet.vect for tweet in user1.tweets]) | numpy.array |
import argparse
import json
import numpy as np
import pandas as pd
import os
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report,f1_score
from keras.models import Sequential
from keras.layers import Dense, Dropout
from keras import backend as K
from keras.utils.vis_utils import plot_model
from sklearn.externals import joblib
import time
def f1(y_true, y_pred):
def recall(y_true, y_pred):
"""Recall metric.
Only computes a batch-wise average of recall.
Computes the recall, a metric for multi-label classification of
how many relevant items are selected.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
possible_positives = K.sum(K.round(K.clip(y_true, 0, 1)))
recall = true_positives / (possible_positives + K.epsilon())
return recall
def precision(y_true, y_pred):
"""Precision metric.
Only computes a batch-wise average of precision.
Computes the precision, a metric for multi-label classification of
how many selected items are relevant.
"""
true_positives = K.sum(K.round(K.clip(y_true * y_pred, 0, 1)))
predicted_positives = K.sum(K.round(K.clip(y_pred, 0, 1)))
precision = true_positives / (predicted_positives + K.epsilon())
return precision
precision = precision(y_true, y_pred)
recall = recall(y_true, y_pred)
return 2*((precision*recall)/(precision+recall+K.epsilon()))
def get_embeddings(sentences_list,layer_json):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:return: Dictionary with key each sentence of the sentences_list and as value the embedding
'''
sentences = dict()#dict with key the index of each line of the sentences_list.txt and as value the sentence
embeddings = dict()##dict with key the index of each sentence and as value the its embedding
sentence_emb = dict()#key:sentence,value:its embedding
with open(sentences_list,'r') as file:
for index,line in enumerate(file):
sentences[index] = line.strip()
with open(layer_json, 'r',encoding='utf-8') as f:
for line in f:
embeddings[json.loads(line)['linex_index']] = np.asarray(json.loads(line)['features'])
for key,value in sentences.items():
sentence_emb[value] = embeddings[key]
return sentence_emb
def train_classifier(sentences_list,layer_json,dataset_csv,filename):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:param filename: The path of the pickle file that the model will be stored
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = np.asarray(length)
print(length.shape)
label = np.asarray(label)
print(errors)
features = np.concatenate([sentence_emb, previous_emb, next_emb,section_emb], axis=1)
features = np.column_stack([features, length]) # np.append(features,length,axis=1)
print(features.shape)
X_train, X_val, y_train, y_val = train_test_split(features, label, test_size=0.33, random_state=42)
log = LogisticRegression(random_state=0, solver='newton-cg', max_iter=1000, C=0.1)
log.fit(X_train, y_train)
#save the model
_ = joblib.dump(log, filename, compress=9)
predictions = log.predict(X_val)
print("###########################################")
print("Results using embeddings from the",layer_json,"file")
print(classification_report(y_val, predictions))
print("F1 score using Logistic Regression:",f1_score(y_val, predictions))
print("###########################################")
#train a DNN
f1_results = list()
for i in range(3):
model = Sequential()
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dense(128, activation='relu', trainable=True))
model.add(Dropout(0.30))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.25))
model.add(Dense(64, activation='relu', trainable=True))
model.add(Dropout(0.35))
model.add(Dense(1, activation='sigmoid'))
# compile network
model.compile(loss='binary_crossentropy', optimizer='sgd', metrics=[f1])
# fit network
model.fit(X_train, y_train, epochs=100, batch_size=64)
loss, f_1 = model.evaluate(X_val, y_val, verbose=1)
print('\nTest F1: %f' % (f_1 * 100))
f1_results.append(f_1)
model = None
print("###########################################")
print("Results using embeddings from the", layer_json, "file")
# evaluate
print(np.mean(f1_results))
print("###########################################")
def parameter_tuning_LR(sentences_list,layer_json,dataset_csv):
'''
:param sentences_list: the path o the sentences.txt
:param layer_json: the path of the json file that contains the embeddings of the sentences
:param dataset_csv: the path of the dataset
:return:
'''
dataset = pd.read_csv(dataset_csv)
bert_dict = get_embeddings(sentences_list,layer_json)
length = list()
sentence_emb = list()
previous_emb = list()
next_list = list()
section_list = list()
label = list()
errors = 0
for row in dataset.iterrows():
sentence = row[1][0].strip()
previous = row[1][1].strip()
nexts = row[1][2].strip()
section = row[1][3].strip()
if sentence in bert_dict:
sentence_emb.append(bert_dict[sentence])
else:
sentence_emb.append(np.zeros(768))
print(sentence)
errors += 1
if previous in bert_dict:
previous_emb.append(bert_dict[previous])
else:
previous_emb.append(np.zeros(768))
if nexts in bert_dict:
next_list.append(bert_dict[nexts])
else:
next_list.append(np.zeros(768))
if section in bert_dict:
section_list.append(bert_dict[section])
else:
section_list.append(np.zeros(768))
length.append(row[1][4])
label.append(row[1][5])
sentence_emb = np.asarray(sentence_emb)
print(sentence_emb.shape)
next_emb = np.asarray(next_list)
print(next_emb.shape)
previous_emb = np.asarray(previous_emb)
print(previous_emb.shape)
section_emb = np.asarray(section_list)
print(sentence_emb.shape)
length = | np.asarray(length) | numpy.asarray |
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]) | numpy.max |
from itertools import product
import numpy as np
import pytest
from alibi_detect.utils.discretizer import Discretizer
x = | np.random.rand(10, 4) | numpy.random.rand |
#
# 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)
tf.random.set_seed(seed)
sample_posterior = lv(inputs, observations=[inputs, targets], training=True, seed=seed2)
tf.random.set_seed(seed)
posterior_expected = np.concatenate([inputs, posteriors.sample(seed=seed2)], axis=-1)
| np.testing.assert_array_equal(sample_posterior, posterior_expected) | numpy.testing.assert_array_equal |
###############################################################################
# @todo add Pilot2-splash-app disclaimer
###############################################################################
""" Get's KRAS states """
import MDAnalysis as mda
from MDAnalysis.analysis import align
from MDAnalysis.lib.mdamath import make_whole
import os
import numpy as np
import math
############## Below section needs to be uncommented ############
import mummi_core
import mummi_ras
from mummi_core.utils import Naming
# # Logger has to be initialized the first thing in the script
from logging import getLogger
LOGGER = getLogger(__name__)
# # Innitilize MuMMI if it has not been done before
# MUMMI_ROOT = mummi.init(True)
# This is needed so the Naming works below
#@TODO fix this so we don't have these on import make them as an init
mummi_core.init()
dirKRASStates = Naming.dir_res('states')
dirKRASStructures = Naming.dir_res('structures')
# #RAS_ONLY_macrostate = np.loadtxt(os.path.join(dirKRASStates, "RAS-ONLY.microstates.txt"))
RAS_ONLY_macrostate = np.loadtxt(os.path.join(dirKRASStates, "ras-states.txt"),comments='#')
# #RAS_RAF_macrostate = np.loadtxt(os.path.join(dirKRASStates, "RAS-RAF.microstates.txt"))
RAS_RAF_macrostate = np.loadtxt(os.path.join(dirKRASStates, "ras-raf-states.txt"),comments='#') # Note diffrent number of columns so index change below
# TODO: CS, my edits to test
# RAS_ONLY_macrostate = np.loadtxt('ras-states.txt')
# RAS_RAF_macrostate = np.loadtxt('ras-raf-states.txt')
############## above section needs to be uncommented ############
# TODO: CS, my edits to test
# TODO: TSC, The reference structure has to currently be set as the 'RAS-ONLY-reference-structure.gro'
# TODO: TSC, path to the reference structure is: mummi_resources/structures/
kras_ref_universe = mda.Universe(os.path.join(dirKRASStructures, "RAS-ONLY-reference-structure.gro"))
# kras_ref_universe = mda.Universe("RAS-ONLY-reference-structure.gro")
# kras_ref_universe = mda.Universe('AA_pfpatch_000000004641_RAS_RAF2_411.gro')
# TODO: CS, not using these for x4 proteins; instead using protein_systems below to set num_res
######### Below hard codes the number of residues within RAS-only and RAS-RAF ##########
RAS_only_num_res = 184
RAS_RAF_num_res = 320
######### Above hard codes the number of residues within RAS-only and RAS-RAF ##########
####### This can be removed
# def get_kras(syst, kras_start):
# """Gets all atoms for a KRAS protein starting at 'kras_start'."""
# return syst.atoms[kras_start:kras_start+428]
####### This can be removed
def get_segids(u):
"""Identifies the list of segments within the system. Only needs to be called x1 time"""
segs = u.segments
segs = segs.segids
ras_segids = []
rasraf_segids = []
for i in range(len(segs)):
# print(segs[i])
if segs[i][-3:] == 'RAS':
ras_segids.append(segs[i])
if segs[i][-3:] == 'RAF':
rasraf_segids.append(segs[i])
return ras_segids, rasraf_segids
def get_protein_info(u,tag):
"""Uses the segments identified in get_segids to make a list of all proteins in the systems.\
Outputs a list of the first residue number of the protein, and whether it is 'RAS-ONLY', or 'RAS-RAF'.\
The 'tag' input defines what is used to identify the first residue of the protein. i.e. 'resname ACE1 and name BB'.\
Only needs to be called x1 time"""
ras_segids, rasraf_segids = get_segids(u)
if len(ras_segids) > 0:
RAS = u.select_atoms('segid '+ras_segids[0]+' and '+str(tag))
else:
RAS = []
if len(rasraf_segids) > 0:
RAF = u.select_atoms('segid '+rasraf_segids[0]+' and '+str(tag))
else:
RAF = []
protein_info = []#np.empty([len(RAS)+len(RAF),2])
for i in range(len(RAS)):
protein_info.append((RAS[i].resid,'RAS-ONLY'))
for i in range(len(RAF)):
protein_info.append((RAF[i].resid,'RAS-RAF'))
######## sort protein info
protein_info = sorted(protein_info)
######## sort protein info
return protein_info
def get_ref_kras():
"""Gets the reference KRAS struct. Only called x1 time when class is loaded"""
start_of_g_ref = kras_ref_universe.residues[0].resid
ref_selection = 'resid '+str(start_of_g_ref)+':'+str(start_of_g_ref+24)+' ' +\
str(start_of_g_ref+38)+':'+str(start_of_g_ref+54)+' ' +\
str(start_of_g_ref+67)+':'+str(start_of_g_ref+164)+' ' +\
'and (name CA or name BB)'
r2_26r40_56r69_166_ref = kras_ref_universe.select_atoms(str(ref_selection))
return kras_ref_universe.select_atoms(str(ref_selection)).positions - kras_ref_universe.select_atoms(str(ref_selection)).center_of_mass()
# Load inital ref frames (only need to do this once)
ref0 = get_ref_kras()
def getKRASstates(u,kras_indices):
"""Gets states for all KRAS proteins in path."""
# res_shift = 8
# all_glycine = u.select_atoms("resname GLY")
# kras_indices = []
# for i in range(0, len(all_glycine), 26):
# kras_indices.append(all_glycine[i].index)
########## Below is taken out of the function so it is only done once #########
# kras_indices = get_protein_info(u,'resname ACE1 and name BB')
########## Above is taken out of the function so it is only done once #########
# CS, for x4 cases:
# [{protein_x4: (protein_type, num_res)}]
protein_systems = [{'ras4a': ('RAS-ONLY', 185),
'ras4araf': ('RAS-RAF', 321),
'ras': ('RAS-ONLY', 184),
'rasraf': ('RAS-RAF', 320)}]
ALLOUT = []
for k in range(len(kras_indices)):
start_of_g = kras_indices[k][0]
protein_x4 = str(kras_indices[k][1])
try:
protein_type = [item[protein_x4] for item in protein_systems][0][0] # 'RAS-ONLY' OR 'RAS-RAF'
num_res = [item[protein_x4] for item in protein_systems][0][1]
except:
LOGGER.error('Check KRas naming between modules')
raise Exception('Error: unknown KRas name')
# TODO: CS, replacing this comment section with the above, to handle x4 protein types
# ---------------------------------------
# ALLOUT = []
# for k in range(len(kras_indices)):
# start_of_g = kras_indices[k][0]
# protein_type = str(kras_indices[k][1])
# ########## BELOW SECTION TO DETERMINE WHICH RESIDUES ARE PART OF THE PROTEIN GROUP - NEEDED FOR PBC REMOVAL ##############
# ########## POTENTIALLY REDO WITH A 'HARD-CODED' NUMBER OF RESIDUES PER PROTEIN GROUP (WHETHER RAS-ONLY OR RAS-RAF) #######
# ########## HAS BEEN REDONE WITH A 'HARD-CODED' NUMBER OF RESIDUES PER PROTEIN GROUP (WHETHER RAS-ONLY OR RAS-RAF) ########
# # if len(kras_indices) == 1:
# # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(len(u.residues))+' and name BB') ####### HAS TO BE FIXED FOR BACKBONE ATOMS FOR SPECIFIC PROTEIN
# # elif len(kras_indices) > 1:
# # if k == len(kras_indices)-1:
# # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(len(u.residues))+' and name BB')
# # else:
# # krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(kras_indices[k+1][0])+' and name BB')
# ########## ABOVE SECTION TO DETERMINE WHICH RESIDUES ARE PART OF THE PROTEIN GROUP - NEEDED FOR PBC REMOVAL ##############
#
# ########## Below hard codes the number of residues/beads in the RAS-ONLY and RAS-RAF simulations #########################
# if protein_type == 'RAS-ONLY':
# num_res = RAS_only_num_res
# elif protein_type == 'RAS-RAF':
# num_res = RAS_RAF_num_res
# ########## Above hard codes the number of residues/beads in the RAS-ONLY and RAS-RAF simulations #########################
# ---------------------------------------
# TODO: TSC, I changed the selection below, which can be used for the make_whole...
# krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+num_res)+' and (name CA or name BB)')
krases0_BB = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+num_res))
krases0_BB.guess_bonds()
r2_26r40_56r69_166 = u.select_atoms('resid '+str(start_of_g)+':'+str(start_of_g+24)+' ' +\
str(start_of_g+38)+':'+str(start_of_g+54)+' ' +\
str(start_of_g+67)+':'+str(start_of_g+164)+\
' and (name CA or name BB)')
u_selection = \
'resid '+str(start_of_g)+':'+str(start_of_g+24)+' '+str(start_of_g+38)+':'+str(start_of_g+54)+' ' +\
str(start_of_g+67)+':'+str(start_of_g+164)+' and (name CA or name BB)'
mobile0 = u.select_atoms(str(u_selection)).positions - u.select_atoms(str(u_selection)).center_of_mass()
# TODO: CS, something wrong with ref0 from get_kras_ref()
# just making ref0 = mobile0 to test for now
# ref0 = mobile0
# TSC removed this
R, RMSD_junk = align.rotation_matrix(mobile0, ref0)
######## TODO: TSC, Adjusted for AA lipid names ########
# lipids = u.select_atoms('resname POPX POPC PAPC POPE DIPE DPSM PAPS PAP6 CHOL')
lipids = u.select_atoms('resname POPC PAPC POPE DIPE SSM PAPS SAPI CHL1')
coords = ref0
RotMat = []
OS = []
r152_165 = krases0_BB.select_atoms('resid '+str(start_of_g+150)+':'+str(start_of_g+163)+' and (name CA or name BB)')
r65_74 = krases0_BB.select_atoms('resid '+str(start_of_g+63)+':'+str(start_of_g+72)+' and (name CA or name BB)')
timeframes = []
# TODO: CS, for AA need bonds to run make_whole()
# krases0_BB.guess_bonds()
# TODO: CS, turn off for now to test beyond this point
''' *** for AA, need to bring that back on once all else runs ***
'''
# @Tim and <NAME>. this was commented out - please check.
#make_whole(krases0_BB)
j, rmsd_junk = mda.analysis.align.rotation_matrix((r2_26r40_56r69_166.positions-r2_26r40_56r69_166.center_of_mass()), coords)
RotMat.append(j)
OS.append(r65_74.center_of_mass()-r152_165.center_of_mass())
timeframes.append(u.trajectory.time)
if protein_type == 'RAS-RAF':
z_pos = []
############### NEED TO CONFIRM THE SELECTION OF THE RAF LOOP RESIDUES BELOW ####################
############### TODO: TSC, zshifting is set to -1 (instead of -2), as there are ACE caps that are separate residues in AA
#zshifting=-1
if protein_x4 == 'rasraf':
zshifting = -1
elif protein_x4 == 'ras4araf':
zshifting = 0
else:
zshifting = 0
LOGGER.error('Found unsupported protein_x4 type')
raf_loops_selection = u.select_atoms('resid '+str(start_of_g+zshifting+291)+':'+str(start_of_g+zshifting+294)+' ' +\
str(start_of_g+zshifting+278)+':'+str(start_of_g+zshifting+281)+' ' +\
' and (name CA or name BB)')
############### NEED TO CONFIRM THE SELECTION OF THE RAF LOOP RESIDUES ABOVE ####################
diff = (lipids.center_of_mass()[2]-raf_loops_selection.center_of_mass(unwrap=True)[2])/10
if diff < 0:
diff = diff+(u.dimensions[2]/10)
z_pos.append(diff)
z_pos = np.array(z_pos)
RotMatNP = np.array(RotMat)
OS = np.array(OS)
OA = RotMatNP[:, 2, :]/(((RotMatNP[:, 2, 0]**2)+(RotMatNP[:, 2, 1]**2)+(RotMatNP[:, 2, 2]**2))**0.5)[:, None]
OWAS = | np.arccos(RotMatNP[:, 2, 2]) | numpy.arccos |
from sklearn.metrics import f1_score,accuracy_score
import numpy as np
from utilities.tools import load_model
import pandas as pd
def predict_MSRP_test_data(n_models,nb_words,nlp_f,test_data_1,test_data_2,test_labels):
models=[]
n_h_features=nlp_f.shape[1]
print('loading the models...')
for i in range(n_models):
models.append(load_model(i+1,nb_words,n_h_features))
preds=[]
print('predicting the test data...\n')
i=0
for m in models:
i+=1
preds_prob=m.predict([test_data_1, test_data_2,nlp_f], batch_size=64, verbose=0)
preds.append(preds_prob[:,1])
preds=np.asarray(preds)
final_labels=np.zeros(len(test_data_1),dtype=int)
#average the predicttion
for i in range(len(test_data_1)):
final_labels[i]=round(np.mean(preds[:,i]))
if i%100==0:
print(i ,' out of ',len(test_data_1))
print("test data accuracy: ", accuracy_score(final_labels,test_labels))
print("test data f_measure: ", f1_score(final_labels, test_labels))
submission = pd.DataFrame({"Quality": final_labels})
submission.to_csv("predictions/MSRP.tsv", index=True,index_label='test_id')
def predict_Quora_test_data(n_models,nb_words,nlp_f,test_data_1,test_data_2):
models=[]
n_h_features=nlp_f.shape[1]
print('loading the models...')
for i in range(n_models):
models.append(load_model(i+1,nb_words,n_h_features))
preds=[]
print('predicting the test data...\n')
i=0
for m in models:
i+=1
preds_prob=m.predict([test_data_1, test_data_2,nlp_f], batch_size=125, verbose=0)
preds.append(preds_prob[:,1])
preds=np.asarray(preds)
final_labels=np.zeros(len(test_data_1),dtype=float)
#average the predicttion
for i in range(len(test_data_1)):
final_labels[i]= | np.mean(preds[:,i]) | numpy.mean |
"""
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) | numpy.empty |
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)
@cache_readonly
def _cached_int64index(self) -> Int64Index:
return Int64Index._simple_new(self._data, name=self.name)
@property
def _int64index(self) -> Int64Index:
# wrap _cached_int64index so we can be sure its name matches self.name
res = self._cached_int64index
res._name = self._name
return res
def _get_data_as_items(self):
""" return a list of tuples of start, stop, step """
rng = self._range
return [("start", rng.start), ("stop", rng.stop), ("step", rng.step)]
def __reduce__(self):
d = self._get_attributes_dict()
d.update(dict(self._get_data_as_items()))
return ibase._new_Index, (type(self), d), None
# --------------------------------------------------------------------
# Rendering Methods
def _format_attrs(self):
"""
Return a list of tuples of the (attr, formatted_value)
"""
attrs = self._get_data_as_items()
if self.name is not None:
attrs.append(("name", ibase.default_pprint(self.name)))
return attrs
def _format_data(self, name=None):
# we are formatting thru the attributes
return None
def _format_with_header(self, header: list[str], na_rep: str = "NaN") -> list[str]:
if not len(self._range):
return header
first_val_str = str(self._range[0])
last_val_str = str(self._range[-1])
max_length = max(len(first_val_str), len(last_val_str))
return header + [f"{x:<{max_length}}" for x in self._range]
# --------------------------------------------------------------------
_deprecation_message = (
"RangeIndex.{} is deprecated and will be "
"removed in a future version. Use RangeIndex.{} "
"instead"
)
@property
def start(self) -> int:
"""
The value of the `start` parameter (``0`` if this was not supplied).
"""
# GH 25710
return self._range.start
@property
def _start(self) -> int:
"""
The value of the `start` parameter (``0`` if this was not supplied).
.. deprecated:: 0.25.0
Use ``start`` instead.
"""
warnings.warn(
self._deprecation_message.format("_start", "start"),
FutureWarning,
stacklevel=2,
)
return self.start
@property
def stop(self) -> int:
"""
The value of the `stop` parameter.
"""
return self._range.stop
@property
def _stop(self) -> int:
"""
The value of the `stop` parameter.
.. deprecated:: 0.25.0
Use ``stop`` instead.
"""
# GH 25710
warnings.warn(
self._deprecation_message.format("_stop", "stop"),
FutureWarning,
stacklevel=2,
)
return self.stop
@property
def step(self) -> int:
"""
The value of the `step` parameter (``1`` if this was not supplied).
"""
# GH 25710
return self._range.step
@property
def _step(self) -> int:
"""
The value of the `step` parameter (``1`` if this was not supplied).
.. deprecated:: 0.25.0
Use ``step`` instead.
"""
# GH 25710
warnings.warn(
self._deprecation_message.format("_step", "step"),
FutureWarning,
stacklevel=2,
)
return self.step
@cache_readonly
def nbytes(self) -> int:
"""
Return the number of bytes in the underlying data.
"""
rng = self._range
return getsizeof(rng) + sum(
getsizeof(getattr(rng, attr_name))
for attr_name in ["start", "stop", "step"]
)
def memory_usage(self, deep: bool = False) -> int:
"""
Memory usage of my values
Parameters
----------
deep : bool
Introspect the data deeply, interrogate
`object` dtypes for system-level memory consumption
Returns
-------
bytes used
Notes
-----
Memory usage does not include memory consumed by elements that
are not components of the array if deep=False
See Also
--------
numpy.ndarray.nbytes
"""
return self.nbytes
@property
def dtype(self) -> np.dtype:
return | np.dtype(np.int64) | numpy.dtype |
"""
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) | numpy.multiply.reduce |
'''
<NAME>
set up :2020-1-9
intergrate img and label into one file
-- fiducial1024_v1
'''
import argparse
import sys, os
import pickle
import random
import collections
import json
import numpy as np
import scipy.io as io
import scipy.misc as m
import matplotlib.pyplot as plt
import glob
import math
import time
import threading
import multiprocessing as mp
from multiprocessing import Pool
import re
import cv2
# sys.path.append('/lustre/home/gwxie/hope/project/dewarp/datasets/') # /lustre/home/gwxie/program/project/unwarp/perturbed_imgaes/GAN
import utils
def getDatasets(dir):
return os.listdir(dir)
class perturbed(utils.BasePerturbed):
def __init__(self, path, bg_path, save_path, save_suffix):
self.path = path
self.bg_path = bg_path
self.save_path = save_path
self.save_suffix = save_suffix
def save_img(self, m, n, fold_curve='fold', repeat_time=4, fiducial_points = 16, relativeShift_position='relativeShift_v2'):
origin_img = cv2.imread(self.path, flags=cv2.IMREAD_COLOR)
save_img_shape = [512*2, 480*2] # 320
# reduce_value = np.random.choice([2**4, 2**5, 2**6, 2**7, 2**8], p=[0.01, 0.1, 0.4, 0.39, 0.1])
reduce_value = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.02, 0.18, 0.2, 0.3, 0.1, 0.1, 0.08, 0.02])
# reduce_value = np.random.choice([8*2, 16*2, 24*2, 32*2, 40*2, 48*2], p=[0.01, 0.02, 0.2, 0.4, 0.19, 0.18])
# reduce_value = np.random.choice([16, 24, 32, 40, 48, 64], p=[0.01, 0.1, 0.2, 0.4, 0.2, 0.09])
base_img_shrink = save_img_shape[0] - reduce_value
# enlarge_img_shrink = [1024, 768]
# enlarge_img_shrink = [896, 672] # 420
enlarge_img_shrink = [512*4, 480*4] # 420
# enlarge_img_shrink = [896*2, 768*2] # 420
# enlarge_img_shrink = [896, 768] # 420
# enlarge_img_shrink = [768, 576] # 420
# enlarge_img_shrink = [640, 480] # 420
''''''
im_lr = origin_img.shape[0]
im_ud = origin_img.shape[1]
reduce_value_v2 = np.random.choice([2*2, 4*2, 8*2, 16*2, 24*2, 28*2, 32*2, 48*2], p=[0.02, 0.18, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1])
# reduce_value_v2 = np.random.choice([16, 24, 28, 32, 48, 64], p=[0.01, 0.1, 0.2, 0.3, 0.25, 0.14])
if im_lr > im_ud:
im_ud = min(int(im_ud / im_lr * base_img_shrink), save_img_shape[1] - reduce_value_v2)
im_lr = save_img_shape[0] - reduce_value
else:
base_img_shrink = save_img_shape[1] - reduce_value
im_lr = min(int(im_lr / im_ud * base_img_shrink), save_img_shape[0] - reduce_value_v2)
im_ud = base_img_shrink
if round(im_lr / im_ud, 2) < 0.5 or round(im_ud / im_lr, 2) < 0.5:
repeat_time = min(repeat_time, 8)
edge_padding = 3
im_lr -= im_lr % (fiducial_points-1) - (2*edge_padding) # im_lr % (fiducial_points-1) - 1
im_ud -= im_ud % (fiducial_points-1) - (2*edge_padding) # im_ud % (fiducial_points-1) - 1
im_hight = np.linspace(edge_padding, im_lr - edge_padding, fiducial_points, dtype=np.int64)
im_wide = np.linspace(edge_padding, im_ud - edge_padding, fiducial_points, dtype=np.int64)
# im_lr -= im_lr % (fiducial_points-1) - (1+2*edge_padding) # im_lr % (fiducial_points-1) - 1
# im_ud -= im_ud % (fiducial_points-1) - (1+2*edge_padding) # im_ud % (fiducial_points-1) - 1
# im_hight = np.linspace(edge_padding, im_lr - (1+edge_padding), fiducial_points, dtype=np.int64)
# im_wide = np.linspace(edge_padding, im_ud - (1+edge_padding), fiducial_points, dtype=np.int64)
im_x, im_y = np.meshgrid(im_hight, im_wide)
segment_x = (im_lr) // (fiducial_points-1)
segment_y = (im_ud) // (fiducial_points-1)
# plt.plot(im_x, im_y,
# color='limegreen',
# marker='.',
# linestyle='')
# plt.grid(True)
# plt.show()
self.origin_img = cv2.resize(origin_img, (im_ud, im_lr), interpolation=cv2.INTER_CUBIC)
perturbed_bg_ = getDatasets(self.bg_path)
perturbed_bg_img_ = self.bg_path+random.choice(perturbed_bg_)
perturbed_bg_img = cv2.imread(perturbed_bg_img_, flags=cv2.IMREAD_COLOR)
mesh_shape = self.origin_img.shape[:2]
self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 256, dtype=np.float32)#np.zeros_like(perturbed_bg_img)
# self.synthesis_perturbed_img = np.full((enlarge_img_shrink[0], enlarge_img_shrink[1], 3), 0, dtype=np.int16)#np.zeros_like(perturbed_bg_img)
self.new_shape = self.synthesis_perturbed_img.shape[:2]
perturbed_bg_img = cv2.resize(perturbed_bg_img, (save_img_shape[1], save_img_shape[0]), cv2.INPAINT_TELEA)
origin_pixel_position = np.argwhere(np.zeros(mesh_shape, dtype=np.uint32) == 0).reshape(mesh_shape[0], mesh_shape[1], 2)
pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2)
self.perturbed_xy_ = np.zeros((self.new_shape[0], self.new_shape[1], 2))
# self.perturbed_xy_ = pixel_position.copy().astype(np.float32)
# fiducial_points_grid = origin_pixel_position[im_x, im_y]
self.synthesis_perturbed_label = np.zeros((self.new_shape[0], self.new_shape[1], 2))
x_min, y_min, x_max, y_max = self.adjust_position_v2(0, 0, mesh_shape[0], mesh_shape[1], save_img_shape)
origin_pixel_position += [x_min, y_min]
x_min, y_min, x_max, y_max = self.adjust_position(0, 0, mesh_shape[0], mesh_shape[1])
x_shift = random.randint(-enlarge_img_shrink[0]//16, enlarge_img_shrink[0]//16)
y_shift = random.randint(-enlarge_img_shrink[1]//16, enlarge_img_shrink[1]//16)
x_min += x_shift
x_max += x_shift
y_min += y_shift
y_max += y_shift
'''im_x,y'''
im_x += x_min
im_y += y_min
self.synthesis_perturbed_img[x_min:x_max, y_min:y_max] = self.origin_img
self.synthesis_perturbed_label[x_min:x_max, y_min:y_max] = origin_pixel_position
synthesis_perturbed_img_map = self.synthesis_perturbed_img.copy()
synthesis_perturbed_label_map = self.synthesis_perturbed_label.copy()
foreORbackground_label = np.full((mesh_shape), 1, dtype=np.int16)
foreORbackground_label_map = np.full((self.new_shape), 0, dtype=np.int16)
foreORbackground_label_map[x_min:x_max, y_min:y_max] = foreORbackground_label
# synthesis_perturbed_img_map = self.pad(self.synthesis_perturbed_img.copy(), x_min, y_min, x_max, y_max)
# synthesis_perturbed_label_map = self.pad(synthesis_perturbed_label_map, x_min, y_min, x_max, y_max)
'''*****************************************************************'''
is_normalizationFun_mixture = self.is_perform(0.2, 0.8)
# if not is_normalizationFun_mixture:
normalizationFun_0_1 = False
# normalizationFun_0_1 = self.is_perform(0.5, 0.5)
if fold_curve == 'fold':
fold_curve_random = True
# is_normalizationFun_mixture = False
normalizationFun_0_1 = self.is_perform(0.2, 0.8)
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
fold_curve_random = self.is_perform(0.1, 0.9) # False # self.is_perform(0.01, 0.99)
alpha_perturbed = random.randint(80, 160) / 100
# is_normalizationFun_mixture = False # self.is_perform(0.01, 0.99)
synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256)
# synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 0, dtype=np.int16)
synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label)
alpha_perturbed_change = self.is_perform(0.5, 0.5)
p_pp_choice = self.is_perform(0.8, 0.2) if fold_curve == 'fold' else self.is_perform(0.1, 0.9)
for repeat_i in range(repeat_time):
if alpha_perturbed_change:
if fold_curve == 'fold':
if is_normalizationFun_mixture:
alpha_perturbed = random.randint(80, 120) / 100
else:
if normalizationFun_0_1 and repeat_time < 8:
alpha_perturbed = random.randint(50, 70) / 100
else:
alpha_perturbed = random.randint(70, 130) / 100
else:
alpha_perturbed = random.randint(80, 160) / 100
''''''
linspace_x = [0, (self.new_shape[0] - im_lr) // 2 - 1,
self.new_shape[0] - (self.new_shape[0] - im_lr) // 2 - 1, self.new_shape[0] - 1]
linspace_y = [0, (self.new_shape[1] - im_ud) // 2 - 1,
self.new_shape[1] - (self.new_shape[1] - im_ud) // 2 - 1, self.new_shape[1] - 1]
linspace_x_seq = [1, 2, 3]
linspace_y_seq = [1, 2, 3]
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_p = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
if ((r_x == 1 or r_x == 3) and (r_y == 1 or r_y == 3)) and p_pp_choice:
linspace_x_seq.remove(r_x)
linspace_y_seq.remove(r_y)
r_x = random.choice(linspace_x_seq)
r_y = random.choice(linspace_y_seq)
perturbed_pp = np.array(
[random.randint(linspace_x[r_x-1] * 10, linspace_x[r_x] * 10),
random.randint(linspace_y[r_y-1] * 10, linspace_y[r_y] * 10)])/10
# perturbed_p, perturbed_pp = np.array(
# [random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10]) \
# , np.array([random.randint(0, self.new_shape[0] * 10) / 10,
# random.randint(0, self.new_shape[1] * 10) / 10])
# perturbed_p, perturbed_pp = np.array(
# [random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10]) \
# , np.array([random.randint((self.new_shape[0]-im_lr)//2*10, (self.new_shape[0]-(self.new_shape[0]-im_lr)//2) * 10) / 10,
# random.randint((self.new_shape[1]-im_ud)//2*10, (self.new_shape[1]-(self.new_shape[1]-im_ud)//2) * 10) / 10])
''''''
perturbed_vp = perturbed_pp - perturbed_p
perturbed_vp_norm = np.linalg.norm(perturbed_vp)
perturbed_distance_vertex_and_line = np.dot((perturbed_p - pixel_position), perturbed_vp) / perturbed_vp_norm
''''''
# perturbed_v = np.array([random.randint(-3000, 3000) / 100, random.randint(-3000, 3000) / 100])
# perturbed_v = np.array([random.randint(-4000, 4000) / 100, random.randint(-4000, 4000) / 100])
if fold_curve == 'fold' and self.is_perform(0.6, 0.4): # self.is_perform(0.3, 0.7):
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
perturbed_v = np.array([random.randint(-10000, 10000) / 100, random.randint(-10000, 10000) / 100])
# perturbed_v = np.array([random.randint(-11000, 11000) / 100, random.randint(-11000, 11000) / 100])
else:
# perturbed_v = np.array([random.randint(-9000, 9000) / 100, random.randint(-9000, 9000) / 100])
# perturbed_v = np.array([random.randint(-16000, 16000) / 100, random.randint(-16000, 16000) / 100])
perturbed_v = np.array([random.randint(-8000, 8000) / 100, random.randint(-8000, 8000) / 100])
# perturbed_v = np.array([random.randint(-3500, 3500) / 100, random.randint(-3500, 3500) / 100])
# perturbed_v = np.array([random.randint(-600, 600) / 10, random.randint(-600, 600) / 10])
''''''
if fold_curve == 'fold':
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
if is_normalizationFun_mixture:
if self.is_perform(0.5, 0.5):
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
else:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), random.randint(1, 2))
else:
if normalizationFun_0_1:
perturbed_d = self.get_0_1_d(np.abs(perturbed_distance_vertex_and_line), 2)
else:
perturbed_d = np.abs(self.get_normalize(perturbed_distance_vertex_and_line))
''''''
if fold_curve_random:
# omega_perturbed = (alpha_perturbed+0.2) / (perturbed_d + alpha_perturbed)
# omega_perturbed = alpha_perturbed**perturbed_d
omega_perturbed = alpha_perturbed / (perturbed_d + alpha_perturbed)
else:
omega_perturbed = 1 - perturbed_d ** alpha_perturbed
'''shadow'''
if self.is_perform(0.6, 0.4):
synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] = np.minimum(np.maximum(synthesis_perturbed_img_map[x_min:x_max, y_min:y_max] - np.int16(np.round(omega_perturbed[x_min:x_max, y_min:y_max].repeat(3).reshape(x_max-x_min, y_max-y_min, 3) * abs(np.linalg.norm(perturbed_v//2))*np.array([0.4-random.random()*0.1, 0.4-random.random()*0.1, 0.4-random.random()*0.1]))), 0), 255)
''''''
if relativeShift_position in ['position', 'relativeShift_v2']:
self.perturbed_xy_ += np.array([omega_perturbed * perturbed_v[0], omega_perturbed * perturbed_v[1]]).transpose(1, 2, 0)
else:
print('relativeShift_position error')
exit()
'''
flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(
self.new_shape[0] * self.new_shape[1], 2)
vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position)
wts_sum = np.abs(wts).sum(-1)
# flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts)
wts = wts[wts_sum <= 1, :]
vtx = vtx[wts_sum <= 1, :]
synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts)
synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts)
foreORbackground_label = np.zeros(self.new_shape)
foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
# synthesis_perturbed_img = np.around(synthesis_perturbed_img).astype(np.uint8)
synthesis_perturbed_label[:, :, 0] *= foreORbackground_label
synthesis_perturbed_label[:, :, 1] *= foreORbackground_label
synthesis_perturbed_img[:, :, 0] *= foreORbackground_label
synthesis_perturbed_img[:, :, 1] *= foreORbackground_label
synthesis_perturbed_img[:, :, 2] *= foreORbackground_label
self.synthesis_perturbed_img = synthesis_perturbed_img
self.synthesis_perturbed_label = synthesis_perturbed_label
'''
'''perspective'''
perspective_shreshold = random.randint(26, 36)*10 # 280
x_min_per, y_min_per, x_max_per, y_max_per = self.adjust_position(perspective_shreshold, perspective_shreshold, self.new_shape[0]-perspective_shreshold, self.new_shape[1]-perspective_shreshold)
pts1 = np.float32([[x_min_per, y_min_per], [x_max_per, y_min_per], [x_min_per, y_max_per], [x_max_per, y_max_per]])
e_1_ = x_max_per - x_min_per
e_2_ = y_max_per - y_min_per
e_3_ = e_2_
e_4_ = e_1_
perspective_shreshold_h = e_1_*0.02
perspective_shreshold_w = e_2_*0.02
a_min_, a_max_ = 70, 110
# if self.is_perform(1, 0):
if fold_curve == 'curve' and self.is_perform(0.5, 0.5):
if self.is_perform(0.5, 0.5):
while True:
pts2 = np.around(
np.float32([[x_min_per - (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold],
[x_max_per - (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold],
[x_min_per + (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold],
[x_max_per + (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold]])) # right
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
else:
while True:
pts2 = np.around(
np.float32([[x_min_per + (random.random()) * perspective_shreshold, y_min_per - (random.random()) * perspective_shreshold],
[x_max_per + (random.random()) * perspective_shreshold, y_min_per + (random.random()) * perspective_shreshold],
[x_min_per - (random.random()) * perspective_shreshold, y_max_per - (random.random()) * perspective_shreshold],
[x_max_per - (random.random()) * perspective_shreshold, y_max_per + (random.random()) * perspective_shreshold]]))
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
else:
while True:
pts2 = np.around(np.float32([[x_min_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold],
[x_max_per+(random.random()-0.5)*perspective_shreshold, y_min_per+(random.random()-0.5)*perspective_shreshold],
[x_min_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold],
[x_max_per+(random.random()-0.5)*perspective_shreshold, y_max_per+(random.random()-0.5)*perspective_shreshold]]))
e_1 = np.linalg.norm(pts2[0]-pts2[1])
e_2 = np.linalg.norm(pts2[0]-pts2[2])
e_3 = np.linalg.norm(pts2[1]-pts2[3])
e_4 = np.linalg.norm(pts2[2]-pts2[3])
if e_1_+perspective_shreshold_h > e_1 and e_2_+perspective_shreshold_w > e_2 and e_3_+perspective_shreshold_w > e_3 and e_4_+perspective_shreshold_h > e_4 and \
e_1_ - perspective_shreshold_h < e_1 and e_2_ - perspective_shreshold_w < e_2 and e_3_ - perspective_shreshold_w < e_3 and e_4_ - perspective_shreshold_h < e_4 and \
abs(e_1-e_4) < perspective_shreshold_h and abs(e_2-e_3) < perspective_shreshold_w:
a0_, a1_, a2_, a3_ = self.get_angle_4(pts2)
if (a0_ > a_min_ and a0_ < a_max_) or (a1_ > a_min_ and a1_ < a_max_) or (a2_ > a_min_ and a2_ < a_max_) or (a3_ > a_min_ and a3_ < a_max_):
break
M = cv2.getPerspectiveTransform(pts1, pts2)
one = np.ones((self.new_shape[0], self.new_shape[1], 1), dtype=np.int16)
matr = np.dstack((pixel_position, one))
new = np.dot(M, matr.reshape(-1, 3).T).T.reshape(self.new_shape[0], self.new_shape[1], 3)
x = new[:, :, 0]/new[:, :, 2]
y = new[:, :, 1]/new[:, :, 2]
perturbed_xy_ = np.dstack((x, y))
# perturbed_xy_round_int = np.around(cv2.bilateralFilter(perturbed_xy_round_int, 9, 75, 75))
# perturbed_xy_round_int = np.around(cv2.blur(perturbed_xy_, (17, 17)))
# perturbed_xy_round_int = cv2.blur(perturbed_xy_round_int, (17, 17))
# perturbed_xy_round_int = cv2.GaussianBlur(perturbed_xy_round_int, (7, 7), 0)
perturbed_xy_ = perturbed_xy_-np.min(perturbed_xy_.T.reshape(2, -1), 1)
# perturbed_xy_round_int = np.around(perturbed_xy_round_int-np.min(perturbed_xy_round_int.T.reshape(2, -1), 1)).astype(np.int16)
self.perturbed_xy_ += perturbed_xy_
'''perspective end'''
'''to img'''
flat_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(
self.new_shape[0] * self.new_shape[1], 2)
# self.perturbed_xy_ = cv2.blur(self.perturbed_xy_, (7, 7))
self.perturbed_xy_ = cv2.GaussianBlur(self.perturbed_xy_, (7, 7), 0)
'''get fiducial points'''
fiducial_points_coordinate = self.perturbed_xy_[im_x, im_y]
vtx, wts = self.interp_weights(self.perturbed_xy_.reshape(self.new_shape[0] * self.new_shape[1], 2), flat_position)
wts_sum = np.abs(wts).sum(-1)
# flat_img.reshape(flat_shape[0] * flat_shape[1], 3)[:] = interpolate(pixel, vtx, wts)
wts = wts[wts_sum <= 1, :]
vtx = vtx[wts_sum <= 1, :]
synthesis_perturbed_img.reshape(self.new_shape[0] * self.new_shape[1], 3)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_img_map.reshape(self.new_shape[0] * self.new_shape[1], 3), vtx, wts)
synthesis_perturbed_label.reshape(self.new_shape[0] * self.new_shape[1], 2)[wts_sum <= 1,
:] = self.interpolate(synthesis_perturbed_label_map.reshape(self.new_shape[0] * self.new_shape[1], 2), vtx, wts)
foreORbackground_label = np.zeros(self.new_shape)
foreORbackground_label.reshape(self.new_shape[0] * self.new_shape[1], 1)[wts_sum <= 1, :] = self.interpolate(foreORbackground_label_map.reshape(self.new_shape[0] * self.new_shape[1], 1), vtx, wts)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
self.synthesis_perturbed_img = synthesis_perturbed_img
self.synthesis_perturbed_label = synthesis_perturbed_label
self.foreORbackground_label = foreORbackground_label
'''draw fiducial points
stepSize = 0
fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_img.copy()
for l in fiducial_points_coordinate.astype(np.int64).reshape(-1,2):
cv2.circle(fiducial_points_synthesis_perturbed_img, (l[1] + math.ceil(stepSize / 2), l[0] + math.ceil(stepSize / 2)), 5, (0, 0, 255), -1)
cv2.imwrite('/lustre/home/gwxie/program/project/unwarp/unwarp_perturbed/TPS/img/cv_TPS_large.jpg', fiducial_points_synthesis_perturbed_img)
'''
'''clip'''
perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = -1, -1, self.new_shape[0], self.new_shape[1]
for x in range(self.new_shape[0] // 2, perturbed_x_max):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and perturbed_x_max - 1 > x:
perturbed_x_max = x
break
for x in range(self.new_shape[0] // 2, perturbed_x_min, -1):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and x > 0:
perturbed_x_min = x
break
for y in range(self.new_shape[1] // 2, perturbed_y_max):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and perturbed_y_max - 1 > y:
perturbed_y_max = y
break
for y in range(self.new_shape[1] // 2, perturbed_y_min, -1):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and y > 0:
perturbed_y_min = y
break
if perturbed_x_min == 0 or perturbed_x_max == self.new_shape[0] or perturbed_y_min == self.new_shape[1] or perturbed_y_max == self.new_shape[1]:
raise Exception('clip error')
if perturbed_x_max - perturbed_x_min < im_lr//2 or perturbed_y_max - perturbed_y_min < im_ud//2:
raise Exception('clip error')
perfix_ = self.save_suffix+'_'+str(m)+'_'+str(n)
is_shrink = False
if perturbed_x_max - perturbed_x_min > save_img_shape[0] or perturbed_y_max - perturbed_y_min > save_img_shape[1]:
is_shrink = True
synthesis_perturbed_img = cv2.resize(self.synthesis_perturbed_img[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR)
synthesis_perturbed_label = cv2.resize(self.synthesis_perturbed_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR)
foreORbackground_label = cv2.resize(self.foreORbackground_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max].copy(), (im_ud, im_lr), interpolation=cv2.INTER_LINEAR)
foreORbackground_label[foreORbackground_label < 0.99] = 0
foreORbackground_label[foreORbackground_label >= 0.99] = 1
'''shrink fiducial points'''
center_x_l, center_y_l = perturbed_x_min + (perturbed_x_max - perturbed_x_min) // 2, perturbed_y_min + (perturbed_y_max - perturbed_y_min) // 2
fiducial_points_coordinate_copy = fiducial_points_coordinate.copy()
shrink_x = im_lr/(perturbed_x_max - perturbed_x_min)
shrink_y = im_ud/(perturbed_y_max - perturbed_y_min)
fiducial_points_coordinate *= [shrink_x, shrink_y]
center_x_l *= shrink_x
center_y_l *= shrink_y
# fiducial_points_coordinate[1:, 1:] *= [shrink_x, shrink_y]
# fiducial_points_coordinate[1:, :1, 0] *= shrink_x
# fiducial_points_coordinate[:1, 1:, 1] *= shrink_y
# perturbed_x_min_copy, perturbed_y_min_copy, perturbed_x_max_copy, perturbed_y_max_copy = perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max
perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = self.adjust_position_v2(0, 0, im_lr, im_ud, self.new_shape)
self.synthesis_perturbed_img = np.full_like(self.synthesis_perturbed_img, 256)
self.synthesis_perturbed_label = np.zeros_like(self.synthesis_perturbed_label)
self.foreORbackground_label = np.zeros_like(self.foreORbackground_label)
self.synthesis_perturbed_img[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_img
self.synthesis_perturbed_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_label
self.foreORbackground_label[perturbed_x_min:perturbed_x_max, perturbed_y_min:perturbed_y_max] = foreORbackground_label
center_x, center_y = perturbed_x_min + (perturbed_x_max - perturbed_x_min) // 2, perturbed_y_min + (perturbed_y_max - perturbed_y_min) // 2
if is_shrink:
fiducial_points_coordinate += [center_x-center_x_l, center_y-center_y_l]
'''draw fiducial points
stepSize = 0
fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_img.copy()
for l in fiducial_points_coordinate.astype(np.int64).reshape(-1, 2):
cv2.circle(fiducial_points_synthesis_perturbed_img,
(l[1] + math.ceil(stepSize / 2), l[0] + math.ceil(stepSize / 2)), 5, (0, 0, 255), -1)
cv2.imwrite('/lustre/home/gwxie/program/project/unwarp/unwarp_perturbed/TPS/img/cv_TPS_small.jpg',fiducial_points_synthesis_perturbed_img)
'''
self.new_shape = save_img_shape
self.synthesis_perturbed_img = self.synthesis_perturbed_img[
center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2,
center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2,
:].copy()
self.synthesis_perturbed_label = self.synthesis_perturbed_label[
center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2,
center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2,
:].copy()
self.foreORbackground_label = self.foreORbackground_label[
center_x - self.new_shape[0] // 2:center_x + self.new_shape[0] // 2,
center_y - self.new_shape[1] // 2:center_y + self.new_shape[1] // 2].copy()
perturbed_x_ = max(self.new_shape[0] - (perturbed_x_max - perturbed_x_min), 0)
perturbed_x_min = perturbed_x_ // 2
perturbed_x_max = self.new_shape[0] - perturbed_x_ // 2 if perturbed_x_%2 == 0 else self.new_shape[0] - (perturbed_x_ // 2 + 1)
perturbed_y_ = max(self.new_shape[1] - (perturbed_y_max - perturbed_y_min), 0)
perturbed_y_min = perturbed_y_ // 2
perturbed_y_max = self.new_shape[1] - perturbed_y_ // 2 if perturbed_y_%2 == 0 else self.new_shape[1] - (perturbed_y_ // 2 + 1)
'''clip
perturbed_x_min, perturbed_y_min, perturbed_x_max, perturbed_y_max = -1, -1, self.new_shape[0], self.new_shape[1]
for x in range(self.new_shape[0] // 2, perturbed_x_max):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and perturbed_x_max - 1 > x:
perturbed_x_max = x
break
for x in range(self.new_shape[0] // 2, perturbed_x_min, -1):
if np.sum(self.synthesis_perturbed_img[x, :]) == 768 * self.new_shape[1] and x > 0:
perturbed_x_min = x
break
for y in range(self.new_shape[1] // 2, perturbed_y_max):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and perturbed_y_max - 1 > y:
perturbed_y_max = y
break
for y in range(self.new_shape[1] // 2, perturbed_y_min, -1):
if np.sum(self.synthesis_perturbed_img[:, y]) == 768 * self.new_shape[0] and y > 0:
perturbed_y_min = y
break
center_x, center_y = perturbed_x_min+(perturbed_x_max - perturbed_x_min)//2, perturbed_y_min+(perturbed_y_max - perturbed_y_min)//2
perfix_ = self.save_suffix+'_'+str(m)+'_'+str(n)
self.new_shape = save_img_shape
perturbed_x_ = max(self.new_shape[0] - (perturbed_x_max - perturbed_x_min), 0)
perturbed_x_min = perturbed_x_ // 2
perturbed_x_max = self.new_shape[0] - perturbed_x_ // 2 if perturbed_x_%2 == 0 else self.new_shape[0] - (perturbed_x_ // 2 + 1)
perturbed_y_ = max(self.new_shape[1] - (perturbed_y_max - perturbed_y_min), 0)
perturbed_y_min = perturbed_y_ // 2
perturbed_y_max = self.new_shape[1] - perturbed_y_ // 2 if perturbed_y_%2 == 0 else self.new_shape[1] - (perturbed_y_ // 2 + 1)
self.synthesis_perturbed_img = self.synthesis_perturbed_img[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2, :].copy()
self.synthesis_perturbed_label = self.synthesis_perturbed_label[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2, :].copy()
self.foreORbackground_label = self.foreORbackground_label[center_x-self.new_shape[0]//2:center_x+self.new_shape[0]//2, center_y-self.new_shape[1]//2:center_y+self.new_shape[1]//2].copy()
'''
'''save'''
pixel_position = np.argwhere(np.zeros(self.new_shape, dtype=np.uint32) == 0).reshape(self.new_shape[0], self.new_shape[1], 2)
if relativeShift_position == 'relativeShift_v2':
self.synthesis_perturbed_label -= pixel_position
fiducial_points_coordinate -= [center_x - self.new_shape[0] // 2, center_y - self.new_shape[1] // 2]
self.synthesis_perturbed_label[:, :, 0] *= self.foreORbackground_label
self.synthesis_perturbed_label[:, :, 1] *= self.foreORbackground_label
self.synthesis_perturbed_img[:, :, 0] *= self.foreORbackground_label
self.synthesis_perturbed_img[:, :, 1] *= self.foreORbackground_label
self.synthesis_perturbed_img[:, :, 2] *= self.foreORbackground_label
'''
synthesis_perturbed_img_filter = self.synthesis_perturbed_img.copy()
synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0)
# if self.is_perform(0.9, 0.1) or repeat_time > 5:
# # if self.is_perform(0.1, 0.9) and repeat_time > 9:
# # synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (7, 7), 0)
# # else:
# synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (5, 5), 0)
# else:
# synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0)
self.synthesis_perturbed_img[self.foreORbackground_label == 1] = synthesis_perturbed_img_filter[self.foreORbackground_label == 1]
'''
'''
perturbed_bg_img = perturbed_bg_img.astype(np.float32)
perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label
self.synthesis_perturbed_img += perturbed_bg_img
HSV
perturbed_bg_img = perturbed_bg_img.astype(np.float32)
if self.is_perform(0.1, 0.9):
if self.is_perform(0.2, 0.8):
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_RGB2HSV)
H_, S_, V_ = (random.random()-0.2)*20, (random.random()-0.2)/8, (random.random()-0.2)*20
synthesis_perturbed_img_clip_HSV[:, :, 0], synthesis_perturbed_img_clip_HSV[:, :, 1], synthesis_perturbed_img_clip_HSV[:, :, 2] = synthesis_perturbed_img_clip_HSV[:, :, 0]-H_, synthesis_perturbed_img_clip_HSV[:, :, 1]-S_, synthesis_perturbed_img_clip_HSV[:, :, 2]-V_
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_HSV2RGB)
perturbed_bg_img[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1-self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
else:
perturbed_bg_img_HSV = perturbed_bg_img
perturbed_bg_img_HSV = cv2.cvtColor(perturbed_bg_img_HSV, cv2.COLOR_RGB2HSV)
H_, S_, V_ = (random.random()-0.5)*20, (random.random()-0.5)/8, (random.random()-0.2)*20
perturbed_bg_img_HSV[:, :, 0], perturbed_bg_img_HSV[:, :, 1], perturbed_bg_img_HSV[:, :, 2] = perturbed_bg_img_HSV[:, :, 0]-H_, perturbed_bg_img_HSV[:, :, 1]-S_, perturbed_bg_img_HSV[:, :, 2]-V_
perturbed_bg_img_HSV = cv2.cvtColor(perturbed_bg_img_HSV, cv2.COLOR_HSV2RGB)
perturbed_bg_img_HSV[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 2] *= 1-self.foreORbackground_label
self.synthesis_perturbed_img += perturbed_bg_img_HSV
# self.synthesis_perturbed_img[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771]
else:
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
# synthesis_perturbed_img_clip_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img[np.sum(self.synthesis_perturbed_img, 2) == 771]
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_RGB2HSV)
H_, S_, V_ = (random.random()-0.5)*20, (random.random()-0.5)/10, (random.random()-0.4)*20
synthesis_perturbed_img_clip_HSV[:, :, 0], synthesis_perturbed_img_clip_HSV[:, :, 1], synthesis_perturbed_img_clip_HSV[:, :, 2] = synthesis_perturbed_img_clip_HSV[:, :, 0]-H_, synthesis_perturbed_img_clip_HSV[:, :, 1]-S_, synthesis_perturbed_img_clip_HSV[:, :, 2]-V_
synthesis_perturbed_img_clip_HSV = cv2.cvtColor(synthesis_perturbed_img_clip_HSV, cv2.COLOR_HSV2RGB)
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
'''
'''HSV_v2'''
perturbed_bg_img = perturbed_bg_img.astype(np.float32)
# if self.is_perform(1, 0):
# if self.is_perform(1, 0):
if self.is_perform(0.1, 0.9):
if self.is_perform(0.2, 0.8):
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
synthesis_perturbed_img_clip_HSV = self.HSV_v1(synthesis_perturbed_img_clip_HSV)
perturbed_bg_img[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1-self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
else:
perturbed_bg_img_HSV = perturbed_bg_img
perturbed_bg_img_HSV = self.HSV_v1(perturbed_bg_img_HSV)
perturbed_bg_img_HSV[:, :, 0] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 1] *= 1-self.foreORbackground_label
perturbed_bg_img_HSV[:, :, 2] *= 1-self.foreORbackground_label
self.synthesis_perturbed_img += perturbed_bg_img_HSV
# self.synthesis_perturbed_img[np.sum(self.synthesis_perturbed_img, 2) == 771] = perturbed_bg_img_HSV[np.sum(self.synthesis_perturbed_img, 2) == 771]
else:
synthesis_perturbed_img_clip_HSV = self.synthesis_perturbed_img.copy()
perturbed_bg_img[:, :, 0] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 1] *= 1 - self.foreORbackground_label
perturbed_bg_img[:, :, 2] *= 1 - self.foreORbackground_label
synthesis_perturbed_img_clip_HSV += perturbed_bg_img
synthesis_perturbed_img_clip_HSV = self.HSV_v1(synthesis_perturbed_img_clip_HSV)
self.synthesis_perturbed_img = synthesis_perturbed_img_clip_HSV
''''''
# cv2.imwrite(self.save_path+'clip/'+perfix_+'_'+fold_curve+str(perturbed_time)+'-'+str(repeat_time)+'.png', synthesis_perturbed_img_clip)
self.synthesis_perturbed_img[self.synthesis_perturbed_img < 0] = 0
self.synthesis_perturbed_img[self.synthesis_perturbed_img > 255] = 255
self.synthesis_perturbed_img = np.around(self.synthesis_perturbed_img).astype(np.uint8)
label = np.zeros_like(self.synthesis_perturbed_img, dtype=np.float32)
label[:, :, :2] = self.synthesis_perturbed_label
label[:, :, 2] = self.foreORbackground_label
# grey = np.around(self.synthesis_perturbed_img[:, :, 0] * 0.2989 + self.synthesis_perturbed_img[:, :, 1] * 0.5870 + self.synthesis_perturbed_img[:, :, 0] * 0.1140).astype(np.int16)
# synthesis_perturbed_grey = np.concatenate((grey.reshape(self.new_shape[0], self.new_shape[1], 1), label), axis=2)
synthesis_perturbed_color = np.concatenate((self.synthesis_perturbed_img, label), axis=2)
self.synthesis_perturbed_color = np.zeros_like(synthesis_perturbed_color, dtype=np.float32)
# self.synthesis_perturbed_grey = np.zeros_like(synthesis_perturbed_grey, dtype=np.float32)
reduce_value_x = int(round(min((random.random() / 2) * (self.new_shape[0] - (perturbed_x_max - perturbed_x_min)), min(reduce_value, reduce_value_v2))))
reduce_value_y = int(round(min((random.random() / 2) * (self.new_shape[1] - (perturbed_y_max - perturbed_y_min)), min(reduce_value, reduce_value_v2))))
perturbed_x_min = max(perturbed_x_min - reduce_value_x, 0)
perturbed_x_max = min(perturbed_x_max + reduce_value_x, self.new_shape[0])
perturbed_y_min = max(perturbed_y_min - reduce_value_y, 0)
perturbed_y_max = min(perturbed_y_max + reduce_value_y, self.new_shape[1])
if im_lr >= im_ud:
self.synthesis_perturbed_color[:, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_color[:, perturbed_y_min:perturbed_y_max, :]
# self.synthesis_perturbed_grey[:, perturbed_y_min:perturbed_y_max, :] = synthesis_perturbed_grey[:, perturbed_y_min:perturbed_y_max, :]
else:
self.synthesis_perturbed_color[perturbed_x_min:perturbed_x_max, :, :] = synthesis_perturbed_color[perturbed_x_min:perturbed_x_max, :, :]
# self.synthesis_perturbed_grey[perturbed_x_min:perturbed_x_max, :, :] = synthesis_perturbed_grey[perturbed_x_min:perturbed_x_max, :, :]
'''blur'''
if self.is_perform(0.1, 0.9):
synthesis_perturbed_img_filter = self.synthesis_perturbed_color[:, :, :3].copy()
if self.is_perform(0.1, 0.9):
synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (5, 5), 0)
else:
synthesis_perturbed_img_filter = cv2.GaussianBlur(synthesis_perturbed_img_filter, (3, 3), 0)
if self.is_perform(0.5, 0.5):
self.synthesis_perturbed_color[:, :, :3][self.synthesis_perturbed_color[:, :, 5] == 1] = synthesis_perturbed_img_filter[self.synthesis_perturbed_color[:, :, 5] == 1]
else:
self.synthesis_perturbed_color[:, :, :3] = synthesis_perturbed_img_filter
fiducial_points_coordinate = fiducial_points_coordinate[:, :, ::-1]
'''draw fiducial points'''
stepSize = 0
fiducial_points_synthesis_perturbed_img = self.synthesis_perturbed_color[:, :, :3].copy()
for l in fiducial_points_coordinate.astype(np.int64).reshape(-1, 2):
cv2.circle(fiducial_points_synthesis_perturbed_img, (l[0] + math.ceil(stepSize / 2), l[1] + math.ceil(stepSize / 2)), 2, (0, 0, 255), -1)
cv2.imwrite(self.save_path + 'fiducial_points/' + perfix_ + '_' + fold_curve + '.png', fiducial_points_synthesis_perturbed_img)
cv2.imwrite(self.save_path + 'png/' + perfix_ + '_' + fold_curve + '.png', self.synthesis_perturbed_color[:, :, :3])
'''forward-begin'''
self.forward_mapping = np.full((save_img_shape[0], save_img_shape[1], 2), 0, dtype=np.float32)
forward_mapping = np.full((save_img_shape[0], save_img_shape[1], 2), 0, dtype=np.float32)
forward_position = (self.synthesis_perturbed_color[:, :, 3:5] + pixel_position)[self.synthesis_perturbed_color[:, :, 5] != 0, :]
flat_position = np.argwhere( | np.zeros(save_img_shape, dtype=np.uint32) | 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)
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) | numpy.linspace |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * | np.ones(100) | numpy.ones |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray',
linestyle='dashed')
plt.xlim(3.4 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/neural_network.png')
plt.show()
# plot 6a
np.random.seed(0)
time = np.linspace(0, 5 * np.pi, 1001)
knots_51 = np.linspace(0, 5 * np.pi, 51)
time_series = np.cos(2 * time) + np.cos(4 * time) + np.cos(8 * time)
noise = np.random.normal(0, 1, len(time_series))
time_series += noise
advemdpy = EMD(time=time, time_series=time_series)
imfs_51, hts_51, ifs_51 = advemdpy.empirical_mode_decomposition(knots=knots_51, max_imfs=3,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_31 = np.linspace(0, 5 * np.pi, 31)
imfs_31, hts_31, ifs_31 = advemdpy.empirical_mode_decomposition(knots=knots_31, max_imfs=2,
edge_effect='symmetric_anchor', verbose=False)[:3]
knots_11 = np.linspace(0, 5 * np.pi, 11)
imfs_11, hts_11, ifs_11 = advemdpy.empirical_mode_decomposition(knots=knots_11, max_imfs=1,
edge_effect='symmetric_anchor', verbose=False)[:3]
fig, axs = plt.subplots(3, 1)
plt.suptitle(textwrap.fill('Comparison of Trends Extracted with Different Knot Sequences', 40))
plt.subplots_adjust(hspace=0.1)
axs[0].plot(time, time_series, label='Time series')
axs[0].plot(time, imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 1, IMF 2, & IMF 3 with 51 knots', 21))
print(f'DFA fluctuation with 51 knots: {np.round(np.var(time_series - (imfs_51[1, :] + imfs_51[2, :] + imfs_51[3, :])), 3)}')
for knot in knots_51:
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[0].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1, label='Knots')
axs[0].set_xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi, 5 * np.pi])
axs[0].set_xticklabels(['', '', '', '', '', ''])
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), 5.5 * np.ones(101), 'k--')
axs[0].plot(np.linspace(0.95 * np.pi, 1.55 * np.pi, 101), -5.5 * np.ones(101), 'k--')
axs[0].plot(0.95 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--')
axs[0].plot(1.55 * np.pi * np.ones(101), np.linspace(-5.5, 5.5, 101), 'k--', label='Zoomed region')
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, 0.5), fontsize=8)
axs[1].plot(time, time_series, label='Time series')
axs[1].plot(time, imfs_31[1, :] + imfs_31[2, :], label=textwrap.fill('Sum of IMF 1 and IMF 2 with 31 knots', 19))
axs[1].plot(time, imfs_51[2, :] + imfs_51[3, :], label=textwrap.fill('Sum of IMF 2 and IMF 3 with 51 knots', 19))
print(f'DFA fluctuation with 31 knots: {np.round(np.var(time_series - (imfs_31[1, :] + imfs_31[2, :])), 3)}')
for knot in knots_31:
axs[1].plot(knot * np.ones(101), np.linspace(-5, 5, 101), '--', c='grey', zorder=1)
axs[1].plot(knot * np.ones(101), | np.linspace(-5, 5, 101) | numpy.linspace |
import matplotlib.pyplot as plt
import numpy as np
from fears.utils import results_manager, plotter, dir_manager
import os
suffix = '07212021_0001'
data_folder = 'results_' + suffix
exp_info_file = 'experiment_info_' + suffix + '.p'
exp_folders,exp_info = results_manager.get_experiment_results(data_folder,
exp_info_file)
max_cells = exp_info.populations[0].max_cells
n_sims = exp_info.n_sims
k_abs = exp_info.slopes
exp_folders.reverse()
k_abs = | np.flip(k_abs) | numpy.flip |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.ones_like |
"""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)) | numpy.empty |
# ________
# /
# \ /
# \ /
# \/
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) | numpy.linspace |
""" Unit tests for the system interface."""
import unittest
from six import assertRaisesRegex
from six.moves import cStringIO
import numpy as np
from openmdao.api import Problem, Group, IndepVarComp, ExecComp
from openmdao.test_suite.components.options_feature_vector import VectorDoublingComp
from openmdao.utils.assert_utils import assert_rel_error, assert_warning
class TestSystem(unittest.TestCase):
def test_vector_context_managers(self):
g1 = Group()
g1.add_subsystem('Indep', IndepVarComp('a', 5.0), promotes=['a'])
g2 = g1.add_subsystem('G2', Group(), promotes=['*'])
g2.add_subsystem('C1', ExecComp('b=2*a'), promotes=['a', 'b'])
model = Group()
model.add_subsystem('G1', g1, promotes=['b'])
model.add_subsystem('Sink', ExecComp('c=2*b'), promotes=['b'])
p = Problem(model=model)
p.set_solver_print(level=0)
# Test pre-setup errors
with self.assertRaises(Exception) as cm:
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(str(cm.exception),
"Group: Cannot get vectors because setup has not yet been called.")
with self.assertRaises(Exception) as cm:
d_inputs, d_outputs, d_residuals = model.get_linear_vectors('vec')
self.assertEqual(str(cm.exception),
"Group: Cannot get vectors because setup has not yet been called.")
p.setup()
p.run_model()
# Test inputs with original values
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(inputs['G1.G2.C1.a'], 5.)
inputs, outputs, residuals = g1.get_nonlinear_vectors()
self.assertEqual(inputs['G2.C1.a'], 5.)
# Test inputs after setting a new value
inputs, outputs, residuals = g2.get_nonlinear_vectors()
inputs['C1.a'] = -1.
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(inputs['G1.G2.C1.a'], -1.)
inputs, outputs, residuals = g1.get_nonlinear_vectors()
self.assertEqual(inputs['G2.C1.a'], -1.)
# Test outputs with original values
inputs, outputs, residuals = model.get_nonlinear_vectors()
self.assertEqual(outputs['G1.G2.C1.b'], 10.)
inputs, outputs, residuals = g2.get_nonlinear_vectors()
# Test outputs after setting a new value
inputs, outputs, residuals = model.get_nonlinear_vectors()
outputs['G1.G2.C1.b'] = 123.
self.assertEqual(outputs['G1.G2.C1.b'], 123.)
inputs, outputs, residuals = g2.get_nonlinear_vectors()
outputs['C1.b'] = 789.
self.assertEqual(outputs['C1.b'], 789.)
# Test residuals
inputs, outputs, residuals = model.get_nonlinear_vectors()
residuals['G1.G2.C1.b'] = 99.0
self.assertEqual(residuals['G1.G2.C1.b'], 99.0)
# Test linear
d_inputs, d_outputs, d_residuals = model.get_linear_vectors('linear')
d_outputs['G1.G2.C1.b'] = 10.
self.assertEqual(d_outputs['G1.G2.C1.b'], 10.)
# Test linear with invalid vec_name
with self.assertRaises(Exception) as cm:
d_inputs, d_outputs, d_residuals = model.get_linear_vectors('bad_name')
self.assertEqual(str(cm.exception),
"Group (<model>): There is no linear vector named %s" % 'bad_name')
def test_set_checks_shape(self):
indep = IndepVarComp()
indep.add_output('a')
indep.add_output('x', shape=(5, 1))
g1 = Group()
g1.add_subsystem('Indep', indep, promotes=['a', 'x'])
g2 = g1.add_subsystem('G2', Group(), promotes=['*'])
g2.add_subsystem('C1', ExecComp('b=2*a'), promotes=['a', 'b'])
g2.add_subsystem('C2', ExecComp('y=2*x',
x=np.zeros((5, 1)),
y= | np.zeros((5, 1)) | numpy.zeros |
# 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) | numpy.cos |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = | np.hstack((weights, 0)) | 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) | numpy.random.randn |
import os
import string
from collections import Counter
from datetime import datetime
from functools import partial
from pathlib import Path
from typing import Optional
import numpy as np
import pandas as pd
from scipy.stats.stats import chisquare
from tangled_up_in_unicode import block, block_abbr, category, category_long, script
from pandas_profiling.config import Settings
from pandas_profiling.model.summary_helpers_image import (
extract_exif,
hash_image,
is_image_truncated,
open_image,
)
def mad(arr: np.ndarray) -> np.ndarray:
"""Median Absolute Deviation: a "Robust" version of standard deviation.
Indices variability of the sample.
https://en.wikipedia.org/wiki/Median_absolute_deviation
"""
return np.median(np.abs(arr - np.median(arr)))
def named_aggregate_summary(series: pd.Series, key: str) -> dict:
summary = {
f"max_{key}": np.max(series),
f"mean_{key}": np.mean(series),
f"median_{key}": np.median(series),
f"min_{key}": np.min(series),
}
return summary
def length_summary(series: pd.Series, summary: dict = None) -> dict:
if summary is None:
summary = {}
length = series.str.len()
summary.update({"length": length})
summary.update(named_aggregate_summary(length, "length"))
return summary
def file_summary(series: pd.Series) -> dict:
"""
Args:
series: series to summarize
Returns:
"""
# Transform
stats = series.map(lambda x: os.stat(x))
def convert_datetime(x: float) -> str:
return datetime.fromtimestamp(x).strftime("%Y-%m-%d %H:%M:%S")
# Transform some more
summary = {
"file_size": stats.map(lambda x: x.st_size),
"file_created_time": stats.map(lambda x: x.st_ctime).map(convert_datetime),
"file_accessed_time": stats.map(lambda x: x.st_atime).map(convert_datetime),
"file_modified_time": stats.map(lambda x: x.st_mtime).map(convert_datetime),
}
return summary
def path_summary(series: pd.Series) -> dict:
"""
Args:
series: series to summarize
Returns:
"""
# TODO: optimize using value counts
summary = {
"common_prefix": os.path.commonprefix(series.values.tolist())
or "No common prefix",
"stem_counts": series.map(lambda x: os.path.splitext(x)[0]).value_counts(),
"suffix_counts": series.map(lambda x: os.path.splitext(x)[1]).value_counts(),
"name_counts": series.map(lambda x: os.path.basename(x)).value_counts(),
"parent_counts": series.map(lambda x: os.path.dirname(x)).value_counts(),
"anchor_counts": series.map(lambda x: os.path.splitdrive(x)[0]).value_counts(),
}
summary["n_stem_unique"] = len(summary["stem_counts"])
summary["n_suffix_unique"] = len(summary["suffix_counts"])
summary["n_name_unique"] = len(summary["name_counts"])
summary["n_parent_unique"] = len(summary["parent_counts"])
summary["n_anchor_unique"] = len(summary["anchor_counts"])
return summary
def url_summary(series: pd.Series) -> dict:
"""
Args:
series: series to summarize
Returns:
"""
summary = {
"scheme_counts": series.map(lambda x: x.scheme).value_counts(),
"netloc_counts": series.map(lambda x: x.netloc).value_counts(),
"path_counts": series.map(lambda x: x.path).value_counts(),
"query_counts": series.map(lambda x: x.query).value_counts(),
"fragment_counts": series.map(lambda x: x.fragment).value_counts(),
}
return summary
def count_duplicate_hashes(image_descriptions: dict) -> int:
"""
Args:
image_descriptions:
Returns:
"""
counts = pd.Series(
[x["hash"] for x in image_descriptions if "hash" in x]
).value_counts()
return counts.sum() - len(counts)
def extract_exif_series(image_exifs: list) -> dict:
"""
Args:
image_exifs:
Returns:
"""
exif_keys = []
exif_values: dict = {}
for image_exif in image_exifs:
# Extract key
exif_keys.extend(list(image_exif.keys()))
# Extract values per key
for exif_key, exif_val in image_exif.items():
if exif_key not in exif_values:
exif_values[exif_key] = []
exif_values[exif_key].append(exif_val)
series = {"exif_keys": pd.Series(exif_keys, dtype=object).value_counts().to_dict()}
for k, v in exif_values.items():
series[k] = pd.Series(v).value_counts()
return series
def extract_image_information(
path: Path, exif: bool = False, hash: bool = False
) -> dict:
"""Extracts all image information per file, as opening files is slow
Args:
path: Path to the image
exif: extract exif information
hash: calculate hash (for duplicate detection)
Returns:
A dict containing image information
"""
information: dict = {}
image = open_image(path)
information["opened"] = image is not None
if image is not None:
information["truncated"] = is_image_truncated(image)
if not information["truncated"]:
information["size"] = image.size
if exif:
information["exif"] = extract_exif(image)
if hash:
information["hash"] = hash_image(image)
return information
def image_summary(series: pd.Series, exif: bool = False, hash: bool = False) -> dict:
"""
Args:
series: series to summarize
exif: extract exif information
hash: calculate hash (for duplicate detection)
Returns:
"""
image_information = series.apply(
partial(extract_image_information, exif=exif, hash=hash)
)
summary = {
"n_truncated": sum(
[1 for x in image_information if "truncated" in x and x["truncated"]]
),
"image_dimensions": pd.Series(
[x["size"] for x in image_information if "size" in x],
name="image_dimensions",
),
}
image_widths = summary["image_dimensions"].map(lambda x: x[0])
summary.update(named_aggregate_summary(image_widths, "width"))
image_heights = summary["image_dimensions"].map(lambda x: x[1])
summary.update(named_aggregate_summary(image_heights, "height"))
image_areas = image_widths * image_heights
summary.update(named_aggregate_summary(image_areas, "area"))
if hash:
summary["n_duplicate_hash"] = count_duplicate_hashes(image_information)
if exif:
exif_series = extract_exif_series(
[x["exif"] for x in image_information if "exif" in x]
)
summary["exif_keys_counts"] = exif_series["exif_keys"]
summary["exif_data"] = exif_series
return summary
def get_character_counts(series: pd.Series) -> Counter:
"""Function to return the character counts
Args:
series: the Series to process
Returns:
A dict with character counts
"""
return Counter(series.str.cat())
def counter_to_series(counter: Counter) -> pd.Series:
if not counter:
return pd.Series([], dtype=object)
counter_as_tuples = counter.most_common()
items, counts = zip(*counter_as_tuples)
return pd.Series(counts, index=items)
def unicode_summary(series: pd.Series) -> dict:
# Unicode Character Summaries (category and script name)
character_counts = get_character_counts(series)
character_counts_series = counter_to_series(character_counts)
char_to_block = {key: block(key) for key in character_counts.keys()}
char_to_category_short = {key: category(key) for key in character_counts.keys()}
char_to_script = {key: script(key) for key in character_counts.keys()}
summary = {
"n_characters": len(character_counts_series),
"character_counts": character_counts_series,
"category_alias_values": {
key: category_long(value) for key, value in char_to_category_short.items()
},
"block_alias_values": {
key: block_abbr(value) for key, value in char_to_block.items()
},
}
# Retrieve original distribution
block_alias_counts: Counter = Counter()
per_block_char_counts: dict = {
k: Counter() for k in summary["block_alias_values"].values()
}
for char, n_char in character_counts.items():
block_name = summary["block_alias_values"][char]
block_alias_counts[block_name] += n_char
per_block_char_counts[block_name][char] = n_char
summary["block_alias_counts"] = counter_to_series(block_alias_counts)
summary["block_alias_char_counts"] = {
k: counter_to_series(v) for k, v in per_block_char_counts.items()
}
script_counts: Counter = Counter()
per_script_char_counts: dict = {k: Counter() for k in char_to_script.values()}
for char, n_char in character_counts.items():
script_name = char_to_script[char]
script_counts[script_name] += n_char
per_script_char_counts[script_name][char] = n_char
summary["script_counts"] = counter_to_series(script_counts)
summary["script_char_counts"] = {
k: counter_to_series(v) for k, v in per_script_char_counts.items()
}
category_alias_counts: Counter = Counter()
per_category_alias_char_counts: dict = {
k: Counter() for k in summary["category_alias_values"].values()
}
for char, n_char in character_counts.items():
category_alias_name = summary["category_alias_values"][char]
category_alias_counts[category_alias_name] += n_char
per_category_alias_char_counts[category_alias_name][char] += n_char
summary["category_alias_counts"] = counter_to_series(category_alias_counts)
summary["category_alias_char_counts"] = {
k: counter_to_series(v) for k, v in per_category_alias_char_counts.items()
}
# Unique counts
summary["n_category"] = len(summary["category_alias_counts"])
summary["n_scripts"] = len(summary["script_counts"])
summary["n_block_alias"] = len(summary["block_alias_counts"])
if len(summary["category_alias_counts"]) > 0:
summary["category_alias_counts"].index = summary[
"category_alias_counts"
].index.str.replace("_", " ")
return summary
def histogram_compute(
config: Settings,
finite_values: np.ndarray,
n_unique: int,
name: str = "histogram",
weights: Optional[np.ndarray] = None,
) -> dict:
stats = {}
bins = config.plot.histogram.bins
bins_arg = "auto" if bins == 0 else min(bins, n_unique)
stats[name] = np.histogram(finite_values, bins=bins_arg, weights=weights)
max_bins = config.plot.histogram.max_bins
if bins_arg == "auto" and len(stats[name][1]) > max_bins:
stats[name] = | np.histogram(finite_values, bins=max_bins, weights=None) | numpy.histogram |
import copy
import functools
import itertools
import numbers
import warnings
from collections import defaultdict
from datetime import timedelta
from distutils.version import LooseVersion
from typing import (
Any,
Dict,
Hashable,
Mapping,
Optional,
Sequence,
Tuple,
TypeVar,
Union,
)
import numpy as np
import pandas as pd
import xarray as xr # only for Dataset and DataArray
from . import arithmetic, common, dtypes, duck_array_ops, indexing, nputils, ops, utils
from .indexing import (
BasicIndexer,
OuterIndexer,
PandasIndexAdapter,
VectorizedIndexer,
as_indexable,
)
from .npcompat import IS_NEP18_ACTIVE
from .options import _get_keep_attrs
from .pycompat import (
cupy_array_type,
dask_array_type,
integer_types,
is_duck_dask_array,
)
from .utils import (
OrderedSet,
_default,
decode_numpy_dict_values,
drop_dims_from_indexers,
either_dict_or_kwargs,
ensure_us_time_resolution,
infix_dims,
is_duck_array,
)
NON_NUMPY_SUPPORTED_ARRAY_TYPES = (
(
indexing.ExplicitlyIndexed,
pd.Index,
)
+ dask_array_type
+ cupy_array_type
)
# https://github.com/python/mypy/issues/224
BASIC_INDEXING_TYPES = integer_types + (slice,) # type: ignore
VariableType = TypeVar("VariableType", bound="Variable")
"""Type annotation to be used when methods of Variable return self or a copy of self.
When called from an instance of a subclass, e.g. IndexVariable, mypy identifies the
output as an instance of the subclass.
Usage::
class Variable:
def f(self: VariableType, ...) -> VariableType:
...
"""
class MissingDimensionsError(ValueError):
"""Error class used when we can't safely guess a dimension name."""
# inherits from ValueError for backward compatibility
# TODO: move this to an xarray.exceptions module?
def as_variable(obj, name=None) -> "Union[Variable, IndexVariable]":
"""Convert an object into a Variable.
Parameters
----------
obj : object
Object to convert into a Variable.
- If the object is already a Variable, return a shallow copy.
- Otherwise, if the object has 'dims' and 'data' attributes, convert
it into a new Variable.
- If all else fails, attempt to convert the object into a Variable by
unpacking it into the arguments for creating a new Variable.
name : str, optional
If provided:
- `obj` can be a 1D array, which is assumed to label coordinate values
along a dimension of this given name.
- Variables with name matching one of their dimensions are converted
into `IndexVariable` objects.
Returns
-------
var : Variable
The newly created variable.
"""
from .dataarray import DataArray
# TODO: consider extending this method to automatically handle Iris and
if isinstance(obj, DataArray):
# extract the primary Variable from DataArrays
obj = obj.variable
if isinstance(obj, Variable):
obj = obj.copy(deep=False)
elif isinstance(obj, tuple):
try:
obj = Variable(*obj)
except (TypeError, ValueError) as error:
# use .format() instead of % because it handles tuples consistently
raise error.__class__(
"Could not convert tuple of form "
"(dims, data[, attrs, encoding]): "
"{} to Variable.".format(obj)
)
elif utils.is_scalar(obj):
obj = Variable([], obj)
elif isinstance(obj, (pd.Index, IndexVariable)) and obj.name is not None:
obj = Variable(obj.name, obj)
elif isinstance(obj, (set, dict)):
raise TypeError("variable {!r} has invalid type {!r}".format(name, type(obj)))
elif name is not None:
data = as_compatible_data(obj)
if data.ndim != 1:
raise MissingDimensionsError(
"cannot set variable %r with %r-dimensional data "
"without explicit dimension names. Pass a tuple of "
"(dims, data) instead." % (name, data.ndim)
)
obj = Variable(name, data, fastpath=True)
else:
raise TypeError(
"unable to convert object into a variable without an "
"explicit list of dimensions: %r" % obj
)
if name is not None and name in obj.dims:
# convert the Variable into an Index
if obj.ndim != 1:
raise MissingDimensionsError(
"%r has more than 1-dimension and the same name as one of its "
"dimensions %r. xarray disallows such variables because they "
"conflict with the coordinates used to label "
"dimensions." % (name, obj.dims)
)
obj = obj.to_index_variable()
return obj
def _maybe_wrap_data(data):
"""
Put pandas.Index and numpy.ndarray arguments in adapter objects to ensure
they can be indexed properly.
NumpyArrayAdapter, PandasIndexAdapter and LazilyOuterIndexedArray should
all pass through unmodified.
"""
if isinstance(data, pd.Index):
return PandasIndexAdapter(data)
return data
def _possibly_convert_objects(values):
"""Convert arrays of datetime.datetime and datetime.timedelta objects into
datetime64 and timedelta64, according to the pandas convention. Also used for
validating that datetime64 and timedelta64 objects are within the valid date
range for ns precision, as pandas will raise an error if they are not.
"""
return np.asarray(pd.Series(values.ravel())).reshape(values.shape)
def as_compatible_data(data, fastpath=False):
"""Prepare and wrap data to put in a Variable.
- If data does not have the necessary attributes, convert it to ndarray.
- If data has dtype=datetime64, ensure that it has ns precision. If it's a
pandas.Timestamp, convert it to datetime64.
- If data is already a pandas or xarray object (other than an Index), just
use the values.
Finally, wrap it up with an adapter if necessary.
"""
if fastpath and getattr(data, "ndim", 0) > 0:
# can't use fastpath (yet) for scalars
return _maybe_wrap_data(data)
if isinstance(data, Variable):
return data.data
if isinstance(data, NON_NUMPY_SUPPORTED_ARRAY_TYPES):
return _maybe_wrap_data(data)
if isinstance(data, tuple):
data = utils.to_0d_object_array(data)
if isinstance(data, pd.Timestamp):
# TODO: convert, handle datetime objects, too
data = np.datetime64(data.value, "ns")
if isinstance(data, timedelta):
data = np.timedelta64(getattr(data, "value", data), "ns")
# we don't want nested self-described arrays
data = getattr(data, "values", data)
if isinstance(data, np.ma.MaskedArray):
mask = np.ma.getmaskarray(data)
if mask.any():
dtype, fill_value = dtypes.maybe_promote(data.dtype)
data = np.asarray(data, dtype=dtype)
data[mask] = fill_value
else:
data = np.asarray(data)
if not isinstance(data, np.ndarray):
if hasattr(data, "__array_function__"):
if IS_NEP18_ACTIVE:
return data
else:
raise TypeError(
"Got an NumPy-like array type providing the "
"__array_function__ protocol but NEP18 is not enabled. "
"Check that numpy >= v1.16 and that the environment "
'variable "NUMPY_EXPERIMENTAL_ARRAY_FUNCTION" is set to '
'"1"'
)
# validate whether the data is valid data types.
data = np.asarray(data)
if isinstance(data, np.ndarray):
if data.dtype.kind == "O":
data = _possibly_convert_objects(data)
elif data.dtype.kind == "M":
data = _possibly_convert_objects(data)
elif data.dtype.kind == "m":
data = _possibly_convert_objects(data)
return _maybe_wrap_data(data)
def _as_array_or_item(data):
"""Return the given values as a numpy array, or as an individual item if
it's a 0d datetime64 or timedelta64 array.
Importantly, this function does not copy data if it is already an ndarray -
otherwise, it will not be possible to update Variable values in place.
This function mostly exists because 0-dimensional ndarrays with
dtype=datetime64 are broken :(
https://github.com/numpy/numpy/issues/4337
https://github.com/numpy/numpy/issues/7619
TODO: remove this (replace with np.asarray) once these issues are fixed
"""
if isinstance(data, cupy_array_type):
data = data.get()
else:
data = np.asarray(data)
if data.ndim == 0:
if data.dtype.kind == "M":
data = np.datetime64(data, "ns")
elif data.dtype.kind == "m":
data = np.timedelta64(data, "ns")
return data
class Variable(
common.AbstractArray, arithmetic.SupportsArithmetic, utils.NdimSizeLenMixin
):
"""A netcdf-like variable consisting of dimensions, data and attributes
which describe a single Array. A single Variable object is not fully
described outside the context of its parent Dataset (if you want such a
fully described object, use a DataArray instead).
The main functional difference between Variables and numpy arrays is that
numerical operations on Variables implement array broadcasting by dimension
name. For example, adding an Variable with dimensions `('time',)` to
another Variable with dimensions `('space',)` results in a new Variable
with dimensions `('time', 'space')`. Furthermore, numpy reduce operations
like ``mean`` or ``sum`` are overwritten to take a "dimension" argument
instead of an "axis".
Variables are light-weight objects used as the building block for datasets.
They are more primitive objects, so operations with them provide marginally
higher performance than using DataArrays. However, manipulating data in the
form of a Dataset or DataArray should almost always be preferred, because
they can use more complete metadata in context of coordinate labels.
"""
__slots__ = ("_dims", "_data", "_attrs", "_encoding")
def __init__(self, dims, data, attrs=None, encoding=None, fastpath=False):
"""
Parameters
----------
dims : str or sequence of str
Name(s) of the the data dimension(s). Must be either a string (only
for 1D data) or a sequence of strings with length equal to the
number of dimensions.
data : array_like
Data array which supports numpy-like data access.
attrs : dict_like or None, optional
Attributes to assign to the new variable. If None (default), an
empty attribute dictionary is initialized.
encoding : dict_like or None, optional
Dictionary specifying how to encode this array's data into a
serialized format like netCDF4. Currently used keys (for netCDF)
include '_FillValue', 'scale_factor', 'add_offset' and 'dtype'.
Well-behaved code to serialize a Variable should ignore
unrecognized encoding items.
"""
self._data = as_compatible_data(data, fastpath=fastpath)
self._dims = self._parse_dimensions(dims)
self._attrs = None
self._encoding = None
if attrs is not None:
self.attrs = attrs
if encoding is not None:
self.encoding = encoding
@property
def dtype(self):
return self._data.dtype
@property
def shape(self):
return self._data.shape
@property
def nbytes(self):
return self.size * self.dtype.itemsize
@property
def _in_memory(self):
return isinstance(self._data, (np.ndarray, np.number, PandasIndexAdapter)) or (
isinstance(self._data, indexing.MemoryCachedArray)
and isinstance(self._data.array, indexing.NumpyIndexingAdapter)
)
@property
def data(self):
if is_duck_array(self._data):
return self._data
else:
return self.values
@data.setter
def data(self, data):
data = as_compatible_data(data)
if data.shape != self.shape:
raise ValueError(
f"replacement data must match the Variable's shape. "
f"replacement data has shape {data.shape}; Variable has shape {self.shape}"
)
self._data = data
def astype(
self: VariableType,
dtype,
*,
order=None,
casting=None,
subok=None,
copy=None,
keep_attrs=True,
) -> VariableType:
"""
Copy of the Variable object, with data cast to a specified type.
Parameters
----------
dtype : str or dtype
Typecode or data-type to which the array is cast.
order : {'C', 'F', 'A', 'K'}, optional
Controls the memory layout order of the result. ‘C’ means C order,
‘F’ means Fortran order, ‘A’ means ‘F’ order if all the arrays are
Fortran contiguous, ‘C’ order otherwise, and ‘K’ means as close to
the order the array elements appear in memory as possible.
casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
Controls what kind of data casting may occur.
* 'no' means the data types should not be cast at all.
* 'equiv' means only byte-order changes are allowed.
* 'safe' means only casts which can preserve values are allowed.
* 'same_kind' means only safe casts or casts within a kind,
like float64 to float32, are allowed.
* 'unsafe' means any data conversions may be done.
subok : bool, optional
If True, then sub-classes will be passed-through, otherwise the
returned array will be forced to be a base-class array.
copy : bool, optional
By default, astype always returns a newly allocated array. If this
is set to False and the `dtype` requirement is satisfied, the input
array is returned instead of a copy.
keep_attrs : bool, optional
By default, astype keeps attributes. Set to False to remove
attributes in the returned object.
Returns
-------
out : same as object
New object with data cast to the specified type.
Notes
-----
The ``order``, ``casting``, ``subok`` and ``copy`` arguments are only passed
through to the ``astype`` method of the underlying array when a value
different than ``None`` is supplied.
Make sure to only supply these arguments if the underlying array class
supports them.
See also
--------
numpy.ndarray.astype
dask.array.Array.astype
sparse.COO.astype
"""
from .computation import apply_ufunc
kwargs = dict(order=order, casting=casting, subok=subok, copy=copy)
kwargs = {k: v for k, v in kwargs.items() if v is not None}
return apply_ufunc(
duck_array_ops.astype,
self,
dtype,
kwargs=kwargs,
keep_attrs=keep_attrs,
dask="allowed",
)
def load(self, **kwargs):
"""Manually trigger loading of this variable's data from disk or a
remote source into memory and return this variable.
Normally, it should not be necessary to call this method in user code,
because all xarray functions should either work on deferred data or
load data automatically.
Parameters
----------
**kwargs : dict
Additional keyword arguments passed on to ``dask.array.compute``.
See Also
--------
dask.array.compute
"""
if is_duck_dask_array(self._data):
self._data = as_compatible_data(self._data.compute(**kwargs))
elif not is_duck_array(self._data):
self._data = np.asarray(self._data)
return self
def compute(self, **kwargs):
"""Manually trigger loading of this variable's data from disk or a
remote source into memory and return a new variable. The original is
left unaltered.
Normally, it should not be necessary to call this method in user code,
because all xarray functions should either work on deferred data or
load data automatically.
Parameters
----------
**kwargs : dict
Additional keyword arguments passed on to ``dask.array.compute``.
See Also
--------
dask.array.compute
"""
new = self.copy(deep=False)
return new.load(**kwargs)
def __dask_tokenize__(self):
# Use v.data, instead of v._data, in order to cope with the wrappers
# around NetCDF and the like
from dask.base import normalize_token
return normalize_token((type(self), self._dims, self.data, self._attrs))
def __dask_graph__(self):
if is_duck_dask_array(self._data):
return self._data.__dask_graph__()
else:
return None
def __dask_keys__(self):
return self._data.__dask_keys__()
def __dask_layers__(self):
return self._data.__dask_layers__()
@property
def __dask_optimize__(self):
return self._data.__dask_optimize__
@property
def __dask_scheduler__(self):
return self._data.__dask_scheduler__
def __dask_postcompute__(self):
array_func, array_args = self._data.__dask_postcompute__()
return (
self._dask_finalize,
(array_func, array_args, self._dims, self._attrs, self._encoding),
)
def __dask_postpersist__(self):
array_func, array_args = self._data.__dask_postpersist__()
return (
self._dask_finalize,
(array_func, array_args, self._dims, self._attrs, self._encoding),
)
@staticmethod
def _dask_finalize(results, array_func, array_args, dims, attrs, encoding):
data = array_func(results, *array_args)
return Variable(dims, data, attrs=attrs, encoding=encoding)
@property
def values(self):
"""The variable's data as a numpy.ndarray"""
return _as_array_or_item(self._data)
@values.setter
def values(self, values):
self.data = values
def to_base_variable(self):
"""Return this variable as a base xarray.Variable"""
return Variable(
self.dims, self._data, self._attrs, encoding=self._encoding, fastpath=True
)
to_variable = utils.alias(to_base_variable, "to_variable")
def to_index_variable(self):
"""Return this variable as an xarray.IndexVariable"""
return IndexVariable(
self.dims, self._data, self._attrs, encoding=self._encoding, fastpath=True
)
to_coord = utils.alias(to_index_variable, "to_coord")
def to_index(self):
"""Convert this variable to a pandas.Index"""
return self.to_index_variable().to_index()
def to_dict(self, data=True):
"""Dictionary representation of variable."""
item = {"dims": self.dims, "attrs": decode_numpy_dict_values(self.attrs)}
if data:
item["data"] = ensure_us_time_resolution(self.values).tolist()
else:
item.update({"dtype": str(self.dtype), "shape": self.shape})
return item
@property
def dims(self):
"""Tuple of dimension names with which this variable is associated."""
return self._dims
@dims.setter
def dims(self, value):
self._dims = self._parse_dimensions(value)
def _parse_dimensions(self, dims):
if isinstance(dims, str):
dims = (dims,)
dims = tuple(dims)
if len(dims) != self.ndim:
raise ValueError(
"dimensions %s must have the same length as the "
"number of data dimensions, ndim=%s" % (dims, self.ndim)
)
return dims
def _item_key_to_tuple(self, key):
if utils.is_dict_like(key):
return tuple(key.get(dim, slice(None)) for dim in self.dims)
else:
return key
def _broadcast_indexes(self, key):
"""Prepare an indexing key for an indexing operation.
Parameters
-----------
key: int, slice, array-like, dict or tuple of integer, slice and array-like
Any valid input for indexing.
Returns
-------
dims : tuple
Dimension of the resultant variable.
indexers : IndexingTuple subclass
Tuple of integer, array-like, or slices to use when indexing
self._data. The type of this argument indicates the type of
indexing to perform, either basic, outer or vectorized.
new_order : Optional[Sequence[int]]
Optional reordering to do on the result of indexing. If not None,
the first len(new_order) indexing should be moved to these
positions.
"""
key = self._item_key_to_tuple(key) # key is a tuple
# key is a tuple of full size
key = indexing.expanded_indexer(key, self.ndim)
# Convert a scalar Variable to an integer
key = tuple(
k.data.item() if isinstance(k, Variable) and k.ndim == 0 else k for k in key
)
# Convert a 0d-array to an integer
key = tuple(
k.item() if isinstance(k, np.ndarray) and k.ndim == 0 else k for k in key
)
if all(isinstance(k, BASIC_INDEXING_TYPES) for k in key):
return self._broadcast_indexes_basic(key)
self._validate_indexers(key)
# Detect it can be mapped as an outer indexer
# If all key is unlabeled, or
# key can be mapped as an OuterIndexer.
if all(not isinstance(k, Variable) for k in key):
return self._broadcast_indexes_outer(key)
# If all key is 1-dimensional and there are no duplicate labels,
# key can be mapped as an OuterIndexer.
dims = []
for k, d in zip(key, self.dims):
if isinstance(k, Variable):
if len(k.dims) > 1:
return self._broadcast_indexes_vectorized(key)
dims.append(k.dims[0])
elif not isinstance(k, integer_types):
dims.append(d)
if len(set(dims)) == len(dims):
return self._broadcast_indexes_outer(key)
return self._broadcast_indexes_vectorized(key)
def _broadcast_indexes_basic(self, key):
dims = tuple(
dim for k, dim in zip(key, self.dims) if not isinstance(k, integer_types)
)
return dims, BasicIndexer(key), None
def _validate_indexers(self, key):
""" Make sanity checks """
for dim, k in zip(self.dims, key):
if isinstance(k, BASIC_INDEXING_TYPES):
pass
else:
if not isinstance(k, Variable):
k = np.asarray(k)
if k.ndim > 1:
raise IndexError(
"Unlabeled multi-dimensional array cannot be "
"used for indexing: {}".format(k)
)
if k.dtype.kind == "b":
if self.shape[self.get_axis_num(dim)] != len(k):
raise IndexError(
"Boolean array size {:d} is used to index array "
"with shape {:s}.".format(len(k), str(self.shape))
)
if k.ndim > 1:
raise IndexError(
"{}-dimensional boolean indexing is "
"not supported. ".format(k.ndim)
)
if getattr(k, "dims", (dim,)) != (dim,):
raise IndexError(
"Boolean indexer should be unlabeled or on the "
"same dimension to the indexed array. Indexer is "
"on {:s} but the target dimension is {:s}.".format(
str(k.dims), dim
)
)
def _broadcast_indexes_outer(self, key):
dims = tuple(
k.dims[0] if isinstance(k, Variable) else dim
for k, dim in zip(key, self.dims)
if not isinstance(k, integer_types)
)
new_key = []
for k in key:
if isinstance(k, Variable):
k = k.data
if not isinstance(k, BASIC_INDEXING_TYPES):
k = np.asarray(k)
if k.size == 0:
# Slice by empty list; numpy could not infer the dtype
k = k.astype(int)
elif k.dtype.kind == "b":
(k,) = np.nonzero(k)
new_key.append(k)
return dims, OuterIndexer(tuple(new_key)), None
def _nonzero(self):
""" Equivalent numpy's nonzero but returns a tuple of Varibles. """
# TODO we should replace dask's native nonzero
# after https://github.com/dask/dask/issues/1076 is implemented.
nonzeros = np.nonzero(self.data)
return tuple(Variable((dim), nz) for nz, dim in zip(nonzeros, self.dims))
def _broadcast_indexes_vectorized(self, key):
variables = []
out_dims_set = OrderedSet()
for dim, value in zip(self.dims, key):
if isinstance(value, slice):
out_dims_set.add(dim)
else:
variable = (
value
if isinstance(value, Variable)
else as_variable(value, name=dim)
)
if variable.dtype.kind == "b": # boolean indexing case
(variable,) = variable._nonzero()
variables.append(variable)
out_dims_set.update(variable.dims)
variable_dims = set()
for variable in variables:
variable_dims.update(variable.dims)
slices = []
for i, (dim, value) in enumerate(zip(self.dims, key)):
if isinstance(value, slice):
if dim in variable_dims:
# We only convert slice objects to variables if they share
# a dimension with at least one other variable. Otherwise,
# we can equivalently leave them as slices aknd transpose
# the result. This is significantly faster/more efficient
# for most array backends.
values = np.arange(*value.indices(self.sizes[dim]))
variables.insert(i - len(slices), Variable((dim,), values))
else:
slices.append((i, value))
try:
variables = _broadcast_compat_variables(*variables)
except ValueError:
raise IndexError(f"Dimensions of indexers mismatch: {key}")
out_key = [variable.data for variable in variables]
out_dims = tuple(out_dims_set)
slice_positions = set()
for i, value in slices:
out_key.insert(i, value)
new_position = out_dims.index(self.dims[i])
slice_positions.add(new_position)
if slice_positions:
new_order = [i for i in range(len(out_dims)) if i not in slice_positions]
else:
new_order = None
return out_dims, VectorizedIndexer(tuple(out_key)), new_order
def __getitem__(self: VariableType, key) -> VariableType:
"""Return a new Variable object whose contents are consistent with
getting the provided key from the underlying data.
NB. __getitem__ and __setitem__ implement xarray-style indexing,
where if keys are unlabeled arrays, we index the array orthogonally
with them. If keys are labeled array (such as Variables), they are
broadcasted with our usual scheme and then the array is indexed with
the broadcasted key, like numpy's fancy indexing.
If you really want to do indexing like `x[x > 0]`, manipulate the numpy
array `x.values` directly.
"""
dims, indexer, new_order = self._broadcast_indexes(key)
data = as_indexable(self._data)[indexer]
if new_order:
data = duck_array_ops.moveaxis(data, range(len(new_order)), new_order)
return self._finalize_indexing_result(dims, data)
def _finalize_indexing_result(self: VariableType, dims, data) -> VariableType:
"""Used by IndexVariable to return IndexVariable objects when possible."""
return type(self)(dims, data, self._attrs, self._encoding, fastpath=True)
def _getitem_with_mask(self, key, fill_value=dtypes.NA):
"""Index this Variable with -1 remapped to fill_value."""
# TODO(shoyer): expose this method in public API somewhere (isel?) and
# use it for reindex.
# TODO(shoyer): add a sanity check that all other integers are
# non-negative
# TODO(shoyer): add an optimization, remapping -1 to an adjacent value
# that is actually indexed rather than mapping it to the last value
# along each axis.
if fill_value is dtypes.NA:
fill_value = dtypes.get_fill_value(self.dtype)
dims, indexer, new_order = self._broadcast_indexes(key)
if self.size:
if is_duck_dask_array(self._data):
# dask's indexing is faster this way; also vindex does not
# support negative indices yet:
# https://github.com/dask/dask/pull/2967
actual_indexer = indexing.posify_mask_indexer(indexer)
else:
actual_indexer = indexer
data = as_indexable(self._data)[actual_indexer]
mask = indexing.create_mask(indexer, self.shape, data)
# we need to invert the mask in order to pass data first. This helps
# pint to choose the correct unit
# TODO: revert after https://github.com/hgrecco/pint/issues/1019 is fixed
data = duck_array_ops.where(np.logical_not(mask), data, fill_value)
else:
# array cannot be indexed along dimensions of size 0, so just
# build the mask directly instead.
mask = indexing.create_mask(indexer, self.shape)
data = np.broadcast_to(fill_value, getattr(mask, "shape", ()))
if new_order:
data = duck_array_ops.moveaxis(data, range(len(new_order)), new_order)
return self._finalize_indexing_result(dims, data)
def __setitem__(self, key, value):
"""__setitem__ is overloaded to access the underlying numpy values with
orthogonal indexing.
See __getitem__ for more details.
"""
dims, index_tuple, new_order = self._broadcast_indexes(key)
if not isinstance(value, Variable):
value = as_compatible_data(value)
if value.ndim > len(dims):
raise ValueError(
"shape mismatch: value array of shape %s could not be "
"broadcast to indexing result with %s dimensions"
% (value.shape, len(dims))
)
if value.ndim == 0:
value = Variable((), value)
else:
value = Variable(dims[-value.ndim :], value)
# broadcast to become assignable
value = value.set_dims(dims).data
if new_order:
value = duck_array_ops.asarray(value)
value = value[(len(dims) - value.ndim) * (np.newaxis,) + (Ellipsis,)]
value = duck_array_ops.moveaxis(value, new_order, range(len(new_order)))
indexable = as_indexable(self._data)
indexable[index_tuple] = value
@property
def attrs(self) -> Dict[Hashable, Any]:
"""Dictionary of local attributes on this variable."""
if self._attrs is None:
self._attrs = {}
return self._attrs
@attrs.setter
def attrs(self, value: Mapping[Hashable, Any]) -> None:
self._attrs = dict(value)
@property
def encoding(self):
"""Dictionary of encodings on this variable."""
if self._encoding is None:
self._encoding = {}
return self._encoding
@encoding.setter
def encoding(self, value):
try:
self._encoding = dict(value)
except ValueError:
raise ValueError("encoding must be castable to a dictionary")
def copy(self, deep=True, data=None):
"""Returns a copy of this object.
If `deep=True`, the data array is loaded into memory and copied onto
the new object. Dimensions, attributes and encodings are always copied.
Use `data` to create a new object with the same structure as
original but entirely new data.
Parameters
----------
deep : bool, optional
Whether the data array is loaded into memory and copied onto
the new object. Default is True.
data : array_like, optional
Data to use in the new object. Must have same shape as original.
When `data` is used, `deep` is ignored.
Returns
-------
object : Variable
New object with dimensions, attributes, encodings, and optionally
data copied from original.
Examples
--------
Shallow copy versus deep copy
>>> var = xr.Variable(data=[1, 2, 3], dims="x")
>>> var.copy()
<xarray.Variable (x: 3)>
array([1, 2, 3])
>>> var_0 = var.copy(deep=False)
>>> var_0[0] = 7
>>> var_0
<xarray.Variable (x: 3)>
array([7, 2, 3])
>>> var
<xarray.Variable (x: 3)>
array([7, 2, 3])
Changing the data using the ``data`` argument maintains the
structure of the original object, but with the new data. Original
object is unaffected.
>>> var.copy(data=[0.1, 0.2, 0.3])
<xarray.Variable (x: 3)>
array([0.1, 0.2, 0.3])
>>> var
<xarray.Variable (x: 3)>
array([7, 2, 3])
See Also
--------
pandas.DataFrame.copy
"""
if data is None:
data = self._data
if isinstance(data, indexing.MemoryCachedArray):
# don't share caching between copies
data = indexing.MemoryCachedArray(data.array)
if deep:
data = copy.deepcopy(data)
else:
data = as_compatible_data(data)
if self.shape != data.shape:
raise ValueError(
"Data shape {} must match shape of object {}".format(
data.shape, self.shape
)
)
# note:
# dims is already an immutable tuple
# attributes and encoding will be copied when the new Array is created
return self._replace(data=data)
def _replace(
self, dims=_default, data=_default, attrs=_default, encoding=_default
) -> "Variable":
if dims is _default:
dims = copy.copy(self._dims)
if data is _default:
data = copy.copy(self.data)
if attrs is _default:
attrs = copy.copy(self._attrs)
if encoding is _default:
encoding = copy.copy(self._encoding)
return type(self)(dims, data, attrs, encoding, fastpath=True)
def __copy__(self):
return self.copy(deep=False)
def __deepcopy__(self, memo=None):
# memo does nothing but is required for compatibility with
# copy.deepcopy
return self.copy(deep=True)
# mutable objects should not be hashable
# https://github.com/python/mypy/issues/4266
__hash__ = None # type: ignore
@property
def chunks(self):
"""Block dimensions for this array's data or None if it's not a dask
array.
"""
return getattr(self._data, "chunks", None)
_array_counter = itertools.count()
def chunk(self, chunks={}, name=None, lock=False):
"""Coerce this array's data into a dask arrays with the given chunks.
If this variable is a non-dask array, it will be converted to dask
array. If it's a dask array, it will be rechunked to the given chunk
sizes.
If neither chunks is not provided for one or more dimensions, chunk
sizes along that dimension will not be updated; non-dask arrays will be
converted into dask arrays with a single block.
Parameters
----------
chunks : int, tuple or dict, optional
Chunk sizes along each dimension, e.g., ``5``, ``(5, 5)`` or
``{'x': 5, 'y': 5}``.
name : str, optional
Used to generate the name for this array in the internal dask
graph. Does not need not be unique.
lock : optional
Passed on to :py:func:`dask.array.from_array`, if the array is not
already as dask array.
Returns
-------
chunked : xarray.Variable
"""
import dask
import dask.array as da
if chunks is None:
warnings.warn(
"None value for 'chunks' is deprecated. "
"It will raise an error in the future. Use instead '{}'",
category=FutureWarning,
)
chunks = {}
if utils.is_dict_like(chunks):
chunks = {self.get_axis_num(dim): chunk for dim, chunk in chunks.items()}
data = self._data
if is_duck_dask_array(data):
data = data.rechunk(chunks)
else:
if isinstance(data, indexing.ExplicitlyIndexed):
# Unambiguously handle array storage backends (like NetCDF4 and h5py)
# that can't handle general array indexing. For example, in netCDF4 you
# can do "outer" indexing along two dimensions independent, which works
# differently from how NumPy handles it.
# da.from_array works by using lazy indexing with a tuple of slices.
# Using OuterIndexer is a pragmatic choice: dask does not yet handle
# different indexing types in an explicit way:
# https://github.com/dask/dask/issues/2883
data = indexing.ImplicitToExplicitIndexingAdapter(
data, indexing.OuterIndexer
)
if LooseVersion(dask.__version__) < "2.0.0":
kwargs = {}
else:
# All of our lazily loaded backend array classes should use NumPy
# array operations.
kwargs = {"meta": np.ndarray}
else:
kwargs = {}
if utils.is_dict_like(chunks):
chunks = tuple(chunks.get(n, s) for n, s in enumerate(self.shape))
data = da.from_array(data, chunks, name=name, lock=lock, **kwargs)
return type(self)(self.dims, data, self._attrs, self._encoding, fastpath=True)
def _as_sparse(self, sparse_format=_default, fill_value=dtypes.NA):
"""
use sparse-array as backend.
"""
import sparse
# TODO: what to do if dask-backended?
if fill_value is dtypes.NA:
dtype, fill_value = dtypes.maybe_promote(self.dtype)
else:
dtype = dtypes.result_type(self.dtype, fill_value)
if sparse_format is _default:
sparse_format = "coo"
try:
as_sparse = getattr(sparse, f"as_{sparse_format.lower()}")
except AttributeError:
raise ValueError(f"{sparse_format} is not a valid sparse format")
data = as_sparse(self.data.astype(dtype), fill_value=fill_value)
return self._replace(data=data)
def _to_dense(self):
"""
Change backend from sparse to np.array
"""
if hasattr(self._data, "todense"):
return self._replace(data=self._data.todense())
return self.copy(deep=False)
def isel(
self: VariableType,
indexers: Mapping[Hashable, Any] = None,
missing_dims: str = "raise",
**indexers_kwargs: Any,
) -> VariableType:
"""Return a new array indexed along the specified dimension(s).
Parameters
----------
**indexers : {dim: indexer, ...}
Keyword arguments with names matching dimensions and values given
by integers, slice objects or arrays.
missing_dims : {"raise", "warn", "ignore"}, default: "raise"
What to do if dimensions that should be selected from are not present in the
DataArray:
- "raise": raise an exception
- "warning": raise a warning, and ignore the missing dimensions
- "ignore": ignore the missing dimensions
Returns
-------
obj : Array object
A new Array with the selected data and dimensions. In general,
the new variable's data will be a view of this variable's data,
unless numpy fancy indexing was triggered by using an array
indexer, in which case the data will be a copy.
"""
indexers = either_dict_or_kwargs(indexers, indexers_kwargs, "isel")
indexers = drop_dims_from_indexers(indexers, self.dims, missing_dims)
key = tuple(indexers.get(dim, slice(None)) for dim in self.dims)
return self[key]
def squeeze(self, dim=None):
"""Return a new object with squeezed data.
Parameters
----------
dim : None or str or tuple of str, optional
Selects a subset of the length one dimensions. If a dimension is
selected with length greater than one, an error is raised. If
None, all length one dimensions are squeezed.
Returns
-------
squeezed : same type as caller
This object, but with with all or a subset of the dimensions of
length 1 removed.
See Also
--------
numpy.squeeze
"""
dims = common.get_squeeze_dims(self, dim)
return self.isel({d: 0 for d in dims})
def _shift_one_dim(self, dim, count, fill_value=dtypes.NA):
axis = self.get_axis_num(dim)
if count > 0:
keep = slice(None, -count)
elif count < 0:
keep = slice(-count, None)
else:
keep = slice(None)
trimmed_data = self[(slice(None),) * axis + (keep,)].data
if fill_value is dtypes.NA:
dtype, fill_value = dtypes.maybe_promote(self.dtype)
else:
dtype = self.dtype
width = min(abs(count), self.shape[axis])
dim_pad = (width, 0) if count >= 0 else (0, width)
pads = [(0, 0) if d != dim else dim_pad for d in self.dims]
data = duck_array_ops.pad(
trimmed_data.astype(dtype),
pads,
mode="constant",
constant_values=fill_value,
)
if is_duck_dask_array(data):
# chunked data should come out with the same chunks; this makes
# it feasible to combine shifted and unshifted data
# TODO: remove this once dask.array automatically aligns chunks
data = data.rechunk(self.data.chunks)
return type(self)(self.dims, data, self._attrs, fastpath=True)
def shift(self, shifts=None, fill_value=dtypes.NA, **shifts_kwargs):
"""
Return a new Variable with shifted data.
Parameters
----------
shifts : mapping of the form {dim: offset}
Integer offset to shift along each of the given dimensions.
Positive offsets shift to the right; negative offsets shift to the
left.
fill_value: scalar, optional
Value to use for newly missing values
**shifts_kwargs
The keyword arguments form of ``shifts``.
One of shifts or shifts_kwargs must be provided.
Returns
-------
shifted : Variable
Variable with the same dimensions and attributes but shifted data.
"""
shifts = either_dict_or_kwargs(shifts, shifts_kwargs, "shift")
result = self
for dim, count in shifts.items():
result = result._shift_one_dim(dim, count, fill_value=fill_value)
return result
def _pad_options_dim_to_index(
self,
pad_option: Mapping[Hashable, Union[int, Tuple[int, int]]],
fill_with_shape=False,
):
if fill_with_shape:
return [
(n, n) if d not in pad_option else pad_option[d]
for d, n in zip(self.dims, self.data.shape)
]
return [(0, 0) if d not in pad_option else pad_option[d] for d in self.dims]
def pad(
self,
pad_width: Mapping[Hashable, Union[int, Tuple[int, int]]] = None,
mode: str = "constant",
stat_length: Union[
int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]]
] = None,
constant_values: Union[
int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]]
] = None,
end_values: Union[
int, Tuple[int, int], Mapping[Hashable, Tuple[int, int]]
] = None,
reflect_type: str = None,
**pad_width_kwargs: Any,
):
"""
Return a new Variable with padded data.
Parameters
----------
pad_width : mapping of hashable to tuple of int
Mapping with the form of {dim: (pad_before, pad_after)}
describing the number of values padded along each dimension.
{dim: pad} is a shortcut for pad_before = pad_after = pad
mode : str, default: "constant"
See numpy / Dask docs
stat_length : int, tuple or mapping of hashable to tuple
Used in 'maximum', 'mean', 'median', and 'minimum'. Number of
values at edge of each axis used to calculate the statistic value.
constant_values : scalar, tuple or mapping of hashable to tuple
Used in 'constant'. The values to set the padded values for each
axis.
end_values : scalar, tuple or mapping of hashable to tuple
Used in 'linear_ramp'. The values used for the ending value of the
linear_ramp and that will form the edge of the padded array.
reflect_type : {"even", "odd"}, optional
Used in "reflect", and "symmetric". The "even" style is the
default with an unaltered reflection around the edge value. For
the "odd" style, the extended part of the array is created by
subtracting the reflected values from two times the edge value.
**pad_width_kwargs
One of pad_width or pad_width_kwargs must be provided.
Returns
-------
padded : Variable
Variable with the same dimensions and attributes but padded data.
"""
pad_width = either_dict_or_kwargs(pad_width, pad_width_kwargs, "pad")
# change default behaviour of pad with mode constant
if mode == "constant" and (
constant_values is None or constant_values is dtypes.NA
):
dtype, constant_values = dtypes.maybe_promote(self.dtype)
else:
dtype = self.dtype
# create pad_options_kwargs, numpy requires only relevant kwargs to be nonempty
if isinstance(stat_length, dict):
stat_length = self._pad_options_dim_to_index(
stat_length, fill_with_shape=True
)
if isinstance(constant_values, dict):
constant_values = self._pad_options_dim_to_index(constant_values)
if isinstance(end_values, dict):
end_values = self._pad_options_dim_to_index(end_values)
# workaround for bug in Dask's default value of stat_length https://github.com/dask/dask/issues/5303
if stat_length is None and mode in ["maximum", "mean", "median", "minimum"]:
stat_length = [(n, n) for n in self.data.shape] # type: ignore
# change integer values to a tuple of two of those values and change pad_width to index
for k, v in pad_width.items():
if isinstance(v, numbers.Number):
pad_width[k] = (v, v)
pad_width_by_index = self._pad_options_dim_to_index(pad_width)
# create pad_options_kwargs, numpy/dask requires only relevant kwargs to be nonempty
pad_option_kwargs = {}
if stat_length is not None:
pad_option_kwargs["stat_length"] = stat_length
if constant_values is not None:
pad_option_kwargs["constant_values"] = constant_values
if end_values is not None:
pad_option_kwargs["end_values"] = end_values
if reflect_type is not None:
pad_option_kwargs["reflect_type"] = reflect_type # type: ignore
array = duck_array_ops.pad(
self.data.astype(dtype, copy=False),
pad_width_by_index,
mode=mode,
**pad_option_kwargs,
)
return type(self)(self.dims, array)
def _roll_one_dim(self, dim, count):
axis = self.get_axis_num(dim)
count %= self.shape[axis]
if count != 0:
indices = [slice(-count, None), slice(None, -count)]
else:
indices = [slice(None)]
arrays = [self[(slice(None),) * axis + (idx,)].data for idx in indices]
data = duck_array_ops.concatenate(arrays, axis)
if is_duck_dask_array(data):
# chunked data should come out with the same chunks; this makes
# it feasible to combine shifted and unshifted data
# TODO: remove this once dask.array automatically aligns chunks
data = data.rechunk(self.data.chunks)
return type(self)(self.dims, data, self._attrs, fastpath=True)
def roll(self, shifts=None, **shifts_kwargs):
"""
Return a new Variable with rolld data.
Parameters
----------
shifts : mapping of hashable to int
Integer offset to roll along each of the given dimensions.
Positive offsets roll to the right; negative offsets roll to the
left.
**shifts_kwargs
The keyword arguments form of ``shifts``.
One of shifts or shifts_kwargs must be provided.
Returns
-------
shifted : Variable
Variable with the same dimensions and attributes but rolled data.
"""
shifts = either_dict_or_kwargs(shifts, shifts_kwargs, "roll")
result = self
for dim, count in shifts.items():
result = result._roll_one_dim(dim, count)
return result
def transpose(self, *dims) -> "Variable":
"""Return a new Variable object with transposed dimensions.
Parameters
----------
*dims : str, optional
By default, reverse the dimensions. Otherwise, reorder the
dimensions to this order.
Returns
-------
transposed : Variable
The returned object has transposed data and dimensions with the
same attributes as the original.
Notes
-----
This operation returns a view of this variable's data. It is
lazy for dask-backed Variables but not for numpy-backed Variables.
See Also
--------
numpy.transpose
"""
if len(dims) == 0:
dims = self.dims[::-1]
dims = tuple(infix_dims(dims, self.dims))
axes = self.get_axis_num(dims)
if len(dims) < 2 or dims == self.dims:
# no need to transpose if only one dimension
# or dims are in same order
return self.copy(deep=False)
data = as_indexable(self._data).transpose(axes)
return type(self)(dims, data, self._attrs, self._encoding, fastpath=True)
@property
def T(self) -> "Variable":
return self.transpose()
def set_dims(self, dims, shape=None):
"""Return a new variable with given set of dimensions.
This method might be used to attach new dimension(s) to variable.
When possible, this operation does not copy this variable's data.
Parameters
----------
dims : str or sequence of str or dict
Dimensions to include on the new variable. If a dict, values are
used to provide the sizes of new dimensions; otherwise, new
dimensions are inserted with length 1.
Returns
-------
Variable
"""
if isinstance(dims, str):
dims = [dims]
if shape is None and utils.is_dict_like(dims):
shape = dims.values()
missing_dims = set(self.dims) - set(dims)
if missing_dims:
raise ValueError(
"new dimensions %r must be a superset of "
"existing dimensions %r" % (dims, self.dims)
)
self_dims = set(self.dims)
expanded_dims = tuple(d for d in dims if d not in self_dims) + self.dims
if self.dims == expanded_dims:
# don't use broadcast_to unless necessary so the result remains
# writeable if possible
expanded_data = self.data
elif shape is not None:
dims_map = dict(zip(dims, shape))
tmp_shape = tuple(dims_map[d] for d in expanded_dims)
expanded_data = duck_array_ops.broadcast_to(self.data, tmp_shape)
else:
expanded_data = self.data[(None,) * (len(expanded_dims) - self.ndim)]
expanded_var = Variable(
expanded_dims, expanded_data, self._attrs, self._encoding, fastpath=True
)
return expanded_var.transpose(*dims)
def _stack_once(self, dims, new_dim):
if not set(dims) <= set(self.dims):
raise ValueError("invalid existing dimensions: %s" % dims)
if new_dim in self.dims:
raise ValueError(
"cannot create a new dimension with the same "
"name as an existing dimension"
)
if len(dims) == 0:
# don't stack
return self.copy(deep=False)
other_dims = [d for d in self.dims if d not in dims]
dim_order = other_dims + list(dims)
reordered = self.transpose(*dim_order)
new_shape = reordered.shape[: len(other_dims)] + (-1,)
new_data = reordered.data.reshape(new_shape)
new_dims = reordered.dims[: len(other_dims)] + (new_dim,)
return Variable(new_dims, new_data, self._attrs, self._encoding, fastpath=True)
def stack(self, dimensions=None, **dimensions_kwargs):
"""
Stack any number of existing dimensions into a single new dimension.
New dimensions will be added at the end, and the order of the data
along each new dimension will be in contiguous (C) order.
Parameters
----------
dimensions : mapping of hashable to tuple of hashable
Mapping of form new_name=(dim1, dim2, ...) describing the
names of new dimensions, and the existing dimensions that
they replace.
**dimensions_kwargs
The keyword arguments form of ``dimensions``.
One of dimensions or dimensions_kwargs must be provided.
Returns
-------
stacked : Variable
Variable with the same attributes but stacked data.
See also
--------
Variable.unstack
"""
dimensions = either_dict_or_kwargs(dimensions, dimensions_kwargs, "stack")
result = self
for new_dim, dims in dimensions.items():
result = result._stack_once(dims, new_dim)
return result
def _unstack_once(self, dims, old_dim):
new_dim_names = tuple(dims.keys())
new_dim_sizes = tuple(dims.values())
if old_dim not in self.dims:
raise ValueError("invalid existing dimension: %s" % old_dim)
if set(new_dim_names).intersection(self.dims):
raise ValueError(
"cannot create a new dimension with the same "
"name as an existing dimension"
)
if np.prod(new_dim_sizes) != self.sizes[old_dim]:
raise ValueError(
"the product of the new dimension sizes must "
"equal the size of the old dimension"
)
other_dims = [d for d in self.dims if d != old_dim]
dim_order = other_dims + [old_dim]
reordered = self.transpose(*dim_order)
new_shape = reordered.shape[: len(other_dims)] + new_dim_sizes
new_data = reordered.data.reshape(new_shape)
new_dims = reordered.dims[: len(other_dims)] + new_dim_names
return Variable(new_dims, new_data, self._attrs, self._encoding, fastpath=True)
def unstack(self, dimensions=None, **dimensions_kwargs):
"""
Unstack an existing dimension into multiple new dimensions.
New dimensions will be added at the end, and the order of the data
along each new dimension will be in contiguous (C) order.
Parameters
----------
dimensions : mapping of hashable to mapping of hashable to int
Mapping of the form old_dim={dim1: size1, ...} describing the
names of existing dimensions, and the new dimensions and sizes
that they map to.
**dimensions_kwargs
The keyword arguments form of ``dimensions``.
One of dimensions or dimensions_kwargs must be provided.
Returns
-------
unstacked : Variable
Variable with the same attributes but unstacked data.
See also
--------
Variable.stack
"""
dimensions = either_dict_or_kwargs(dimensions, dimensions_kwargs, "unstack")
result = self
for old_dim, dims in dimensions.items():
result = result._unstack_once(dims, old_dim)
return result
def fillna(self, value):
return ops.fillna(self, value)
def where(self, cond, other=dtypes.NA):
return ops.where_method(self, cond, other)
def reduce(
self,
func,
dim=None,
axis=None,
keep_attrs=None,
keepdims=False,
**kwargs,
):
"""Reduce this array by applying `func` along some dimension(s).
Parameters
----------
func : callable
Function which can be called in the form
`func(x, axis=axis, **kwargs)` to return the result of reducing an
np.ndarray over an integer valued axis.
dim : str or sequence of str, optional
Dimension(s) over which to apply `func`.
axis : int or sequence of int, optional
Axis(es) over which to apply `func`. Only one of the 'dim'
and 'axis' arguments can be supplied. If neither are supplied, then
the reduction is calculated over the flattened array (by calling
`func(x)` without an axis argument).
keep_attrs : bool, optional
If True, the variable's attributes (`attrs`) will be copied from
the original object to the new one. If False (default), the new
object will be returned without attributes.
keepdims : bool, default: False
If True, the dimensions which are reduced are left in the result
as dimensions of size one
**kwargs : dict
Additional keyword arguments passed on to `func`.
Returns
-------
reduced : Array
Array with summarized data and the indicated dimension(s)
removed.
"""
if dim == ...:
dim = None
if dim is not None and axis is not None:
raise ValueError("cannot supply both 'axis' and 'dim' arguments")
if dim is not None:
axis = self.get_axis_num(dim)
with warnings.catch_warnings():
warnings.filterwarnings(
"ignore", r"Mean of empty slice", category=RuntimeWarning
)
if axis is not None:
data = func(self.data, axis=axis, **kwargs)
else:
data = func(self.data, **kwargs)
if getattr(data, "shape", ()) == self.shape:
dims = self.dims
else:
removed_axes = (
range(self.ndim) if axis is None else np.atleast_1d(axis) % self.ndim
)
if keepdims:
# Insert np.newaxis for removed dims
slices = tuple(
np.newaxis if i in removed_axes else slice(None, None)
for i in range(self.ndim)
)
if getattr(data, "shape", None) is None:
# Reduce has produced a scalar value, not an array-like
data = np.asanyarray(data)[slices]
else:
data = data[slices]
dims = self.dims
else:
dims = [
adim for n, adim in enumerate(self.dims) if n not in removed_axes
]
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
attrs = self._attrs if keep_attrs else None
return Variable(dims, data, attrs=attrs)
@classmethod
def concat(cls, variables, dim="concat_dim", positions=None, shortcut=False):
"""Concatenate variables along a new or existing dimension.
Parameters
----------
variables : iterable of Variable
Arrays to stack together. Each variable is expected to have
matching dimensions and shape except for along the stacked
dimension.
dim : str or DataArray, optional
Name of the dimension to stack along. This can either be a new
dimension name, in which case it is added along axis=0, or an
existing dimension name, in which case the location of the
dimension is unchanged. Where to insert the new dimension is
determined by the first variable.
positions : None or list of array-like, optional
List of integer arrays which specifies the integer positions to
which to assign each dataset along the concatenated dimension.
If not supplied, objects are concatenated in the provided order.
shortcut : bool, optional
This option is used internally to speed-up groupby operations.
If `shortcut` is True, some checks of internal consistency between
arrays to concatenate are skipped.
Returns
-------
stacked : Variable
Concatenated Variable formed by stacking all the supplied variables
along the given dimension.
"""
if not isinstance(dim, str):
(dim,) = dim.dims
# can't do this lazily: we need to loop through variables at least
# twice
variables = list(variables)
first_var = variables[0]
arrays = [v.data for v in variables]
if dim in first_var.dims:
axis = first_var.get_axis_num(dim)
dims = first_var.dims
data = duck_array_ops.concatenate(arrays, axis=axis)
if positions is not None:
# TODO: deprecate this option -- we don't need it for groupby
# any more.
indices = nputils.inverse_permutation(np.concatenate(positions))
data = duck_array_ops.take(data, indices, axis=axis)
else:
axis = 0
dims = (dim,) + first_var.dims
data = duck_array_ops.stack(arrays, axis=axis)
attrs = dict(first_var.attrs)
encoding = dict(first_var.encoding)
if not shortcut:
for var in variables:
if var.dims != first_var.dims:
raise ValueError(
f"Variable has dimensions {list(var.dims)} but first Variable has dimensions {list(first_var.dims)}"
)
return cls(dims, data, attrs, encoding)
def equals(self, other, equiv=duck_array_ops.array_equiv):
"""True if two Variables have the same dimensions and values;
otherwise False.
Variables can still be equal (like pandas objects) if they have NaN
values in the same locations.
This method is necessary because `v1 == v2` for Variables
does element-wise comparisons (like numpy.ndarrays).
"""
other = getattr(other, "variable", other)
try:
return self.dims == other.dims and (
self._data is other._data or equiv(self.data, other.data)
)
except (TypeError, AttributeError):
return False
def broadcast_equals(self, other, equiv=duck_array_ops.array_equiv):
"""True if two Variables have the values after being broadcast against
each other; otherwise False.
Variables can still be equal (like pandas objects) if they have NaN
values in the same locations.
"""
try:
self, other = broadcast_variables(self, other)
except (ValueError, AttributeError):
return False
return self.equals(other, equiv=equiv)
def identical(self, other, equiv=duck_array_ops.array_equiv):
"""Like equals, but also checks attributes."""
try:
return utils.dict_equiv(self.attrs, other.attrs) and self.equals(
other, equiv=equiv
)
except (TypeError, AttributeError):
return False
def no_conflicts(self, other, equiv=duck_array_ops.array_notnull_equiv):
"""True if the intersection of two Variable's non-null data is
equal; otherwise false.
Variables can thus still be equal if there are locations where either,
or both, contain NaN values.
"""
return self.broadcast_equals(other, equiv=equiv)
def quantile(
self, q, dim=None, interpolation="linear", keep_attrs=None, skipna=True
):
"""Compute the qth quantile of the data along the specified dimension.
Returns the qth quantiles(s) of the array elements.
Parameters
----------
q : float or sequence of float
Quantile to compute, which must be between 0 and 1
inclusive.
dim : str or sequence of str, optional
Dimension(s) over which to apply quantile.
interpolation : {"linear", "lower", "higher", "midpoint", "nearest"}, default: "linear"
This optional parameter specifies the interpolation method to
use when the desired quantile lies between two data points
``i < j``:
* linear: ``i + (j - i) * fraction``, where ``fraction`` is
the fractional part of the index surrounded by ``i`` and
``j``.
* lower: ``i``.
* higher: ``j``.
* nearest: ``i`` or ``j``, whichever is nearest.
* midpoint: ``(i + j) / 2``.
keep_attrs : bool, optional
If True, the variable's attributes (`attrs`) will be copied from
the original object to the new one. If False (default), the new
object will be returned without attributes.
Returns
-------
quantiles : Variable
If `q` is a single quantile, then the result
is a scalar. If multiple percentiles are given, first axis of
the result corresponds to the quantile and a quantile dimension
is added to the return array. The other dimensions are the
dimensions that remain after the reduction of the array.
See Also
--------
numpy.nanquantile, pandas.Series.quantile, Dataset.quantile,
DataArray.quantile
"""
from .computation import apply_ufunc
_quantile_func = np.nanquantile if skipna else np.quantile
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
scalar = utils.is_scalar(q)
q = np.atleast_1d(np.asarray(q, dtype=np.float64))
if dim is None:
dim = self.dims
if utils.is_scalar(dim):
dim = [dim]
def _wrapper(npa, **kwargs):
# move quantile axis to end. required for apply_ufunc
return np.moveaxis(_quantile_func(npa, **kwargs), 0, -1)
axis = np.arange(-1, -1 * len(dim) - 1, -1)
result = apply_ufunc(
_wrapper,
self,
input_core_dims=[dim],
exclude_dims=set(dim),
output_core_dims=[["quantile"]],
output_dtypes=[np.float64],
dask_gufunc_kwargs=dict(output_sizes={"quantile": len(q)}),
dask="parallelized",
kwargs={"q": q, "axis": axis, "interpolation": interpolation},
)
# for backward compatibility
result = result.transpose("quantile", ...)
if scalar:
result = result.squeeze("quantile")
if keep_attrs:
result.attrs = self._attrs
return result
def rank(self, dim, pct=False):
"""Ranks the data.
Equal values are assigned a rank that is the average of the ranks that
would have been otherwise assigned to all of the values within that
set. Ranks begin at 1, not 0. If `pct`, computes percentage ranks.
NaNs in the input array are returned as NaNs.
The `bottleneck` library is required.
Parameters
----------
dim : str
Dimension over which to compute rank.
pct : bool, optional
If True, compute percentage ranks, otherwise compute integer ranks.
Returns
-------
ranked : Variable
See Also
--------
Dataset.rank, DataArray.rank
"""
import bottleneck as bn
data = self.data
if is_duck_dask_array(data):
raise TypeError(
"rank does not work for arrays stored as dask "
"arrays. Load the data via .compute() or .load() "
"prior to calling this method."
)
elif not isinstance(data, np.ndarray):
raise TypeError(
"rank is not implemented for {} objects.".format(type(data))
)
axis = self.get_axis_num(dim)
func = bn.nanrankdata if self.dtype.kind == "f" else bn.rankdata
ranked = func(data, axis=axis)
if pct:
count = np.sum(~np.isnan(data), axis=axis, keepdims=True)
ranked /= count
return Variable(self.dims, ranked)
def rolling_window(
self, dim, window, window_dim, center=False, fill_value=dtypes.NA
):
"""
Make a rolling_window along dim and add a new_dim to the last place.
Parameters
----------
dim : str
Dimension over which to compute rolling_window.
For nd-rolling, should be list of dimensions.
window : int
Window size of the rolling
For nd-rolling, should be list of integers.
window_dim : str
New name of the window dimension.
For nd-rolling, should be list of integers.
center : bool, default: False
If True, pad fill_value for both ends. Otherwise, pad in the head
of the axis.
fill_value
value to be filled.
Returns
-------
Variable that is a view of the original array with a added dimension of
size w.
The return dim: self.dims + (window_dim, )
The return shape: self.shape + (window, )
Examples
--------
>>> v = Variable(("a", "b"), np.arange(8).reshape((2, 4)))
>>> v.rolling_window("b", 3, "window_dim")
<xarray.Variable (a: 2, b: 4, window_dim: 3)>
array([[[nan, nan, 0.],
[nan, 0., 1.],
[ 0., 1., 2.],
[ 1., 2., 3.]],
<BLANKLINE>
[[nan, nan, 4.],
[nan, 4., 5.],
[ 4., 5., 6.],
[ 5., 6., 7.]]])
>>> v.rolling_window("b", 3, "window_dim", center=True)
<xarray.Variable (a: 2, b: 4, window_dim: 3)>
array([[[nan, 0., 1.],
[ 0., 1., 2.],
[ 1., 2., 3.],
[ 2., 3., nan]],
<BLANKLINE>
[[nan, 4., 5.],
[ 4., 5., 6.],
[ 5., 6., 7.],
[ 6., 7., nan]]])
"""
if fill_value is dtypes.NA: # np.nan is passed
dtype, fill_value = dtypes.maybe_promote(self.dtype)
array = self.astype(dtype, copy=False).data
else:
dtype = self.dtype
array = self.data
if isinstance(dim, list):
assert len(dim) == len(window)
assert len(dim) == len(window_dim)
assert len(dim) == len(center)
else:
dim = [dim]
window = [window]
window_dim = [window_dim]
center = [center]
axis = [self.get_axis_num(d) for d in dim]
new_dims = self.dims + tuple(window_dim)
return Variable(
new_dims,
duck_array_ops.rolling_window(
array, axis=axis, window=window, center=center, fill_value=fill_value
),
)
def coarsen(
self, windows, func, boundary="exact", side="left", keep_attrs=None, **kwargs
):
"""
Apply reduction function.
"""
windows = {k: v for k, v in windows.items() if k in self.dims}
if not windows:
return self.copy()
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
if keep_attrs:
_attrs = self.attrs
else:
_attrs = None
reshaped, axes = self._coarsen_reshape(windows, boundary, side)
if isinstance(func, str):
name = func
func = getattr(duck_array_ops, name, None)
if func is None:
raise NameError(f"{name} is not a valid method.")
return self._replace(data=func(reshaped, axis=axes, **kwargs), attrs=_attrs)
def _coarsen_reshape(self, windows, boundary, side):
"""
Construct a reshaped-array for coarsen
"""
if not utils.is_dict_like(boundary):
boundary = {d: boundary for d in windows.keys()}
if not utils.is_dict_like(side):
side = {d: side for d in windows.keys()}
# remove unrelated dimensions
boundary = {k: v for k, v in boundary.items() if k in windows}
side = {k: v for k, v in side.items() if k in windows}
for d, window in windows.items():
if window <= 0:
raise ValueError(f"window must be > 0. Given {window}")
variable = self
for d, window in windows.items():
# trim or pad the object
size = variable.shape[self._get_axis_num(d)]
n = int(size / window)
if boundary[d] == "exact":
if n * window != size:
raise ValueError(
"Could not coarsen a dimension of size {} with "
"window {}".format(size, window)
)
elif boundary[d] == "trim":
if side[d] == "left":
variable = variable.isel({d: slice(0, window * n)})
else:
excess = size - window * n
variable = variable.isel({d: slice(excess, None)})
elif boundary[d] == "pad": # pad
pad = window * n - size
if pad < 0:
pad += window
if side[d] == "left":
pad_width = {d: (0, pad)}
else:
pad_width = {d: (pad, 0)}
variable = variable.pad(pad_width, mode="constant")
else:
raise TypeError(
"{} is invalid for boundary. Valid option is 'exact', "
"'trim' and 'pad'".format(boundary[d])
)
shape = []
axes = []
axis_count = 0
for i, d in enumerate(variable.dims):
if d in windows:
size = variable.shape[i]
shape.append(int(size / windows[d]))
shape.append(windows[d])
axis_count += 1
axes.append(i + axis_count)
else:
shape.append(variable.shape[i])
return variable.data.reshape(shape), tuple(axes)
def isnull(self, keep_attrs: bool = None):
"""Test each value in the array for whether it is a missing value.
Returns
-------
isnull : Variable
Same type and shape as object, but the dtype of the data is bool.
See Also
--------
pandas.isnull
Examples
--------
>>> var = xr.Variable("x", [1, np.nan, 3])
>>> var
<xarray.Variable (x: 3)>
array([ 1., nan, 3.])
>>> var.isnull()
<xarray.Variable (x: 3)>
array([False, True, False])
"""
from .computation import apply_ufunc
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
return apply_ufunc(
duck_array_ops.isnull,
self,
dask="allowed",
keep_attrs=keep_attrs,
)
def notnull(self, keep_attrs: bool = None):
"""Test each value in the array for whether it is not a missing value.
Returns
-------
notnull : Variable
Same type and shape as object, but the dtype of the data is bool.
See Also
--------
pandas.notnull
Examples
--------
>>> var = xr.Variable("x", [1, np.nan, 3])
>>> var
<xarray.Variable (x: 3)>
array([ 1., nan, 3.])
>>> var.notnull()
<xarray.Variable (x: 3)>
array([ True, False, True])
"""
from .computation import apply_ufunc
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=False)
return apply_ufunc(
duck_array_ops.notnull,
self,
dask="allowed",
keep_attrs=keep_attrs,
)
@property
def real(self):
return type(self)(self.dims, self.data.real, self._attrs)
@property
def imag(self):
return type(self)(self.dims, self.data.imag, self._attrs)
def __array_wrap__(self, obj, context=None):
return Variable(self.dims, obj)
@staticmethod
def _unary_op(f):
@functools.wraps(f)
def func(self, *args, **kwargs):
keep_attrs = kwargs.pop("keep_attrs", None)
if keep_attrs is None:
keep_attrs = _get_keep_attrs(default=True)
with np.errstate(all="ignore"):
result = self.__array_wrap__(f(self.data, *args, **kwargs))
if keep_attrs:
result.attrs = self.attrs
return result
return func
@staticmethod
def _binary_op(f, reflexive=False, **ignored_kwargs):
@functools.wraps(f)
def func(self, other):
if isinstance(other, (xr.DataArray, xr.Dataset)):
return NotImplemented
self_data, other_data, dims = _broadcast_compat_data(self, other)
keep_attrs = _get_keep_attrs(default=False)
attrs = self._attrs if keep_attrs else None
with np.errstate(all="ignore"):
new_data = (
f(self_data, other_data)
if not reflexive
else f(other_data, self_data)
)
result = Variable(dims, new_data, attrs=attrs)
return result
return func
@staticmethod
def _inplace_binary_op(f):
@functools.wraps(f)
def func(self, other):
if isinstance(other, xr.Dataset):
raise TypeError("cannot add a Dataset to a Variable in-place")
self_data, other_data, dims = _broadcast_compat_data(self, other)
if dims != self.dims:
raise ValueError("dimensions cannot change for in-place operations")
with | np.errstate(all="ignore") | numpy.errstate |
# ________
# /
# \ /
# \ /
# \/
import random
import textwrap
import emd_mean
import AdvEMDpy
import emd_basis
import emd_utils
import numpy as np
import pandas as pd
import cvxpy as cvx
import seaborn as sns
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from scipy.ndimage import gaussian_filter
from emd_utils import time_extension, Utility
from scipy.interpolate import CubicSpline
from emd_hilbert import Hilbert, hilbert_spectrum
from emd_preprocess import Preprocess
from emd_mean import Fluctuation
from AdvEMDpy import EMD
# alternate packages
from PyEMD import EMD as pyemd0215
import emd as emd040
sns.set(style='darkgrid')
pseudo_alg_time = np.linspace(0, 2 * np.pi, 1001)
pseudo_alg_time_series = np.sin(pseudo_alg_time) + np.sin(5 * pseudo_alg_time)
pseudo_utils = Utility(time=pseudo_alg_time, time_series=pseudo_alg_time_series)
# plot 0 - addition
fig = plt.figure(figsize=(9, 4))
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('First Iteration of Sifting Algorithm')
plt.plot(pseudo_alg_time, pseudo_alg_time_series, label=r'$h_{(1,0)}(t)$', zorder=1)
plt.scatter(pseudo_alg_time[pseudo_utils.max_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.max_bool_func_1st_order_fd()],
c='r', label=r'$M(t_i)$', zorder=2)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) + 1, '--', c='r', label=r'$\tilde{h}_{(1,0)}^M(t)$', zorder=4)
plt.scatter(pseudo_alg_time[pseudo_utils.min_bool_func_1st_order_fd()],
pseudo_alg_time_series[pseudo_utils.min_bool_func_1st_order_fd()],
c='c', label=r'$m(t_j)$', zorder=3)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time) - 1, '--', c='c', label=r'$\tilde{h}_{(1,0)}^m(t)$', zorder=5)
plt.plot(pseudo_alg_time, np.sin(pseudo_alg_time), '--', c='purple', label=r'$\tilde{h}_{(1,0)}^{\mu}(t)$', zorder=5)
plt.yticks(ticks=[-2, -1, 0, 1, 2])
plt.xticks(ticks=[0, np.pi, 2 * np.pi],
labels=[r'0', r'$\pi$', r'$2\pi$'])
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.95, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/pseudo_algorithm.png')
plt.show()
knots = np.arange(12)
time = np.linspace(0, 11, 1101)
basis = emd_basis.Basis(time=time, time_series=time)
b_spline_basis = basis.cubic_b_spline(knots)
chsi_basis = basis.chsi_basis(knots)
# plot 1
plt.title('Non-Natural Cubic B-Spline Bases at Boundary')
plt.plot(time[500:], b_spline_basis[2, 500:].T, '--', label=r'$ B_{-3,4}(t) $')
plt.plot(time[500:], b_spline_basis[3, 500:].T, '--', label=r'$ B_{-2,4}(t) $')
plt.plot(time[500:], b_spline_basis[4, 500:].T, '--', label=r'$ B_{-1,4}(t) $')
plt.plot(time[500:], b_spline_basis[5, 500:].T, '--', label=r'$ B_{0,4}(t) $')
plt.plot(time[500:], b_spline_basis[6, 500:].T, '--', label=r'$ B_{1,4}(t) $')
plt.xticks([5, 6], [r'$ \tau_0 $', r'$ \tau_1 $'])
plt.xlim(4.4, 6.6)
plt.plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
plt.legend(loc='upper left')
plt.savefig('jss_figures/boundary_bases.png')
plt.show()
# plot 1a - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
knots_uniform = np.linspace(0, 2 * np.pi, 51)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs = emd.empirical_mode_decomposition(knots=knots_uniform, edge_effect='anti-symmetric', verbose=False)[0]
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Uniform Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Uniform Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Uniform Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots_uniform[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots_uniform)):
axs[i].plot(knots_uniform[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_uniform.png')
plt.show()
# plot 1b - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=1, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Statically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Statically Optimised Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Statically Optimised Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots)):
axs[i].plot(knots[j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_1.png')
plt.show()
# plot 1c - addition
knot_demonstrate_time = np.linspace(0, 2 * np.pi, 1001)
knot_demonstrate_time_series = np.sin(knot_demonstrate_time) + np.sin(5 * knot_demonstrate_time)
emd = EMD(time=knot_demonstrate_time, time_series=knot_demonstrate_time_series)
imfs, _, _, _, knots, _, _ = emd.empirical_mode_decomposition(edge_effect='anti-symmetric',
optimise_knots=2, verbose=False)
fig, axs = plt.subplots(3, 1)
fig.subplots_adjust(hspace=0.6)
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Time Series and Dynamically Optimised Knots')
axs[0].plot(knot_demonstrate_time, knot_demonstrate_time_series, Linewidth=2, zorder=100)
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].set_title('IMF 1 and Dynamically Knots')
axs[1].plot(knot_demonstrate_time, imfs[1, :], Linewidth=2, zorder=100)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[1].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[2].set_title('IMF 2 and Dynamically Knots')
axs[2].plot(knot_demonstrate_time, imfs[2, :], Linewidth=2, zorder=100)
axs[2].set_yticks(ticks=[-2, 0, 2])
axs[2].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[2].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[0].plot(knots[0][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[0].legend(loc='lower left')
axs[1].plot(knots[1][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
axs[2].plot(knots[2][0] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey', label='Knots')
for i in range(3):
for j in range(1, len(knots[i])):
axs[i].plot(knots[i][j] * np.ones(101), np.linspace(-2, 2, 101), '--', c='grey')
plt.savefig('jss_figures/knot_2.png')
plt.show()
# plot 1d - addition
window = 81
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Filtering Demonstration')
axs[1].set_title('Zoomed Region')
preprocess_time = pseudo_alg_time.copy()
np.random.seed(1)
random.seed(1)
preprocess_time_series = pseudo_alg_time_series + np.random.normal(0, 0.1, len(preprocess_time))
for i in random.sample(range(1000), 500):
preprocess_time_series[i] += np.random.normal(0, 1)
preprocess = Preprocess(time=preprocess_time, time_series=preprocess_time_series)
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[0].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[0].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[0].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[0].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple', label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.mean_filter(window_width=window)[1], label=textwrap.fill('Mean filter', 12))
axs[1].plot(preprocess_time, preprocess.median_filter(window_width=window)[1], label=textwrap.fill('Median filter', 13))
axs[1].plot(preprocess_time, preprocess.winsorize(window_width=window, a=0.8)[1], label=textwrap.fill('Windsorize filter', 12))
axs[1].plot(preprocess_time, preprocess.winsorize_interpolate(window_width=window, a=0.8)[1],
label=textwrap.fill('Windsorize interpolation filter', 14))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.90)[1], c='grey',
label=textwrap.fill('Quantile window', 12))
axs[1].plot(preprocess_time, preprocess.quantile_filter(window_width=window, q=0.10)[1], c='grey')
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.05, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_filter.png')
plt.show()
# plot 1e - addition
fig, axs = plt.subplots(2, 1)
fig.subplots_adjust(hspace=0.4)
figure_size = plt.gcf().get_size_inches()
factor = 0.8
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
axs[0].set_title('Preprocess Smoothing Demonstration')
axs[1].set_title('Zoomed Region')
axs[0].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[0].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[0].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[0].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
downsampled_and_decimated = preprocess.downsample()
axs[0].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 11))
downsampled = preprocess.downsample(decimate=False)
axs[0].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), -3 * np.ones(101), '--', c='black',
label=textwrap.fill('Zoomed region', 10))
axs[0].plot(np.linspace(0.85 * np.pi, 1.15 * np.pi, 101), 3 * np.ones(101), '--', c='black')
axs[0].plot(0.85 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].plot(1.15 * np.pi * np.ones(101), np.linspace(-3, 3, 101), '--', c='black')
axs[0].set_yticks(ticks=[-2, 0, 2])
axs[0].set_xticks(ticks=[0, np.pi, 2 * np.pi])
axs[0].set_xticklabels(labels=['0', r'$\pi$', r'$2\pi$'])
axs[1].plot(preprocess_time, preprocess_time_series, label='x(t)')
axs[1].plot(pseudo_alg_time, pseudo_alg_time_series, '--', c='purple',
label=textwrap.fill('Noiseless time series', 12))
axs[1].plot(preprocess_time, preprocess.hp()[1],
label=textwrap.fill('Hodrick-Prescott smoothing', 12))
axs[1].plot(preprocess_time, preprocess.hw(order=51)[1],
label=textwrap.fill('Henderson-Whittaker smoothing', 13))
axs[1].plot(downsampled_and_decimated[0], downsampled_and_decimated[1],
label=textwrap.fill('Downsampled & decimated', 13))
axs[1].plot(downsampled[0], downsampled[1],
label=textwrap.fill('Downsampled', 13))
axs[1].set_xlim(0.85 * np.pi, 1.15 * np.pi)
axs[1].set_ylim(-3, 3)
axs[1].set_yticks(ticks=[-2, 0, 2])
axs[1].set_xticks(ticks=[np.pi])
axs[1].set_xticklabels(labels=[r'$\pi$'])
box_0 = axs[0].get_position()
axs[0].set_position([box_0.x0 - 0.06, box_0.y0, box_0.width * 0.85, box_0.height])
axs[0].legend(loc='center left', bbox_to_anchor=(1, -0.15))
box_1 = axs[1].get_position()
axs[1].set_position([box_1.x0 - 0.06, box_1.y0, box_1.width * 0.85, box_1.height])
plt.savefig('jss_figures/preprocess_smooth.png')
plt.show()
# plot 2
fig, axs = plt.subplots(1, 2, sharey=True)
axs[0].set_title('Cubic B-Spline Bases')
axs[0].plot(time, b_spline_basis[2, :].T, '--', label='Basis 1')
axs[0].plot(time, b_spline_basis[3, :].T, '--', label='Basis 2')
axs[0].plot(time, b_spline_basis[4, :].T, '--', label='Basis 3')
axs[0].plot(time, b_spline_basis[5, :].T, '--', label='Basis 4')
axs[0].legend(loc='upper left')
axs[0].plot(5 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].plot(6 * np.ones(100), np.linspace(-0.2, 0.8, 100), 'k-')
axs[0].set_xticks([5, 6])
axs[0].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[0].set_xlim(4.5, 6.5)
axs[1].set_title('Cubic Hermite Spline Bases')
axs[1].plot(time, chsi_basis[10, :].T, '--')
axs[1].plot(time, chsi_basis[11, :].T, '--')
axs[1].plot(time, chsi_basis[12, :].T, '--')
axs[1].plot(time, chsi_basis[13, :].T, '--')
axs[1].plot(5 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].plot(6 * np.ones(100), np.linspace(-0.2, 1.2, 100), 'k-')
axs[1].set_xticks([5, 6])
axs[1].set_xticklabels([r'$ \tau_k $', r'$ \tau_{k+1} $'])
axs[1].set_xlim(4.5, 6.5)
plt.savefig('jss_figures/comparing_bases.png')
plt.show()
# plot 3
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_dash = maxima_y[-1] * np.ones_like(max_dash_time)
min_dash_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_dash = minima_y[-1] * np.ones_like(min_dash_time)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
max_discard = maxima_y[-1]
max_discard_time = minima_x[-1] - maxima_x[-1] + minima_x[-1]
max_discard_dash_time = np.linspace(max_discard_time - width, max_discard_time + width, 101)
max_discard_dash = max_discard * np.ones_like(max_discard_dash_time)
dash_2_time = np.linspace(minima_x[-1], max_discard_time, 101)
dash_2 = np.linspace(minima_y[-1], max_discard, 101)
end_point_time = time[-1]
end_point = time_series[-1]
time_reflect = np.linspace((5 - a) * np.pi, (5 + a) * np.pi, 101)
time_series_reflect = np.flip(np.cos(np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)) + np.cos(5 * np.linspace((5 - 2.6 * a) * np.pi,
(5 - a) * np.pi, 101)))
time_series_anti_reflect = time_series_reflect[0] - time_series_reflect
utils = emd_utils.Utility(time=time, time_series=time_series_anti_reflect)
anti_max_bool = utils.max_bool_func_1st_order_fd()
anti_max_point_time = time_reflect[anti_max_bool]
anti_max_point = time_series_anti_reflect[anti_max_bool]
utils = emd_utils.Utility(time=time, time_series=time_series_reflect)
no_anchor_max_time = time_reflect[utils.max_bool_func_1st_order_fd()]
no_anchor_max = time_series_reflect[utils.max_bool_func_1st_order_fd()]
point_1 = 5.4
length_distance = np.linspace(maxima_y[-1], minima_y[-1], 101)
length_distance_time = point_1 * np.pi * np.ones_like(length_distance)
length_time = np.linspace(point_1 * np.pi - width, point_1 * np.pi + width, 101)
length_top = maxima_y[-1] * np.ones_like(length_time)
length_bottom = minima_y[-1] * np.ones_like(length_time)
point_2 = 5.2
length_distance_2 = np.linspace(time_series[-1], minima_y[-1], 101)
length_distance_time_2 = point_2 * np.pi * np.ones_like(length_distance_2)
length_time_2 = np.linspace(point_2 * np.pi - width, point_2 * np.pi + width, 101)
length_top_2 = time_series[-1] * np.ones_like(length_time_2)
length_bottom_2 = minima_y[-1] * np.ones_like(length_time_2)
symmetry_axis_1_time = minima_x[-1] * np.ones(101)
symmetry_axis_2_time = time[-1] * np.ones(101)
symmetry_axis = np.linspace(-2, 2, 101)
end_time = np.linspace(time[-1] - width, time[-1] + width, 101)
end_signal = time_series[-1] * np.ones_like(end_time)
anti_symmetric_time = np.linspace(time[-1] - 0.5, time[-1] + 0.5, 101)
anti_symmetric_signal = time_series[-1] * np.ones_like(anti_symmetric_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Symmetry Edge Effects Example')
plt.plot(time_reflect, time_series_reflect, 'g--', LineWidth=2, label=textwrap.fill('Symmetric signal', 10))
plt.plot(time_reflect[:51], time_series_anti_reflect[:51], '--', c='purple', LineWidth=2,
label=textwrap.fill('Anti-symmetric signal', 10))
plt.plot(max_dash_time, max_dash, 'k-')
plt.plot(min_dash_time, min_dash, 'k-')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(length_distance_time, length_distance, 'k--')
plt.plot(length_distance_time_2, length_distance_2, 'k--')
plt.plot(length_time, length_top, 'k-')
plt.plot(length_time, length_bottom, 'k-')
plt.plot(length_time_2, length_top_2, 'k-')
plt.plot(length_time_2, length_bottom_2, 'k-')
plt.plot(end_time, end_signal, 'k-')
plt.plot(symmetry_axis_1_time, symmetry_axis, 'r--', zorder=1)
plt.plot(anti_symmetric_time, anti_symmetric_signal, 'r--', zorder=1)
plt.plot(symmetry_axis_2_time, symmetry_axis, 'r--', label=textwrap.fill('Axes of symmetry', 10), zorder=1)
plt.text(5.1 * np.pi, -0.7, r'$\beta$L')
plt.text(5.34 * np.pi, -0.05, 'L')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(max_discard_time, max_discard, c='purple', zorder=4, label=textwrap.fill('Symmetric Discard maxima', 10))
plt.scatter(end_point_time, end_point, c='orange', zorder=4, label=textwrap.fill('Symmetric Anchor maxima', 10))
plt.scatter(anti_max_point_time, anti_max_point, c='green', zorder=4, label=textwrap.fill('Anti-Symmetric maxima', 10))
plt.scatter(no_anchor_max_time, no_anchor_max, c='gray', zorder=4, label=textwrap.fill('Symmetric maxima', 10))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_symmetry_anti.png')
plt.show()
# plot 4
a = 0.21
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
max_dash_1 = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_dash_2 = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_dash_time_1 = maxima_x[-1] * np.ones_like(max_dash_1)
max_dash_time_2 = maxima_x[-2] * np.ones_like(max_dash_1)
min_dash_1 = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_dash_2 = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_dash_time_1 = minima_x[-1] * np.ones_like(min_dash_1)
min_dash_time_2 = minima_x[-2] * np.ones_like(min_dash_1)
dash_1_time = np.linspace(maxima_x[-1], minima_x[-1], 101)
dash_1 = np.linspace(maxima_y[-1], minima_y[-1], 101)
dash_2_time = np.linspace(maxima_x[-1], minima_x[-2], 101)
dash_2 = np.linspace(maxima_y[-1], minima_y[-2], 101)
s1 = (minima_y[-2] - maxima_y[-1]) / (minima_x[-2] - maxima_x[-1])
slope_based_maximum_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
slope_based_maximum = minima_y[-1] + (slope_based_maximum_time - minima_x[-1]) * s1
max_dash_time_3 = slope_based_maximum_time * np.ones_like(max_dash_1)
max_dash_3 = np.linspace(slope_based_maximum - width, slope_based_maximum + width, 101)
dash_3_time = np.linspace(minima_x[-1], slope_based_maximum_time, 101)
dash_3 = np.linspace(minima_y[-1], slope_based_maximum, 101)
s2 = (minima_y[-1] - maxima_y[-1]) / (minima_x[-1] - maxima_x[-1])
slope_based_minimum_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
slope_based_minimum = slope_based_maximum - (slope_based_maximum_time - slope_based_minimum_time) * s2
min_dash_time_3 = slope_based_minimum_time * np.ones_like(min_dash_1)
min_dash_3 = np.linspace(slope_based_minimum - width, slope_based_minimum + width, 101)
dash_4_time = np.linspace(slope_based_maximum_time, slope_based_minimum_time)
dash_4 = np.linspace(slope_based_maximum, slope_based_minimum)
maxima_dash = np.linspace(2.5 - width, 2.5 + width, 101)
maxima_dash_time_1 = maxima_x[-2] * np.ones_like(maxima_dash)
maxima_dash_time_2 = maxima_x[-1] * np.ones_like(maxima_dash)
maxima_dash_time_3 = slope_based_maximum_time * np.ones_like(maxima_dash)
maxima_line_dash_time = np.linspace(maxima_x[-2], slope_based_maximum_time, 101)
maxima_line_dash = 2.5 * np.ones_like(maxima_line_dash_time)
minima_dash = np.linspace(-3.4 - width, -3.4 + width, 101)
minima_dash_time_1 = minima_x[-2] * np.ones_like(minima_dash)
minima_dash_time_2 = minima_x[-1] * np.ones_like(minima_dash)
minima_dash_time_3 = slope_based_minimum_time * np.ones_like(minima_dash)
minima_line_dash_time = np.linspace(minima_x[-2], slope_based_minimum_time, 101)
minima_line_dash = -3.4 * np.ones_like(minima_line_dash_time)
# slightly edit signal to make difference between slope-based method and improved slope-based method more clear
time_series[time >= minima_x[-1]] = 1.5 * (time_series[time >= minima_x[-1]] - time_series[time == minima_x[-1]]) + \
time_series[time == minima_x[-1]]
improved_slope_based_maximum_time = time[-1]
improved_slope_based_maximum = time_series[-1]
improved_slope_based_minimum_time = slope_based_minimum_time
improved_slope_based_minimum = improved_slope_based_maximum + s2 * (improved_slope_based_minimum_time -
improved_slope_based_maximum_time)
min_dash_4 = np.linspace(improved_slope_based_minimum - width, improved_slope_based_minimum + width, 101)
min_dash_time_4 = improved_slope_based_minimum_time * np.ones_like(min_dash_4)
dash_final_time = np.linspace(improved_slope_based_maximum_time, improved_slope_based_minimum_time, 101)
dash_final = np.linspace(improved_slope_based_maximum, improved_slope_based_minimum, 101)
ax = plt.subplot(111)
figure_size = plt.gcf().get_size_inches()
factor = 0.9
plt.gcf().set_size_inches((figure_size[0], factor * figure_size[1]))
plt.gcf().subplots_adjust(bottom=0.10)
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.title('Slope-Based Edge Effects Example')
plt.plot(max_dash_time_1, max_dash_1, 'k-')
plt.plot(max_dash_time_2, max_dash_2, 'k-')
plt.plot(max_dash_time_3, max_dash_3, 'k-')
plt.plot(min_dash_time_1, min_dash_1, 'k-')
plt.plot(min_dash_time_2, min_dash_2, 'k-')
plt.plot(min_dash_time_3, min_dash_3, 'k-')
plt.plot(min_dash_time_4, min_dash_4, 'k-')
plt.plot(maxima_dash_time_1, maxima_dash, 'k-')
plt.plot(maxima_dash_time_2, maxima_dash, 'k-')
plt.plot(maxima_dash_time_3, maxima_dash, 'k-')
plt.plot(minima_dash_time_1, minima_dash, 'k-')
plt.plot(minima_dash_time_2, minima_dash, 'k-')
plt.plot(minima_dash_time_3, minima_dash, 'k-')
plt.text(4.34 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.74 * np.pi, -3.2, r'$\Delta{t^{min}_{m}}$')
plt.text(4.12 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.50 * np.pi, 2, r'$\Delta{t^{max}_{M}}$')
plt.text(4.30 * np.pi, 0.35, r'$s_1$')
plt.text(4.43 * np.pi, -0.20, r'$s_2$')
plt.text(4.30 * np.pi + (minima_x[-1] - minima_x[-2]), 0.35 + (minima_y[-1] - minima_y[-2]), r'$s_1$')
plt.text(4.43 * np.pi + (slope_based_minimum_time - minima_x[-1]),
-0.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.text(4.50 * np.pi + (slope_based_minimum_time - minima_x[-1]),
1.20 + (slope_based_minimum - minima_y[-1]), r'$s_2$')
plt.plot(minima_line_dash_time, minima_line_dash, 'k--')
plt.plot(maxima_line_dash_time, maxima_line_dash, 'k--')
plt.plot(dash_1_time, dash_1, 'k--')
plt.plot(dash_2_time, dash_2, 'k--')
plt.plot(dash_3_time, dash_3, 'k--')
plt.plot(dash_4_time, dash_4, 'k--')
plt.plot(dash_final_time, dash_final, 'k--')
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.scatter(slope_based_maximum_time, slope_based_maximum, c='orange', zorder=4,
label=textwrap.fill('Slope-based maximum', 11))
plt.scatter(slope_based_minimum_time, slope_based_minimum, c='purple', zorder=4,
label=textwrap.fill('Slope-based minimum', 11))
plt.scatter(improved_slope_based_maximum_time, improved_slope_based_maximum, c='deeppink', zorder=4,
label=textwrap.fill('Improved slope-based maximum', 11))
plt.scatter(improved_slope_based_minimum_time, improved_slope_based_minimum, c='dodgerblue', zorder=4,
label=textwrap.fill('Improved slope-based minimum', 11))
plt.xlim(3.9 * np.pi, 5.5 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-3, -2, -1, 0, 1, 2), ('-3', '-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.85, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_slope_based.png')
plt.show()
# plot 5
a = 0.25
width = 0.2
time = np.linspace(0, (5 - a) * np.pi, 1001)
time_series = np.cos(time) + np.cos(5 * time)
utils = emd_utils.Utility(time=time, time_series=time_series)
max_bool = utils.max_bool_func_1st_order_fd()
maxima_x = time[max_bool]
maxima_y = time_series[max_bool]
min_bool = utils.min_bool_func_1st_order_fd()
minima_x = time[min_bool]
minima_y = time_series[min_bool]
A2 = np.abs(maxima_y[-2] - minima_y[-2]) / 2
A1 = np.abs(maxima_y[-1] - minima_y[-1]) / 2
P2 = 2 * np.abs(maxima_x[-2] - minima_x[-2])
P1 = 2 * np.abs(maxima_x[-1] - minima_x[-1])
Huang_time = (P1 / P2) * (time[time >= maxima_x[-2]] - time[time == maxima_x[-2]]) + maxima_x[-1]
Huang_wave = (A1 / A2) * (time_series[time >= maxima_x[-2]] - time_series[time == maxima_x[-2]]) + maxima_y[-1]
Coughlin_time = Huang_time
Coughlin_wave = A1 * np.cos(2 * np.pi * (1 / P1) * (Coughlin_time - Coughlin_time[0]))
Average_max_time = maxima_x[-1] + (maxima_x[-1] - maxima_x[-2])
Average_max = (maxima_y[-2] + maxima_y[-1]) / 2
Average_min_time = minima_x[-1] + (minima_x[-1] - minima_x[-2])
Average_min = (minima_y[-2] + minima_y[-1]) / 2
utils_Huang = emd_utils.Utility(time=time, time_series=Huang_wave)
Huang_max_bool = utils_Huang.max_bool_func_1st_order_fd()
Huang_min_bool = utils_Huang.min_bool_func_1st_order_fd()
utils_Coughlin = emd_utils.Utility(time=time, time_series=Coughlin_wave)
Coughlin_max_bool = utils_Coughlin.max_bool_func_1st_order_fd()
Coughlin_min_bool = utils_Coughlin.min_bool_func_1st_order_fd()
Huang_max_time = Huang_time[Huang_max_bool]
Huang_max = Huang_wave[Huang_max_bool]
Huang_min_time = Huang_time[Huang_min_bool]
Huang_min = Huang_wave[Huang_min_bool]
Coughlin_max_time = Coughlin_time[Coughlin_max_bool]
Coughlin_max = Coughlin_wave[Coughlin_max_bool]
Coughlin_min_time = Coughlin_time[Coughlin_min_bool]
Coughlin_min = Coughlin_wave[Coughlin_min_bool]
max_2_x_time = np.linspace(maxima_x[-2] - width, maxima_x[-2] + width, 101)
max_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
max_2_x = maxima_y[-2] * np.ones_like(max_2_x_time)
min_2_x_time = np.linspace(minima_x[-2] - width, minima_x[-2] + width, 101)
min_2_x_time_side = np.linspace(5.3 * np.pi - width, 5.3 * np.pi + width, 101)
min_2_x = minima_y[-2] * np.ones_like(min_2_x_time)
dash_max_min_2_x = np.linspace(minima_y[-2], maxima_y[-2], 101)
dash_max_min_2_x_time = 5.3 * np.pi * np.ones_like(dash_max_min_2_x)
max_2_y = np.linspace(maxima_y[-2] - width, maxima_y[-2] + width, 101)
max_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
max_2_y_time = maxima_x[-2] * np.ones_like(max_2_y)
min_2_y = np.linspace(minima_y[-2] - width, minima_y[-2] + width, 101)
min_2_y_side = np.linspace(-1.8 - width, -1.8 + width, 101)
min_2_y_time = minima_x[-2] * np.ones_like(min_2_y)
dash_max_min_2_y_time = np.linspace(minima_x[-2], maxima_x[-2], 101)
dash_max_min_2_y = -1.8 * np.ones_like(dash_max_min_2_y_time)
max_1_x_time = np.linspace(maxima_x[-1] - width, maxima_x[-1] + width, 101)
max_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
max_1_x = maxima_y[-1] * np.ones_like(max_1_x_time)
min_1_x_time = np.linspace(minima_x[-1] - width, minima_x[-1] + width, 101)
min_1_x_time_side = np.linspace(5.4 * np.pi - width, 5.4 * np.pi + width, 101)
min_1_x = minima_y[-1] * np.ones_like(min_1_x_time)
dash_max_min_1_x = np.linspace(minima_y[-1], maxima_y[-1], 101)
dash_max_min_1_x_time = 5.4 * np.pi * np.ones_like(dash_max_min_1_x)
max_1_y = np.linspace(maxima_y[-1] - width, maxima_y[-1] + width, 101)
max_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
max_1_y_time = maxima_x[-1] * np.ones_like(max_1_y)
min_1_y = np.linspace(minima_y[-1] - width, minima_y[-1] + width, 101)
min_1_y_side = np.linspace(-2.1 - width, -2.1 + width, 101)
min_1_y_time = minima_x[-1] * np.ones_like(min_1_y)
dash_max_min_1_y_time = np.linspace(minima_x[-1], maxima_x[-1], 101)
dash_max_min_1_y = -2.1 * np.ones_like(dash_max_min_1_y_time)
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Characteristic Wave Effects Example')
plt.plot(time, time_series, LineWidth=2, label='Signal')
plt.scatter(Huang_max_time, Huang_max, c='magenta', zorder=4, label=textwrap.fill('Huang maximum', 10))
plt.scatter(Huang_min_time, Huang_min, c='lime', zorder=4, label=textwrap.fill('Huang minimum', 10))
plt.scatter(Coughlin_max_time, Coughlin_max, c='darkorange', zorder=4,
label=textwrap.fill('Coughlin maximum', 14))
plt.scatter(Coughlin_min_time, Coughlin_min, c='dodgerblue', zorder=4,
label=textwrap.fill('Coughlin minimum', 14))
plt.scatter(Average_max_time, Average_max, c='orangered', zorder=4,
label=textwrap.fill('Average maximum', 14))
plt.scatter(Average_min_time, Average_min, c='cyan', zorder=4,
label=textwrap.fill('Average minimum', 14))
plt.scatter(maxima_x, maxima_y, c='r', zorder=4, label='Maxima')
plt.scatter(minima_x, minima_y, c='b', zorder=4, label='Minima')
plt.plot(Huang_time, Huang_wave, '--', c='darkviolet', label=textwrap.fill('Huang Characteristic Wave', 14))
plt.plot(Coughlin_time, Coughlin_wave, '--', c='darkgreen', label=textwrap.fill('Coughlin Characteristic Wave', 14))
plt.plot(max_2_x_time, max_2_x, 'k-')
plt.plot(max_2_x_time_side, max_2_x, 'k-')
plt.plot(min_2_x_time, min_2_x, 'k-')
plt.plot(min_2_x_time_side, min_2_x, 'k-')
plt.plot(dash_max_min_2_x_time, dash_max_min_2_x, 'k--')
plt.text(5.16 * np.pi, 0.85, r'$2a_2$')
plt.plot(max_2_y_time, max_2_y, 'k-')
plt.plot(max_2_y_time, max_2_y_side, 'k-')
plt.plot(min_2_y_time, min_2_y, 'k-')
plt.plot(min_2_y_time, min_2_y_side, 'k-')
plt.plot(dash_max_min_2_y_time, dash_max_min_2_y, 'k--')
plt.text(4.08 * np.pi, -2.2, r'$\frac{p_2}{2}$')
plt.plot(max_1_x_time, max_1_x, 'k-')
plt.plot(max_1_x_time_side, max_1_x, 'k-')
plt.plot(min_1_x_time, min_1_x, 'k-')
plt.plot(min_1_x_time_side, min_1_x, 'k-')
plt.plot(dash_max_min_1_x_time, dash_max_min_1_x, 'k--')
plt.text(5.42 * np.pi, -0.1, r'$2a_1$')
plt.plot(max_1_y_time, max_1_y, 'k-')
plt.plot(max_1_y_time, max_1_y_side, 'k-')
plt.plot(min_1_y_time, min_1_y, 'k-')
plt.plot(min_1_y_time, min_1_y_side, 'k-')
plt.plot(dash_max_min_1_y_time, dash_max_min_1_y, 'k--')
plt.text(4.48 * np.pi, -2.5, r'$\frac{p_1}{2}$')
plt.xlim(3.9 * np.pi, 5.6 * np.pi)
plt.xticks((4 * np.pi, 5 * np.pi), (r'4$\pi$', r'5$\pi$'))
plt.yticks((-2, -1, 0, 1, 2), ('-2', '-1', '0', '1', '2'))
box_0 = ax.get_position()
ax.set_position([box_0.x0 - 0.05, box_0.y0, box_0.width * 0.84, box_0.height])
ax.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.savefig('jss_figures/edge_effects_characteristic_wave.png')
plt.show()
# plot 6
t = np.linspace(5, 95, 100)
signal_orig = np.cos(2 * np.pi * t / 50) + 0.6 * np.cos(2 * np.pi * t / 25) + 0.5 * np.sin(2 * np.pi * t / 200)
util_nn = emd_utils.Utility(time=t, time_series=signal_orig)
maxima = signal_orig[util_nn.max_bool_func_1st_order_fd()]
minima = signal_orig[util_nn.min_bool_func_1st_order_fd()]
cs_max = CubicSpline(t[util_nn.max_bool_func_1st_order_fd()], maxima)
cs_min = CubicSpline(t[util_nn.min_bool_func_1st_order_fd()], minima)
time = np.linspace(0, 5 * np.pi, 1001)
lsq_signal = np.cos(time) + np.cos(5 * time)
knots = np.linspace(0, 5 * np.pi, 101)
time_extended = time_extension(time)
time_series_extended = np.zeros_like(time_extended) / 0
time_series_extended[int(len(lsq_signal) - 1):int(2 * (len(lsq_signal) - 1) + 1)] = lsq_signal
neural_network_m = 200
neural_network_k = 100
# forward ->
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[(-(neural_network_m + neural_network_k - col)):(-(neural_network_m - col))]
P[-1, col] = 1 # for additive constant
t = lsq_signal[-neural_network_m:]
# test - top
seed_weights = np.ones(neural_network_k) / neural_network_k
weights = 0 * seed_weights.copy()
train_input = P[:-1, :]
lr = 0.01
for iterations in range(1000):
output = np.matmul(weights, train_input)
error = (t - output)
gradients = error * (- train_input)
# guess average gradients
average_gradients = np.mean(gradients, axis=1)
# steepest descent
max_gradient_vector = average_gradients * (np.abs(average_gradients) == max(np.abs(average_gradients)))
adjustment = - lr * average_gradients
# adjustment = - lr * max_gradient_vector
weights += adjustment
# test - bottom
weights_right = np.hstack((weights, 0))
max_count_right = 0
min_count_right = 0
i_right = 0
while ((max_count_right < 1) or (min_count_right < 1)) and (i_right < len(lsq_signal) - 1):
time_series_extended[int(2 * (len(lsq_signal) - 1) + 1 + i_right)] = \
sum(weights_right * np.hstack((time_series_extended[
int(2 * (len(lsq_signal) - 1) + 1 - neural_network_k + i_right):
int(2 * (len(lsq_signal) - 1) + 1 + i_right)], 1)))
i_right += 1
if i_right > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_right += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)],
time_series=time_series_extended[int(2 * (len(lsq_signal) - 1) + 1):
int(2 * (len(lsq_signal) - 1) + 1 + i_right + 1)])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_right += 1
# backward <-
P = np.zeros((int(neural_network_k + 1), neural_network_m))
for col in range(neural_network_m):
P[:-1, col] = lsq_signal[int(col + 1):int(col + neural_network_k + 1)]
P[-1, col] = 1 # for additive constant
t = lsq_signal[:neural_network_m]
vx = cvx.Variable(int(neural_network_k + 1))
objective = cvx.Minimize(cvx.norm((2 * (vx * P) + 1 - t), 2)) # linear activation function is arbitrary
prob = cvx.Problem(objective)
result = prob.solve(verbose=True, solver=cvx.ECOS)
weights_left = np.array(vx.value)
max_count_left = 0
min_count_left = 0
i_left = 0
while ((max_count_left < 1) or (min_count_left < 1)) and (i_left < len(lsq_signal) - 1):
time_series_extended[int(len(lsq_signal) - 2 - i_left)] = \
2 * sum(weights_left * np.hstack((time_series_extended[int(len(lsq_signal) - 1 - i_left):
int(len(lsq_signal) - 1 - i_left + neural_network_k)],
1))) + 1
i_left += 1
if i_left > 1:
emd_utils_max = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_max.max_bool_func_1st_order_fd()) > 0:
max_count_left += 1
emd_utils_min = \
emd_utils.Utility(time=time_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))],
time_series=time_series_extended[int(len(lsq_signal) - 1 - i_left):int(len(lsq_signal))])
if sum(emd_utils_min.min_bool_func_1st_order_fd()) > 0:
min_count_left += 1
lsq_utils = emd_utils.Utility(time=time, time_series=lsq_signal)
utils_extended = emd_utils.Utility(time=time_extended, time_series=time_series_extended)
maxima = lsq_signal[lsq_utils.max_bool_func_1st_order_fd()]
maxima_time = time[lsq_utils.max_bool_func_1st_order_fd()]
maxima_extrapolate = time_series_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
maxima_extrapolate_time = time_extended[utils_extended.max_bool_func_1st_order_fd()][-1]
minima = lsq_signal[lsq_utils.min_bool_func_1st_order_fd()]
minima_time = time[lsq_utils.min_bool_func_1st_order_fd()]
minima_extrapolate = time_series_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
minima_extrapolate_time = time_extended[utils_extended.min_bool_func_1st_order_fd()][-2:]
ax = plt.subplot(111)
plt.gcf().subplots_adjust(bottom=0.10)
plt.title('Single Neuron Neural Network Example')
plt.plot(time, lsq_signal, zorder=2, label='Signal')
plt.plot(time_extended, time_series_extended, c='g', zorder=1, label=textwrap.fill('Extrapolated signal', 12))
plt.scatter(maxima_time, maxima, c='r', zorder=3, label='Maxima')
plt.scatter(minima_time, minima, c='b', zorder=3, label='Minima')
plt.scatter(maxima_extrapolate_time, maxima_extrapolate, c='magenta', zorder=3,
label=textwrap.fill('Extrapolated maxima', 12))
plt.scatter(minima_extrapolate_time, minima_extrapolate, c='cyan', zorder=4,
label=textwrap.fill('Extrapolated minima', 12))
plt.plot(((time[-302] + time[-301]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k',
label=textwrap.fill('Neural network inputs', 13))
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time[-302] + time[-301]) / 2), ((time[-302] + time[-301]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='k')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1002]) / 2),
((time_extended[-1001] + time_extended[-1002]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='k')
plt.plot(((time_extended[-1001] + time_extended[-1002]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='k')
plt.plot(((time[-202] + time[-201]) / 2) * np.ones(100), np.linspace(-2.75, 2.75, 100), c='gray', linestyle='dashed',
label=textwrap.fill('Neural network targets', 13))
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
-2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time[-202] + time[-201]) / 2), ((time[-202] + time[-201]) / 2) + 0.1, 100),
2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), -2.75 * np.ones(100), c='gray')
plt.plot(np.linspace(((time_extended[-1001] + time_extended[-1000]) / 2),
((time_extended[-1001] + time_extended[-1000]) / 2) - 0.1, 100), 2.75 * np.ones(100), c='gray')
plt.plot(((time_extended[-1001] + time_extended[-1000]) / 2) * | np.ones(100) | numpy.ones |
# 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") | numpy.ones |
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,)) | numpy.array |
# -*- coding: utf-8 -*-
import argparse
import os
import shutil
import time
import numpy as np
import random
from collections import OrderedDict
import torch
import torch.backends.cudnn as cudnn
from callbacks import AverageMeter
from data_utils.causal_data_loader_frames import VideoFolder
from utils import save_results
from tqdm import tqdm
parser = argparse.ArgumentParser(description='Counterfactual CAR')
# Path, dataset and log related arguments
parser.add_argument('--root_frames', type=str, default='/mnt/data1/home/sunpengzhan/sth-sth-v2/',
help='path to the folder with frames')
parser.add_argument('--json_data_train', type=str, default='../data/dataset_splits/compositional/train.json',
help='path to the json file with train video meta data')
parser.add_argument('--json_data_val', type=str, default='../data/dataset_splits/compositional/validation.json',
help='path to the json file with validation video meta data')
parser.add_argument('--json_file_labels', type=str, default='../data/dataset_splits/compositional/labels.json',
help='path to the json file with ground truth labels')
parser.add_argument('--dataset', default='smth_smth',
help='which dataset to train')
parser.add_argument('--logname', default='my_method',
help='name of the experiment for checkpoints and logs')
parser.add_argument('--print_freq', '-p', default=20, type=int,
metavar='N', help='print frequency (default: 20)')
parser.add_argument('--ckpt', default='./ckpt',
help='folder to output checkpoints')
parser.add_argument('--resume_vision', default='', type=str, metavar='PATH',
help='path to latest checkpoint (default: none)')
parser.add_argument('--resume_coord', default='', type=str, metavar='PATH',
help='path to latest checkpoint (default: none)')
parser.add_argument('--resume_fusion', default='', type=str, metavar='PATH',
help='path to latest checkpoint (default: none)')
# model, image&feature dim and training related arguments
parser.add_argument('--model_vision', default='rgb_roi')
parser.add_argument('--model_coord', default='interaction')
parser.add_argument('--model_fusion', default='concat_fusion')
parser.add_argument('--fusion_function', default='fused_sum', type=str,
help='function for fusing activations from each branch')
parser.add_argument('--img_feature_dim', default=512, type=int, metavar='N',
help='intermediate feature dimension for image-based features')
parser.add_argument('--coord_feature_dim', default=512, type=int, metavar='N',
help='intermediate feature dimension for coord-based features')
parser.add_argument('--size', default=224, type=int, metavar='N',
help='primary image input size')
parser.add_argument('--num_boxes', default=4, type=int,
help='num of boxes for each image')
parser.add_argument('--num_frames', default=16, type=int,
help='num of frames for the model')
parser.add_argument('--num_classes', default=174, type=int,
help='num of class in the model')
parser.add_argument('--epochs', default=30, type=int, metavar='N',
help='number of total epochs to run')
parser.add_argument('--start_epoch', default=None, type=int, metavar='N',
help='manual epoch number (useful on restarts)')
parser.add_argument('--batch_size', '-b', default=16, type=int,
metavar='N', help='mini-batch size')
parser.add_argument('--lr', '--learning-rate', default=0.01, type=float,
metavar='LR', help='initial learning rate')
parser.add_argument('--lr_steps', default=[24, 35, 45], type=float, nargs="+",
metavar='LRSteps', help='epochs to decay learning rate by 10')
parser.add_argument('--momentum', default=0.9, type=float, metavar='M',
help='momentum')
parser.add_argument('--weight_decay', '--wd', default=0.0001, type=float,
metavar='W', help='weight decay (default: 1e-4)')
parser.add_argument('--clip_gradient', '-cg', default=5, type=float,
metavar='W', help='gradient norm clipping (default: 5)')
parser.add_argument('--search_stride', type=int, default=5, help='test performance every n strides')
# train mode, hardware setting and others related arguments
parser.add_argument('-j', '--workers', default=4, type=int, metavar='N',
help='number of data loading workers (default: 4)')
parser.add_argument('-e', '--evaluate', dest='evaluate', action='store_true',
help='evaluate model on validation set')
parser.add_argument('--cf_inference_group', action='store_true', help='counterfactual inference model on validation set')
parser.add_argument('--parallel', default=True, type=bool,
help='whether or not train with multi GPUs')
parser.add_argument('--gpu_index', type=str, default='0, 1, 2, 3', help='the index of gpu you want to use')
best_loss = 1000000
def main():
global args, best_loss
args = parser.parse_args()
os.environ['CUDA_VISIBLE_DEVICES'] = args.gpu_index
print(args)
# create vision model
if args.model_vision == 'global_i3d':
from model.model_lib import VideoGlobalModel as RGBModel
print('global_i3d loaded!!')
elif args.model_vision == 'rgb_roi':
from model.model_lib import BboxVisualModel as RGBModel
print('rgb_roi loaded!!')
else:
print("no such a vision model!")
# create coord model
if args.model_coord == 'interaction':
from model.model_lib import BboxInteractionLatentModel as BboxModel
print('interaction loaded!!')
else:
print("no such a coordinate model!")
# create fusion model
if args.model_fusion == 'concat_fusion':
from model.model_lib import ConcatFusionModel as FusionModel
print('concat_fusion loaded!!')
else:
print('no such a fusion model!')
# load model branch
vision_model = RGBModel(args)
coord_model = BboxModel(args)
fusion_model = FusionModel(args)
# create the fusion function for the activation of three branches
if args.fusion_function == 'fused_sum':
from fusion_function import logsigsum as fusion_func
print('fused_sum loaded!!')
elif args.fusion_function == 'naive_sum':
from fusion_function import naivesum as fusion_func
print('naive_sum loaded!!')
else:
print('no such a fusion function!')
fusion_function = fusion_func()
if args.parallel:
vision_model = torch.nn.DataParallel(vision_model).cuda()
coord_model = torch.nn.DataParallel(coord_model).cuda()
fusion_model = torch.nn.DataParallel(fusion_model).cuda()
else:
vision_model = vision_model.cuda()
coord_model = coord_model.cuda()
fusion_model = fusion_model.cuda()
# optionally resume vision model from a checkpoint
if args.resume_vision:
assert os.path.isfile(args.resume_vision), "No checkpoint found at '{}'".format(args.resume_vision)
print("=> loading checkpoint '{}'".format(args.resume_vision))
checkpoint = torch.load(args.resume_vision)
if args.start_epoch is None:
args.start_epoch = checkpoint['epoch']
best_loss = checkpoint['best_loss']
vision_model.load_state_dict(checkpoint['state_dict'])
print("=> loaded checkpoint '{}' (epoch {})"
.format(args.resume_vision, checkpoint['epoch']))
# optionally resume coord model from a checkpoint
if args.resume_coord:
assert os.path.isfile(args.resume_coord), "No checkpoint found at '{}'".format(args.resume_coord)
print("=> loading checkpoint '{}'".format(args.resume_coord))
checkpoint = torch.load(args.resume_coord)
if args.start_epoch is None:
args.start_epoch = checkpoint['epoch']
best_loss = checkpoint['best_loss']
coord_model.load_state_dict(checkpoint['state_dict'])
print("=> loaded checkpoint '{}' (epoch {})"
.format(args.resume_coord, checkpoint['epoch']))
if args.resume_fusion:
assert os.path.isfile(args.resume_fusion), "No checkpoint found at '{}'".format(args.resume_fusion)
print("=> loading checkpoint '{}'".format(args.resume_fusion))
checkpoint = torch.load(args.resume_fusion)
if args.start_epoch is None:
args.start_epoch = checkpoint['epoch']
best_loss = checkpoint['best_loss']
fusion_model.load_state_dict(checkpoint['state_dict'])
print("=> loaded checkpoint '{}' (epoch {})"
.format(args.resume_fusion, checkpoint['epoch']))
if args.start_epoch is None:
args.start_epoch = 0
cudnn.benchmark = True
# create training and validation dataset
dataset_train = VideoFolder(root=args.root_frames,
num_boxes=args.num_boxes,
file_input=args.json_data_train,
file_labels=args.json_file_labels,
frames_duration=args.num_frames,
args=args,
is_val=False,
if_augment=True,
)
dataset_val = VideoFolder(root=args.root_frames,
num_boxes=args.num_boxes,
file_input=args.json_data_val,
file_labels=args.json_file_labels,
frames_duration=args.num_frames,
args=args,
is_val=True,
if_augment=True,
)
# create training and validation loader
train_loader = torch.utils.data.DataLoader(
dataset_train,
batch_size=args.batch_size, shuffle=True,
num_workers=args.workers, drop_last=True,
pin_memory=True
)
val_loader = torch.utils.data.DataLoader(
dataset_val, drop_last=True,
batch_size=args.batch_size, shuffle=False,
num_workers=args.workers, pin_memory=False
)
model_list = [vision_model, coord_model, fusion_model]
optimizer_vision = torch.optim.SGD(filter(lambda p: p.requires_grad, vision_model.parameters()),
momentum=args.momentum, lr=args.lr, weight_decay=args.weight_decay)
optimizer_coord = torch.optim.SGD(filter(lambda p: p.requires_grad, coord_model.parameters()),
momentum=args.momentum, lr=args.lr, weight_decay=args.weight_decay)
optimizer_fusion = torch.optim.SGD(filter(lambda p: p.requires_grad, fusion_model.parameters()),
momentum=args.momentum, lr=args.lr, weight_decay=args.weight_decay)
optimizer_list = [optimizer_vision, optimizer_coord, optimizer_fusion]
criterion = torch.nn.CrossEntropyLoss()
search_list = np.linspace(0.0, 1.0, 11)
# factual inference (vanilla test stage)
if args.evaluate:
validate(val_loader, model_list, fusion_function, criterion, class_to_idx=dataset_val.classes_dict)
return
# Counterfactual inference by trying a list of hyperparameter
if args.cf_inference_group:
cf_inference_group(val_loader, model_list, fusion_function, search_list,
class_to_idx=dataset_val.classes_dict)
return
print('training begin...')
for epoch in tqdm(range(args.start_epoch, args.epochs)):
adjust_learning_rate(optimizer_vision, epoch, args.lr_steps, 'vision')
adjust_learning_rate(optimizer_coord, epoch, args.lr_steps, 'coord')
adjust_learning_rate(optimizer_fusion, epoch, args.lr_steps, 'fusion')
# train for one epoch
train(train_loader, model_list, fusion_function, optimizer_list, epoch, criterion)
if (epoch+1) >= 30 and (epoch + 1) % args.search_stride == 0:
loss = validate(val_loader, model_list, fusion_function, criterion,
epoch=epoch, class_to_idx=dataset_val.classes_dict)
else:
loss = 100
# remember best loss and save checkpoint
is_best = loss < best_loss
best_loss = min(loss, best_loss)
save_checkpoint(
{
'epoch': epoch + 1,
'state_dict': vision_model.state_dict(),
'best_loss': best_loss,
},
is_best,
os.path.join(args.ckpt, '{}_{}'.format(args.model_vision, args.logname)))
save_checkpoint(
{
'epoch': epoch + 1,
'state_dict': coord_model.state_dict(),
'best_loss': best_loss,
},
is_best,
os.path.join(args.ckpt, '{}_{}'.format(args.model_coord, args.logname)))
save_checkpoint(
{
'epoch': epoch + 1,
'state_dict': fusion_model.state_dict(),
'best_loss': best_loss,
},
is_best,
os.path.join(args.ckpt, '{}_{}'.format(args.model_fusion, args.logname)))
def train(train_loader, model_list, fusion_function,
optimizer_list, epoch, criterion):
global args
batch_time = AverageMeter()
data_time = AverageMeter()
losses = AverageMeter()
acc_top1 = AverageMeter()
acc_top5 = AverageMeter()
# load three model branches
[vision_model, coord_model, fusion_model] = model_list
# load four optimizers, including the one designed for uniform assumption
[optimizer_vision, optimizer_coord, optimizer_fusion] = optimizer_list
# switch to train mode
vision_model.train()
coord_model.train()
fusion_model.train()
end = time.time()
for i, (global_img_tensors, box_tensors, box_categories, video_label) in enumerate(train_loader):
data_time.update(time.time() - end)
# obtain the activation and vision features from vision branch
output_vision, feature_vision = vision_model(global_img_tensors.cuda(), box_categories, box_tensors.cuda(), video_label)
output_vision = output_vision.view((-1, len(train_loader.dataset.classes)))
# obtain the activation and coordinate features from coordinate branch
output_coord, feature_coord = coord_model(global_img_tensors, box_categories.cuda(), box_tensors.cuda(), video_label)
output_coord = output_coord.view((-1, len(train_loader.dataset.classes)))
# detach the computation graph, avoid the gradient confusion
feature_vision_detached = feature_vision.detach()
feature_coord_detached = feature_coord.detach()
# obtain the activation of fusion branch
output_fusion = fusion_model(feature_vision_detached.cuda(), feature_coord_detached.cuda())
output_fusion = output_fusion.view((-1, len(train_loader.dataset.classes)))
output_factual = fusion_function(output_vision, output_coord, output_fusion)
# loss_fusion is the loss of output_fusion(fused, obtained from the fusion_function)
loss_vision = criterion(output_vision, video_label.long().cuda())
loss_coord = criterion(output_coord, video_label.long().cuda())
loss_fusion = criterion(output_fusion, video_label.long().cuda())
loss_factual = criterion(output_factual, video_label.long().cuda())
# Measure the accuracy of the sum of three branch activation results
acc1, acc5 = accuracy(output_factual.cpu(), video_label, topk=(1, 5))
# record the accuracy and loss
losses.update(loss_factual.item(), global_img_tensors.size(0))
acc_top1.update(acc1.item(), global_img_tensors.size(0))
acc_top5.update(acc5.item(), global_img_tensors.size(0))
# refresh the optimizer
optimizer_vision.zero_grad()
optimizer_coord.zero_grad()
optimizer_fusion.zero_grad()
loss = loss_vision + loss_coord + loss_factual
loss.backward()
if args.clip_gradient is not None:
torch.nn.utils.clip_grad_norm_(vision_model.parameters(), args.clip_gradient)
# update the parameter
optimizer_vision.step()
optimizer_coord.step()
optimizer_fusion.step()
batch_time.update(time.time() - end)
end = time.time()
if i % args.print_freq == 0:
print('Epoch: [{0}][{1}/{2}]\t'
'Time {batch_time.val:.3f} ({batch_time.avg:.3f})\t'
'Data {data_time.val:.3f} ({data_time.avg:.3f})\t'
'Loss {loss.val:.4f} ({loss.avg:.4f})\t'
'Acc1 {acc_top1.val:.1f} ({acc_top1.avg:.1f})\t'
'Acc5 {acc_top5.val:.1f} ({acc_top5.avg:.1f})'.format(
epoch, i, len(train_loader), batch_time=batch_time,
data_time=data_time, loss=losses,
acc_top1=acc_top1, acc_top5=acc_top5))
def validate(val_loader, model_list, fusion_function, criterion,
epoch=None, class_to_idx=None):
batch_time = AverageMeter()
losses = AverageMeter()
acc_top1 = AverageMeter()
acc_top5 = AverageMeter()
logits_matrix = []
targets_list = []
# unpack three models
[vision_model, coord_model, fusion_model] = model_list
# switch to evaluate mode
vision_model.eval()
coord_model.eval()
fusion_model.eval()
end = time.time()
for i, (global_img_tensors, box_tensors, box_categories, video_label) in enumerate(val_loader):
# compute output
with torch.no_grad():
output_vision, feature_vision = vision_model(global_img_tensors.cuda(), box_categories, box_tensors.cuda(), video_label)
output_vision = output_vision.view((-1, len(val_loader.dataset.classes)))
output_coord, feature_coord = coord_model(global_img_tensors, box_categories.cuda(), box_tensors.cuda(), video_label)
output_coord = output_coord.view((-1, len(val_loader.dataset.classes)))
# detach the computation graph, avoid the gradient confusion
feature_vision_detached = feature_vision.detach()
feature_coord_detached = feature_coord.detach()
# obtain the activation of fusion branch
output_fusion = fusion_model(feature_vision_detached.cuda(), feature_coord_detached.cuda())
output_fusion = output_fusion.view((-1, len(val_loader.dataset.classes)))
# fuse three outputs
output_factual = fusion_function(output_vision, output_coord, output_fusion)
# warning: loss_fusion is the loss of output_fusion(fused, obtained from the fusion_function)
loss_vision = criterion(output_vision, video_label.long().cuda())
loss_coord = criterion(output_coord, video_label.long().cuda())
loss_fusion = criterion(output_factual, video_label.long().cuda())
# statistic result from fusion_branch or value after fusion function
output = output_factual
loss = loss_vision
acc1, acc5 = accuracy(output.cpu(), video_label, topk=(1, 5))
if args.evaluate:
logits_matrix.append(output.cpu().data.numpy())
targets_list.append(video_label.cpu().numpy())
# measure accuracy and record loss
losses.update(loss.item(), global_img_tensors.size(0))
acc_top1.update(acc1.item(), global_img_tensors.size(0))
acc_top5.update(acc5.item(), global_img_tensors.size(0))
# measure elapsed time
batch_time.update(time.time() - end)
end = time.time()
if i % args.print_freq == 0 or i + 1 == len(val_loader):
print('Test: [{0}/{1}]\t'
'Time {batch_time.val:.3f} ({batch_time.avg:.3f})\t'
'Loss {loss.val:.4f} ({loss.avg:.4f})\t'
'Acc1 {acc_top1.val:.1f} ({acc_top1.avg:.1f})\t'
'Acc5 {acc_top5.val:.1f} ({acc_top5.avg:.1f})\t'.format(
i, len(val_loader), batch_time=batch_time, loss=losses,
acc_top1=acc_top1, acc_top5=acc_top5,
))
if args.evaluate:
logits_matrix = np.concatenate(logits_matrix)
targets_list = np.concatenate(targets_list)
save_results(logits_matrix, targets_list, class_to_idx, args)
return losses.avg
def cf_inference_group(val_loader, model_list, fusion_function, search_list, class_to_idx=None):
batch_time = AverageMeter()
search_length = len(search_list)
search_dict = {}
for i in range(search_length):
search_dict['acc_1_alpha_{}'.format(round(search_list[i], 1))] = AverageMeter()
search_dict['acc_5_alpha_{}'.format(round(search_list[i], 1))] = AverageMeter()
[vision_model, coord_model, fusion_model] = model_list
# switch to evaluate mode
vision_model.eval()
coord_model.eval()
fusion_model.eval()
end = time.time()
for i, (global_img_tensors, box_tensors, box_categories, video_label) in enumerate(val_loader):
# compute output
with torch.no_grad():
# factual inference
output_vision, feature_vision = vision_model(global_img_tensors.cuda(), box_categories, box_tensors.cuda(),
video_label)
output_vision = output_vision.view((-1, len(val_loader.dataset.classes)))
output_coord, feature_coord = coord_model(global_img_tensors, box_categories.cuda(), box_tensors.cuda(),
video_label)
output_coord = output_coord.view((-1, len(val_loader.dataset.classes)))
# obtain the activation of fusion branch
output_fusion = fusion_model(feature_vision.cuda(), feature_coord.cuda())
output_fusion = output_fusion.view((-1, len(val_loader.dataset.classes)))
# fuse three outputs
output_factual = fusion_function(output_vision, output_coord, output_fusion)
# counterfactual inference
output_vision_subtrahend = output_vision
output_counterfactual = fusion_function(output_vision_subtrahend, torch.tensor(0.0), torch.tensor(0.0))
for j in range(search_length):
weight = search_list[j]
output_debiased = output_factual - output_counterfactual * weight
acc1, acc5 = accuracy(output_debiased.cpu(), video_label, topk=(1, 5))
search_dict['acc_1_alpha_{}'.format(round(search_list[j], 1))].update(acc1.item(), global_img_tensors.size(0))
search_dict['acc_5_alpha_{}'.format(round(search_list[j], 1))].update(acc5.item(), global_img_tensors.size(0))
# measure elapsed time
batch_time.update(time.time() - end)
end = time.time()
if i % args.print_freq == 0 or i + 1 == len(val_loader):
print('Cf-Inference: [{0}/{1}]\t'
'Time {batch_time.val:.3f} ({batch_time.avg:.3f})\t'
'Acc1_0.0 {acc_top1_00.val:.1f} ({acc_top1_00.avg:.1f})\t'
'Acc1_0.2 {acc_top1_02.val:.1f} ({acc_top1_02.avg:.1f})\t'
'Acc1_0.5 {acc_top1_05.val:.1f} ({acc_top1_05.avg:.1f})\t'
'Acc1_0.8 {acc_top1_08.val:.1f} ({acc_top1_08.avg:.1f})\t'
'Acc1_1.0 {acc_top1_10.val:.1f} ({acc_top1_10.avg:.1f})'.format(
i, len(val_loader), batch_time=batch_time, acc_top1_00=search_dict['acc_1_alpha_0.0'],
acc_top1_02=search_dict['acc_1_alpha_0.2'], acc_top1_05=search_dict['acc_1_alpha_0.5'],
acc_top1_08=search_dict['acc_1_alpha_0.8'], acc_top1_10=search_dict['acc_1_alpha_1.0']))
for k in range(search_length):
print(search_list[k], search_dict['acc_1_alpha_{}'.format(round(search_list[k], 1))].avg,
search_dict['acc_5_alpha_{}'.format(round(search_list[k], 1))].avg)
return
def save_checkpoint(state, is_best, filename):
torch.save(state, filename + '_latest.pth.tar')
if is_best:
shutil.copyfile(filename + '_latest.pth.tar', filename + '_best.pth.tar')
def adjust_learning_rate(optimizer, epoch, lr_steps, branch_name=None):
"""Sets the learning rate to the initial LR decayed by 10"""
decay = 0.1 ** (sum(epoch >= | np.array(lr_steps) | numpy.array |
#
# 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) | numpy.random.randn |
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)
@cache_readonly
def _cached_int64index(self) -> Int64Index:
return Int64Index._simple_new(self._data, name=self.name)
@property
def _int64index(self) -> Int64Index:
# wrap _cached_int64index so we can be sure its name matches self.name
res = self._cached_int64index
res._name = self._name
return res
def _get_data_as_items(self):
""" return a list of tuples of start, stop, step """
rng = self._range
return [("start", rng.start), ("stop", rng.stop), ("step", rng.step)]
def __reduce__(self):
d = self._get_attributes_dict()
d.update(dict(self._get_data_as_items()))
return ibase._new_Index, (type(self), d), None
# --------------------------------------------------------------------
# Rendering Methods
def _format_attrs(self):
"""
Return a list of tuples of the (attr, formatted_value)
"""
attrs = self._get_data_as_items()
if self.name is not None:
attrs.append(("name", ibase.default_pprint(self.name)))
return attrs
def _format_data(self, name=None):
# we are formatting thru the attributes
return None
def _format_with_header(self, header: list[str], na_rep: str = "NaN") -> list[str]:
if not len(self._range):
return header
first_val_str = str(self._range[0])
last_val_str = str(self._range[-1])
max_length = max(len(first_val_str), len(last_val_str))
return header + [f"{x:<{max_length}}" for x in self._range]
# --------------------------------------------------------------------
_deprecation_message = (
"RangeIndex.{} is deprecated and will be "
"removed in a future version. Use RangeIndex.{} "
"instead"
)
@property
def start(self) -> int:
"""
The value of the `start` parameter (``0`` if this was not supplied).
"""
# GH 25710
return self._range.start
@property
def _start(self) -> int:
"""
The value of the `start` parameter (``0`` if this was not supplied).
.. deprecated:: 0.25.0
Use ``start`` instead.
"""
warnings.warn(
self._deprecation_message.format("_start", "start"),
FutureWarning,
stacklevel=2,
)
return self.start
@property
def stop(self) -> int:
"""
The value of the `stop` parameter.
"""
return self._range.stop
@property
def _stop(self) -> int:
"""
The value of the `stop` parameter.
.. deprecated:: 0.25.0
Use ``stop`` instead.
"""
# GH 25710
warnings.warn(
self._deprecation_message.format("_stop", "stop"),
FutureWarning,
stacklevel=2,
)
return self.stop
@property
def step(self) -> int:
"""
The value of the `step` parameter (``1`` if this was not supplied).
"""
# GH 25710
return self._range.step
@property
def _step(self) -> int:
"""
The value of the `step` parameter (``1`` if this was not supplied).
.. deprecated:: 0.25.0
Use ``step`` instead.
"""
# GH 25710
warnings.warn(
self._deprecation_message.format("_step", "step"),
FutureWarning,
stacklevel=2,
)
return self.step
@cache_readonly
def nbytes(self) -> int:
"""
Return the number of bytes in the underlying data.
"""
rng = self._range
return getsizeof(rng) + sum(
getsizeof(getattr(rng, attr_name))
for attr_name in ["start", "stop", "step"]
)
def memory_usage(self, deep: bool = False) -> int:
"""
Memory usage of my values
Parameters
----------
deep : bool
Introspect the data deeply, interrogate
`object` dtypes for system-level memory consumption
Returns
-------
bytes used
Notes
-----
Memory usage does not include memory consumed by elements that
are not components of the array if deep=False
See Also
--------
numpy.ndarray.nbytes
"""
return self.nbytes
@property
def dtype(self) -> np.dtype:
return np.dtype(np.int64)
@property
def is_unique(self) -> bool:
""" return if the index has unique values """
return True
@cache_readonly
def is_monotonic_increasing(self) -> bool:
return self._range.step > 0 or len(self) <= 1
@cache_readonly
def is_monotonic_decreasing(self) -> bool:
return self._range.step < 0 or len(self) <= 1
def __contains__(self, key: Any) -> bool:
hash(key)
try:
key = ensure_python_int(key)
except TypeError:
return False
return key in self._range
@property
def inferred_type(self) -> str:
return "integer"
# --------------------------------------------------------------------
# Indexing Methods
@doc(Int64Index.get_loc)
def get_loc(self, key, method=None, tolerance=None):
if method is None and tolerance is None:
if is_integer(key) or (is_float(key) and key.is_integer()):
new_key = int(key)
try:
return self._range.index(new_key)
except ValueError as err:
raise KeyError(key) from err
raise KeyError(key)
return super().get_loc(key, method=method, tolerance=tolerance)
def _get_indexer(
self,
target: Index,
method: str | None = None,
limit: int | None = None,
tolerance=None,
) -> np.ndarray:
# -> np.ndarray[np.intp]
if com.any_not_none(method, tolerance, limit):
return super()._get_indexer(
target, method=method, tolerance=tolerance, limit=limit
)
if self.step > 0:
start, stop, step = self.start, self.stop, self.step
else:
# GH 28678: work on reversed range for simplicity
reverse = self._range[::-1]
start, stop, step = reverse.start, reverse.stop, reverse.step
if not is_signed_integer_dtype(target):
# checks/conversions/roundings are delegated to general method
return super()._get_indexer(target, method=method, tolerance=tolerance)
target_array = np.asarray(target)
locs = target_array - start
valid = (locs % step == 0) & (locs >= 0) & (target_array < stop)
locs[~valid] = -1
locs[valid] = locs[valid] / step
if step != self.step:
# We reversed this range: transform to original locs
locs[valid] = len(self) - 1 - locs[valid]
return ensure_platform_int(locs)
# --------------------------------------------------------------------
def repeat(self, repeats, axis=None) -> Int64Index:
return self._int64index.repeat(repeats, axis=axis)
def delete(self, loc) -> Int64Index: # type: ignore[override]
return self._int64index.delete(loc)
def take(
self, indices, axis: int = 0, allow_fill: bool = True, fill_value=None, **kwargs
) -> Int64Index:
with rewrite_exception("Int64Index", type(self).__name__):
return self._int64index.take(
indices,
axis=axis,
allow_fill=allow_fill,
fill_value=fill_value,
**kwargs,
)
def tolist(self) -> list[int]:
return list(self._range)
@doc(Int64Index.__iter__)
def __iter__(self):
yield from self._range
@doc(Int64Index._shallow_copy)
def _shallow_copy(self, values, name: Hashable = no_default):
name = self.name if name is no_default else name
if values.dtype.kind == "f":
return Float64Index(values, name=name)
return Int64Index._simple_new(values, name=name)
def _view(self: RangeIndex) -> RangeIndex:
result = type(self)._simple_new(self._range, name=self._name)
result._cache = self._cache
return result
@doc(Int64Index.copy)
def copy(
self,
name: Hashable = None,
deep: bool = False,
dtype: Dtype | None = None,
names=None,
):
name = self._validate_names(name=name, names=names, deep=deep)[0]
new_index = self._rename(name=name)
if dtype:
warnings.warn(
"parameter dtype is deprecated and will be removed in a future "
"version. Use the astype method instead.",
FutureWarning,
stacklevel=2,
)
new_index = new_index.astype(dtype)
return new_index
def _minmax(self, meth: str):
no_steps = len(self) - 1
if no_steps == -1:
return np.nan
elif (meth == "min" and self.step > 0) or (meth == "max" and self.step < 0):
return self.start
return self.start + self.step * no_steps
def min(self, axis=None, skipna: bool = True, *args, **kwargs) -> int:
"""The minimum value of the RangeIndex"""
nv.validate_minmax_axis(axis)
nv.validate_min(args, kwargs)
return self._minmax("min")
def max(self, axis=None, skipna: bool = True, *args, **kwargs) -> int:
"""The maximum value of the RangeIndex"""
nv.validate_minmax_axis(axis)
nv.validate_max(args, kwargs)
return self._minmax("max")
def argsort(self, *args, **kwargs) -> np.ndarray:
"""
Returns the indices that would sort the index and its
underlying data.
Returns
-------
np.ndarray[np.intp]
See Also
--------
numpy.ndarray.argsort
"""
ascending = kwargs.pop("ascending", True) # EA compat
nv.validate_argsort(args, kwargs)
if self._range.step > 0:
result = np.arange(len(self), dtype=np.intp)
else:
result = np.arange(len(self) - 1, -1, -1, dtype=np.intp)
if not ascending:
result = result[::-1]
return result
def factorize(
self, sort: bool = False, na_sentinel: int | None = -1
) -> tuple[np.ndarray, RangeIndex]:
codes = np.arange(len(self), dtype=np.intp)
uniques = self
if sort and self.step < 0:
codes = codes[::-1]
uniques = uniques[::-1]
return codes, uniques
def equals(self, other: object) -> bool:
"""
Determines if two Index objects contain the same elements.
"""
if isinstance(other, RangeIndex):
return self._range == other._range
return super().equals(other)
# --------------------------------------------------------------------
# Set Operations
def _intersection(self, other: Index, sort=False):
if not isinstance(other, RangeIndex):
# Int64Index
return super()._intersection(other, sort=sort)
if not len(self) or not len(other):
return self._simple_new(_empty_range)
first = self._range[::-1] if self.step < 0 else self._range
second = other._range[::-1] if other.step < 0 else other._range
# check whether intervals intersect
# deals with in- and decreasing ranges
int_low = max(first.start, second.start)
int_high = min(first.stop, second.stop)
if int_high <= int_low:
return self._simple_new(_empty_range)
# Method hint: linear Diophantine equation
# solve intersection problem
# performance hint: for identical step sizes, could use
# cheaper alternative
gcd, s, _ = self._extended_gcd(first.step, second.step)
# check whether element sets intersect
if (first.start - second.start) % gcd:
return self._simple_new(_empty_range)
# calculate parameters for the RangeIndex describing the
# intersection disregarding the lower bounds
tmp_start = first.start + (second.start - first.start) * first.step // gcd * s
new_step = first.step * second.step // gcd
new_range = range(tmp_start, int_high, new_step)
new_index = self._simple_new(new_range)
# adjust index to limiting interval
new_start = new_index._min_fitting_element(int_low)
new_range = range(new_start, new_index.stop, new_index.step)
new_index = self._simple_new(new_range)
if (self.step < 0 and other.step < 0) is not (new_index.step < 0):
new_index = new_index[::-1]
if sort is None:
new_index = new_index.sort_values()
return new_index
def _min_fitting_element(self, lower_limit: int) -> int:
"""Returns the smallest element greater than or equal to the limit"""
no_steps = -(-(lower_limit - self.start) // abs(self.step))
return self.start + abs(self.step) * no_steps
def _max_fitting_element(self, upper_limit: int) -> int:
"""Returns the largest element smaller than or equal to the limit"""
no_steps = (upper_limit - self.start) // abs(self.step)
return self.start + abs(self.step) * no_steps
def _extended_gcd(self, a: int, b: int) -> tuple[int, int, int]:
"""
Extended Euclidean algorithms to solve Bezout's identity:
a*x + b*y = gcd(x, y)
Finds one particular solution for x, y: s, t
Returns: gcd, s, t
"""
s, old_s = 0, 1
t, old_t = 1, 0
r, old_r = b, a
while r:
quotient = old_r // r
old_r, r = r, old_r - quotient * r
old_s, s = s, old_s - quotient * s
old_t, t = t, old_t - quotient * t
return old_r, old_s, old_t
def _union(self, other: Index, sort):
"""
Form the union of two Index objects and sorts if possible
Parameters
----------
other : Index or array-like
sort : False or None, default None
Whether to sort resulting index. ``sort=None`` returns a
monotonically increasing ``RangeIndex`` if possible or a sorted
``Int64Index`` if not. ``sort=False`` always returns an
unsorted ``Int64Index``
.. versionadded:: 0.25.0
Returns
-------
union : Index
"""
if isinstance(other, RangeIndex) and sort is None:
start_s, step_s = self.start, self.step
end_s = self.start + self.step * (len(self) - 1)
start_o, step_o = other.start, other.step
end_o = other.start + other.step * (len(other) - 1)
if self.step < 0:
start_s, step_s, end_s = end_s, -step_s, start_s
if other.step < 0:
start_o, step_o, end_o = end_o, -step_o, start_o
if len(self) == 1 and len(other) == 1:
step_s = step_o = abs(self.start - other.start)
elif len(self) == 1:
step_s = step_o
elif len(other) == 1:
step_o = step_s
start_r = min(start_s, start_o)
end_r = max(end_s, end_o)
if step_o == step_s:
if (
(start_s - start_o) % step_s == 0
and (start_s - end_o) <= step_s
and (start_o - end_s) <= step_s
):
return type(self)(start_r, end_r + step_s, step_s)
if (
(step_s % 2 == 0)
and (abs(start_s - start_o) <= step_s / 2)
and (abs(end_s - end_o) <= step_s / 2)
):
return type(self)(start_r, end_r + step_s / 2, step_s / 2)
elif step_o % step_s == 0:
if (
(start_o - start_s) % step_s == 0
and (start_o + step_s >= start_s)
and (end_o - step_s <= end_s)
):
return type(self)(start_r, end_r + step_s, step_s)
elif step_s % step_o == 0:
if (
(start_s - start_o) % step_o == 0
and (start_s + step_o >= start_o)
and (end_s - step_o <= end_o)
):
return type(self)(start_r, end_r + step_o, step_o)
return self._int64index._union(other, sort=sort)
def _difference(self, other, sort=None):
# optimized set operation if we have another RangeIndex
self._validate_sort_keyword(sort)
self._assert_can_do_setop(other)
other, result_name = self._convert_can_do_setop(other)
if not isinstance(other, RangeIndex):
return super()._difference(other, sort=sort)
res_name = ops.get_op_result_name(self, other)
first = self._range[::-1] if self.step < 0 else self._range
overlap = self.intersection(other)
if overlap.step < 0:
overlap = overlap[::-1]
if len(overlap) == 0:
return self.rename(name=res_name)
if len(overlap) == len(self):
return self[:0].rename(res_name)
if not isinstance(overlap, RangeIndex):
# We won't end up with RangeIndex, so fall back
return super()._difference(other, sort=sort)
if overlap.step != first.step:
# In some cases we might be able to get a RangeIndex back,
# but not worth the effort.
return super()._difference(other, sort=sort)
if overlap[0] == first.start:
# The difference is everything after the intersection
new_rng = range(overlap[-1] + first.step, first.stop, first.step)
elif overlap[-1] == first[-1]:
# The difference is everything before the intersection
new_rng = range(first.start, overlap[0], first.step)
else:
# The difference is not range-like
return super()._difference(other, sort=sort)
new_index = type(self)._simple_new(new_rng, name=res_name)
if first is not self._range:
new_index = new_index[::-1]
return new_index
def symmetric_difference(self, other, result_name: Hashable = None, sort=None):
if not isinstance(other, RangeIndex) or sort is not None:
return super().symmetric_difference(other, result_name, sort)
left = self.difference(other)
right = other.difference(self)
result = left.union(right)
if result_name is not None:
result = result.rename(result_name)
return result
# --------------------------------------------------------------------
def _concat(self, indexes: list[Index], name: Hashable) -> Index:
"""
Overriding parent method for the case of all RangeIndex instances.
When all members of "indexes" are of type RangeIndex: result will be
RangeIndex if possible, Int64Index otherwise. E.g.:
indexes = [RangeIndex(3), RangeIndex(3, 6)] -> RangeIndex(6)
indexes = [RangeIndex(3), RangeIndex(4, 6)] -> Int64Index([0,1,2,4,5])
"""
if not all(isinstance(x, RangeIndex) for x in indexes):
return super()._concat(indexes, name)
elif len(indexes) == 1:
return indexes[0]
rng_indexes = cast(List[RangeIndex], indexes)
start = step = next_ = None
# Filter the empty indexes
non_empty_indexes = [obj for obj in rng_indexes if len(obj)]
for obj in non_empty_indexes:
rng = obj._range
if start is None:
# This is set by the first non-empty index
start = rng.start
if step is None and len(rng) > 1:
step = rng.step
elif step is None:
# First non-empty index had only one element
if rng.start == start:
values = | np.concatenate([x._values for x in rng_indexes]) | numpy.concatenate |
# 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) | 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.) | numpy.arange |
from __future__ import division
from math import sqrt as sqrt
from itertools import product as product
import torch
import numpy as np
import cv2
from lib.utils.visualize_utils import TBWriter
def vis(func):
"""tensorboard visualization if has writer as input"""
def wrapper(*args, **kw):
return func(*args, **kw) if kw['tb_writer'] is not None else None
return wrapper
class PriorBoxBase(object):
"""Compute priorbox coordinates in center-offset form for each source
feature map.
"""
def __init__(self, cfg):
super(PriorBoxBase, self).__init__()
self.image_size = cfg.MODEL.IMAGE_SIZE
self._steps = cfg.MODEL.STEPS
self._cfg_list = []
self._prior_cfg = {}
self._clip = cfg.MODEL.CLIP
self._variance = cfg.MODEL.VARIANCE
for v in self._variance:
if v <= 0:
raise ValueError('Variances must be greater than 0')
def _setup(self, cfg):
num_feat = len(self._steps)
for item in self._cfg_list:
if item not in cfg.MODEL:
raise Exception("wrong anchor config!")
if len(cfg.MODEL[item]) != num_feat and len(cfg.MODEL[item]) != 0:
raise Exception("config {} length does not match step length!".format(item))
self._prior_cfg[item] = cfg.MODEL[item]
@property
def num_priors(self):
"""allow prior num calculation before knowing feature map size"""
assert self._prior_cfg is not {}
return [int(len(self._create_prior(0, 0, k)) / 4) for k in range(len(self._steps))]
def _create_prior(self, cx, cy, k):
raise NotImplementedError
@vis
def _image_proc(self, image=None, tb_writer=None):
# TODO test with image
if isinstance(image, type(None)):
image = np.ones((self.image_size[1], self.image_size[0], 3))
elif isinstance(image, str):
image = cv2.imread(image, -1)
image = cv2.resize(image, (self.image_size[1], self.image_size[0]))
return image
@vis
def _prior_vis(self, anchor, image_ori, feat_idx, tb_writer=None):
# TODO add output path to the signature
writer = tb_writer.writer
prior_num = self.num_priors[feat_idx]
# transform coordinates
scale = [self.image_size[1], self.image_size[0], self.image_size[1], self.image_size[0]]
bboxs = | np.array(anchor) | numpy.array |
from abc import ABCMeta, abstractmethod
import os
from vmaf.tools.misc import make_absolute_path, run_process
from vmaf.tools.stats import ListStats
__copyright__ = "Copyright 2016-2018, Netflix, Inc."
__license__ = "Apache, Version 2.0"
import re
import numpy as np
import ast
from vmaf import ExternalProgramCaller, to_list
from vmaf.config import VmafConfig, VmafExternalConfig
from vmaf.core.executor import Executor
from vmaf.core.result import Result
from vmaf.tools.reader import YuvReader
class FeatureExtractor(Executor):
"""
FeatureExtractor takes in a list of assets, and run feature extraction on
them, and return a list of corresponding results. A FeatureExtractor must
specify a unique type and version combination (by the TYPE and VERSION
attribute), so that the Result generated by it can be identified.
A derived class of FeatureExtractor must:
1) Override TYPE and VERSION
2) Override _generate_result(self, asset), which call a
command-line executable and generate feature scores in a log file.
3) Override _get_feature_scores(self, asset), which read the feature
scores from the log file, and return the scores in a dictionary format.
For an example, follow VmafFeatureExtractor.
"""
__metaclass__ = ABCMeta
@property
@abstractmethod
def ATOM_FEATURES(self):
raise NotImplementedError
def _read_result(self, asset):
result = {}
result.update(self._get_feature_scores(asset))
executor_id = self.executor_id
return Result(asset, executor_id, result)
@classmethod
def get_scores_key(cls, atom_feature):
return "{type}_{atom_feature}_scores".format(
type=cls.TYPE, atom_feature=atom_feature)
@classmethod
def get_score_key(cls, atom_feature):
return "{type}_{atom_feature}_score".format(
type=cls.TYPE, atom_feature=atom_feature)
def _get_feature_scores(self, asset):
# routine to read the feature scores from the log file, and return
# the scores in a dictionary format.
log_file_path = self._get_log_file_path(asset)
atom_feature_scores_dict = {}
atom_feature_idx_dict = {}
for atom_feature in self.ATOM_FEATURES:
atom_feature_scores_dict[atom_feature] = []
atom_feature_idx_dict[atom_feature] = 0
with open(log_file_path, 'rt') as log_file:
for line in log_file.readlines():
for atom_feature in self.ATOM_FEATURES:
re_template = "{af}: ([0-9]+) ([a-zA-Z0-9.-]+)".format(af=atom_feature)
mo = re.match(re_template, line)
if mo:
cur_idx = int(mo.group(1))
assert cur_idx == atom_feature_idx_dict[atom_feature]
# parse value, allowing NaN and inf
val = float(mo.group(2))
if np.isnan(val) or np.isinf(val):
val = None
atom_feature_scores_dict[atom_feature].append(val)
atom_feature_idx_dict[atom_feature] += 1
continue
len_score = len(atom_feature_scores_dict[self.ATOM_FEATURES[0]])
assert len_score != 0
for atom_feature in self.ATOM_FEATURES[1:]:
assert len_score == len(atom_feature_scores_dict[atom_feature]), \
"Feature data possibly corrupt. Run cleanup script and try again."
feature_result = {}
for atom_feature in self.ATOM_FEATURES:
scores_key = self.get_scores_key(atom_feature)
feature_result[scores_key] = atom_feature_scores_dict[atom_feature]
return feature_result
class VmafFeatureExtractor(FeatureExtractor):
TYPE = "VMAF_feature"
# VERSION = '0.1' # vmaf_study; Anush's VIF fix
# VERSION = '0.2' # expose vif_num, vif_den, adm_num, adm_den, anpsnr
# VERSION = '0.2.1' # expose vif num/den of each scale
# VERSION = '0.2.2' # adm abs-->fabs, corrected border handling, uniform reading with option of offset for input YUV, updated VIF corner case
# VERSION = '0.2.2b' # expose adm_den/num_scalex
# VERSION = '0.2.3' # AVX for VMAF convolution; update adm features by folding noise floor into per coef
# VERSION = '0.2.4' # Fix a bug in adm feature passing scale into dwt_quant_step
# VERSION = '0.2.4b' # Modify by adding ADM noise floor outside cube root; add derived feature motion2
VERSION = '0.2.4c' # Modify by moving motion2 to c code
ATOM_FEATURES = ['vif', 'adm', 'ansnr', 'motion', 'motion2',
'vif_num', 'vif_den', 'adm_num', 'adm_den', 'anpsnr',
'vif_num_scale0', 'vif_den_scale0',
'vif_num_scale1', 'vif_den_scale1',
'vif_num_scale2', 'vif_den_scale2',
'vif_num_scale3', 'vif_den_scale3',
'adm_num_scale0', 'adm_den_scale0',
'adm_num_scale1', 'adm_den_scale1',
'adm_num_scale2', 'adm_den_scale2',
'adm_num_scale3', 'adm_den_scale3',
]
DERIVED_ATOM_FEATURES = ['vif_scale0', 'vif_scale1', 'vif_scale2', 'vif_scale3',
'vif2', 'adm2', 'adm3',
'adm_scale0', 'adm_scale1', 'adm_scale2', 'adm_scale3',
]
ADM2_CONSTANT = 0
ADM_SCALE_CONSTANT = 0
def _generate_result(self, asset):
# routine to call the command-line executable and generate feature
# scores in the log file.
quality_width, quality_height = asset.quality_width_height
log_file_path = self._get_log_file_path(asset)
yuv_type=self._get_workfile_yuv_type(asset)
ref_path=asset.ref_workfile_path
dis_path=asset.dis_workfile_path
w=quality_width
h=quality_height
logger = self.logger
ExternalProgramCaller.call_vmaf_feature(yuv_type, ref_path, dis_path, w, h, log_file_path, logger)
@classmethod
def _post_process_result(cls, result):
# override Executor._post_process_result
result = super(VmafFeatureExtractor, cls)._post_process_result(result)
# adm2 =
# (adm_num + ADM2_CONSTANT) / (adm_den + ADM2_CONSTANT)
adm2_scores_key = cls.get_scores_key('adm2')
adm_num_scores_key = cls.get_scores_key('adm_num')
adm_den_scores_key = cls.get_scores_key('adm_den')
result.result_dict[adm2_scores_key] = list(
(np.array(result.result_dict[adm_num_scores_key]) + cls.ADM2_CONSTANT) /
(np.array(result.result_dict[adm_den_scores_key]) + cls.ADM2_CONSTANT)
)
# vif_scalei = vif_num_scalei / vif_den_scalei, i = 0, 1, 2, 3
vif_num_scale0_scores_key = cls.get_scores_key('vif_num_scale0')
vif_den_scale0_scores_key = cls.get_scores_key('vif_den_scale0')
vif_num_scale1_scores_key = cls.get_scores_key('vif_num_scale1')
vif_den_scale1_scores_key = cls.get_scores_key('vif_den_scale1')
vif_num_scale2_scores_key = cls.get_scores_key('vif_num_scale2')
vif_den_scale2_scores_key = cls.get_scores_key('vif_den_scale2')
vif_num_scale3_scores_key = cls.get_scores_key('vif_num_scale3')
vif_den_scale3_scores_key = cls.get_scores_key('vif_den_scale3')
vif_scale0_scores_key = cls.get_scores_key('vif_scale0')
vif_scale1_scores_key = cls.get_scores_key('vif_scale1')
vif_scale2_scores_key = cls.get_scores_key('vif_scale2')
vif_scale3_scores_key = cls.get_scores_key('vif_scale3')
result.result_dict[vif_scale0_scores_key] = list(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key]))
)
result.result_dict[vif_scale1_scores_key] = list(
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key]))
)
result.result_dict[vif_scale2_scores_key] = list(
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key]))
)
result.result_dict[vif_scale3_scores_key] = list(
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
)
# vif2 =
# ((vif_num_scale0 / vif_den_scale0) + (vif_num_scale1 / vif_den_scale1) +
# (vif_num_scale2 / vif_den_scale2) + (vif_num_scale3 / vif_den_scale3)) / 4.0
vif_scores_key = cls.get_scores_key('vif2')
result.result_dict[vif_scores_key] = list(
(
(np.array(result.result_dict[vif_num_scale0_scores_key])
/ np.array(result.result_dict[vif_den_scale0_scores_key])) +
(np.array(result.result_dict[vif_num_scale1_scores_key])
/ np.array(result.result_dict[vif_den_scale1_scores_key])) +
(np.array(result.result_dict[vif_num_scale2_scores_key])
/ np.array(result.result_dict[vif_den_scale2_scores_key])) +
(np.array(result.result_dict[vif_num_scale3_scores_key])
/ np.array(result.result_dict[vif_den_scale3_scores_key]))
) / 4.0
)
# adm_scalei = adm_num_scalei / adm_den_scalei, i = 0, 1, 2, 3
adm_num_scale0_scores_key = cls.get_scores_key('adm_num_scale0')
adm_den_scale0_scores_key = cls.get_scores_key('adm_den_scale0')
adm_num_scale1_scores_key = cls.get_scores_key('adm_num_scale1')
adm_den_scale1_scores_key = cls.get_scores_key('adm_den_scale1')
adm_num_scale2_scores_key = cls.get_scores_key('adm_num_scale2')
adm_den_scale2_scores_key = cls.get_scores_key('adm_den_scale2')
adm_num_scale3_scores_key = cls.get_scores_key('adm_num_scale3')
adm_den_scale3_scores_key = cls.get_scores_key('adm_den_scale3')
adm_scale0_scores_key = cls.get_scores_key('adm_scale0')
adm_scale1_scores_key = cls.get_scores_key('adm_scale1')
adm_scale2_scores_key = cls.get_scores_key('adm_scale2')
adm_scale3_scores_key = cls.get_scores_key('adm_scale3')
result.result_dict[adm_scale0_scores_key] = list(
(np.array(result.result_dict[adm_num_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale0_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale1_scores_key] = list(
(np.array(result.result_dict[adm_num_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale1_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale2_scores_key] = list(
(np.array(result.result_dict[adm_num_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
/ (np.array(result.result_dict[adm_den_scale2_scores_key]) + cls.ADM_SCALE_CONSTANT)
)
result.result_dict[adm_scale3_scores_key] = list(
(np.array(result.result_dict[adm_num_scale3_scores_key]) + 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]) | 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]) | numpy.any |
"""Bindings for the Barnes Hut TSNE algorithm with fast nearest neighbors
Refs:
References
[1] <NAME>, L.J.P.; Hinton, G.E. Visualizing High-Dimensional Data
Using t-SNE. Journal of Machine Learning Research 9:2579-2605, 2008.
[2] <NAME>, L.J.P. t-Distributed Stochastic Neighbor Embedding
http://homepage.tudelft.nl/19j49/t-SNE.html
"""
import numpy as N
import ctypes
import os
import pkg_resources
def ord_string(s):
b = bytearray()
arr = b.extend(map(ord, s))
return N.array([x for x in b] + [0]).astype(N.uint8)
class TSNE(object):
def __init__(self,
n_components=2,
perplexity=50.0,
early_exaggeration=2.0,
learning_rate=200.0,
num_neighbors=1023,
force_magnify_iters=250,
pre_momentum=0.5,
post_momentum=0.8,
theta=0.5,
epssq=0.0025,
n_iter=1000,
n_iter_without_progress=1000,
min_grad_norm=1e-7,
perplexity_epsilon=1e-3,
metric='euclidean',
init='random',
return_style='once',
num_snapshots=5,
verbose=0,
random_seed=None,
use_interactive=False,
viz_timeout=10000,
viz_server="tcp://localhost:5556",
dump_points=False,
dump_file="dump.txt",
dump_interval=1,
print_interval=10,
device=0,
):
"""Initialization method for barnes hut T-SNE class.
"""
# Initialize the variables
self.n_components = int(n_components)
if self.n_components != 2:
raise ValueError('The current barnes-hut implementation does not support projection into dimensions other than 2 for now.')
self.perplexity = float(perplexity)
self.early_exaggeration = float(early_exaggeration)
self.learning_rate = float(learning_rate)
self.n_iter = int(n_iter)
self.n_iter_without_progress = int(n_iter_without_progress)
self.min_grad_norm = float(min_grad_norm)
if metric not in ['euclidean']:
raise ValueError('Non-Euclidean metrics are not currently supported. Please use metric=\'euclidean\' for now.')
else:
self.metric = metric
if init not in ['random']:
raise ValueError('Non-Random initialization is not currently supported. Please use init=\'random\' for now.')
else:
self.init = init
self.verbose = int(verbose)
# Initialize non-sklearn variables
self.num_neighbors = int(num_neighbors)
self.force_magnify_iters = int(force_magnify_iters)
self.perplexity_epsilon = float(perplexity_epsilon)
self.pre_momentum = float(pre_momentum)
self.post_momentum = float(post_momentum)
self.theta = float(theta)
self.epssq =float(epssq)
self.device = int(device)
self.print_interval = int(print_interval)
# Point dumpoing
self.dump_file = str(dump_file)
self.dump_points = bool(dump_points)
self.dump_interval = int(dump_interval)
# Viz
self.use_interactive = bool(use_interactive)
self.viz_server = str(viz_server)
self.viz_timeout = int(viz_timeout)
# Return style
if return_style not in ['once','snapshots']:
raise ValueError('Invalid return style...')
elif return_style == 'once':
self.return_style = 0
elif return_style == 'snapshots':
self.return_style = 1
self.num_snapshots = int(num_snapshots)
# Build the hooks for the BH T-SNE library
self._path = pkg_resources.resource_filename('tsnecuda','') # Load from current location
# self._faiss_lib = N.ctypeslib.load_library('libfaiss', self._path) # Load the ctypes library
# self._gpufaiss_lib = N.ctypeslib.load_library('libgpufaiss', self._path) # Load the ctypes library
self._lib = N.ctypeslib.load_library('libtsnecuda', self._path) # Load the ctypes library
# Hook the BH T-SNE function
self._lib.pymodule_bh_tsne.restype = None
self._lib.pymodule_bh_tsne.argtypes = [
N.ctypeslib.ndpointer(N.float32, ndim=2, flags='ALIGNED, F_CONTIGUOUS, WRITEABLE'), # result
N.ctypeslib.ndpointer(N.float32, ndim=2, flags='ALIGNED, CONTIGUOUS'), # points
ctypes.POINTER(N.ctypeslib.c_intp), # dims
ctypes.c_float, # Perplexity
ctypes.c_float, # Learning Rate
ctypes.c_float, # Magnitude Factor
ctypes.c_int, # Num Neighbors
ctypes.c_int, # Iterations
ctypes.c_int, # Iterations no progress
ctypes.c_int, # Force Magnify iterations
ctypes.c_float, # Perplexity search epsilon
ctypes.c_float, # pre-exaggeration momentum
ctypes.c_float, # post-exaggeration momentum
ctypes.c_float, # Theta
ctypes.c_float, # epssq
ctypes.c_float, # Minimum gradient norm
ctypes.c_int, # Initialization types
N.ctypeslib.ndpointer(N.float32, ndim=2, flags='ALIGNED, F_CONTIGUOUS'), # Initialization Data
ctypes.c_bool, # Dump points
N.ctypeslib.ndpointer(N.uint8, flags='ALIGNED, CONTIGUOUS'), # Dump File
ctypes.c_int, # Dump interval
ctypes.c_bool, # Use interactive
N.ctypeslib.ndpointer(N.uint8, flags='ALIGNED, CONTIGUOUS'), # Viz Server
ctypes.c_int, # Viz timeout
ctypes.c_int, # Verbosity
ctypes.c_int, # Print interval
ctypes.c_int, # GPU Device
ctypes.c_int, # Return style
ctypes.c_int ] # Number of snapshots
def fit_transform(self, X, y=None):
"""Fit X into an embedded space and return that transformed output.
Arguments:
X {array} -- Input array, shape: (n_points, n_dimensions)
Keyword Arguments:
y {None} -- Ignored (default: {None})
"""
# Setup points/embedding requirements
self.points = N.require(X, N.float32, ['CONTIGUOUS', 'ALIGNED'])
self.embedding = | N.zeros(shape=(X.shape[0],self.n_components)) | numpy.zeros |
"""
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) | numpy.compat.isfileobj |
'''
<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]) | numpy.linalg.norm |
"""
This code is used to scrape ScienceDirect of publication urls and write them to
a text file in the current directory for later use.
"""
import selenium
from selenium import webdriver
import numpy as np
import pandas as pd
import bs4
from bs4 import BeautifulSoup
import time
from sklearn.utils import shuffle
def scrape_page(driver):
"""
This method finds all the publication result web elements on the webpage.
Parameters
----------
driver (Selenium webdriver object) : Instance of the webdriver class e.g.
webdriver.Chrome()
Returns
-------
elems (list) : A list of all scraped hrefs from the page
"""
elems = driver.find_elements_by_class_name('ResultItem')
return elems
def clean(elems):
"""
This method takes a list of scraped selenium web elements
and filters/ returns only the hrefs leading to publications.
Filtering includes removing all urls with keywords that are indicative of
non-html links.
Parameters
----------
elems (list) : The list of hrefs to be filtered
Returns
-------
urls (list) : The new list of hrefs, which should be the same as the list
displayed on gui ScienceDirect
"""
titles = []
urls = []
for elem in elems:
href_child = elem.find_element_by_css_selector('a[href]')
url = href_child.get_attribute('href')
title = href_child.text
titles.append(title)
urls.append(url)
return urls, titles
def build_url_list(gui_prefix,search_terms,journal_list):
"""
This method takes the list of journals and creates a tiple nested dictionary
containing all accessible urls to each page, in each year, for each journal,
for a given search on sciencedirect.
"""
dict1 = {}
years = np.arange(1995,2020)
for journal in journal_list:
dict2 = {}
for year in years:
dict3 = {}
for i in range(60):
url = gui_prefix + search_terms + '&show=100'+ '&articleTypes=FLA%2CREV' + '&years='+ str(year)
if i != 0:
url = url + '&offset=' + str(i) +'00'
url = url + '&pub=' + journal
dict3[i] = url
dict2[year] = dict3
dict1[journal] = dict2
return dict1
def proxify(scraped_urls,uw_prefix):
"""
This method takes a list of scraped urls and turns them into urls that
go through the UW Library proxy so that all of them are full access.
Parameters
----------
scraped_urls (list) : The list of URLs to be converted
uw_prefix (str) : The string that all URLs which go through the UW Library
Proxy start with.
Returns
-------
proxy_urls (list) : The list of converted URLs which go through UW Library
proxy
"""
proxy_urls = []
for url in scraped_urls:
sd_id = url[-17:]
newlink = uw_prefix + sd_id
if sd_id.startswith('S'):
proxy_urls.append(newlink)
return proxy_urls
def write_urls(urls,titles,file,journal,year):
"""
This method takes a list of urls and writes them to a desired text file.
Parameters
----------
urls (list) : The list of URLs to be saved.
file (file object) : The opened .txt file which will be written to.
year (str or int) : The year associated with the publication date.
Returns
-------
Does not return anything
"""
for link,title in zip(urls,titles):
line = link + ',' + title + ',' + journal + ',' + str(year)
file.write(line)
file.write('\n')
def find_pubTitle(driver,journal):
"""
This method finds the identifying number for a specific journal. This
identifying number is added to the gui query URL to ensure only publciations
from the desired journal are being found.
"""
pub_elems = driver.find_elements_by_css_selector('input[id*=publicationTitles]')
pub_names = []
for elem in pub_elems:
pub_name = elem.get_attribute("name")
if pub_name == journal:
return elem.get_attribute('id')[-6:] #returns the identifying number
#for that journal
df = pd.read_excel('elsevier_journals.xls')
df.Full_Category = df.Full_Category.str.lower() # lowercase topics for searching
df = df.drop_duplicates(subset = 'Journal_Title') # drop any duplicate journals
df = shuffle(df,random_state = 42)
# The set of default strings that will be used to sort which journals we want
journal_strings = ['chemistry','energy','molecular','atomic','chemical','biochem'
,'organic','polymer','chemical engineering','biotech','coloid']
name = df.Full_Category.str.contains # making this an easier command to type
# new dataframe full of only journals who's topic description contained the
# desired keywords
df2 = df[name('polymer') | name('chemistry') | name('energy')
| name('molecular') | name('colloid') | name('biochem')
| name('organic') | name('biotech') | name('chemical')]
journal_list = df2.Journal_Title # Series of only the journals to be searched
gui_prefix = 'https://www.sciencedirect.com/search/advanced?qs='
search_terms = 'chemistry%20OR%20molecule%20OR%20polymer%20OR%20organic'
url_dict = build_url_list(gui_prefix,search_terms,journal_list)
driver = webdriver.Chrome()
uw_prefix = 'https://www-sciencedirect-com.offcampus.lib.washington.edu/science/article/pii/'
filename = input("Input filename with .txt extension for URL storage: ")
url_counter = 0
master_list = []
file = open(filename,'a+')
for journal in journal_list:
for year in | np.arange(1995,2020) | numpy.arange |
"""Test the search module"""
from collections.abc import Iterable, Sized
from io import StringIO
from itertools import chain, product
from functools import partial
import pickle
import sys
from types import GeneratorType
import re
import numpy as np
import scipy.sparse as sp
import pytest
from sklearn.utils.fixes import sp_version
from sklearn.utils._testing import assert_raises
from sklearn.utils._testing import assert_warns
from sklearn.utils._testing import assert_warns_message
from sklearn.utils._testing import assert_raise_message
from sklearn.utils._testing import assert_array_equal
from sklearn.utils._testing import assert_array_almost_equal
from sklearn.utils._testing import assert_allclose
from sklearn.utils._testing import assert_almost_equal
from sklearn.utils._testing import ignore_warnings
from sklearn.utils._mocking import CheckingClassifier, MockDataFrame
from scipy.stats import bernoulli, expon, uniform
from sklearn.base import BaseEstimator, ClassifierMixin
from sklearn.base import clone
from sklearn.exceptions import NotFittedError
from sklearn.datasets import make_classification
from sklearn.datasets import make_blobs
from sklearn.datasets import make_multilabel_classification
from sklearn.model_selection import fit_grid_point
from sklearn.model_selection import train_test_split
from sklearn.model_selection import KFold
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import StratifiedShuffleSplit
from sklearn.model_selection import LeaveOneGroupOut
from sklearn.model_selection import LeavePGroupsOut
from sklearn.model_selection import GroupKFold
from sklearn.model_selection import GroupShuffleSplit
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import RandomizedSearchCV
from sklearn.model_selection import ParameterGrid
from sklearn.model_selection import ParameterSampler
from sklearn.model_selection._search import BaseSearchCV
from sklearn.model_selection._validation import FitFailedWarning
from sklearn.svm import LinearSVC, SVC
from sklearn.tree import DecisionTreeRegressor
from sklearn.tree import DecisionTreeClassifier
from sklearn.cluster import KMeans
from sklearn.neighbors import KernelDensity
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import f1_score
from sklearn.metrics import recall_score
from sklearn.metrics import accuracy_score
from sklearn.metrics import make_scorer
from sklearn.metrics import roc_auc_score
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.impute import SimpleImputer
from sklearn.pipeline import Pipeline
from sklearn.linear_model import Ridge, SGDClassifier, LinearRegression
from sklearn.experimental import enable_hist_gradient_boosting # noqa
from sklearn.ensemble import HistGradientBoostingClassifier
from sklearn.model_selection.tests.common import OneTimeSplitter
# Neither of the following two estimators inherit from BaseEstimator,
# to test hyperparameter search on user-defined classifiers.
class MockClassifier:
"""Dummy classifier to test the parameter search algorithms"""
def __init__(self, foo_param=0):
self.foo_param = foo_param
def fit(self, X, Y):
assert len(X) == len(Y)
self.classes_ = np.unique(Y)
return self
def predict(self, T):
return T.shape[0]
def transform(self, X):
return X + self.foo_param
def inverse_transform(self, X):
return X - self.foo_param
predict_proba = predict
predict_log_proba = predict
decision_function = predict
def score(self, X=None, Y=None):
if self.foo_param > 1:
score = 1.
else:
score = 0.
return score
def get_params(self, deep=False):
return {'foo_param': self.foo_param}
def set_params(self, **params):
self.foo_param = params['foo_param']
return self
class LinearSVCNoScore(LinearSVC):
"""An LinearSVC classifier that has no score method."""
@property
def score(self):
raise AttributeError
X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
y = np.array([1, 1, 2, 2])
def assert_grid_iter_equals_getitem(grid):
assert list(grid) == [grid[i] for i in range(len(grid))]
@pytest.mark.parametrize("klass", [ParameterGrid,
partial(ParameterSampler, n_iter=10)])
@pytest.mark.parametrize(
"input, error_type, error_message",
[(0, TypeError, r'Parameter .* is not a dict or a list \(0\)'),
([{'foo': [0]}, 0], TypeError, r'Parameter .* is not a dict \(0\)'),
({'foo': 0}, TypeError, "Parameter.* value is not iterable .*"
r"\(key='foo', value=0\)")]
)
def test_validate_parameter_input(klass, input, error_type, error_message):
with pytest.raises(error_type, match=error_message):
klass(input)
def test_parameter_grid():
# Test basic properties of ParameterGrid.
params1 = {"foo": [1, 2, 3]}
grid1 = ParameterGrid(params1)
assert isinstance(grid1, Iterable)
assert isinstance(grid1, Sized)
assert len(grid1) == 3
assert_grid_iter_equals_getitem(grid1)
params2 = {"foo": [4, 2],
"bar": ["ham", "spam", "eggs"]}
grid2 = ParameterGrid(params2)
assert len(grid2) == 6
# loop to assert we can iterate over the grid multiple times
for i in range(2):
# tuple + chain transforms {"a": 1, "b": 2} to ("a", 1, "b", 2)
points = set(tuple(chain(*(sorted(p.items())))) for p in grid2)
assert (points ==
set(("bar", x, "foo", y)
for x, y in product(params2["bar"], params2["foo"])))
assert_grid_iter_equals_getitem(grid2)
# Special case: empty grid (useful to get default estimator settings)
empty = ParameterGrid({})
assert len(empty) == 1
assert list(empty) == [{}]
assert_grid_iter_equals_getitem(empty)
assert_raises(IndexError, lambda: empty[1])
has_empty = ParameterGrid([{'C': [1, 10]}, {}, {'C': [.5]}])
assert len(has_empty) == 4
assert list(has_empty) == [{'C': 1}, {'C': 10}, {}, {'C': .5}]
assert_grid_iter_equals_getitem(has_empty)
def test_grid_search():
# Test that the best estimator contains the right value for foo_param
clf = MockClassifier()
grid_search = GridSearchCV(clf, {'foo_param': [1, 2, 3]}, cv=3, verbose=3)
# make sure it selects the smallest parameter in case of ties
old_stdout = sys.stdout
sys.stdout = StringIO()
grid_search.fit(X, y)
sys.stdout = old_stdout
assert grid_search.best_estimator_.foo_param == 2
assert_array_equal(grid_search.cv_results_["param_foo_param"].data,
[1, 2, 3])
# Smoke test the score etc:
grid_search.score(X, y)
grid_search.predict_proba(X)
grid_search.decision_function(X)
grid_search.transform(X)
# Test exception handling on scoring
grid_search.scoring = 'sklearn'
assert_raises(ValueError, grid_search.fit, X, y)
def test_grid_search_pipeline_steps():
# check that parameters that are estimators are cloned before fitting
pipe = Pipeline([('regressor', LinearRegression())])
param_grid = {'regressor': [LinearRegression(), Ridge()]}
grid_search = GridSearchCV(pipe, param_grid, cv=2)
grid_search.fit(X, y)
regressor_results = grid_search.cv_results_['param_regressor']
assert isinstance(regressor_results[0], LinearRegression)
assert isinstance(regressor_results[1], Ridge)
assert not hasattr(regressor_results[0], 'coef_')
assert not hasattr(regressor_results[1], 'coef_')
assert regressor_results[0] is not grid_search.best_estimator_
assert regressor_results[1] is not grid_search.best_estimator_
# check that we didn't modify the parameter grid that was passed
assert not hasattr(param_grid['regressor'][0], 'coef_')
assert not hasattr(param_grid['regressor'][1], 'coef_')
@pytest.mark.parametrize("SearchCV", [GridSearchCV, RandomizedSearchCV])
def test_SearchCV_with_fit_params(SearchCV):
X = np.arange(100).reshape(10, 10)
y = np.array([0] * 5 + [1] * 5)
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) | numpy.arange |
# pylint: disable=protected-access
"""
Test the wrappers for the C API.
"""
import os
from contextlib import contextmanager
import numpy as np
import numpy.testing as npt
import pandas as pd
import pytest
import xarray as xr
from packaging.version import Version
from pygmt import Figure, clib
from pygmt.clib.conversion import dataarray_to_matrix
from pygmt.clib.session import FAMILIES, VIAS
from pygmt.exceptions import (
GMTCLibError,
GMTCLibNoSessionError,
GMTInvalidInput,
GMTVersionError,
)
from pygmt.helpers import GMTTempFile
TEST_DATA_DIR = os.path.join(os.path.dirname(__file__), "data")
with clib.Session() as _lib:
gmt_version = Version(_lib.info["version"])
@contextmanager
def mock(session, func, returns=None, mock_func=None):
"""
Mock a GMT C API function to make it always return a given value.
Used to test that exceptions are raised when API functions fail by
producing a NULL pointer as output or non-zero status codes.
Needed because it's not easy to get some API functions to fail without
inducing a Segmentation Fault (which is a good thing because libgmt usually
only fails with errors).
"""
if mock_func is None:
def mock_api_function(*args): # pylint: disable=unused-argument
"""
A mock GMT API function that always returns a given value.
"""
return returns
mock_func = mock_api_function
get_libgmt_func = session.get_libgmt_func
def mock_get_libgmt_func(name, argtypes=None, restype=None):
"""
Return our mock function.
"""
if name == func:
return mock_func
return get_libgmt_func(name, argtypes, restype)
setattr(session, "get_libgmt_func", mock_get_libgmt_func)
yield
setattr(session, "get_libgmt_func", get_libgmt_func)
def test_getitem():
"""
Test that I can get correct constants from the C lib.
"""
ses = clib.Session()
assert ses["GMT_SESSION_EXTERNAL"] != -99999
assert ses["GMT_MODULE_CMD"] != -99999
assert ses["GMT_PAD_DEFAULT"] != -99999
assert ses["GMT_DOUBLE"] != -99999
with pytest.raises(GMTCLibError):
ses["A_WHOLE_LOT_OF_JUNK"] # pylint: disable=pointless-statement
def test_create_destroy_session():
"""
Test that create and destroy session are called without errors.
"""
# Create two session and make sure they are not pointing to the same memory
session1 = clib.Session()
session1.create(name="test_session1")
assert session1.session_pointer is not None
session2 = clib.Session()
session2.create(name="test_session2")
assert session2.session_pointer is not None
assert session2.session_pointer != session1.session_pointer
session1.destroy()
session2.destroy()
# Create and destroy a session twice
ses = clib.Session()
for __ in range(2):
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
ses.create("session1")
assert ses.session_pointer is not None
ses.destroy()
with pytest.raises(GMTCLibNoSessionError):
ses.session_pointer # pylint: disable=pointless-statement
def test_create_session_fails():
"""
Check that an exception is raised when failing to create a session.
"""
ses = clib.Session()
with mock(ses, "GMT_Create_Session", returns=None):
with pytest.raises(GMTCLibError):
ses.create("test-session-name")
# Should fail if trying to create a session before destroying the old one.
ses.create("test1")
with pytest.raises(GMTCLibError):
ses.create("test2")
def test_destroy_session_fails():
"""
Fail to destroy session when given bad input.
"""
ses = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
ses.destroy()
ses.create("test-session")
with mock(ses, "GMT_Destroy_Session", returns=1):
with pytest.raises(GMTCLibError):
ses.destroy()
ses.destroy()
def test_call_module():
"""
Run a command to see if call_module works.
"""
data_fname = os.path.join(TEST_DATA_DIR, "points.txt")
out_fname = "test_call_module.txt"
with clib.Session() as lib:
with GMTTempFile() as out_fname:
lib.call_module("info", "{} -C ->{}".format(data_fname, out_fname.name))
assert os.path.exists(out_fname.name)
output = out_fname.read().strip()
assert output == "11.5309 61.7074 -2.9289 7.8648 0.1412 0.9338"
def test_call_module_invalid_arguments():
"""
Fails for invalid module arguments.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("info", "bogus-data.bla")
def test_call_module_invalid_name():
"""
Fails when given bad input.
"""
with clib.Session() as lib:
with pytest.raises(GMTCLibError):
lib.call_module("meh", "")
def test_call_module_error_message():
"""
Check is the GMT error message was captured.
"""
with clib.Session() as lib:
try:
lib.call_module("info", "bogus-data.bla")
except GMTCLibError as error:
assert "Module 'info' failed with status code" in str(error)
assert "gmtinfo [ERROR]: Cannot find file bogus-data.bla" in str(error)
def test_method_no_session():
"""
Fails when not in a session.
"""
# Create an instance of Session without "with" so no session is created.
lib = clib.Session()
with pytest.raises(GMTCLibNoSessionError):
lib.call_module("gmtdefaults", "")
with pytest.raises(GMTCLibNoSessionError):
lib.session_pointer # pylint: disable=pointless-statement
def test_parse_constant_single():
"""
Parsing a single family argument correctly.
"""
lib = clib.Session()
for family in FAMILIES:
parsed = lib._parse_constant(family, valid=FAMILIES)
assert parsed == lib[family]
def test_parse_constant_composite():
"""
Parsing a composite constant argument (separated by |) correctly.
"""
lib = clib.Session()
test_cases = ((family, via) for family in FAMILIES for via in VIAS)
for family, via in test_cases:
composite = "|".join([family, via])
expected = lib[family] + lib[via]
parsed = lib._parse_constant(composite, valid=FAMILIES, valid_modifiers=VIAS)
assert parsed == expected
def test_parse_constant_fails():
"""
Check if the function fails when given bad input.
"""
lib = clib.Session()
test_cases = [
"SOME_random_STRING",
"GMT_IS_DATASET|GMT_VIA_MATRIX|GMT_VIA_VECTOR",
"GMT_IS_DATASET|NOT_A_PROPER_VIA",
"NOT_A_PROPER_FAMILY|GMT_VIA_MATRIX",
"NOT_A_PROPER_FAMILY|ALSO_INVALID",
]
for test_case in test_cases:
with pytest.raises(GMTInvalidInput):
lib._parse_constant(test_case, valid=FAMILIES, valid_modifiers=VIAS)
# Should also fail if not given valid modifiers but is using them anyway.
# This should work...
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=VIAS
)
# But this shouldn't.
with pytest.raises(GMTInvalidInput):
lib._parse_constant(
"GMT_IS_DATASET|GMT_VIA_MATRIX", valid=FAMILIES, valid_modifiers=None
)
def test_create_data_dataset():
"""
Run the function to make sure it doesn't fail badly.
"""
with clib.Session() as lib:
# Dataset from vectors
data_vector = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_VECTOR",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0], # columns, rows, layers, dtype
)
# Dataset from matrices
data_matrix = lib.create_data(
family="GMT_IS_DATASET|GMT_VIA_MATRIX",
geometry="GMT_IS_POINT",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
assert data_vector != data_matrix
def test_create_data_grid_dim():
"""
Create a grid ignoring range and inc.
"""
with clib.Session() as lib:
# Grids from matrices using dim
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[10, 20, 1, 0],
)
def test_create_data_grid_range():
"""
Create a grid specifying range and inc instead of dim.
"""
with clib.Session() as lib:
# Grids from matrices using range and int
lib.create_data(
family="GMT_IS_GRID|GMT_VIA_MATRIX",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
def test_create_data_fails():
"""
Check that create_data raises exceptions for invalid input and output.
"""
# Passing in invalid mode
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="Not_a_valid_mode",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# Passing in invalid geometry
with pytest.raises(GMTInvalidInput):
with clib.Session() as lib:
lib.create_data(
family="GMT_IS_GRID",
geometry="Not_a_valid_geometry",
mode="GMT_CONTAINER_ONLY",
dim=[0, 0, 1, 0],
ranges=[150.0, 250.0, -20.0, 20.0],
inc=[0.1, 0.2],
)
# If the data pointer returned is None (NULL pointer)
with pytest.raises(GMTCLibError):
with clib.Session() as lib:
with mock(lib, "GMT_Create_Data", returns=None):
lib.create_data(
family="GMT_IS_DATASET",
geometry="GMT_IS_SURFACE",
mode="GMT_CONTAINER_ONLY",
dim=[11, 10, 2, 0],
)
def test_virtual_file():
"""
Test passing in data via a virtual file with a Dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (5, 3)
for dtype in dtypes:
with clib.Session() as lib:
family = "GMT_IS_DATASET|GMT_VIA_MATRIX"
geometry = "GMT_IS_POINT"
dataset = lib.create_data(
family=family,
geometry=geometry,
mode="GMT_CONTAINER_ONLY",
dim=[shape[1], shape[0], 1, 0], # columns, rows, layers, dtype
)
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
lib.put_matrix(dataset, matrix=data)
# Add the dataset to a virtual file and pass it along to gmt info
vfargs = (family, geometry, "GMT_IN|GMT_IS_REFERENCE", dataset)
with lib.open_virtual_file(*vfargs) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds)
assert output == expected
def test_virtual_file_fails():
"""
Check that opening and closing virtual files raises an exception for non-
zero return codes.
"""
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IN|GMT_IS_REFERENCE",
None,
)
# Mock Open_VirtualFile to test the status check when entering the context.
# If the exception is raised, the code won't get to the closing of the
# virtual file.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=1):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
print("Should not get to this code")
# Test the status check when closing the virtual file
# Mock the opening to return 0 (success) so that we don't open a file that
# we won't close later.
with clib.Session() as lib, mock(lib, "GMT_Open_VirtualFile", returns=0), mock(
lib, "GMT_Close_VirtualFile", returns=1
):
with pytest.raises(GMTCLibError):
with lib.open_virtual_file(*vfargs):
pass
print("Shouldn't get to this code either")
def test_virtual_file_bad_direction():
"""
Test passing an invalid direction argument.
"""
with clib.Session() as lib:
vfargs = (
"GMT_IS_DATASET|GMT_VIA_MATRIX",
"GMT_IS_POINT",
"GMT_IS_GRID", # The invalid direction argument
0,
)
with pytest.raises(GMTInvalidInput):
with lib.open_virtual_file(*vfargs):
print("This should have failed")
def test_virtualfile_from_vectors():
"""
Test the automation for transforming vectors to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
size = 10
for dtype in dtypes:
x = np.arange(size, dtype=dtype)
y = np.arange(size, size * 2, 1, dtype=dtype)
z = np.arange(size * 2, size * 3, 1, dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(i.min(), i.max()) for i in (x, y, z)]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_one_string_or_object_column(dtype):
"""
Test passing in one column with string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings = np.array(["a", "bc", "defg", "hijklmn", "opqrst"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(f"{i}\t{j}\t{k}\n" for i, j, k in zip(x, y, strings))
assert output == expected
@pytest.mark.parametrize("dtype", [str, object])
def test_virtualfile_from_vectors_two_string_or_object_columns(dtype):
"""
Test passing in two columns of string or object dtype into virtual file
dataset.
"""
size = 5
x = np.arange(size, dtype=np.int32)
y = np.arange(size, size * 2, 1, dtype=np.int32)
strings1 = np.array(["a", "bc", "def", "ghij", "klmno"], dtype=dtype)
strings2 = np.array(["pqrst", "uvwx", "yz!", "@#", "$"], dtype=dtype)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, strings1, strings2) as vfile:
with GMTTempFile() as outfile:
lib.call_module("convert", f"{vfile} ->{outfile.name}")
output = outfile.read(keep_tabs=True)
expected = "".join(
f"{h}\t{i}\t{j} {k}\n" for h, i, j, k in zip(x, y, strings1, strings2)
)
assert output == expected
def test_virtualfile_from_vectors_transpose():
"""
Test transforming matrix columns to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (7, 5)
for dtype in dtypes:
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(*data.T) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} -C ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["{:.0f}\t{:.0f}".format(col.min(), col.max()) for col in data.T]
)
expected = "{}\n".format(bounds)
assert output == expected
def test_virtualfile_from_vectors_diff_size():
"""
Test the function fails for arrays of different sizes.
"""
x = np.arange(5)
y = np.arange(6)
with clib.Session() as lib:
with pytest.raises(GMTInvalidInput):
with lib.virtualfile_from_vectors(x, y):
print("This should have failed")
def test_virtualfile_from_matrix():
"""
Test transforming a matrix to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (7, 5)
for dtype in dtypes:
data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
with clib.Session() as lib:
with lib.virtualfile_from_matrix(data) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(shape[0], bounds)
assert output == expected
def test_virtualfile_from_matrix_slice():
"""
Test transforming a slice of a larger array to virtual file dataset.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
shape = (10, 6)
for dtype in dtypes:
full_data = np.arange(shape[0] * shape[1], dtype=dtype).reshape(shape)
rows = 5
cols = 3
data = full_data[:rows, :cols]
with clib.Session() as lib:
with lib.virtualfile_from_matrix(data) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(col.min(), col.max()) for col in data.T]
)
expected = "<matrix memory>: N = {}\t{}\n".format(rows, bounds)
assert output == expected
def test_virtualfile_from_vectors_pandas():
"""
Pass vectors to a dataset using pandas Series.
"""
dtypes = "float32 float64 int32 int64 uint32 uint64".split()
size = 13
for dtype in dtypes:
data = pd.DataFrame(
data=dict(
x=np.arange(size, dtype=dtype),
y=np.arange(size, size * 2, 1, dtype=dtype),
z=np.arange(size * 2, size * 3, 1, dtype=dtype),
)
)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(data.x, data.y, data.z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
[
"<{:.0f}/{:.0f}>".format(i.min(), i.max())
for i in (data.x, data.y, data.z)
]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
def test_virtualfile_from_vectors_arraylike():
"""
Pass array-like vectors to a dataset.
"""
size = 13
x = list(range(0, size, 1))
y = tuple(range(size, size * 2, 1))
z = range(size * 2, size * 3, 1)
with clib.Session() as lib:
with lib.virtualfile_from_vectors(x, y, z) as vfile:
with GMTTempFile() as outfile:
lib.call_module("info", "{} ->{}".format(vfile, outfile.name))
output = outfile.read(keep_tabs=True)
bounds = "\t".join(
["<{:.0f}/{:.0f}>".format(min(i), max(i)) for i in (x, y, z)]
)
expected = "<vector memory>: N = {}\t{}\n".format(size, bounds)
assert output == expected
def test_extract_region_fails():
"""
Check that extract region fails if nothing has been plotted.
"""
Figure()
with pytest.raises(GMTCLibError):
with clib.Session() as lib:
lib.extract_region()
def test_extract_region_two_figures():
"""
Extract region should handle multiple figures existing at the same time.
"""
# Make two figures before calling extract_region to make sure that it's
# getting from the current figure, not the last figure.
fig1 = Figure()
region1 = np.array([0, 10, -20, -10])
fig1.coast(region=region1, projection="M6i", frame=True, land="black")
fig2 = Figure()
fig2.basemap(region="US.HI+r5", projection="M6i", frame=True)
# Activate the first figure and extract the region from it
# Use in a different session to avoid any memory problems.
with clib.Session() as lib:
lib.call_module("figure", "{} -".format(fig1._name))
with clib.Session() as lib:
wesn1 = lib.extract_region()
npt.assert_allclose(wesn1, region1)
# Now try it with the second one
with clib.Session() as lib:
lib.call_module("figure", "{} -".format(fig2._name))
with clib.Session() as lib:
wesn2 = lib.extract_region()
npt.assert_allclose(wesn2, np.array([-165.0, -150.0, 15.0, 25.0]))
def test_write_data_fails():
"""
Check that write data raises an exception for non-zero return codes.
"""
# It's hard to make the C API function fail without causing a Segmentation
# Fault. Can't test this if by giving a bad file name because if
# output=='', GMT will just write to stdout and spaces are valid file
# names. Use a mock instead just to exercise this part of the code.
with clib.Session() as lib:
with mock(lib, "GMT_Write_Data", returns=1):
with pytest.raises(GMTCLibError):
lib.write_data(
"GMT_IS_VECTOR",
"GMT_IS_POINT",
"GMT_WRITE_SET",
[1] * 6,
"some-file-name",
None,
)
def test_dataarray_to_matrix_works():
"""
Check that dataarray_to_matrix returns correct output.
"""
data = np.diag(v=np.arange(3))
x = np.linspace(start=0, stop=4, num=3)
y = np.linspace(start=5, stop=9, num=3)
grid = xr.DataArray(data, coords=[("y", y), ("x", x)])
matrix, region, inc = dataarray_to_matrix(grid)
npt.assert_allclose(actual=matrix, desired=np.flipud(data))
npt.assert_allclose(actual=region, desired=[x.min(), x.max(), y.min(), y.max()])
npt.assert_allclose(actual=inc, desired=[x[1] - x[0], y[1] - y[0]])
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) | numpy.arange |