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"""
Test used to verify PyWavelets Continuous Wavelet Transform computation
accuracy against MathWorks Wavelet Toolbox.
"""
from __future__ import division, print_function, absolute_import
import warnings
import numpy as np
import pytest
from numpy.testing import assert_
import pywt
from pywt._pytest import (uses_pymatbridge, uses_precomputed, size_set,
matlab_result_dict_cwt)
families = ('gaus', 'mexh', 'morl', 'cgau', 'shan', 'fbsp', 'cmor')
wavelets = sum([pywt.wavelist(name) for name in families], [])
def _get_data_sizes(w):
""" Return the sizes to test for wavelet w. """
if size_set == 'full':
data_sizes = list(range(100, 101)) + \
[100, 200, 500, 1000, 50000]
else:
data_sizes = (1000, 1000 + 1)
return data_sizes
def _get_scales(w):
""" Return the scales to test for wavelet w. """
if size_set == 'full':
scales = (1, np.arange(1, 3), np.arange(1, 4), np.arange(1, 5))
else:
scales = (1, np.arange(1, 3))
return scales
@uses_pymatbridge # skip this case if precomputed results are used instead
@pytest.mark.slow
def test_accuracy_pymatbridge_cwt():
Matlab = pytest.importorskip("pymatbridge.Matlab")
mlab = Matlab()
rstate = np.random.RandomState(1234)
# max RMSE (was 1.0e-10, is reduced to 5.0e-5 due to different coefficients)
epsilon = 1e-15
epsilon_psi = 1e-15
mlab.start()
try:
for wavelet in wavelets:
with warnings.catch_warnings():
warnings.simplefilter('ignore', FutureWarning)
w = pywt.ContinuousWavelet(wavelet)
if np.any((wavelet == np.array(['shan', 'cmor'])),axis=0):
mlab.set_variable('wavelet', wavelet+str(w.bandwidth_frequency)+'-'+str(w.center_frequency))
elif wavelet == 'fbsp':
mlab.set_variable('wavelet', wavelet+str(w.fbsp_order)+'-'+str(w.bandwidth_frequency)+'-'+str(w.center_frequency))
else:
mlab.set_variable('wavelet', wavelet)
mlab_code = ("psi = wavefun(wavelet,10)")
res = mlab.run_code(mlab_code)
psi = np.asarray(mlab.get_variable('psi'))
_check_accuracy_psi(w, psi, wavelet, epsilon_psi)
for N in _get_data_sizes(w):
data = rstate.randn(N)
mlab.set_variable('data', data)
for scales in _get_scales(w):
coefs = _compute_matlab_result(data, wavelet, scales, mlab)
_check_accuracy(data, w, scales, coefs, wavelet, epsilon)
finally:
mlab.stop()
@uses_precomputed # skip this case if pymatbridge + Matlab are being used
@pytest.mark.slow
def test_accuracy_precomputed_cwt():
# Keep this specific random seed to match the precomputed Matlab result.
rstate = np.random.RandomState(1234)
# has to be improved
epsilon = 2e-15
epsilon32 = 1e-5
epsilon_psi = 1e-15
for wavelet in wavelets:
with warnings.catch_warnings():
warnings.simplefilter('ignore', FutureWarning)
w = pywt.ContinuousWavelet(wavelet)
w32 = pywt.ContinuousWavelet(wavelet,dtype=np.float32)
psi = _load_matlab_result_psi(wavelet)
_check_accuracy_psi(w, psi, wavelet, epsilon_psi)
for N in _get_data_sizes(w):
data = rstate.randn(N)
data32 = data.astype(np.float32)
scales_count = 0
for scales in _get_scales(w):
scales_count += 1
coefs = _load_matlab_result(data, wavelet, scales_count)
_check_accuracy(data, w, scales, coefs, wavelet, epsilon)
_check_accuracy(data32, w32, scales, coefs, wavelet, epsilon32)
def _compute_matlab_result(data, wavelet, scales, mlab):
""" Compute the result using MATLAB.
This function assumes that the Matlab variables `wavelet` and `data` have
already been set externally.
"""
mlab.set_variable('scales', scales)
mlab_code = ("coefs = cwt(data, scales, wavelet)")
res = mlab.run_code(mlab_code)
if not res['success']:
raise RuntimeError("Matlab failed to execute the provided code. "
"Check that the wavelet toolbox is installed.")
# need np.asarray because sometimes the output is a single float64
coefs = np.asarray(mlab.get_variable('coefs'))
return coefs
def _load_matlab_result(data, wavelet, scales):
""" Load the precomputed result.
"""
N = len(data)
coefs_key = '_'.join([str(scales), wavelet, str(N), 'coefs'])
if (coefs_key not in matlab_result_dict_cwt):
raise KeyError(
"Precompted Matlab result not found for wavelet: "
"{0}, mode: {1}, size: {2}".format(wavelet, scales, N))
coefs = matlab_result_dict_cwt[coefs_key]
return coefs
def _load_matlab_result_psi(wavelet):
""" Load the precomputed result.
"""
psi_key = '_'.join([wavelet, 'psi'])
if (psi_key not in matlab_result_dict_cwt):
raise KeyError(
"Precompted Matlab psi result not found for wavelet: "
"{0}}".format(wavelet))
psi = matlab_result_dict_cwt[psi_key]
return psi
def _check_accuracy(data, w, scales, coefs, wavelet, epsilon):
# PyWavelets result
coefs_pywt, freq = pywt.cwt(data, scales, w)
# coefs from Matlab are from R2012a which is missing the complex conjugate
# as shown in Eq. 2 of Torrence and Compo. We take the complex conjugate of
# the precomputed Matlab result to account for this.
coefs = np.conj(coefs)
# calculate error measures
err = coefs_pywt - coefs
rms = np.real(np.sqrt(np.mean(np.conj(err) * err)))
msg = ('[RMS > EPSILON] for Scale: %s, Wavelet: %s, '
'Length: %d, rms=%.3g' % (scales, wavelet, len(data), rms))
assert_(rms < epsilon, msg=msg)
def _check_accuracy_psi(w, psi, wavelet, epsilon):
# PyWavelets result
psi_pywt, x = w.wavefun(length=1024)
# calculate error measures
err = psi_pywt.flatten() - psi.flatten()
rms = np.real(np.sqrt(np.mean(np.conj(err) * err)))
msg = ('[RMS > EPSILON] for Wavelet: %s, '
'rms=%.3g' % (wavelet, rms))
assert_(rms < epsilon, msg=msg)
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