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"""
Test used to verify PyWavelets Discrete Wavelet Transform computation
accuracy against MathWorks Wavelet Toolbox.
"""
from __future__ import division, print_function, absolute_import
import numpy as np
import pytest
from numpy.testing import assert_
import pywt
from pywt._pytest import (uses_pymatbridge, uses_precomputed, size_set)
from pywt._pytest import matlab_result_dict_dwt as matlab_result_dict
# list of mode names in pywt and matlab
modes = [('zero', 'zpd'),
('constant', 'sp0'),
('symmetric', 'sym'),
('reflect', 'symw'),
('periodic', 'ppd'),
('smooth', 'sp1'),
('periodization', 'per'),
# TODO: Now have implemented asymmetric modes too.
# Would be nice to update the Matlab data to test these as well.
('antisymmetric', 'asym'),
('antireflect', 'asymw'),
]
families = ('db', 'sym', 'coif', 'bior', 'rbio')
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(w.dec_len, 40)) + \
[100, 200, 500, 1000, 50000]
else:
data_sizes = (w.dec_len, w.dec_len + 1)
return data_sizes
@uses_pymatbridge
@pytest.mark.slow
def test_accuracy_pymatbridge():
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 = 5.0e-5
epsilon_pywt_coeffs = 1.0e-10
mlab.start()
try:
for wavelet in wavelets:
w = pywt.Wavelet(wavelet)
mlab.set_variable('wavelet', wavelet)
for N in _get_data_sizes(w):
data = rstate.randn(N)
mlab.set_variable('data', data)
for pmode, mmode in modes:
ma, md = _compute_matlab_result(data, wavelet, mmode, mlab)
_check_accuracy(data, w, pmode, ma, md, wavelet, epsilon)
ma, md = _load_matlab_result_pywt_coeffs(data, wavelet, mmode)
_check_accuracy(data, w, pmode, ma, md, wavelet, epsilon_pywt_coeffs)
finally:
mlab.stop()
@uses_precomputed
@pytest.mark.slow
def test_accuracy_precomputed():
# Keep this specific random seed to match the precomputed Matlab result.
rstate = np.random.RandomState(1234)
# max RMSE (was 1.0e-10, is reduced to 5.0e-5 due to different coefficients)
epsilon = 5.0e-5
epsilon_pywt_coeffs = 1.0e-10
for wavelet in wavelets:
w = pywt.Wavelet(wavelet)
for N in _get_data_sizes(w):
data = rstate.randn(N)
for pmode, mmode in modes:
ma, md = _load_matlab_result(data, wavelet, mmode)
_check_accuracy(data, w, pmode, ma, md, wavelet, epsilon)
ma, md = _load_matlab_result_pywt_coeffs(data, wavelet, mmode)
_check_accuracy(data, w, pmode, ma, md, wavelet, epsilon_pywt_coeffs)
def _compute_matlab_result(data, wavelet, mmode, mlab):
""" Compute the result using MATLAB.
This function assumes that the Matlab variables `wavelet` and `data` have
already been set externally.
"""
if np.any((wavelet == np.array(['coif6', 'coif7', 'coif8', 'coif9', 'coif10', 'coif11', 'coif12', 'coif13', 'coif14', 'coif15', 'coif16', 'coif17'])),axis=0):
w = pywt.Wavelet(wavelet)
mlab.set_variable('Lo_D', w.dec_lo)
mlab.set_variable('Hi_D', w.dec_hi)
mlab_code = ("[ma, md] = dwt(data, Lo_D, Hi_D, 'mode', '%s');" % mmode)
else:
mlab_code = "[ma, md] = dwt(data, wavelet, 'mode', '%s');" % mmode
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
ma = np.asarray(mlab.get_variable('ma'))
md = np.asarray(mlab.get_variable('md'))
return ma, md
def _load_matlab_result(data, wavelet, mmode):
""" Load the precomputed result.
"""
N = len(data)
ma_key = '_'.join([mmode, wavelet, str(N), 'ma'])
md_key = '_'.join([mmode, wavelet, str(N), 'md'])
if (ma_key not in matlab_result_dict) or \
(md_key not in matlab_result_dict):
raise KeyError(
"Precompted Matlab result not found for wavelet: "
"{0}, mode: {1}, size: {2}".format(wavelet, mmode, N))
ma = matlab_result_dict[ma_key]
md = matlab_result_dict[md_key]
return ma, md
def _load_matlab_result_pywt_coeffs(data, wavelet, mmode):
""" Load the precomputed result.
"""
N = len(data)
ma_key = '_'.join([mmode, wavelet, str(N), 'ma_pywtCoeffs'])
md_key = '_'.join([mmode, wavelet, str(N), 'md_pywtCoeffs'])
if (ma_key not in matlab_result_dict) or \
(md_key not in matlab_result_dict):
raise KeyError(
"Precompted Matlab result not found for wavelet: "
"{0}, mode: {1}, size: {2}".format(wavelet, mmode, N))
ma = matlab_result_dict[ma_key]
md = matlab_result_dict[md_key]
return ma, md
def _check_accuracy(data, w, pmode, ma, md, wavelet, epsilon):
# PyWavelets result
pa, pd = pywt.dwt(data, w, pmode)
# calculate error measures
rms_a = np.sqrt(np.mean((pa - ma) ** 2))
rms_d = np.sqrt(np.mean((pd - md) ** 2))
msg = ('[RMS_A > EPSILON] for Mode: %s, Wavelet: %s, '
'Length: %d, rms=%.3g' % (pmode, wavelet, len(data), rms_a))
assert_(rms_a < epsilon, msg=msg)
msg = ('[RMS_D > EPSILON] for Mode: %s, Wavelet: %s, '
'Length: %d, rms=%.3g' % (pmode, wavelet, len(data), rms_d))
assert_(rms_d < epsilon, msg=msg)
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