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