170 lines
6.4 KiB
Python
170 lines
6.4 KiB
Python
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from numpy.testing import assert_allclose, assert_raises, assert_, assert_equal
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import pywt
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float_dtypes = [np.float32, np.float64, np.complex64, np.complex128]
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real_dtypes = [np.float32, np.float64]
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def _sign(x):
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# Matlab-like sign function (numpy uses a different convention).
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return x / np.abs(x)
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def _soft(x, thresh):
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"""soft thresholding supporting complex values.
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Notes
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-----
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This version is not robust to zeros in x.
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"""
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return _sign(x) * np.maximum(np.abs(x) - thresh, 0)
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def test_threshold():
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data = np.linspace(1, 4, 7)
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# soft
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soft_result = [0., 0., 0., 0.5, 1., 1.5, 2.]
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assert_allclose(pywt.threshold(data, 2, 'soft'),
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np.array(soft_result), rtol=1e-12)
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assert_allclose(pywt.threshold(-data, 2, 'soft'),
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-np.array(soft_result), rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'soft'),
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[[0, 1]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'soft'),
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[[0, 0]] * 2, rtol=1e-12)
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# soft thresholding complex values
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assert_allclose(pywt.threshold([[1j, 2j]] * 2, 1, 'soft'),
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[[0j, 1j]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1+1j, 2+2j]] * 2, 6, 'soft'),
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[[0, 0]] * 2, rtol=1e-12)
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complex_data = [[1+2j, 2+2j]]*2
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for thresh in [1, 2]:
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assert_allclose(pywt.threshold(complex_data, thresh, 'soft'),
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_soft(complex_data, thresh), rtol=1e-12)
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# test soft thresholding with non-default substitute argument
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s = 5
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assert_allclose(pywt.threshold([[1j, 2]] * 2, 1.5, 'soft', substitute=s),
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[[s, 0.5]] * 2, rtol=1e-12)
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# soft: no divide by zero warnings when input contains zeros
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assert_allclose(pywt.threshold(np.zeros(16), 2, 'soft'),
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np.zeros(16), rtol=1e-12)
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# hard
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hard_result = [0., 0., 2., 2.5, 3., 3.5, 4.]
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assert_allclose(pywt.threshold(data, 2, 'hard'),
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np.array(hard_result), rtol=1e-12)
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assert_allclose(pywt.threshold(-data, 2, 'hard'),
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-np.array(hard_result), rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'hard'),
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[[1, 2]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'hard'),
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[[0, 2]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'hard', substitute=s),
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[[s, 2]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1+1j, 2+2j]] * 2, 2, 'hard'),
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[[0, 2+2j]] * 2, rtol=1e-12)
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# greater
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greater_result = [0., 0., 2., 2.5, 3., 3.5, 4.]
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assert_allclose(pywt.threshold(data, 2, 'greater'),
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np.array(greater_result), rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'greater'),
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[[1, 2]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'greater'),
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[[0, 2]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'greater', substitute=s),
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[[s, 2]] * 2, rtol=1e-12)
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# greater doesn't allow complex-valued inputs
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assert_raises(ValueError, pywt.threshold, [1j, 2j], 2, 'greater')
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# less
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assert_allclose(pywt.threshold(data, 2, 'less'),
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np.array([1., 1.5, 2., 0., 0., 0., 0.]), rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'less'),
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[[1, 0]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 1, 'less', substitute=s),
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[[1, s]] * 2, rtol=1e-12)
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assert_allclose(pywt.threshold([[1, 2]] * 2, 2, 'less'),
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[[1, 2]] * 2, rtol=1e-12)
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# less doesn't allow complex-valued inputs
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assert_raises(ValueError, pywt.threshold, [1j, 2j], 2, 'less')
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# invalid
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assert_raises(ValueError, pywt.threshold, data, 2, 'foo')
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def test_nonnegative_garotte():
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thresh = 0.3
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data_real = np.linspace(-1, 1, 100)
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for dtype in float_dtypes:
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if dtype in real_dtypes:
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data = np.asarray(data_real, dtype=dtype)
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else:
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data = np.asarray(data_real + 0.1j, dtype=dtype)
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d_hard = pywt.threshold(data, thresh, 'hard')
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d_soft = pywt.threshold(data, thresh, 'soft')
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d_garotte = pywt.threshold(data, thresh, 'garotte')
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# check dtypes
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assert_equal(d_hard.dtype, data.dtype)
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assert_equal(d_soft.dtype, data.dtype)
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assert_equal(d_garotte.dtype, data.dtype)
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# values < threshold are zero
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lt = np.where(np.abs(data) < thresh)
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assert_(np.all(d_garotte[lt] == 0))
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# values > than the threshold are intermediate between soft and hard
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gt = np.where(np.abs(data) > thresh)
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gt_abs_garotte = np.abs(d_garotte[gt])
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assert_(np.all(gt_abs_garotte < np.abs(d_hard[gt])))
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assert_(np.all(gt_abs_garotte > np.abs(d_soft[gt])))
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def test_threshold_firm():
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thresh = 0.2
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thresh2 = 3 * thresh
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data_real = np.linspace(-1, 1, 100)
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for dtype in float_dtypes:
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if dtype in real_dtypes:
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data = np.asarray(data_real, dtype=dtype)
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else:
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data = np.asarray(data_real + 0.1j, dtype=dtype)
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if data.real.dtype == np.float32:
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rtol = atol = 1e-6
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else:
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rtol = atol = 1e-14
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d_hard = pywt.threshold(data, thresh, 'hard')
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d_soft = pywt.threshold(data, thresh, 'soft')
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d_firm = pywt.threshold_firm(data, thresh, thresh2)
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# check dtypes
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assert_equal(d_hard.dtype, data.dtype)
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assert_equal(d_soft.dtype, data.dtype)
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assert_equal(d_firm.dtype, data.dtype)
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# values < threshold are zero
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lt = np.where(np.abs(data) < thresh)
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assert_(np.all(d_firm[lt] == 0))
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# values > than the threshold are equal to hard-thresholding
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gt = np.where(np.abs(data) >= thresh2)
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assert_allclose(np.abs(d_hard[gt]), np.abs(d_firm[gt]),
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rtol=rtol, atol=atol)
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# other values are intermediate between soft and hard thresholding
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mt = np.where(np.logical_and(np.abs(data) > thresh,
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np.abs(data) < thresh2))
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mt_abs_firm = np.abs(d_firm[mt])
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assert_(np.all(mt_abs_firm < np.abs(d_hard[mt])))
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assert_(np.all(mt_abs_firm > np.abs(d_soft[mt])))
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