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#!/usr/bin/env python
from __future__ import division, print_function, absolute_import
import numpy as np
from itertools import combinations
from numpy.testing import assert_allclose, assert_, assert_raises, assert_equal
import pywt
# Check that float32, float64, complex64, complex128 are preserved.
# Other real types get converted to float64.
# complex256 gets converted to complex128
dtypes_in = [np.int8, np.float16, np.float32, np.float64, np.complex64,
np.complex128]
dtypes_out = [np.float64, np.float32, np.float32, np.float64, np.complex64,
np.complex128]
# test complex256 as well if it is available
try:
dtypes_in += [np.complex256, ]
dtypes_out += [np.complex128, ]
except AttributeError:
pass
def test_dwtn_input():
# Array-like must be accepted
pywt.dwtn([1, 2, 3, 4], 'haar')
# Others must not
data = dict()
assert_raises(TypeError, pywt.dwtn, data, 'haar')
# Must be at least 1D
assert_raises(ValueError, pywt.dwtn, 2, 'haar')
def test_3D_reconstruct():
data = np.array([
[[0, 4, 1, 5, 1, 4],
[0, 5, 26, 3, 2, 1],
[5, 8, 2, 33, 4, 9],
[2, 5, 19, 4, 19, 1]],
[[1, 5, 1, 2, 3, 4],
[7, 12, 6, 52, 7, 8],
[2, 12, 3, 52, 6, 8],
[5, 2, 6, 78, 12, 2]]])
wavelet = pywt.Wavelet('haar')
for mode in pywt.Modes.modes:
d = pywt.dwtn(data, wavelet, mode=mode)
assert_allclose(data, pywt.idwtn(d, wavelet, mode=mode),
rtol=1e-13, atol=1e-13)
def test_dwdtn_idwtn_allwavelets():
rstate = np.random.RandomState(1234)
r = rstate.randn(16, 16)
# test 2D case only for all wavelet types
wavelist = pywt.wavelist()
if 'dmey' in wavelist:
wavelist.remove('dmey')
for wavelet in wavelist:
if wavelet in ['cmor', 'shan', 'fbsp']:
# skip these CWT families to avoid warnings
continue
if isinstance(pywt.DiscreteContinuousWavelet(wavelet), pywt.Wavelet):
for mode in pywt.Modes.modes:
coeffs = pywt.dwtn(r, wavelet, mode=mode)
assert_allclose(pywt.idwtn(coeffs, wavelet, mode=mode),
r, rtol=1e-7, atol=1e-7)
def test_stride():
wavelet = pywt.Wavelet('haar')
for dtype in ('float32', 'float64'):
data = np.array([[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]],
dtype=dtype)
for mode in pywt.Modes.modes:
expected = pywt.dwtn(data, wavelet)
strided = np.ones((3, 12), dtype=data.dtype)
strided[::-1, ::2] = data
strided_dwtn = pywt.dwtn(strided[::-1, ::2], wavelet)
for key in expected.keys():
assert_allclose(strided_dwtn[key], expected[key])
def test_byte_offset():
wavelet = pywt.Wavelet('haar')
for dtype in ('float32', 'float64'):
data = np.array([[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]],
dtype=dtype)
for mode in pywt.Modes.modes:
expected = pywt.dwtn(data, wavelet)
padded = np.ones((3, 6), dtype=np.dtype({'data': (data.dtype, 0),
'pad': ('byte', data.dtype.itemsize)},
align=True))
padded[:] = data
padded_dwtn = pywt.dwtn(padded['data'], wavelet)
for key in expected.keys():
assert_allclose(padded_dwtn[key], expected[key])
def test_3D_reconstruct_complex():
# All dimensions even length so `take` does not need to be specified
data = np.array([
[[0, 4, 1, 5, 1, 4],
[0, 5, 26, 3, 2, 1],
[5, 8, 2, 33, 4, 9],
[2, 5, 19, 4, 19, 1]],
[[1, 5, 1, 2, 3, 4],
[7, 12, 6, 52, 7, 8],
[2, 12, 3, 52, 6, 8],
[5, 2, 6, 78, 12, 2]]])
data = data + 1j
wavelet = pywt.Wavelet('haar')
d = pywt.dwtn(data, wavelet)
# idwtn creates even-length shapes (2x dwtn size)
original_shape = tuple([slice(None, s) for s in data.shape])
assert_allclose(data, pywt.idwtn(d, wavelet)[original_shape],
rtol=1e-13, atol=1e-13)
def test_idwtn_idwt2():
data = np.array([
[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]])
wavelet = pywt.Wavelet('haar')
LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
for mode in pywt.Modes.modes:
assert_allclose(pywt.idwt2((LL, (HL, LH, HH)), wavelet, mode=mode),
pywt.idwtn(d, wavelet, mode=mode),
rtol=1e-14, atol=1e-14)
def test_idwtn_idwt2_complex():
data = np.array([
[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]])
data = data + 1j
wavelet = pywt.Wavelet('haar')
LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
for mode in pywt.Modes.modes:
assert_allclose(pywt.idwt2((LL, (HL, LH, HH)), wavelet, mode=mode),
pywt.idwtn(d, wavelet, mode=mode),
rtol=1e-14, atol=1e-14)
def test_idwtn_missing():
# Test to confirm missing data behave as zeroes
data = np.array([
[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]])
wavelet = pywt.Wavelet('haar')
coefs = pywt.dwtn(data, wavelet)
# No point removing zero, or all
for num_missing in range(1, len(coefs)):
for missing in combinations(coefs.keys(), num_missing):
missing_coefs = coefs.copy()
for key in missing:
del missing_coefs[key]
LL = missing_coefs.get('aa', None)
HL = missing_coefs.get('da', None)
LH = missing_coefs.get('ad', None)
HH = missing_coefs.get('dd', None)
assert_allclose(pywt.idwt2((LL, (HL, LH, HH)), wavelet),
pywt.idwtn(missing_coefs, 'haar'), atol=1e-15)
def test_idwtn_all_coeffs_None():
coefs = dict(aa=None, da=None, ad=None, dd=None)
assert_raises(ValueError, pywt.idwtn, coefs, 'haar')
def test_error_on_invalid_keys():
data = np.array([
[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]])
wavelet = pywt.Wavelet('haar')
LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
# unexpected key
d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH, 'ff': LH}
assert_raises(ValueError, pywt.idwtn, d, wavelet)
# mismatched key lengths
d = {'a': LL, 'da': HL, 'ad': LH, 'dd': HH}
assert_raises(ValueError, pywt.idwtn, d, wavelet)
def test_error_mismatched_size():
data = np.array([
[0, 4, 1, 5, 1, 4],
[0, 5, 6, 3, 2, 1],
[2, 5, 19, 4, 19, 1]])
wavelet = pywt.Wavelet('haar')
LL, (HL, LH, HH) = pywt.dwt2(data, wavelet)
# Pass/fail depends on first element being shorter than remaining ones so
# set 3/4 to an incorrect size to maximize chances. Order of dict items
# is random so may not trigger on every test run. Dict is constructed
# inside idwtn function so no use using an OrderedDict here.
LL = LL[:, :-1]
LH = LH[:, :-1]
HH = HH[:, :-1]
d = {'aa': LL, 'da': HL, 'ad': LH, 'dd': HH}
assert_raises(ValueError, pywt.idwtn, d, wavelet)
def test_dwt2_idwt2_dtypes():
wavelet = pywt.Wavelet('haar')
for dt_in, dt_out in zip(dtypes_in, dtypes_out):
x = np.ones((4, 4), dtype=dt_in)
errmsg = "wrong dtype returned for {0} input".format(dt_in)
cA, (cH, cV, cD) = pywt.dwt2(x, wavelet)
assert_(cA.dtype == cH.dtype == cV.dtype == cD.dtype,
"dwt2: " + errmsg)
x_roundtrip = pywt.idwt2((cA, (cH, cV, cD)), wavelet)
assert_(x_roundtrip.dtype == dt_out, "idwt2: " + errmsg)
def test_dwtn_axes():
data = np.array([[0, 1, 2, 3],
[1, 1, 1, 1],
[1, 4, 2, 8]])
data = data + 1j*data # test with complex data
coefs = pywt.dwtn(data, 'haar', axes=(1,))
expected_a = list(map(lambda x: pywt.dwt(x, 'haar')[0], data))
assert_equal(coefs['a'], expected_a)
expected_d = list(map(lambda x: pywt.dwt(x, 'haar')[1], data))
assert_equal(coefs['d'], expected_d)
coefs = pywt.dwtn(data, 'haar', axes=(1, 1))
expected_aa = list(map(lambda x: pywt.dwt(x, 'haar')[0], expected_a))
assert_equal(coefs['aa'], expected_aa)
expected_ad = list(map(lambda x: pywt.dwt(x, 'haar')[1], expected_a))
assert_equal(coefs['ad'], expected_ad)
def test_idwtn_axes():
data = np.array([[0, 1, 2, 3],
[1, 1, 1, 1],
[1, 4, 2, 8]])
data = data + 1j*data # test with complex data
coefs = pywt.dwtn(data, 'haar', axes=(1, 1))
assert_allclose(pywt.idwtn(coefs, 'haar', axes=(1, 1)), data, atol=1e-14)
def test_idwt2_none_coeffs():
data = np.array([[0, 1, 2, 3],
[1, 1, 1, 1],
[1, 4, 2, 8]])
data = data + 1j*data # test with complex data
cA, (cH, cV, cD) = pywt.dwt2(data, 'haar', axes=(1, 1))
# verify setting coefficients to None is the same as zeroing them
cD = np.zeros_like(cD)
result_zeros = pywt.idwt2((cA, (cH, cV, cD)), 'haar', axes=(1, 1))
cD = None
result_none = pywt.idwt2((cA, (cH, cV, cD)), 'haar', axes=(1, 1))
assert_equal(result_zeros, result_none)
def test_idwtn_none_coeffs():
data = np.array([[0, 1, 2, 3],
[1, 1, 1, 1],
[1, 4, 2, 8]])
data = data + 1j*data # test with complex data
coefs = pywt.dwtn(data, 'haar', axes=(1, 1))
# verify setting coefficients to None is the same as zeroing them
coefs['dd'] = np.zeros_like(coefs['dd'])
result_zeros = pywt.idwtn(coefs, 'haar', axes=(1, 1))
coefs['dd'] = None
result_none = pywt.idwtn(coefs, 'haar', axes=(1, 1))
assert_equal(result_zeros, result_none)
def test_idwt2_axes():
data = np.array([[0, 1, 2, 3],
[1, 1, 1, 1],
[1, 4, 2, 8]])
coefs = pywt.dwt2(data, 'haar', axes=(1, 1))
assert_allclose(pywt.idwt2(coefs, 'haar', axes=(1, 1)), data, atol=1e-14)
# too many axes
assert_raises(ValueError, pywt.idwt2, coefs, 'haar', axes=(0, 1, 1))
def test_idwt2_axes_subsets():
data = np.array(np.random.standard_normal((4, 4, 4)))
# test all combinations of 2 out of 3 axes transformed
for axes in combinations((0, 1, 2), 2):
coefs = pywt.dwt2(data, 'haar', axes=axes)
assert_allclose(pywt.idwt2(coefs, 'haar', axes=axes), data, atol=1e-14)
def test_idwtn_axes_subsets():
data = np.array(np.random.standard_normal((4, 4, 4, 4)))
# test all combinations of 3 out of 4 axes transformed
for axes in combinations((0, 1, 2, 3), 3):
coefs = pywt.dwtn(data, 'haar', axes=axes)
assert_allclose(pywt.idwtn(coefs, 'haar', axes=axes), data, atol=1e-14)
def test_negative_axes():
data = np.array([[0, 1, 2, 3],
[1, 1, 1, 1],
[1, 4, 2, 8]])
coefs1 = pywt.dwtn(data, 'haar', axes=(1, 1))
coefs2 = pywt.dwtn(data, 'haar', axes=(-1, -1))
assert_equal(coefs1, coefs2)
rec1 = pywt.idwtn(coefs1, 'haar', axes=(1, 1))
rec2 = pywt.idwtn(coefs1, 'haar', axes=(-1, -1))
assert_equal(rec1, rec2)
def test_dwtn_idwtn_dtypes():
wavelet = pywt.Wavelet('haar')
for dt_in, dt_out in zip(dtypes_in, dtypes_out):
x = np.ones((4, 4), dtype=dt_in)
errmsg = "wrong dtype returned for {0} input".format(dt_in)
coeffs = pywt.dwtn(x, wavelet)
for k, v in coeffs.items():
assert_(v.dtype == dt_out, "dwtn: " + errmsg)
x_roundtrip = pywt.idwtn(coeffs, wavelet)
assert_(x_roundtrip.dtype == dt_out, "idwtn: " + errmsg)
def test_idwtn_mixed_complex_dtype():
rstate = np.random.RandomState(0)
x = rstate.randn(8, 8, 8)
x = x + 1j*x
coeffs = pywt.dwtn(x, 'db2')
x_roundtrip = pywt.idwtn(coeffs, 'db2')
assert_allclose(x_roundtrip, x, rtol=1e-10)
# mismatched dtypes OK
coeffs['a' * x.ndim] = coeffs['a' * x.ndim].astype(np.complex64)
x_roundtrip2 = pywt.idwtn(coeffs, 'db2')
assert_allclose(x_roundtrip2, x, rtol=1e-7, atol=1e-7)
assert_(x_roundtrip2.dtype == np.complex128)
def test_idwt2_size_mismatch_error():
LL = np.zeros((6, 6))
LH = HL = HH = np.zeros((5, 5))
assert_raises(ValueError, pywt.idwt2, (LL, (LH, HL, HH)), wavelet='haar')
def test_dwt2_dimension_error():
data = np.ones(16)
wavelet = pywt.Wavelet('haar')
# wrong number of input dimensions
assert_raises(ValueError, pywt.dwt2, data, wavelet)
# too many axes
data2 = np.ones((8, 8))
assert_raises(ValueError, pywt.dwt2, data2, wavelet, axes=(0, 1, 1))
def test_per_axis_wavelets_and_modes():
# tests separate wavelet and edge mode for each axis.
rstate = np.random.RandomState(1234)
data = rstate.randn(16, 16, 16)
# wavelet can be a string or wavelet object
wavelets = (pywt.Wavelet('haar'), 'sym2', 'db4')
# mode can be a string or a Modes enum
modes = ('symmetric', 'periodization',
pywt._extensions._pywt.Modes.reflect)
coefs = pywt.dwtn(data, wavelets, modes)
assert_allclose(pywt.idwtn(coefs, wavelets, modes), data, atol=1e-14)
coefs = pywt.dwtn(data, wavelets[:1], modes)
assert_allclose(pywt.idwtn(coefs, wavelets[:1], modes), data, atol=1e-14)
coefs = pywt.dwtn(data, wavelets, modes[:1])
assert_allclose(pywt.idwtn(coefs, wavelets, modes[:1]), data, atol=1e-14)
# length of wavelets or modes doesn't match the length of axes
assert_raises(ValueError, pywt.dwtn, data, wavelets[:2])
assert_raises(ValueError, pywt.dwtn, data, wavelets, mode=modes[:2])
assert_raises(ValueError, pywt.idwtn, coefs, wavelets[:2])
assert_raises(ValueError, pywt.idwtn, coefs, wavelets, mode=modes[:2])
# dwt2/idwt2 also support per-axis wavelets/modes
data2 = data[..., 0]
coefs2 = pywt.dwt2(data2, wavelets[:2], modes[:2])
assert_allclose(pywt.idwt2(coefs2, wavelets[:2], modes[:2]), data2,
atol=1e-14)
def test_error_on_continuous_wavelet():
# A ValueError is raised if a Continuous wavelet is selected
data = np.ones((16, 16))
for dec_fun, rec_fun in zip([pywt.dwt2, pywt.dwtn],
[pywt.idwt2, pywt.idwtn]):
for cwave in ['morl', pywt.DiscreteContinuousWavelet('morl')]:
assert_raises(ValueError, dec_fun, data, wavelet=cwave)
c = dec_fun(data, 'db1')
assert_raises(ValueError, rec_fun, c, wavelet=cwave)
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