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#!/usr/bin/env python
from __future__ import division, print_function, absolute_import
import numpy as np
from numpy.testing import (assert_allclose, assert_, assert_raises,
assert_array_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_dwt_idwt_basic():
x = [3, 7, 1, 1, -2, 5, 4, 6]
cA, cD = pywt.dwt(x, 'db2')
cA_expect = [5.65685425, 7.39923721, 0.22414387, 3.33677403, 7.77817459]
cD_expect = [-2.44948974, -1.60368225, -4.44140056, -0.41361256,
1.22474487]
assert_allclose(cA, cA_expect)
assert_allclose(cD, cD_expect)
x_roundtrip = pywt.idwt(cA, cD, 'db2')
assert_allclose(x_roundtrip, x, rtol=1e-10)
# mismatched dtypes OK
x_roundtrip2 = pywt.idwt(cA.astype(np.float64), cD.astype(np.float32),
'db2')
assert_allclose(x_roundtrip2, x, rtol=1e-7, atol=1e-7)
assert_(x_roundtrip2.dtype == np.float64)
def test_idwt_mixed_complex_dtype():
x = np.arange(8).astype(float)
x = x + 1j*x[::-1]
cA, cD = pywt.dwt(x, 'db2')
x_roundtrip = pywt.idwt(cA, cD, 'db2')
assert_allclose(x_roundtrip, x, rtol=1e-10)
# mismatched dtypes OK
x_roundtrip2 = pywt.idwt(cA.astype(np.complex128), cD.astype(np.complex64),
'db2')
assert_allclose(x_roundtrip2, x, rtol=1e-7, atol=1e-7)
assert_(x_roundtrip2.dtype == np.complex128)
def test_dwt_idwt_dtypes():
wavelet = pywt.Wavelet('haar')
for dt_in, dt_out in zip(dtypes_in, dtypes_out):
x = np.ones(4, dtype=dt_in)
errmsg = "wrong dtype returned for {0} input".format(dt_in)
cA, cD = pywt.dwt(x, wavelet)
assert_(cA.dtype == cD.dtype == dt_out, "dwt: " + errmsg)
x_roundtrip = pywt.idwt(cA, cD, wavelet)
assert_(x_roundtrip.dtype == dt_out, "idwt: " + errmsg)
def test_dwt_idwt_basic_complex():
x = np.asarray([3, 7, 1, 1, -2, 5, 4, 6])
x = x + 0.5j*x
cA, cD = pywt.dwt(x, 'db2')
cA_expect = np.asarray([5.65685425, 7.39923721, 0.22414387, 3.33677403,
7.77817459])
cA_expect = cA_expect + 0.5j*cA_expect
cD_expect = np.asarray([-2.44948974, -1.60368225, -4.44140056, -0.41361256,
1.22474487])
cD_expect = cD_expect + 0.5j*cD_expect
assert_allclose(cA, cA_expect)
assert_allclose(cD, cD_expect)
x_roundtrip = pywt.idwt(cA, cD, 'db2')
assert_allclose(x_roundtrip, x, rtol=1e-10)
def test_dwt_idwt_partial_complex():
x = np.asarray([3, 7, 1, 1, -2, 5, 4, 6])
x = x + 0.5j*x
cA, cD = pywt.dwt(x, 'haar')
cA_rec_expect = np.array([5.0+2.5j, 5.0+2.5j, 1.0+0.5j, 1.0+0.5j,
1.5+0.75j, 1.5+0.75j, 5.0+2.5j, 5.0+2.5j])
cA_rec = pywt.idwt(cA, None, 'haar')
assert_allclose(cA_rec, cA_rec_expect)
cD_rec_expect = np.array([-2.0-1.0j, 2.0+1.0j, 0.0+0.0j, 0.0+0.0j,
-3.5-1.75j, 3.5+1.75j, -1.0-0.5j, 1.0+0.5j])
cD_rec = pywt.idwt(None, cD, 'haar')
assert_allclose(cD_rec, cD_rec_expect)
assert_allclose(cA_rec + cD_rec, x)
def test_dwt_wavelet_kwd():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
cA, cD = pywt.dwt(x, wavelet=w, mode='constant')
cA_expect = [4.38354585, 3.80302657, 7.31813271, -0.58565539, 4.09727044,
7.81994027]
cD_expect = [-1.33068221, -2.78795192, -3.16825651, -0.67715519,
-0.09722957, -0.07045258]
assert_allclose(cA, cA_expect)
assert_allclose(cD, cD_expect)
def test_dwt_coeff_len():
x = np.array([3, 7, 1, 1, -2, 5, 4, 6])
w = pywt.Wavelet('sym3')
ln_modes = [pywt.dwt_coeff_len(len(x), w.dec_len, mode) for mode in
pywt.Modes.modes]
expected_result = [6, ] * len(pywt.Modes.modes)
expected_result[pywt.Modes.modes.index('periodization')] = 4
assert_allclose(ln_modes, expected_result)
ln_modes = [pywt.dwt_coeff_len(len(x), w, mode) for mode in
pywt.Modes.modes]
assert_allclose(ln_modes, expected_result)
def test_idwt_none_input():
# None input equals arrays of zeros of the right length
res1 = pywt.idwt([1, 2, 0, 1], None, 'db2', 'symmetric')
res2 = pywt.idwt([1, 2, 0, 1], [0, 0, 0, 0], 'db2', 'symmetric')
assert_allclose(res1, res2, rtol=1e-15, atol=1e-15)
res1 = pywt.idwt(None, [1, 2, 0, 1], 'db2', 'symmetric')
res2 = pywt.idwt([0, 0, 0, 0], [1, 2, 0, 1], 'db2', 'symmetric')
assert_allclose(res1, res2, rtol=1e-15, atol=1e-15)
# Only one argument at a time can be None
assert_raises(ValueError, pywt.idwt, None, None, 'db2', 'symmetric')
def test_idwt_invalid_input():
# Too short, min length is 4 for 'db4':
assert_raises(ValueError, pywt.idwt, [1, 2, 4], [4, 1, 3], 'db4', 'symmetric')
def test_dwt_single_axis():
x = [[3, 7, 1, 1],
[-2, 5, 4, 6]]
cA, cD = pywt.dwt(x, 'db2', axis=-1)
cA0, cD0 = pywt.dwt(x[0], 'db2')
cA1, cD1 = pywt.dwt(x[1], 'db2')
assert_allclose(cA[0], cA0)
assert_allclose(cA[1], cA1)
assert_allclose(cD[0], cD0)
assert_allclose(cD[1], cD1)
def test_idwt_single_axis():
x = [[3, 7, 1, 1],
[-2, 5, 4, 6]]
x = np.asarray(x)
x = x + 1j*x # test with complex data
cA, cD = pywt.dwt(x, 'db2', axis=-1)
x0 = pywt.idwt(cA[0], cD[0], 'db2', axis=-1)
x1 = pywt.idwt(cA[1], cD[1], 'db2', axis=-1)
assert_allclose(x[0], x0)
assert_allclose(x[1], x1)
def test_dwt_invalid_input():
x = np.arange(1)
assert_raises(ValueError, pywt.dwt, x, 'db2', 'reflect')
assert_raises(ValueError, pywt.dwt, x, 'haar', 'antireflect')
def test_dwt_axis_arg():
x = [[3, 7, 1, 1],
[-2, 5, 4, 6]]
cA_, cD_ = pywt.dwt(x, 'db2', axis=-1)
cA, cD = pywt.dwt(x, 'db2', axis=1)
assert_allclose(cA_, cA)
assert_allclose(cD_, cD)
def test_dwt_axis_invalid_input():
x = np.ones((3,1))
assert_raises(ValueError, pywt.dwt, x, 'db2', 'reflect')
def test_idwt_axis_arg():
x = [[3, 7, 1, 1],
[-2, 5, 4, 6]]
cA, cD = pywt.dwt(x, 'db2', axis=1)
x_ = pywt.idwt(cA, cD, 'db2', axis=-1)
x = pywt.idwt(cA, cD, 'db2', axis=1)
assert_allclose(x_, x)
def test_dwt_idwt_axis_excess():
x = [[3, 7, 1, 1],
[-2, 5, 4, 6]]
# can't transform over axes that aren't there
assert_raises(ValueError,
pywt.dwt, x, 'db2', 'symmetric', axis=2)
assert_raises(ValueError,
pywt.idwt, [1, 2, 4], [4, 1, 3], 'db2', 'symmetric', axis=1)
def test_error_on_continuous_wavelet():
# A ValueError is raised if a Continuous wavelet is selected
data = np.ones((32, ))
for cwave in ['morl', pywt.DiscreteContinuousWavelet('morl')]:
assert_raises(ValueError, pywt.dwt, data, cwave)
cA, cD = pywt.dwt(data, 'db1')
assert_raises(ValueError, pywt.idwt, cA, cD, cwave)
def test_dwt_zero_size_axes():
# raise on empty input array
assert_raises(ValueError, pywt.dwt, [], 'db2')
# >1D case uses a different code path so check there as well
x = np.ones((1, 4))[0:0, :] # 2D with a size zero axis
assert_raises(ValueError, pywt.dwt, x, 'db2', axis=0)
def test_pad_1d():
x = [1, 2, 3]
assert_array_equal(pywt.pad(x, (4, 6), 'periodization'),
[1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2])
assert_array_equal(pywt.pad(x, (4, 6), 'periodic'),
[3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3])
assert_array_equal(pywt.pad(x, (4, 6), 'constant'),
[1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3])
assert_array_equal(pywt.pad(x, (4, 6), 'zero'),
[0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0])
assert_array_equal(pywt.pad(x, (4, 6), 'smooth'),
[-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
assert_array_equal(pywt.pad(x, (4, 6), 'symmetric'),
[3, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3])
assert_array_equal(pywt.pad(x, (4, 6), 'antisymmetric'),
[3, -3, -2, -1, 1, 2, 3, -3, -2, -1, 1, 2, 3])
assert_array_equal(pywt.pad(x, (4, 6), 'reflect'),
[1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1])
assert_array_equal(pywt.pad(x, (4, 6), 'antireflect'),
[-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
# equivalence of various pad_width formats
assert_array_equal(pywt.pad(x, 4, 'periodic'),
pywt.pad(x, (4, 4), 'periodic'))
assert_array_equal(pywt.pad(x, (4, ), 'periodic'),
pywt.pad(x, (4, 4), 'periodic'))
assert_array_equal(pywt.pad(x, [(4, 4)], 'periodic'),
pywt.pad(x, (4, 4), 'periodic'))
def test_pad_errors():
# negative pad width
x = [1, 2, 3]
assert_raises(ValueError, pywt.pad, x, -2, 'periodic')
# wrong length pad width
assert_raises(ValueError, pywt.pad, x, (1, 1, 1), 'periodic')
# invalid mode name
assert_raises(ValueError, pywt.pad, x, 2, 'bad_mode')
def test_pad_nd():
for ndim in [2, 3]:
x = np.arange(4**ndim).reshape((4, ) * ndim)
if ndim == 2:
pad_widths = [(2, 1), (2, 3)]
else:
pad_widths = [(2, 1), ] * ndim
for mode in pywt.Modes.modes:
xp = pywt.pad(x, pad_widths, mode)
# expected result is the same as applying along axes separably
xp_expected = x.copy()
for ax in range(ndim):
xp_expected = np.apply_along_axis(pywt.pad,
ax,
xp_expected,
pad_widths=[pad_widths[ax]],
mode=mode)
assert_array_equal(xp, xp_expected)
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