def _grouped_and_flat_arrays(shapes, dtype):
"""Return a grouped and flat list of arrays with specified shapes.
The lists are constructed as if they were used in a wavelet transform,
i.e. the array with shape ``shapes[0]`` appears once, while the
others appear ``2 ** ndim - 1`` times each.
"""
space = odl.discr_sequence_space(shape=shapes[0], dtype=dtype)
array = noise_array(space).reshape(space.shape)
grouped_list = [array]
flat_list = [array.ravel()]
ndim = space.ndim
for shape in shapes[1:]:
space = odl.discr_sequence_space(shape=shape, dtype=dtype)
arrays = [noise_array(space).reshape(shape)
for _ in range(2 ** ndim - 1)]
grouped_list.append(tuple(arrays))
flat_list.extend([arr.ravel() for arr in arrays])
return grouped_list, flat_list
def _grouped_and_flat_arrays(shapes, dtype):
"""Return a grouped and flat list of arrays with specified shapes.
The lists are constructed as if they were used in a wavelet transform,
i.e. the array with shape ``shapes[0]`` appears once, while the
others appear ``2 ** ndim - 1`` times each.
"""
space = odl.discr_sequence_space(shape=shapes[0], dtype=dtype)
array = noise_array(space).reshape(space.shape)
grouped_list = [array]
flat_list = [array.ravel()]
ndim = space.ndim
for shape in shapes[1:]:
space = odl.discr_sequence_space(shape=shape, dtype=dtype)
arrays = [noise_array(space).reshape(shape)
for _ in range(2 ** ndim - 1)]
grouped_list.append(tuple(arrays))
flat_list.extend([arr.ravel() for arr in arrays])
return grouped_list, flat_list
def test_explicit_example(odl_floating_dtype):
"""Comparison with hand-calculated wavelet transform."""
dtype = odl_floating_dtype
space = odl.uniform_discr([0, 0], [1, 1], (16, 15), dtype=dtype)
x = noise_array(space).reshape(space.shape)
# We use a Daubechies-2 wavelet
wavelet = pywt.Wavelet('db2')
filter_l = np.array(wavelet.dec_lo)
filter_h = np.array(wavelet.dec_hi)
# Build the 2D filters
filter_ll = filter_l[:, None] * filter_l[None, :]
filter_lh = filter_l[:, None] * filter_h[None, :]
filter_hl = filter_h[:, None] * filter_l[None, :]
filter_hh = filter_h[:, None] * filter_h[None, :]
# Convolve x with 2D filters (implicitly uses zero-padding)
conv_ll = convolve(x, filter_ll)
conv_lh = convolve(x, filter_lh)
conv_hl = convolve(x, filter_hl)
conv_hh = convolve(x, filter_hh)
# Downsampling by factor 2, taking the odd indices, gives the wavelet
# coefficients
coeff_aa = conv_ll[1::2, 1::2]
coeff_ad = conv_lh[1::2, 1::2]
coeff_da = conv_hl[1::2, 1::2]
coeff_dd = conv_hh[1::2, 1::2]
# Compare with single-level wavelet trafo (zero padding)
coeffs = pywt_single_level_decomp(x, wavelet='db2', mode='zero')
approx, details = coeffs
assert all_almost_equal(approx, coeff_aa)
assert all_almost_equal(details, [coeff_ad, coeff_da, coeff_dd])
# Second level, continuing with the level 1 approximation coefficient
coeff_2_aa = convolve(coeff_aa, filter_ll)[1::2, 1::2]
coeff_2_ad = convolve(coeff_aa, filter_lh)[1::2, 1::2]
coeff_2_da = convolve(coeff_aa, filter_hl)[1::2, 1::2]
coeff_2_dd = convolve(coeff_aa, filter_hh)[1::2, 1::2]
# Compare with multi-level wavelet trafo (zero padding)
coeffs = pywt_multi_level_decomp(x, wavelet='db2', mode='zero', nlevels=2)
approx_2, details_2, details_1 = coeffs
assert all_almost_equal(approx_2, coeff_2_aa)
assert all_almost_equal(details_1, [coeff_ad, coeff_da, coeff_dd])
assert all_almost_equal(details_2, [coeff_2_ad, coeff_2_da, coeff_2_dd])
def test_explicit_example(floating_dtype):
"""Comparison with hand-calculated wavelet transform."""
space = odl.uniform_discr([0, 0], [1, 1], (16, 15), dtype=floating_dtype)
x = noise_array(space).reshape(space.shape)
# We use a Daubechies-2 wavelet
wavelet = pywt.Wavelet('db2')
filter_l = np.array(wavelet.dec_lo)
filter_h = np.array(wavelet.dec_hi)
# Build the 2D filters
filter_ll = filter_l[:, None] * filter_l[None, :]
filter_lh = filter_l[:, None] * filter_h[None, :]
filter_hl = filter_h[:, None] * filter_l[None, :]
filter_hh = filter_h[:, None] * filter_h[None, :]
# Convolve x with 2D filters (implicitly uses zero-padding)
conv_ll = convolve(x, filter_ll)
conv_lh = convolve(x, filter_lh)
conv_hl = convolve(x, filter_hl)
conv_hh = convolve(x, filter_hh)
# Downsampling by factor 2, taking the odd indices, gives the wavelet
# coefficients
coeff_aa = conv_ll[1::2, 1::2]
coeff_ad = conv_lh[1::2, 1::2]
coeff_da = conv_hl[1::2, 1::2]
coeff_dd = conv_hh[1::2, 1::2]
# Compare with single-level wavelet trafo (zero padding)
coeffs = pywt_single_level_decomp(x, wavelet='db2', mode='zero')
approx, details = coeffs
assert all_almost_equal(approx, coeff_aa)
assert all_almost_equal(details, [coeff_ad, coeff_da, coeff_dd])
# Second level, continuing with the level 1 approximation coefficient
coeff_2_aa = convolve(coeff_aa, filter_ll)[1::2, 1::2]
coeff_2_ad = convolve(coeff_aa, filter_lh)[1::2, 1::2]
coeff_2_da = convolve(coeff_aa, filter_hl)[1::2, 1::2]
coeff_2_dd = convolve(coeff_aa, filter_hh)[1::2, 1::2]
# Compare with multi-level wavelet trafo (zero padding)
coeffs = pywt_multi_level_decomp(x, wavelet='db2', mode='zero', nlevels=2)
approx_2, details_2, details_1 = coeffs
assert all_almost_equal(approx_2, coeff_2_aa)
assert all_almost_equal(details_1, [coeff_ad, coeff_da, coeff_dd])
assert all_almost_equal(details_2, [coeff_2_ad, coeff_2_da, coeff_2_dd])
def test_vector_class_init(fn):
# Test that code runs
arr = noise_array(fn)
NumpyFnVector(fn, arr)
# Space has to be an actual space
for non_space in [1, complex, np.array([1, 2])]:
with pytest.raises(TypeError):
NumpyFnVector(non_space, arr)
# Data has to be a numpy array
with pytest.raises(TypeError):
NumpyFnVector(fn, list(arr))
# Data has to be a numpy array or correct dtype
with pytest.raises(TypeError):
NumpyFnVector(fn, arr.astype(int))
def _pos_array(fn):
"""Create an array with positive real entries as weight in `fn`."""
return np.abs(noise_array(fn)) + 0.1
def test_vector_class_init(fn):
# Test that code runs
arr = noise_array(fn)
NumpyFnVector(fn, arr)
