def test_theano_operator():
"""Test the ODL->Theano operator wrapper."""
# Define ODL operator
matrix = np.random.rand(3, 2)
odl_op = odl.MatrixOperator(matrix)
# Define evaluation points
x = [1., 2.]
dy = [1., 2., 3.]
# Create Theano placeholders
x_theano = T.dvector()
dy_theano = T.dvector()
# Create Theano layer from odl operator
odl_op_layer = odl.contrib.theano.TheanoOperator(odl_op)
# Build computation graphs
y_theano = odl_op_layer(x_theano)
y_theano_func = theano.function([x_theano], y_theano)
dy_theano_func = theano.function([x_theano, dy_theano],
T.Rop(y_theano, x_theano, dy_theano))
# Evaluate using Theano
result = y_theano_func(x)
expected = odl_op(x)
assert all_almost_equal(result, expected)
# Evaluate the adjoint of the derivative, called gradient in Theano
result = dy_theano_func(x, dy)
expected = odl_op.derivative(x).adjoint(dy)
assert all_almost_equal(result, expected)
def test_as_tensorflow_layer():
# Define ODL operator
matrix = np.random.rand(3, 2)
odl_op = odl.MatrixOperator(matrix)
# Define evaluation points
x = np.random.rand(2)
z = np.random.rand(3)
# Add empty axes for batch and channel
x_tf = tf.constant(x)[None, ..., None]
z_tf = tf.constant(z)[None, ..., None]
# Create tensorflow layer from odl operator
odl_op_layer = odl.contrib.tensorflow.as_tensorflow_layer(
odl_op, 'MatrixOperator')
y_tf = odl_op_layer(x_tf)
# Evaluate using tensorflow
result = y_tf.eval().ravel()
expected = odl_op(x)
assert all_almost_equal(result, expected)
# Evaluate the adjoint of the derivative, called gradient in tensorflow
result = tf.gradients(y_tf, [x_tf], z_tf)[0].eval().ravel()
expected = odl_op.derivative(x).adjoint(z)
assert all_almost_equal(result, expected)
def test_reciprocal_grid_nd_axes():
grid = odl.uniform_grid([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
axes_list = [[1, -1], [0], 0, [0, 2, 1], [2, 0]]
for axes in axes_list:
active = np.zeros(grid.ndim, dtype=bool)
active[axes] = True
inactive = np.logical_not(active)
true_recip_stride = np.empty(grid.ndim)
true_recip_stride[active] = 2 * np.pi / (s[active] * n[active])
true_recip_stride[inactive] = s[inactive]
# Without shift altogether
rgrid = reciprocal_grid(grid, shift=False, axes=axes,
halfcomplex=False)
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt[active], -rgrid.max_pt[active])
assert all_equal(rgrid.min_pt[inactive], grid.min_pt[inactive])
assert all_equal(rgrid.max_pt[inactive], grid.max_pt[inactive])
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, axes=axes,
halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_reciprocal_grid_nd_axes():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
axes_list = [[1, -1], [0], 0, [0, 2, 1], [2, 0]]
for axes in axes_list:
active = np.zeros(grid.ndim, dtype=bool)
active[axes] = True
inactive = np.logical_not(active)
true_recip_stride = np.empty(grid.ndim)
true_recip_stride[active] = 2 * np.pi / (s[active] * n[active])
true_recip_stride[inactive] = s[inactive]
# Without shift altogether
rgrid = reciprocal_grid(grid, shift=False, axes=axes,
halfcomplex=False)
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt[active], -rgrid.max_pt[active])
assert all_equal(rgrid.min_pt[inactive], grid.min_pt[inactive])
assert all_equal(rgrid.max_pt[inactive], grid.max_pt[inactive])
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, axes=axes,
halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_pyfftw_call_plan_preserve_input(planning):
for shape in [(10,), (3, 4)]:
arr = _random_array(shape, dtype='complex128')
arr_cpy = arr.copy()
idft_scaling = np.prod(shape)
true_idft = np.fft.ifftn(arr) * idft_scaling
idft_arr = np.empty(shape, dtype='complex128')
pyfftw_call(arr, idft_arr, direction='backward', halfcomplex=False,
planning=planning)
assert all_almost_equal(arr, arr_cpy) # Input perserved
assert all_almost_equal(idft_arr, true_idft)
def test_pyfftw_call_backward_with_axes(floating_dtype):
if floating_dtype == np.dtype('float16'): # not supported, skipping
return
halfcomplex, in_dtype = _params_from_dtype(floating_dtype)
shape = (3, 4, 5)
test_axes = [(0, 1), [1], (-1,), (1, 0), (-1, -2, -3)]
for axes in test_axes:
# Only the shape indexed by axes count for the scaling
active_shape = np.take(shape, axes)
idft_scaling = np.prod(active_shape)
if halfcomplex:
arr = _random_array(_halfcomplex_shape(shape, axes), in_dtype)
true_idft = (np.fft.irfftn(arr, s=active_shape, axes=axes) *
idft_scaling)
else:
arr = _random_array(shape, in_dtype)
true_idft = (np.fft.ifftn(arr, s=active_shape, axes=axes) *
idft_scaling)
idft_arr = np.empty(shape, dtype=floating_dtype)
pyfftw_call(arr, idft_arr, direction='backward', axes=axes,
halfcomplex=halfcomplex)
assert all_almost_equal(idft_arr, true_idft)
def test_pyfftw_call_threads():
shape = (3, 4, 5)
arr = _random_array(shape, dtype='complex64')
true_dft = np.fft.fftn(arr)
dft_arr = np.empty(shape, dtype='complex64')
pyfftw_call(arr, dft_arr, direction='forward', preserve_input=False,
threads=4)
assert all_almost_equal(dft_arr, true_dft)
shape = (1000,) # Trigger cpu_count() as number of threads
arr = _random_array(shape, dtype='complex64')
true_dft = np.fft.fftn(arr)
dft_arr = np.empty(shape, dtype='complex64')
pyfftw_call(arr, dft_arr, direction='forward', preserve_input=False)
assert all_almost_equal(dft_arr, true_dft)
def test_reciprocal_grid_nd():
grid = odl.uniform_grid([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
true_recip_stride = 2 * np.pi / (s * n)
# Without shift altogether
rgrid = reciprocal_grid(grid, shift=False, halfcomplex=False)
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt, -rgrid.max_pt)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_reciprocal_grid_nd():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
true_recip_stride = 2 * np.pi / (s * n)
# Without shift altogether
rgrid = reciprocal_grid(grid, shift=False, halfcomplex=False)
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt, -rgrid.max_pt)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_pyfftw_call_forward_real_not_halfcomplex():
# Test against Numpy's FFT
for shape in [(10,), (3, 4, 5)]:
arr = _random_array(shape, dtype='float64')
true_dft = np.fft.fftn(arr)
dft_arr = np.empty(shape, dtype='complex128')
pyfftw_call(arr, dft_arr, direction='forward', halfcomplex=False)
assert all_almost_equal(dft_arr, true_dft)
def test_pyfftw_call_forward_with_plan():
for shape in [(10,), (3, 4, 5)]:
arr = _random_array(shape, dtype='complex128')
arr_cpy = arr.copy()
true_dft = np.fft.fftn(arr)
# First run, create plan
dft_arr = np.empty(shape, dtype='complex128')
plan = pyfftw_call(arr, dft_arr, direction='forward',
halfcomplex=False, planning_effort='measure')
# Second run, reuse with fresh output array
dft_arr = np.empty(shape, dtype='complex128')
pyfftw_call(arr, dft_arr, direction='forward', fftw_plan=plan,
halfcomplex=False)
assert all_almost_equal(arr, arr_cpy) # Input perserved
assert all_almost_equal(dft_arr, true_dft)
def test_reciprocal_grid_nd_shift_list():
grid = odl.uniform_sampling([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
shift = [False, True, False]
true_recip_stride = 2 * np.pi / (s * n)
# Shift only the even dimension, then zero must be contained
rgrid = reciprocal_grid(grid, shift=shift, halfcomplex=False)
noshift = np.where(np.logical_not(shift))
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt[noshift], -rgrid.max_pt[noshift])
assert all_almost_equal(rgrid[n // 2], [0] * 3)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_reciprocal_grid_nd_shift_list():
grid = odl.uniform_grid([0] * 3, [1] * 3, shape=(3, 4, 5))
s = grid.stride
n = np.array(grid.shape)
shift = [False, True, False]
true_recip_stride = 2 * np.pi / (s * n)
# Shift only the even dimension, then zero must be contained
rgrid = reciprocal_grid(grid, shift=shift, halfcomplex=False)
noshift = np.where(np.logical_not(shift))
assert all_equal(rgrid.shape, n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
assert all_almost_equal(rgrid.min_pt[noshift], -rgrid.max_pt[noshift])
assert all_almost_equal(rgrid[n // 2], [0] * 3)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=False)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_pyfftw_call_backward_real_not_halfcomplex():
# Test against Numpy's IFFT, no normalization
for shape in [(10,), (3, 4, 5)]:
# Scaling happens wrt output (large) shape
idft_scaling = np.prod(shape)
arr = _random_array(shape, dtype='float64')
true_idft = np.fft.ifftn(arr) * idft_scaling
idft_arr = np.empty(shape, dtype='complex128')
pyfftw_call(arr, idft_arr, direction='backward', halfcomplex=False)
assert all_almost_equal(idft_arr, true_idft)
def test_dft_preprocess_data_halfcomplex(sign):
shape = (2, 3, 4)
# With shift
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append(1 - 2 * ((i + j + k) % 2))
arr = np.ones(shape, dtype='float64')
preproc = dft_preprocess_data(arr, shift=True, sign=sign) # out-of-place
out = np.empty_like(arr)
dft_preprocess_data(arr, shift=True, out=out, sign=sign) # in-place
dft_preprocess_data(arr, shift=True, out=arr, sign=sign) # in-place
assert all_almost_equal(preproc.ravel(), correct_arr)
assert all_almost_equal(arr.ravel(), correct_arr)
assert all_almost_equal(out.ravel(), correct_arr)
# Without shift
imag = 1j if sign == '-' else -1j
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
argsum = sum((idx * (1 - 1 / shp))
for idx, shp in zip((i, j, k), shape))
correct_arr.append(np.exp(imag * np.pi * argsum))
arr = np.ones(shape, dtype='float64')
preproc = dft_preprocess_data(arr, shift=False, sign=sign)
assert all_almost_equal(preproc.ravel(), correct_arr)
# Non-float input works, too
arr = np.ones(shape, dtype='int')
preproc = dft_preprocess_data(arr, shift=False, sign=sign)
assert all_almost_equal(preproc.ravel(), correct_arr)
# In-place modification not possible for float array and no shift
arr = np.ones(shape, dtype='float64')
with pytest.raises(ValueError):
dft_preprocess_data(arr, shift=False, out=arr, sign=sign)
def test_dft_preprocess_data_halfcomplex(sign):
shape = (2, 3, 4)
# With shift
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append(1 - 2 * ((i + j + k) % 2))
arr = np.ones(shape, dtype='float64')
preproc = dft_preprocess_data(arr, shift=True, sign=sign) # out-of-place
out = np.empty_like(arr)
dft_preprocess_data(arr, shift=True, out=out, sign=sign) # in-place
dft_preprocess_data(arr, shift=True, out=arr, sign=sign) # in-place
assert all_almost_equal(preproc.ravel(), correct_arr)
assert all_almost_equal(arr.ravel(), correct_arr)
assert all_almost_equal(out.ravel(), correct_arr)
# Without shift
imag = 1j if sign == '-' else -1j
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
argsum = sum((idx * (1 - 1 / shp))
for idx, shp in zip((i, j, k), shape))
correct_arr.append(np.exp(imag * np.pi * argsum))
arr = np.ones(shape, dtype='float64')
preproc = dft_preprocess_data(arr, shift=False, sign=sign)
assert all_almost_equal(preproc.ravel(), correct_arr)
# Non-float input works, too
arr = np.ones(shape, dtype='int')
preproc = dft_preprocess_data(arr, shift=False, sign=sign)
assert all_almost_equal(preproc.ravel(), correct_arr)
# In-place modification not possible for float array and no shift
arr = np.ones(shape, dtype='float64')
with pytest.raises(ValueError):
dft_preprocess_data(arr, shift=False, out=arr, sign=sign)
def test_reciprocal_grid_1d(halfcomplex, shift, parity):
shape = 10 if parity == 'even' else 11
grid = odl.uniform_grid(0, 1, shape=shape)
s = grid.stride
n = np.array(grid.shape)
rgrid = reciprocal_grid(grid, shift=shift, halfcomplex=halfcomplex)
# Independent of halfcomplex, shift and parity
true_recip_stride = 2 * np.pi / (s * n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
if halfcomplex:
assert all_equal(rgrid.shape, n // 2 + 1)
if parity == 'odd' and shift:
# Max point should be half a negative recip stride
assert all_almost_equal(rgrid.max_pt, -true_recip_stride / 2)
elif parity == 'even' and not shift:
# Max point should be half a positive recip stride
assert all_almost_equal(rgrid.max_pt, true_recip_stride / 2)
elif (parity == 'odd' and not shift) or (parity == 'even' and shift):
# Max should be zero
assert all_almost_equal(rgrid.max_pt, 0)
else:
raise RuntimeError('parameter combination not covered')
else: # halfcomplex = False
assert all_equal(rgrid.shape, n)
if (parity == 'even' and shift) or (parity == 'odd' and not shift):
# Zero should be at index n // 2
assert all_almost_equal(rgrid[n // 2], 0)
elif (parity == 'odd' and shift) or (parity == 'even' and not shift):
# No point should be closer to 0 than half a recip stride
atol = 0.999 * true_recip_stride / 2
assert not rgrid.approx_contains(0, atol=atol)
else:
raise RuntimeError('parameter combination not covered')
if not shift:
# Grid Should be symmetric
assert all_almost_equal(rgrid.min_pt, -rgrid.max_pt)
if parity == 'odd':
# Midpoint should be 0
assert all_almost_equal(rgrid.mid_pt, 0)
# Inverting should give back the original
irgrid = realspace_grid(rgrid,
grid.min_pt,
halfcomplex=halfcomplex,
halfcx_parity=parity)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_dft_preprocess_data_with_axes(sign):
shape = (2, 3, 4)
axes = 1 # Only middle index counts
correct_arr = []
for _, j, __ in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append(1 - 2 * (j % 2))
arr = np.ones(shape, dtype='complex64')
dft_preprocess_data(arr, shift=True, axes=axes, out=arr, sign=sign)
assert all_almost_equal(arr.ravel(), correct_arr)
axes = [0, -1] # First and last
correct_arr = []
for i, _, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append(1 - 2 * ((i + k) % 2))
arr = np.ones(shape, dtype='complex64')
dft_preprocess_data(arr, shift=True, axes=axes, out=arr, sign=sign)
assert all_almost_equal(arr.ravel(), correct_arr)
def test_dft_preprocess_data_with_axes(sign):
shape = (2, 3, 4)
axes = 1 # Only middle index counts
correct_arr = []
for _, j, __ in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append(1 - 2 * (j % 2))
arr = np.ones(shape, dtype='complex64')
dft_preprocess_data(arr, shift=True, axes=axes, out=arr, sign=sign)
assert all_almost_equal(arr.ravel(), correct_arr)
axes = [0, -1] # First and last
correct_arr = []
for i, _, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append(1 - 2 * ((i + k) % 2))
arr = np.ones(shape, dtype='complex64')
dft_preprocess_data(arr, shift=True, axes=axes, out=arr, sign=sign)
assert all_almost_equal(arr.ravel(), correct_arr)
def test_dft_preprocess_data(sign):
shape = (2, 3, 4)
# With shift
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append((1 + 1j) * (1 - 2 * ((i + j + k) % 2)))
arr = np.ones(shape, dtype='complex64') * (1 + 1j)
preproc = dft_preprocess_data(arr, shift=True, sign=sign) # out-of-place
dft_preprocess_data(arr, shift=True, out=arr, sign=sign) # in-place
assert all_almost_equal(preproc.ravel(), correct_arr)
assert all_almost_equal(arr.ravel(), correct_arr)
# Without shift
imag = 1j if sign == '-' else -1j
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
argsum = sum((idx * (1 - 1 / shp))
for idx, shp in zip((i, j, k), shape))
correct_arr.append((1 + 1j) * np.exp(imag * np.pi * argsum))
arr = np.ones(shape, dtype='complex64') * (1 + 1j)
dft_preprocess_data(arr, shift=False, out=arr, sign=sign)
assert all_almost_equal(arr.ravel(), correct_arr)
# Bad input
with pytest.raises(ValueError):
dft_preprocess_data(arr, out=arr, sign=1)
arr = np.zeros(shape, dtype='S2')
with pytest.raises(ValueError):
dft_preprocess_data(arr)
def test_dft_preprocess_data(sign):
shape = (2, 3, 4)
# With shift
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
correct_arr.append((1 + 1j) * (1 - 2 * ((i + j + k) % 2)))
arr = np.ones(shape, dtype='complex64') * (1 + 1j)
preproc = dft_preprocess_data(arr, shift=True, sign=sign) # out-of-place
dft_preprocess_data(arr, shift=True, out=arr, sign=sign) # in-place
assert all_almost_equal(preproc.ravel(), correct_arr)
assert all_almost_equal(arr.ravel(), correct_arr)
# Without shift
imag = 1j if sign == '-' else -1j
correct_arr = []
for i, j, k in product(range(shape[0]), range(shape[1]), range(shape[2])):
argsum = sum((idx * (1 - 1 / shp))
for idx, shp in zip((i, j, k), shape))
correct_arr.append((1 + 1j) * np.exp(imag * np.pi * argsum))
arr = np.ones(shape, dtype='complex64') * (1 + 1j)
dft_preprocess_data(arr, shift=False, out=arr, sign=sign)
assert all_almost_equal(arr.ravel(), correct_arr)
# Bad input
with pytest.raises(ValueError):
dft_preprocess_data(arr, out=arr, sign=1)
arr = np.zeros(shape, dtype='S2')
with pytest.raises(ValueError):
dft_preprocess_data(arr)
def test_fourier_trafo_inverse(impl, sign):
# Test if the inverse really is the inverse
def char_interval(x):
return (x >= 0) & (x <= 1)
# Complex-to-complex
discr = odl.uniform_discr(-2, 2, 40, impl='numpy', dtype='complex64')
discr_char = discr.element(char_interval)
ft = FourierTransform(discr, sign=sign, impl=impl)
assert all_almost_equal(ft.inverse(ft(char_interval)), discr_char)
assert all_almost_equal(ft.adjoint(ft(char_interval)), discr_char)
# Half-complex
discr = odl.uniform_discr(-2, 2, 40, impl='numpy', dtype='float32')
ft = FourierTransform(discr, impl=impl, halfcomplex=True)
assert all_almost_equal(ft.inverse(ft(char_interval)), discr_char)
def char_rect(x):
return (x[0] >= 0) & (x[0] <= 1) & (x[1] >= 0) & (x[1] <= 1)
# 2D with axes, C2C
discr = odl.uniform_discr([-2, -2], [2, 2], (20, 10),
impl='numpy',
dtype='complex64')
discr_rect = discr.element(char_rect)
for axes in [(0, ), 1]:
ft = FourierTransform(discr, sign=sign, impl=impl, axes=axes)
assert all_almost_equal(ft.inverse(ft(char_rect)), discr_rect)
assert all_almost_equal(ft.adjoint(ft(char_rect)), discr_rect)
# 2D with axes, halfcomplex
discr = odl.uniform_discr([-2, -2], [2, 2], (20, 10),
impl='numpy',
dtype='float32')
discr_rect = discr.element(char_rect)
for halfcomplex in [False, True]:
if halfcomplex and sign == '+':
continue # cannot mix halfcomplex with sign
for axes in [(0, ), (1, )]:
ft = FourierTransform(discr,
sign=sign,
impl=impl,
axes=axes,
halfcomplex=halfcomplex)
assert all_almost_equal(ft.inverse(ft(char_rect)), discr_rect)
assert all_almost_equal(ft.adjoint(ft(char_rect)), discr_rect)
def test_reciprocal_grid_1d(halfcomplex, shift, parity):
shape = 10 if parity == 'even' else 11
grid = odl.uniform_sampling(0, 1, shape=shape)
s = grid.stride
n = np.array(grid.shape)
rgrid = reciprocal_grid(grid, shift=shift, halfcomplex=halfcomplex)
# Independent of halfcomplex, shift and parity
true_recip_stride = 2 * np.pi / (s * n)
assert all_almost_equal(rgrid.stride, true_recip_stride)
if halfcomplex:
assert all_equal(rgrid.shape, n // 2 + 1)
if parity == 'odd' and shift:
# Max point should be half a negative recip stride
assert all_almost_equal(rgrid.max_pt, -true_recip_stride / 2)
elif parity == 'even' and not shift:
# Max point should be half a positive recip stride
assert all_almost_equal(rgrid.max_pt, true_recip_stride / 2)
elif (parity == 'odd' and not shift) or (parity == 'even' and shift):
# Max should be zero
assert all_almost_equal(rgrid.max_pt, 0)
else:
raise RuntimeError('parameter combination not covered')
else: # halfcomplex = False
assert all_equal(rgrid.shape, n)
if (parity == 'even' and shift) or (parity == 'odd' and not shift):
# Zero should be at index n // 2
assert all_almost_equal(rgrid[n // 2], 0)
elif (parity == 'odd' and shift) or (parity == 'even' and not shift):
# No point should be closer to 0 than half a recip stride
atol = 0.999 * true_recip_stride / 2
assert not rgrid.approx_contains(0, atol=atol)
else:
raise RuntimeError('parameter combination not covered')
if not shift:
# Grid Should be symmetric
assert all_almost_equal(rgrid.min_pt, -rgrid.max_pt)
if parity == 'odd':
# Midpoint should be 0
assert all_almost_equal(rgrid.mid_pt, 0)
# Inverting should give back the original
irgrid = realspace_grid(rgrid, grid.min_pt, halfcomplex=halfcomplex,
halfcx_parity=parity)
assert irgrid.approx_equals(grid, atol=1e-6)
def test_dft_sign(impl):
# Test if the FT sign behaves as expected, i.e. that the FT with sign
# '+' and '-' have same real parts and opposite imaginary parts.
# 2d, complex, all ones and random back & forth
shape = (4, 5)
dft_dom = odl.discr_sequence_space(shape, dtype='complex64')
dft_minus = DiscreteFourierTransform(domain=dft_dom, impl=impl, sign='-')
dft_plus = DiscreteFourierTransform(domain=dft_dom, impl=impl, sign='+')
arr = dft_dom.element([[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 1, 0],
[0, 0, 0, 0, 0]])
arr_dft_minus = dft_minus(arr, flags=('FFTW_ESTIMATE', ))
arr_dft_plus = dft_plus(arr, flags=('FFTW_ESTIMATE', ))
assert all_almost_equal(arr_dft_minus.real, arr_dft_plus.real)
assert all_almost_equal(arr_dft_minus.imag, -arr_dft_plus.imag)
assert all_almost_equal(dft_minus.inverse(arr_dft_minus), arr)
assert all_almost_equal(dft_plus.inverse(arr_dft_plus), arr)
assert all_almost_equal(dft_minus.inverse.inverse(arr), dft_minus(arr))
assert all_almost_equal(dft_plus.inverse.inverse(arr), dft_plus(arr))
# 2d, halfcomplex, first axis
shape = (4, 5)
axes = (0, )
dft_dom = odl.discr_sequence_space(shape, dtype='float32')
arr = dft_dom.element([[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 1, 0],
[0, 0, 0, 0, 0]])
dft = DiscreteFourierTransform(domain=dft_dom,
impl=impl,
halfcomplex=True,
sign='-',
axes=axes)
arr_dft_minus = dft(arr, flags=('FFTW_ESTIMATE', ))
arr_idft_minus = dft.inverse(arr_dft_minus, flags=('FFTW_ESTIMATE', ))
assert all_almost_equal(arr_idft_minus, arr)
with pytest.raises(ValueError):
DiscreteFourierTransform(domain=dft_dom,
impl=impl,
halfcomplex=True,
sign='+',
axes=axes)
def test_fourier_trafo_inverse(impl, sign):
# Test if the inverse really is the inverse
def char_interval(x):
return (x >= 0) & (x <= 1)
# Complex-to-complex
discr = odl.uniform_discr(-2, 2, 40, impl="numpy", dtype="complex64")
discr_char = discr.element(char_interval)
ft = FourierTransform(discr, sign=sign, impl=impl)
assert all_almost_equal(ft.inverse(ft(char_interval)), discr_char)
assert all_almost_equal(ft.adjoint(ft(char_interval)), discr_char)
# Half-complex
discr = odl.uniform_discr(-2, 2, 40, impl="numpy", dtype="float32")
ft = FourierTransform(discr, impl=impl, halfcomplex=True)
assert all_almost_equal(ft.inverse(ft(char_interval)), discr_char)
def char_rect(x):
return (x[0] >= 0) & (x[0] <= 1) & (x[1] >= 0) & (x[1] <= 1)
# 2D with axes, C2C
discr = odl.uniform_discr([-2, -2], [2, 2], (20, 10), impl="numpy", dtype="complex64")
discr_rect = discr.element(char_rect)
for axes in [(0,), 1]:
ft = FourierTransform(discr, sign=sign, impl=impl, axes=axes)
assert all_almost_equal(ft.inverse(ft(char_rect)), discr_rect)
assert all_almost_equal(ft.adjoint(ft(char_rect)), discr_rect)
# 2D with axes, halfcomplex
discr = odl.uniform_discr([-2, -2], [2, 2], (20, 10), impl="numpy", dtype="float32")
discr_rect = discr.element(char_rect)
for halfcomplex in [False, True]:
if halfcomplex and sign == "+":
continue # cannot mix halfcomplex with sign
for axes in [(0,), (1,)]:
ft = FourierTransform(discr, sign=sign, impl=impl, axes=axes, halfcomplex=halfcomplex)
assert all_almost_equal(ft.inverse(ft(char_rect)), discr_rect)
assert all_almost_equal(ft.adjoint(ft(char_rect)), discr_rect)
def test_pyfftw_call_forward(floating_dtype):
# Test against Numpy's FFT
if floating_dtype == np.dtype('float16'): # not supported, skipping
return
halfcomplex, out_dtype = _params_from_dtype(floating_dtype)
for shape in [(10,), (3, 4, 5)]:
arr = _random_array(shape, floating_dtype)
if halfcomplex:
true_dft = np.fft.rfftn(arr)
dft_arr = np.empty(_halfcomplex_shape(shape), dtype=out_dtype)
else:
true_dft = np.fft.fftn(arr)
dft_arr = np.empty(shape, dtype=out_dtype)
pyfftw_call(arr, dft_arr, direction='forward',
halfcomplex=halfcomplex, preserve_input=False)
assert all_almost_equal(dft_arr, true_dft)
def test_pyfftw_call_forward_with_axes(floating_dtype):
if floating_dtype == np.dtype('float16'): # not supported, skipping
return
halfcomplex, out_dtype = _params_from_dtype(floating_dtype)
shape = (3, 4, 5)
test_axes = [(0, 1), [1], (-1,), (1, 0), (-1, -2, -3)]
for axes in test_axes:
arr = _random_array(shape, floating_dtype)
if halfcomplex:
true_dft = np.fft.rfftn(arr, axes=axes)
dft_arr = np.empty(_halfcomplex_shape(shape, axes),
dtype=out_dtype)
else:
true_dft = np.fft.fftn(arr, axes=axes)
dft_arr = np.empty(shape, dtype=out_dtype)
pyfftw_call(arr, dft_arr, direction='forward', axes=axes,
halfcomplex=halfcomplex)
assert all_almost_equal(dft_arr, true_dft)
def test_pyfftw_call_backward(floating_dtype):
# Test against Numpy's IFFT, no normalization
if floating_dtype == np.dtype('float16'): # not supported, skipping
return
halfcomplex, in_dtype = _params_from_dtype(floating_dtype)
for shape in [(10,), (3, 4, 5)]:
# Scaling happens wrt output (large) shape
idft_scaling = np.prod(shape)
if halfcomplex:
arr = _random_array(_halfcomplex_shape(shape), in_dtype)
true_idft = np.fft.irfftn(arr, shape) * idft_scaling
else:
arr = _random_array(shape, in_dtype)
true_idft = np.fft.ifftn(arr) * idft_scaling
idft_arr = np.empty(shape, dtype=floating_dtype)
pyfftw_call(arr, idft_arr, direction='backward',
halfcomplex=halfcomplex)
assert all_almost_equal(idft_arr, true_idft)
def test_theano_gradient():
"""Test the gradient of ODL functionals wrapped as Theano Ops."""
# Define ODL operator
matrix = np.random.rand(3, 2)
odl_op = odl.MatrixOperator(matrix)
# Define evaluation point
x = [1., 2.]
# Define ODL cost and the composed functional
odl_cost = odl.solvers.L2NormSquared(odl_op.range)
odl_functional = odl_cost * odl_op
# Create Theano placeholder
x_theano = T.dvector()
# Create Theano layers from odl operators
odl_op_layer = odl.contrib.theano.TheanoOperator(odl_op)
odl_cost_layer = odl.contrib.theano.TheanoOperator(odl_cost)
# Build computation graph
y_theano = odl_op_layer(x_theano)
cost_theano = odl_cost_layer(y_theano)
cost_theano_func = theano.function([x_theano], cost_theano)
cost_grad_theano = T.grad(cost_theano, x_theano)
cost_grad_theano_func = theano.function([x_theano], cost_grad_theano)
# Evaluate using Theano
result = cost_theano_func(x)
expected = odl_functional(x)
assert result == pytest.approx(expected)
# Evaluate the gradient of the cost, should be 2 * matrix^T.dot(x)
result = cost_grad_theano_func(x)
expected = odl_functional.gradient(x)
assert all_almost_equal(result, expected)
def test_dft_sign(impl):
# Test if the FT sign behaves as expected, i.e. that the FT with sign
# '+' and '-' have same real parts and opposite imaginary parts.
# 2d, complex, all ones and random back & forth
shape = (4, 5)
dft_dom = odl.discr_sequence_space(shape, dtype="complex64")
dft_minus = DiscreteFourierTransform(domain=dft_dom, impl=impl, sign="-")
dft_plus = DiscreteFourierTransform(domain=dft_dom, impl=impl, sign="+")
arr = dft_dom.element([[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 0, 0]])
arr_dft_minus = dft_minus(arr, flags=("FFTW_ESTIMATE",))
arr_dft_plus = dft_plus(arr, flags=("FFTW_ESTIMATE",))
assert all_almost_equal(arr_dft_minus.real, arr_dft_plus.real)
assert all_almost_equal(arr_dft_minus.imag, -arr_dft_plus.imag)
assert all_almost_equal(dft_minus.inverse(arr_dft_minus), arr)
assert all_almost_equal(dft_plus.inverse(arr_dft_plus), arr)
assert all_almost_equal(dft_minus.inverse.inverse(arr), dft_minus(arr))
assert all_almost_equal(dft_plus.inverse.inverse(arr), dft_plus(arr))
# 2d, halfcomplex, first axis
shape = (4, 5)
axes = (0,)
dft_dom = odl.discr_sequence_space(shape, dtype="float32")
arr = dft_dom.element([[0, 0, 0, 0, 0], [0, 0, 1, 1, 0], [0, 0, 1, 1, 0], [0, 0, 0, 0, 0]])
dft = DiscreteFourierTransform(domain=dft_dom, impl=impl, halfcomplex=True, sign="-", axes=axes)
arr_dft_minus = dft(arr, flags=("FFTW_ESTIMATE",))
arr_idft_minus = dft.inverse(arr_dft_minus, flags=("FFTW_ESTIMATE",))
assert all_almost_equal(arr_idft_minus, arr)
with pytest.raises(ValueError):
DiscreteFourierTransform(domain=dft_dom, impl=impl, halfcomplex=True, sign="+", axes=axes)