def test_dft_call(impl):
# 2d, complex, all ones and random back & forth
shape = (4, 5)
dft_dom = odl.discr_sequence_space(shape, dtype="complex64")
dft = DiscreteFourierTransform(domain=dft_dom, impl=impl)
idft = DiscreteFourierTransformInverse(range=dft_dom, impl=impl)
assert dft.domain == idft.range
assert dft.range == idft.domain
one = dft.domain.one()
one_dft1 = dft(one, flags=("FFTW_ESTIMATE",))
one_dft2 = dft.inverse.inverse(one, flags=("FFTW_ESTIMATE",))
one_dft3 = dft.adjoint.adjoint(one, flags=("FFTW_ESTIMATE",))
true_dft = [[20, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] # along all axes by default
assert np.allclose(one_dft1, true_dft)
assert np.allclose(one_dft2, true_dft)
assert np.allclose(one_dft3, true_dft)
one_idft1 = idft(one_dft1, flags=("FFTW_ESTIMATE",))
one_idft2 = dft.inverse(one_dft1, flags=("FFTW_ESTIMATE",))
one_idft3 = dft.adjoint(one_dft1, flags=("FFTW_ESTIMATE",))
assert np.allclose(one_idft1, one)
assert np.allclose(one_idft2, one)
assert np.allclose(one_idft3, one)
rand_arr = noise_element(dft_dom)
rand_arr_dft = dft(rand_arr, flags=("FFTW_ESTIMATE",))
rand_arr_idft = idft(rand_arr_dft, flags=("FFTW_ESTIMATE",))
assert (rand_arr_idft - rand_arr).norm() < 1e-6
# 2d, halfcomplex, first axis
shape = (4, 5)
axes = 0
dft_dom = odl.discr_sequence_space(shape, dtype="float32")
dft = DiscreteFourierTransform(domain=dft_dom, impl=impl, halfcomplex=True, axes=axes)
idft = DiscreteFourierTransformInverse(range=dft_dom, impl=impl, halfcomplex=True, axes=axes)
assert dft.domain == idft.range
assert dft.range == idft.domain
one = dft.domain.one()
one_dft = dft(one, flags=("FFTW_ESTIMATE",))
true_dft = [[4, 4, 4, 4, 4], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]] # transform axis shortened
assert np.allclose(one_dft, true_dft)
one_idft1 = idft(one_dft, flags=("FFTW_ESTIMATE",))
one_idft2 = dft.inverse(one_dft, flags=("FFTW_ESTIMATE",))
assert np.allclose(one_idft1, one)
assert np.allclose(one_idft2, one)
rand_arr = noise_element(dft_dom)
rand_arr_dft = dft(rand_arr, flags=("FFTW_ESTIMATE",))
rand_arr_idft = idft(rand_arr_dft, flags=("FFTW_ESTIMATE",))
assert (rand_arr_idft - rand_arr).norm() < 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_dft_range():
# 1d
shape = 10
dom = odl.discr_sequence_space(shape, dtype='complex128')
fft = DiscreteFourierTransform(dom)
true_ran = odl.discr_sequence_space(shape, dtype='complex128')
assert fft.range == true_ran
# 3d
shape = (3, 4, 5)
ran = odl.discr_sequence_space(shape, dtype='complex64')
fft = DiscreteFourierTransform(ran)
true_ran = odl.discr_sequence_space(shape, dtype='complex64')
assert fft.range == true_ran
# 3d, with axes and halfcomplex
shape = (3, 4, 5)
axes = (-1, -2)
ran_shape = (3, 3, 5)
dom = odl.discr_sequence_space(shape, dtype='float32')
fft = DiscreteFourierTransform(dom, axes=axes, halfcomplex=True)
true_ran = odl.discr_sequence_space(ran_shape, dtype='complex64')
assert fft.range == true_ran
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_dft_init_plan(impl):
# 2d, halfcomplex, first axis
shape = (4, 5)
axes = 0
dft_dom = odl.discr_sequence_space(shape, dtype="float32")
dft = DiscreteFourierTransform(dft_dom, impl=impl, axes=axes, halfcomplex=True)
if impl != "pyfftw":
with pytest.raises(ValueError):
dft.init_fftw_plan()
with pytest.raises(ValueError):
dft.clear_fftw_plan()
else:
dft.init_fftw_plan()
# Make sure plan can be used
dft._fftw_plan(dft.domain.element().asarray(), dft.range.element().asarray())
dft.clear_fftw_plan()
assert dft._fftw_plan is None
def test_dft_init_raise():
# Test different error scenarios
shape = (4, 5)
dom = odl.discr_sequence_space(shape)
dom_f32 = odl.discr_sequence_space(shape, dtype='float32')
# Bad types
with pytest.raises(TypeError):
DiscreteFourierTransform(dom.tspace)
with pytest.raises(TypeError):
DiscreteFourierTransform(dom, dom.tspace)
# Illegal arguments
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, impl='fftw')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, axes=(1, 2))
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, axes=(1, -3))
# Badly shaped range
bad_ran = odl.discr_sequence_space((3, 5), dtype='complex128')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran)
bad_ran = odl.discr_sequence_space((10, 10), dtype='complex128')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran)
bad_ran = odl.discr_sequence_space((4, 5), dtype='complex128')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran, halfcomplex=True)
bad_ran = odl.discr_sequence_space((4, 3), dtype='complex128')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran, halfcomplex=True, axes=(0, ))
# Bad data types
bad_ran = odl.discr_sequence_space(shape, dtype='complex64')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran)
bad_ran = odl.discr_sequence_space(shape, dtype='float64')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran)
bad_ran = odl.discr_sequence_space((4, 3), dtype='float64')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, bad_ran, halfcomplex=True)
bad_ran = odl.discr_sequence_space((4, 3), dtype='complex128')
with pytest.raises(ValueError):
DiscreteFourierTransform(dom_f32, bad_ran, halfcomplex=True)
# Bad sign
with pytest.raises(ValueError):
DiscreteFourierTransform(dom, sign=-1)
def test_dft_init(impl):
# Just check if the code runs at all
shape = (4, 5)
dom = odl.discr_sequence_space(shape)
dom_nonseq = odl.uniform_discr([0, 0], [1, 1], shape)
dom_f32 = odl.discr_sequence_space(shape, dtype='float32')
ran = odl.discr_sequence_space(shape, dtype='complex128')
ran_c64 = odl.discr_sequence_space(shape, dtype='complex64')
ran_hc = odl.discr_sequence_space((3, 5), dtype='complex128')
# Implicit range
DiscreteFourierTransform(dom, impl=impl)
DiscreteFourierTransform(dom_nonseq, impl=impl)
DiscreteFourierTransform(dom_f32, impl=impl)
DiscreteFourierTransform(dom, axes=(0, ), impl=impl)
DiscreteFourierTransform(dom, axes=(0, -1), impl=impl)
DiscreteFourierTransform(dom, axes=(0, ), halfcomplex=True, impl=impl)
DiscreteFourierTransform(dom, impl=impl, sign='+')
# Explicit range
DiscreteFourierTransform(dom, range=ran, impl=impl)
DiscreteFourierTransform(dom_f32, range=ran_c64, impl=impl)
DiscreteFourierTransform(dom, range=ran, axes=(0, ), impl=impl)
DiscreteFourierTransform(dom, range=ran, axes=(0, ), impl=impl, sign='+')
DiscreteFourierTransform(dom, range=ran, axes=(0, -1), impl=impl)
DiscreteFourierTransform(dom,
range=ran_hc,
axes=(0, ),
impl=impl,
halfcomplex=True)
def test_dft_init_plan(impl):
# 2d, halfcomplex, first axis
shape = (4, 5)
axes = 0
dft_dom = odl.discr_sequence_space(shape, dtype='float32')
dft = DiscreteFourierTransform(dft_dom,
impl=impl,
axes=axes,
halfcomplex=True)
if impl != 'pyfftw':
with pytest.raises(ValueError):
dft.init_fftw_plan()
with pytest.raises(ValueError):
dft.clear_fftw_plan()
else:
dft.init_fftw_plan()
# Make sure plan can be used
dft._fftw_plan(dft.domain.element().asarray(),
dft.range.element().asarray())
dft.clear_fftw_plan()
assert dft._fftw_plan is None
def test_dft_call(impl):
# 2d, complex, all ones and random back & forth
shape = (4, 5)
dft_dom = odl.discr_sequence_space(shape, dtype='complex64')
dft = DiscreteFourierTransform(domain=dft_dom, impl=impl)
idft = DiscreteFourierTransformInverse(range=dft_dom, impl=impl)
assert dft.domain == idft.range
assert dft.range == idft.domain
one = dft.domain.one()
one_dft1 = dft(one, flags=('FFTW_ESTIMATE', ))
one_dft2 = dft.inverse.inverse(one, flags=('FFTW_ESTIMATE', ))
one_dft3 = dft.adjoint.adjoint(one, flags=('FFTW_ESTIMATE', ))
true_dft = [
[20, 0, 0, 0, 0], # along all axes by default
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]
]
assert np.allclose(one_dft1, true_dft)
assert np.allclose(one_dft2, true_dft)
assert np.allclose(one_dft3, true_dft)
one_idft1 = idft(one_dft1, flags=('FFTW_ESTIMATE', ))
one_idft2 = dft.inverse(one_dft1, flags=('FFTW_ESTIMATE', ))
one_idft3 = dft.adjoint(one_dft1, flags=('FFTW_ESTIMATE', ))
assert np.allclose(one_idft1, one)
assert np.allclose(one_idft2, one)
assert np.allclose(one_idft3, one)
rand_arr = noise_element(dft_dom)
rand_arr_dft = dft(rand_arr, flags=('FFTW_ESTIMATE', ))
rand_arr_idft = idft(rand_arr_dft, flags=('FFTW_ESTIMATE', ))
assert (rand_arr_idft - rand_arr).norm() < 1e-6
# 2d, halfcomplex, first axis
shape = (4, 5)
axes = 0
dft_dom = odl.discr_sequence_space(shape, dtype='float32')
dft = DiscreteFourierTransform(domain=dft_dom,
impl=impl,
halfcomplex=True,
axes=axes)
idft = DiscreteFourierTransformInverse(range=dft_dom,
impl=impl,
halfcomplex=True,
axes=axes)
assert dft.domain == idft.range
assert dft.range == idft.domain
one = dft.domain.one()
one_dft = dft(one, flags=('FFTW_ESTIMATE', ))
true_dft = [
[4, 4, 4, 4, 4], # transform axis shortened
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0]
]
assert np.allclose(one_dft, true_dft)
one_idft1 = idft(one_dft, flags=('FFTW_ESTIMATE', ))
one_idft2 = dft.inverse(one_dft, flags=('FFTW_ESTIMATE', ))
assert np.allclose(one_idft1, one)
assert np.allclose(one_idft2, one)
rand_arr = noise_element(dft_dom)
rand_arr_dft = dft(rand_arr, flags=('FFTW_ESTIMATE', ))
rand_arr_idft = idft(rand_arr_dft, flags=('FFTW_ESTIMATE', ))
assert (rand_arr_idft - rand_arr).norm() < 1e-6
