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_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_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
