def test_ifft2(self):
x = random((30, 20)) + 1j * random((30, 20))
assert_allclose(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
np.fft.ifft2(x),
atol=1e-6)
assert_allclose(np.fft.ifft2(x) * np.sqrt(30 * 20),
np.fft.ifft2(x, norm="ortho"),
atol=1e-6)
def test_identity(self):
maxlen = 512
x = random(maxlen) + 1j * random(maxlen)
# xr = random(maxlen) # local variable 'xr' is assigned to but never used
for i in range(1, maxlen):
assert_allclose(np.fft.ifft(np.fft.fft(x[0:i])),
x[0:i],
atol=1e-12)
def test_fftn(self):
x = random((30, 20, 10)) + 1j * random((30, 20, 10))
assert_allclose(np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1),
axis=0),
np.fft.fftn(x),
atol=1e-6)
assert_allclose(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
np.fft.fftn(x, norm="ortho"),
atol=1e-6)
def test_ifft(self, norm):
x = random(30) + 1j * random(30)
assert_allclose(x,
np.fft.ifft(np.fft.fft(x, norm=norm), norm=norm),
atol=1e-6)
# Ensure we get the correct error message
with pytest.raises(ValueError):
# ,match='Invalid number of FFT data points'):
np.fft.ifft([], norm=norm)
def test_hfft(self):
x = random(14) + 1j * random(14)
x_herm = np.concatenate((random(1), x, random(1)))
# x = np.concatenate((x_herm, x[::-1].conj()))
x = np.concatenate((x_herm, np.conj(x[::-1])))
assert_allclose(np.fft.fft(x), np.fft.hfft(x_herm), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm) / np.sqrt(30),
np.fft.hfft(x_herm, norm="ortho"),
atol=1e-6)
def test_irfftn(self):
x = random((30, 20, 10))
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x)), atol=1e-6)
assert_allclose(x,
np.fft.irfftn(np.fft.rfftn(x, norm="ortho"),
norm="ortho"),
atol=1e-6)
def test_irfft(self):
x = random(30)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x)), atol=1e-6)
assert_allclose(x,
np.fft.irfft(np.fft.rfft(x, norm="ortho"),
norm="ortho"),
atol=1e-6)
def _test_axes(self, op):
x = random((30, 20, 10))
axes = [(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1),
(2, 1, 0)]
for a in axes:
op_tr = op(np.transpose(x, a))
tr_op = np.transpose(op(x, axes=a), a)
assert_allclose(op_tr, tr_op, atol=1e-6)
def test_rfft(self):
x = random(30)
for n in [x.size, 2 * x.size]:
for norm in [None, 'ortho']:
assert_allclose(np.fft.fft(x, n=n, norm=norm)[:(n // 2 + 1)],
np.fft.rfft(x, n=n, norm=norm),
atol=1e-6)
assert_allclose(np.fft.rfft(x, n=n) / np.sqrt(n),
np.fft.rfft(x, n=n, norm="ortho"),
atol=1e-6)
def test_all_1d_norm_preserving(self):
# verify that round-trip transforms are norm-preserving
x = random(30)
# x_norm = np.linalg.norm(x)
x_norm = numpy.linalg.norm(x)
n = x.size * 2
func_pairs = [
(np.fft.fft, np.fft.ifft),
# (np.fft.rfft, np.fft.irfft),
# hfft: order so the first function takes x.size samples
# (necessary for comparison to x_norm above)
# (np.fft.ihfft, np.fft.hfft),
]
for forw, back in func_pairs:
for n in [x.size, 2 * x.size]:
for norm in [None, 'ortho']:
tmp = forw(x, n=n, norm=norm)
tmp = back(tmp, n=n, norm=norm)
assert_allclose(
x_norm,
# np.linalg.norm(tmp),
numpy.linalg.norm(tmp),
atol=1e-6)
def test_fft(self):
x = random(30) + 1j * random(30)
assert_allclose(fft1(x), np.fft.fft(x), atol=1e-6)
assert_allclose(fft1(x) / np.sqrt(30),
np.fft.fft(x, norm="ortho"),
atol=1e-6)
def test_dtypes(self, dtype):
# make sure that all input precisions are accepted and internally
# converted to 64bit
# x = random(30).astype(dtype)
x = random(30).astype(dtype)
assert_allclose(np.fft.ifft(np.fft.fft(x)), x, atol=1e-6)
def test_rfftn(self):
x = random((30, 20, 10))
assert_allclose(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x), atol=1e-6)
assert_allclose(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
np.fft.rfftn(x, norm="ortho"),
atol=1e-6)