def test_ifftn(self):
x = random((30, 20, 10)) + 1j*random((30, 20, 10))
assert_array_almost_equal(
np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
np.fft.ifftn(x))
assert_array_almost_equal(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
np.fft.ifftn(x, norm="ortho"))
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()))
assert_array_almost_equal(np.fft.fft(x), np.fft.hfft(x_herm))
assert_array_almost_equal(np.fft.hfft(x_herm) / np.sqrt(30),
np.fft.hfft(x_herm, norm="ortho"))
def test_rfft(self):
x = random(30)
for n in [x.size, 2*x.size]:
for norm in [None, 'ortho']:
assert_array_almost_equal(
np.fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
np.fft.rfft(x, n=n, norm=norm))
assert_array_almost_equal(np.fft.rfft(x, n=n) / np.sqrt(n),
np.fft.rfft(x, n=n, norm="ortho"))
def test_all_1d_norm_preserving(self):
# verify that round-trip transforms are norm-preserving
x = random(30)
x_norm = np.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_array_almost_equal(x_norm,
np.linalg.norm(tmp))
def test_irfft2(self):
x = random((30, 20))
assert_array_almost_equal(x, np.fft.irfft2(np.fft.rfft2(x)))
assert_array_almost_equal(
x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"), norm="ortho"))
def test_rfft2(self):
x = random((30, 20))
assert_array_almost_equal(np.fft.fft2(x)[:, :11], np.fft.rfft2(x))
assert_array_almost_equal(np.fft.rfft2(x) / np.sqrt(30 * 20),
np.fft.rfft2(x, norm="ortho"))
def test_fft2(self):
x = random((30, 20)) + 1j*random((30, 20))
assert_array_almost_equal(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
np.fft.fft2(x))
assert_array_almost_equal(np.fft.fft2(x) / np.sqrt(30 * 20),
np.fft.fft2(x, norm="ortho"))
def test_ifft(self):
x = random(30) + 1j*random(30)
assert_array_almost_equal(x, np.fft.ifft(np.fft.fft(x)))
assert_array_almost_equal(
x, np.fft.ifft(np.fft.fft(x, norm="ortho"), norm="ortho"))
def test_fft(self):
x = random(30) + 1j*random(30)
assert_array_almost_equal(fft1(x), np.fft.fft(x))
assert_array_almost_equal(fft1(x) / np.sqrt(30),
np.fft.fft(x, norm="ortho"))
