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import numpy as np
import pytest
from numpy.random import random
from numpy.testing import (
assert_array_equal, assert_raises, assert_allclose, IS_WASM
)
import threading
import queue
def fft1(x):
L = len(x)
phase = -2j * np.pi * (np.arange(L) / L)
phase = np.arange(L).reshape(-1, 1) * phase
return np.sum(x*np.exp(phase), axis=1)
class TestFFTShift:
def test_fft_n(self):
assert_raises(ValueError, np.fft.fft, [1, 2, 3], 0)
class TestFFT1D:
def test_identity(self):
maxlen = 512
x = random(maxlen) + 1j*random(maxlen)
xr = random(maxlen)
for i in range(1, maxlen):
assert_allclose(np.fft.ifft(np.fft.fft(x[0:i])), x[0:i],
atol=1e-12)
assert_allclose(np.fft.irfft(np.fft.rfft(xr[0:i]), i),
xr[0:i], atol=1e-12)
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.fft.fft(x, norm="backward"), atol=1e-6)
assert_allclose(fft1(x) / np.sqrt(30),
np.fft.fft(x, norm="ortho"), atol=1e-6)
assert_allclose(fft1(x) / 30.,
np.fft.fft(x, norm="forward"), atol=1e-6)
@pytest.mark.parametrize('norm', (None, 'backward', 'ortho', 'forward'))
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_fft2(self):
x = random((30, 20)) + 1j*random((30, 20))
assert_allclose(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
np.fft.fft2(x), atol=1e-6)
assert_allclose(np.fft.fft2(x),
np.fft.fft2(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.fft2(x) / np.sqrt(30 * 20),
np.fft.fft2(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.fft2(x) / (30. * 20.),
np.fft.fft2(x, norm="forward"), atol=1e-6)
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.fft.ifft2(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.ifft2(x) * np.sqrt(30 * 20),
np.fft.ifft2(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.ifft2(x) * (30. * 20.),
np.fft.ifft2(x, norm="forward"), atol=1e-6)
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.fft.fftn(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
np.fft.fftn(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.fftn(x) / (30. * 20. * 10.),
np.fft.fftn(x, norm="forward"), atol=1e-6)
def test_ifftn(self):
x = random((30, 20, 10)) + 1j*random((30, 20, 10))
assert_allclose(
np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
np.fft.ifftn(x), atol=1e-6)
assert_allclose(np.fft.ifftn(x),
np.fft.ifftn(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
np.fft.ifftn(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.ifftn(x) * (30. * 20. * 10.),
np.fft.ifftn(x, norm="forward"), atol=1e-6)
def test_rfft(self):
x = random(30)
for n in [x.size, 2*x.size]:
for norm in [None, 'backward', 'ortho', 'forward']:
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.fft.rfft(x, n=n, norm="backward"), 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)
assert_allclose(
np.fft.rfft(x, n=n) / n,
np.fft.rfft(x, n=n, norm="forward"), 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="backward"),
norm="backward"), atol=1e-6)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="ortho"),
norm="ortho"), atol=1e-6)
assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="forward"),
norm="forward"), atol=1e-6)
def test_rfft2(self):
x = random((30, 20))
assert_allclose(np.fft.fft2(x)[:, :11], np.fft.rfft2(x), atol=1e-6)
assert_allclose(np.fft.rfft2(x),
np.fft.rfft2(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.rfft2(x) / np.sqrt(30 * 20),
np.fft.rfft2(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.rfft2(x) / (30. * 20.),
np.fft.rfft2(x, norm="forward"), atol=1e-6)
def test_irfft2(self):
x = random((30, 20))
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x)), atol=1e-6)
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="backward"),
norm="backward"), atol=1e-6)
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"),
norm="ortho"), atol=1e-6)
assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="forward"),
norm="forward"), 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.fft.rfftn(x, norm="backward"), atol=1e-6)
assert_allclose(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
np.fft.rfftn(x, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.rfftn(x) / (30. * 20. * 10.),
np.fft.rfftn(x, norm="forward"), 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="backward"),
norm="backward"), atol=1e-6)
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"),
norm="ortho"), atol=1e-6)
assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="forward"),
norm="forward"), atol=1e-6)
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_allclose(np.fft.fft(x), np.fft.hfft(x_herm), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm),
np.fft.hfft(x_herm, norm="backward"), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm) / np.sqrt(30),
np.fft.hfft(x_herm, norm="ortho"), atol=1e-6)
assert_allclose(np.fft.hfft(x_herm) / 30.,
np.fft.hfft(x_herm, norm="forward"), atol=1e-6)
def test_ihfft(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_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)), atol=1e-6)
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
norm="backward"), norm="backward"), atol=1e-6)
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
norm="ortho"), norm="ortho"), atol=1e-6)
assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
norm="forward"), norm="forward"), atol=1e-6)
@pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
np.fft.rfftn, np.fft.irfftn])
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_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, 'backward', 'ortho', 'forward']:
tmp = forw(x, n=n, norm=norm)
tmp = back(tmp, n=n, norm=norm)
assert_allclose(x_norm,
np.linalg.norm(tmp), atol=1e-6)
@pytest.mark.parametrize("dtype", [np.half, np.single, np.double,
np.longdouble])
def test_dtypes(self, dtype):
# make sure that all input precisions are accepted and internally
# converted to 64bit
x = random(30).astype(dtype)
assert_allclose(np.fft.ifft(np.fft.fft(x)), x, atol=1e-6)
assert_allclose(np.fft.irfft(np.fft.rfft(x)), x, atol=1e-6)
@pytest.mark.parametrize(
"dtype",
[np.float32, np.float64, np.complex64, np.complex128])
@pytest.mark.parametrize("order", ["F", 'non-contiguous'])
@pytest.mark.parametrize(
"fft",
[np.fft.fft, np.fft.fft2, np.fft.fftn,
np.fft.ifft, np.fft.ifft2, np.fft.ifftn])
def test_fft_with_order(dtype, order, fft):
# Check that FFT/IFFT produces identical results for C, Fortran and
# non contiguous arrays
rng = np.random.RandomState(42)
X = rng.rand(8, 7, 13).astype(dtype, copy=False)
# See discussion in pull/14178
_tol = 8.0 * np.sqrt(np.log2(X.size)) * np.finfo(X.dtype).eps
if order == 'F':
Y = np.asfortranarray(X)
else:
# Make a non contiguous array
Y = X[::-1]
X = np.ascontiguousarray(X[::-1])
if fft.__name__.endswith('fft'):
for axis in range(3):
X_res = fft(X, axis=axis)
Y_res = fft(Y, axis=axis)
assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
elif fft.__name__.endswith(('fft2', 'fftn')):
axes = [(0, 1), (1, 2), (0, 2)]
if fft.__name__.endswith('fftn'):
axes.extend([(0,), (1,), (2,), None])
for ax in axes:
X_res = fft(X, axes=ax)
Y_res = fft(Y, axes=ax)
assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
else:
raise ValueError()
@pytest.mark.skipif(IS_WASM, reason="Cannot start thread")
class TestFFTThreadSafe:
threads = 16
input_shape = (800, 200)
def _test_mtsame(self, func, *args):
def worker(args, q):
q.put(func(*args))
q = queue.Queue()
expected = func(*args)
# Spin off a bunch of threads to call the same function simultaneously
t = [threading.Thread(target=worker, args=(args, q))
for i in range(self.threads)]
[x.start() for x in t]
[x.join() for x in t]
# Make sure all threads returned the correct value
for i in range(self.threads):
assert_array_equal(q.get(timeout=5), expected,
'Function returned wrong value in multithreaded context')
def test_fft(self):
a = np.ones(self.input_shape) * 1+0j
self._test_mtsame(np.fft.fft, a)
def test_ifft(self):
a = np.ones(self.input_shape) * 1+0j
self._test_mtsame(np.fft.ifft, a)
def test_rfft(self):
a = np.ones(self.input_shape)
self._test_mtsame(np.fft.rfft, a)
def test_irfft(self):
a = np.ones(self.input_shape) * 1+0j
self._test_mtsame(np.fft.irfft, a)
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