You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
186 lines
6.9 KiB
Python
186 lines
6.9 KiB
Python
6 years ago
|
from __future__ import division, absolute_import, print_function
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from numpy.random import random
|
||
|
|
from numpy.testing import (
|
||
|
|
assert_array_almost_equal, assert_array_equal, assert_raises,
|
||
|
|
)
|
||
|
|
import threading
|
||
|
|
import sys
|
||
|
|
if sys.version_info[0] >= 3:
|
||
|
|
import queue
|
||
|
|
else:
|
||
|
|
import Queue as queue
|
||
|
|
|
||
|
|
|
||
|
|
def fft1(x):
|
||
|
|
L = len(x)
|
||
|
|
phase = -2j*np.pi*(np.arange(L)/float(L))
|
||
|
|
phase = np.arange(L).reshape(-1, 1) * phase
|
||
|
|
return np.sum(x*np.exp(phase), axis=1)
|
||
|
|
|
||
|
|
|
||
|
|
class TestFFTShift(object):
|
||
|
|
|
||
|
|
def test_fft_n(self):
|
||
|
|
assert_raises(ValueError, np.fft.fft, [1, 2, 3], 0)
|
||
|
|
|
||
|
|
|
||
|
|
class TestFFT1D(object):
|
||
|
|
|
||
|
|
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"))
|
||
|
|
|
||
|
|
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_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_ifft2(self):
|
||
|
|
x = random((30, 20)) + 1j*random((30, 20))
|
||
|
|
assert_array_almost_equal(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
|
||
|
|
np.fft.ifft2(x))
|
||
|
|
assert_array_almost_equal(np.fft.ifft2(x) * np.sqrt(30 * 20),
|
||
|
|
np.fft.ifft2(x, norm="ortho"))
|
||
|
|
|
||
|
|
def test_fftn(self):
|
||
|
|
x = random((30, 20, 10)) + 1j*random((30, 20, 10))
|
||
|
|
assert_array_almost_equal(
|
||
|
|
np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1), axis=0),
|
||
|
|
np.fft.fftn(x))
|
||
|
|
assert_array_almost_equal(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
|
||
|
|
np.fft.fftn(x, norm="ortho"))
|
||
|
|
|
||
|
|
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_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_irfft(self):
|
||
|
|
x = random(30)
|
||
|
|
assert_array_almost_equal(x, np.fft.irfft(np.fft.rfft(x)))
|
||
|
|
assert_array_almost_equal(
|
||
|
|
x, np.fft.irfft(np.fft.rfft(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_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_rfftn(self):
|
||
|
|
x = random((30, 20, 10))
|
||
|
|
assert_array_almost_equal(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x))
|
||
|
|
assert_array_almost_equal(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
|
||
|
|
np.fft.rfftn(x, norm="ortho"))
|
||
|
|
|
||
|
|
def test_irfftn(self):
|
||
|
|
x = random((30, 20, 10))
|
||
|
|
assert_array_almost_equal(x, np.fft.irfftn(np.fft.rfftn(x)))
|
||
|
|
assert_array_almost_equal(
|
||
|
|
x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"), 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_ihttf(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(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)))
|
||
|
|
assert_array_almost_equal(
|
||
|
|
x_herm, np.fft.ihfft(np.fft.hfft(x_herm, norm="ortho"),
|
||
|
|
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))
|
||
|
|
|
||
|
|
class TestFFTThreadSafe(object):
|
||
|
|
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)
|