308 lines
12 KiB
Python
308 lines
12 KiB
Python
import numpy as np
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import pytest
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from numpy.random import random
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from numpy.testing import (
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assert_array_equal, assert_raises, assert_allclose
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)
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import threading
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import queue
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def fft1(x):
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L = len(x)
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phase = -2j*np.pi*(np.arange(L)/float(L))
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phase = np.arange(L).reshape(-1, 1) * phase
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return np.sum(x*np.exp(phase), axis=1)
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class TestFFTShift:
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def test_fft_n(self):
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assert_raises(ValueError, np.fft.fft, [1, 2, 3], 0)
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class TestFFT1D:
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def test_identity(self):
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maxlen = 512
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x = random(maxlen) + 1j*random(maxlen)
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xr = random(maxlen)
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for i in range(1, maxlen):
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assert_allclose(np.fft.ifft(np.fft.fft(x[0:i])), x[0:i],
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atol=1e-12)
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assert_allclose(np.fft.irfft(np.fft.rfft(xr[0:i]), i),
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xr[0:i], atol=1e-12)
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def test_fft(self):
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x = random(30) + 1j*random(30)
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assert_allclose(fft1(x), np.fft.fft(x), atol=1e-6)
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assert_allclose(fft1(x), np.fft.fft(x, norm="backward"), atol=1e-6)
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assert_allclose(fft1(x) / np.sqrt(30),
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np.fft.fft(x, norm="ortho"), atol=1e-6)
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assert_allclose(fft1(x) / 30.,
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np.fft.fft(x, norm="forward"), atol=1e-6)
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@pytest.mark.parametrize('norm', (None, 'backward', 'ortho', 'forward'))
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def test_ifft(self, norm):
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x = random(30) + 1j*random(30)
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assert_allclose(
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x, np.fft.ifft(np.fft.fft(x, norm=norm), norm=norm),
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atol=1e-6)
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# Ensure we get the correct error message
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with pytest.raises(ValueError,
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match='Invalid number of FFT data points'):
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np.fft.ifft([], norm=norm)
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def test_fft2(self):
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x = random((30, 20)) + 1j*random((30, 20))
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assert_allclose(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
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np.fft.fft2(x), atol=1e-6)
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assert_allclose(np.fft.fft2(x),
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np.fft.fft2(x, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.fft2(x) / np.sqrt(30 * 20),
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np.fft.fft2(x, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.fft2(x) / (30. * 20.),
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np.fft.fft2(x, norm="forward"), atol=1e-6)
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def test_ifft2(self):
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x = random((30, 20)) + 1j*random((30, 20))
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assert_allclose(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
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np.fft.ifft2(x), atol=1e-6)
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assert_allclose(np.fft.ifft2(x),
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np.fft.ifft2(x, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.ifft2(x) * np.sqrt(30 * 20),
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np.fft.ifft2(x, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.ifft2(x) * (30. * 20.),
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np.fft.ifft2(x, norm="forward"), atol=1e-6)
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def test_fftn(self):
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x = random((30, 20, 10)) + 1j*random((30, 20, 10))
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assert_allclose(
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np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1), axis=0),
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np.fft.fftn(x), atol=1e-6)
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assert_allclose(np.fft.fftn(x),
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np.fft.fftn(x, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
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np.fft.fftn(x, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.fftn(x) / (30. * 20. * 10.),
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np.fft.fftn(x, norm="forward"), atol=1e-6)
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def test_ifftn(self):
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x = random((30, 20, 10)) + 1j*random((30, 20, 10))
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assert_allclose(
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np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
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np.fft.ifftn(x), atol=1e-6)
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assert_allclose(np.fft.ifftn(x),
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np.fft.ifftn(x, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
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np.fft.ifftn(x, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.ifftn(x) * (30. * 20. * 10.),
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np.fft.ifftn(x, norm="forward"), atol=1e-6)
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def test_rfft(self):
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x = random(30)
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for n in [x.size, 2*x.size]:
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for norm in [None, 'backward', 'ortho', 'forward']:
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assert_allclose(
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np.fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
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np.fft.rfft(x, n=n, norm=norm), atol=1e-6)
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assert_allclose(
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np.fft.rfft(x, n=n),
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np.fft.rfft(x, n=n, norm="backward"), atol=1e-6)
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assert_allclose(
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np.fft.rfft(x, n=n) / np.sqrt(n),
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np.fft.rfft(x, n=n, norm="ortho"), atol=1e-6)
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assert_allclose(
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np.fft.rfft(x, n=n) / n,
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np.fft.rfft(x, n=n, norm="forward"), atol=1e-6)
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def test_irfft(self):
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x = random(30)
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assert_allclose(x, np.fft.irfft(np.fft.rfft(x)), atol=1e-6)
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assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="backward"),
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norm="backward"), atol=1e-6)
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assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="ortho"),
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norm="ortho"), atol=1e-6)
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assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="forward"),
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norm="forward"), atol=1e-6)
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def test_rfft2(self):
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x = random((30, 20))
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assert_allclose(np.fft.fft2(x)[:, :11], np.fft.rfft2(x), atol=1e-6)
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assert_allclose(np.fft.rfft2(x),
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np.fft.rfft2(x, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.rfft2(x) / np.sqrt(30 * 20),
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np.fft.rfft2(x, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.rfft2(x) / (30. * 20.),
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np.fft.rfft2(x, norm="forward"), atol=1e-6)
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def test_irfft2(self):
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x = random((30, 20))
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assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x)), atol=1e-6)
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assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="backward"),
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norm="backward"), atol=1e-6)
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assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"),
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norm="ortho"), atol=1e-6)
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assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="forward"),
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norm="forward"), atol=1e-6)
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def test_rfftn(self):
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x = random((30, 20, 10))
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assert_allclose(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x), atol=1e-6)
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assert_allclose(np.fft.rfftn(x),
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np.fft.rfftn(x, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
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np.fft.rfftn(x, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.rfftn(x) / (30. * 20. * 10.),
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np.fft.rfftn(x, norm="forward"), atol=1e-6)
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def test_irfftn(self):
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x = random((30, 20, 10))
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assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x)), atol=1e-6)
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assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="backward"),
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norm="backward"), atol=1e-6)
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assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"),
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norm="ortho"), atol=1e-6)
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assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="forward"),
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norm="forward"), atol=1e-6)
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def test_hfft(self):
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x = random(14) + 1j*random(14)
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x_herm = np.concatenate((random(1), x, random(1)))
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x = np.concatenate((x_herm, x[::-1].conj()))
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assert_allclose(np.fft.fft(x), np.fft.hfft(x_herm), atol=1e-6)
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assert_allclose(np.fft.hfft(x_herm),
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np.fft.hfft(x_herm, norm="backward"), atol=1e-6)
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assert_allclose(np.fft.hfft(x_herm) / np.sqrt(30),
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np.fft.hfft(x_herm, norm="ortho"), atol=1e-6)
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assert_allclose(np.fft.hfft(x_herm) / 30.,
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np.fft.hfft(x_herm, norm="forward"), atol=1e-6)
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def test_ihfft(self):
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x = random(14) + 1j*random(14)
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x_herm = np.concatenate((random(1), x, random(1)))
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x = np.concatenate((x_herm, x[::-1].conj()))
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assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)), atol=1e-6)
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assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
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norm="backward"), norm="backward"), atol=1e-6)
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assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
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norm="ortho"), norm="ortho"), atol=1e-6)
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assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
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norm="forward"), norm="forward"), atol=1e-6)
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@pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
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np.fft.rfftn, np.fft.irfftn])
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def test_axes(self, op):
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x = random((30, 20, 10))
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axes = [(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)]
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for a in axes:
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op_tr = op(np.transpose(x, a))
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tr_op = np.transpose(op(x, axes=a), a)
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assert_allclose(op_tr, tr_op, atol=1e-6)
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def test_all_1d_norm_preserving(self):
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# verify that round-trip transforms are norm-preserving
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x = random(30)
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x_norm = np.linalg.norm(x)
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n = x.size * 2
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func_pairs = [(np.fft.fft, np.fft.ifft),
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(np.fft.rfft, np.fft.irfft),
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# hfft: order so the first function takes x.size samples
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# (necessary for comparison to x_norm above)
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(np.fft.ihfft, np.fft.hfft),
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]
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for forw, back in func_pairs:
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for n in [x.size, 2*x.size]:
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for norm in [None, 'backward', 'ortho', 'forward']:
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tmp = forw(x, n=n, norm=norm)
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tmp = back(tmp, n=n, norm=norm)
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assert_allclose(x_norm,
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np.linalg.norm(tmp), atol=1e-6)
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@pytest.mark.parametrize("dtype", [np.half, np.single, np.double,
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np.longdouble])
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def test_dtypes(self, dtype):
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# make sure that all input precisions are accepted and internally
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# converted to 64bit
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x = random(30).astype(dtype)
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assert_allclose(np.fft.ifft(np.fft.fft(x)), x, atol=1e-6)
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assert_allclose(np.fft.irfft(np.fft.rfft(x)), x, atol=1e-6)
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@pytest.mark.parametrize(
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"dtype",
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[np.float32, np.float64, np.complex64, np.complex128])
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@pytest.mark.parametrize("order", ["F", 'non-contiguous'])
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@pytest.mark.parametrize(
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"fft",
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[np.fft.fft, np.fft.fft2, np.fft.fftn,
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np.fft.ifft, np.fft.ifft2, np.fft.ifftn])
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def test_fft_with_order(dtype, order, fft):
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# Check that FFT/IFFT produces identical results for C, Fortran and
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# non contiguous arrays
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rng = np.random.RandomState(42)
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X = rng.rand(8, 7, 13).astype(dtype, copy=False)
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# See discussion in pull/14178
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_tol = 8.0 * np.sqrt(np.log2(X.size)) * np.finfo(X.dtype).eps
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if order == 'F':
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Y = np.asfortranarray(X)
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else:
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# Make a non contiguous array
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Y = X[::-1]
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X = np.ascontiguousarray(X[::-1])
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if fft.__name__.endswith('fft'):
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for axis in range(3):
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X_res = fft(X, axis=axis)
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Y_res = fft(Y, axis=axis)
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assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
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elif fft.__name__.endswith(('fft2', 'fftn')):
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axes = [(0, 1), (1, 2), (0, 2)]
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if fft.__name__.endswith('fftn'):
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axes.extend([(0,), (1,), (2,), None])
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for ax in axes:
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X_res = fft(X, axes=ax)
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Y_res = fft(Y, axes=ax)
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assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
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else:
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raise ValueError()
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class TestFFTThreadSafe:
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threads = 16
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input_shape = (800, 200)
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def _test_mtsame(self, func, *args):
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def worker(args, q):
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q.put(func(*args))
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q = queue.Queue()
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expected = func(*args)
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# Spin off a bunch of threads to call the same function simultaneously
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t = [threading.Thread(target=worker, args=(args, q))
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for i in range(self.threads)]
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[x.start() for x in t]
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[x.join() for x in t]
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# Make sure all threads returned the correct value
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for i in range(self.threads):
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assert_array_equal(q.get(timeout=5), expected,
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'Function returned wrong value in multithreaded context')
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def test_fft(self):
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a = np.ones(self.input_shape) * 1+0j
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self._test_mtsame(np.fft.fft, a)
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def test_ifft(self):
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a = np.ones(self.input_shape) * 1+0j
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self._test_mtsame(np.fft.ifft, a)
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def test_rfft(self):
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a = np.ones(self.input_shape)
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self._test_mtsame(np.fft.rfft, a)
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def test_irfft(self):
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a = np.ones(self.input_shape) * 1+0j
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self._test_mtsame(np.fft.irfft, a)
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