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365 lines
14 KiB
Python
365 lines
14 KiB
Python
import queue
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import threading
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import multiprocessing
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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_almost_equal, assert_array_equal, assert_allclose
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)
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from pytest import raises as assert_raises
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import scipy.fft as fft
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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(object):
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def test_fft_n(self):
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assert_raises(ValueError, fft.fft, [1, 2, 3], 0)
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class TestFFT1D(object):
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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_array_almost_equal(fft.ifft(fft.fft(x[0:i])), x[0:i],
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decimal=12)
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assert_array_almost_equal(fft.irfft(fft.rfft(xr[0:i]),i),
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xr[0:i], decimal=12)
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def test_fft(self):
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x = random(30) + 1j*random(30)
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expect = fft1(x)
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assert_array_almost_equal(expect, fft.fft(x))
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assert_array_almost_equal(expect, fft.fft(x, norm="backward"))
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assert_array_almost_equal(expect / np.sqrt(30),
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fft.fft(x, norm="ortho"))
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assert_array_almost_equal(expect / 30, fft.fft(x, norm="forward"))
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def test_ifft(self):
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x = random(30) + 1j*random(30)
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assert_array_almost_equal(x, fft.ifft(fft.fft(x)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x, fft.ifft(fft.fft(x, norm=norm), 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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expect = fft.fft(fft.fft(x, axis=1), axis=0)
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assert_array_almost_equal(expect, fft.fft2(x))
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assert_array_almost_equal(expect, fft.fft2(x, norm="backward"))
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assert_array_almost_equal(expect / np.sqrt(30 * 20),
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fft.fft2(x, norm="ortho"))
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assert_array_almost_equal(expect / (30 * 20),
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fft.fft2(x, norm="forward"))
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def test_ifft2(self):
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x = random((30, 20)) + 1j*random((30, 20))
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expect = fft.ifft(fft.ifft(x, axis=1), axis=0)
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assert_array_almost_equal(expect, fft.ifft2(x))
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assert_array_almost_equal(expect, fft.ifft2(x, norm="backward"))
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assert_array_almost_equal(expect * np.sqrt(30 * 20),
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fft.ifft2(x, norm="ortho"))
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assert_array_almost_equal(expect * (30 * 20),
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fft.ifft2(x, norm="forward"))
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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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expect = fft.fft(fft.fft(fft.fft(x, axis=2), axis=1), axis=0)
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assert_array_almost_equal(expect, fft.fftn(x))
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assert_array_almost_equal(expect, fft.fftn(x, norm="backward"))
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assert_array_almost_equal(expect / np.sqrt(30 * 20 * 10),
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fft.fftn(x, norm="ortho"))
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assert_array_almost_equal(expect / (30 * 20 * 10),
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fft.fftn(x, norm="forward"))
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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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expect = fft.ifft(fft.ifft(fft.ifft(x, axis=2), axis=1), axis=0)
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assert_array_almost_equal(expect, fft.ifftn(x))
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assert_array_almost_equal(expect, fft.ifftn(x, norm="backward"))
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assert_array_almost_equal(fft.ifftn(x) * np.sqrt(30 * 20 * 10),
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fft.ifftn(x, norm="ortho"))
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assert_array_almost_equal(expect * (30 * 20 * 10),
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fft.ifftn(x, norm="forward"))
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def test_rfft(self):
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x = random(29)
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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_array_almost_equal(
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fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
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fft.rfft(x, n=n, norm=norm))
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assert_array_almost_equal(fft.rfft(x, n=n) / np.sqrt(n),
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fft.rfft(x, n=n, norm="ortho"))
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def test_irfft(self):
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x = random(30)
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assert_array_almost_equal(x, fft.irfft(fft.rfft(x)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x, fft.irfft(fft.rfft(x, norm=norm), norm=norm))
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def test_rfft2(self):
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x = random((30, 20))
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expect = fft.fft2(x)[:, :11]
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assert_array_almost_equal(expect, fft.rfft2(x))
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assert_array_almost_equal(expect, fft.rfft2(x, norm="backward"))
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assert_array_almost_equal(expect / np.sqrt(30 * 20),
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fft.rfft2(x, norm="ortho"))
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assert_array_almost_equal(expect / (30 * 20),
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fft.rfft2(x, norm="forward"))
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def test_irfft2(self):
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x = random((30, 20))
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assert_array_almost_equal(x, fft.irfft2(fft.rfft2(x)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x, fft.irfft2(fft.rfft2(x, norm=norm), norm=norm))
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def test_rfftn(self):
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x = random((30, 20, 10))
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expect = fft.fftn(x)[:, :, :6]
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assert_array_almost_equal(expect, fft.rfftn(x))
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assert_array_almost_equal(expect, fft.rfftn(x, norm="backward"))
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assert_array_almost_equal(expect / np.sqrt(30 * 20 * 10),
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fft.rfftn(x, norm="ortho"))
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assert_array_almost_equal(expect / (30 * 20 * 10),
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fft.rfftn(x, norm="forward"))
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def test_irfftn(self):
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x = random((30, 20, 10))
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assert_array_almost_equal(x, fft.irfftn(fft.rfftn(x)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x, fft.irfftn(fft.rfftn(x, norm=norm), norm=norm))
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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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expect = fft.fft(x)
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assert_array_almost_equal(expect, fft.hfft(x_herm))
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assert_array_almost_equal(expect, fft.hfft(x_herm, norm="backward"))
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assert_array_almost_equal(expect / np.sqrt(30),
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fft.hfft(x_herm, norm="ortho"))
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assert_array_almost_equal(expect / 30,
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fft.hfft(x_herm, norm="forward"))
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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_array_almost_equal(x_herm, fft.ihfft(fft.hfft(x_herm)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x_herm, fft.ihfft(fft.hfft(x_herm, norm=norm), norm=norm))
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def test_hfft2(self):
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x = random((30, 20))
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assert_array_almost_equal(x, fft.hfft2(fft.ihfft2(x)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x, fft.hfft2(fft.ihfft2(x, norm=norm), norm=norm))
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def test_ihfft2(self):
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x = random((30, 20))
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expect = fft.ifft2(x)[:, :11]
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assert_array_almost_equal(expect, fft.ihfft2(x))
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assert_array_almost_equal(expect, fft.ihfft2(x, norm="backward"))
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assert_array_almost_equal(expect * np.sqrt(30 * 20),
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fft.ihfft2(x, norm="ortho"))
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assert_array_almost_equal(expect * (30 * 20),
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fft.ihfft2(x, norm="forward"))
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def test_hfftn(self):
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x = random((30, 20, 10))
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assert_array_almost_equal(x, fft.hfftn(fft.ihfftn(x)))
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for norm in ["backward", "ortho", "forward"]:
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assert_array_almost_equal(
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x, fft.hfftn(fft.ihfftn(x, norm=norm), norm=norm))
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def test_ihfftn(self):
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x = random((30, 20, 10))
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expect = fft.ifftn(x)[:, :, :6]
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assert_array_almost_equal(expect, fft.ihfftn(x))
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assert_array_almost_equal(expect, fft.ihfftn(x, norm="backward"))
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assert_array_almost_equal(expect * np.sqrt(30 * 20 * 10),
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fft.ihfftn(x, norm="ortho"))
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assert_array_almost_equal(expect * (30 * 20 * 10),
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fft.ihfftn(x, norm="forward"))
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@pytest.mark.parametrize("op", [fft.fftn, fft.ifftn,
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fft.rfftn, fft.irfftn,
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fft.hfftn, fft.ihfftn])
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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_array_almost_equal(op_tr, tr_op)
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@pytest.mark.parametrize("op", [fft.fft2, fft.ifft2,
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fft.rfft2, fft.irfft2,
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fft.hfft2, fft.ihfft2,
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fft.fftn, fft.ifftn,
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fft.rfftn, fft.irfftn,
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fft.hfftn, fft.ihfftn])
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def test_axes_subset_with_shape(self, op):
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x = random((16, 8, 4))
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axes = [(0, 1, 2), (0, 2, 1), (1, 2, 0)]
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for a in axes:
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# different shape on the first two axes
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shape = tuple([2*x.shape[ax] if ax in a[:2] else x.shape[ax]
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for ax in range(x.ndim)])
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# transform only the first two axes
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op_tr = op(np.transpose(x, a), s=shape[:2], axes=(0, 1))
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tr_op = np.transpose(op(x, s=shape[:2], axes=a[:2]), a)
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assert_array_almost_equal(op_tr, tr_op)
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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 = [(fft.fft, fft.ifft),
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(fft.rfft, 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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(fft.ihfft, 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 ['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_array_almost_equal(x_norm,
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np.linalg.norm(tmp))
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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
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x = random(30).astype(dtype)
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assert_array_almost_equal(fft.ifft(fft.fft(x)), x)
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assert_array_almost_equal(fft.irfft(fft.rfft(x)), x)
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assert_array_almost_equal(fft.hfft(fft.ihfft(x), len(x)), x)
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@pytest.mark.parametrize(
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"dtype",
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[np.float32, np.float64, np.longfloat,
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np.complex64, np.complex128, np.longcomplex])
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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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[fft.fft, fft.fft2, fft.fftn,
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fft.ifft, fft.ifft2, 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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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_array_almost_equal(X_res, Y_res)
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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_array_almost_equal(X_res, Y_res)
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else:
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raise ValueError
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class TestFFTThreadSafe(object):
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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, dtype=np.complex128)
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self._test_mtsame(fft.fft, a)
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def test_ifft(self):
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a = np.full(self.input_shape, 1+0j)
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self._test_mtsame(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(fft.rfft, a)
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def test_irfft(self):
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a = np.full(self.input_shape, 1+0j)
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self._test_mtsame(fft.irfft, a)
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def test_hfft(self):
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a = np.ones(self.input_shape, np.complex64)
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self._test_mtsame(fft.hfft, a)
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def test_ihfft(self):
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a = np.ones(self.input_shape)
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self._test_mtsame(fft.ihfft, a)
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@pytest.mark.parametrize("func", [fft.fft, fft.ifft, fft.rfft, fft.irfft])
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def test_multiprocess(func):
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# Test that fft still works after fork (gh-10422)
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with multiprocessing.Pool(2) as p:
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res = p.map(func, [np.ones(100) for _ in range(4)])
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expect = func(np.ones(100))
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for x in res:
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assert_allclose(x, expect)
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class TestIRFFTN(object):
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def test_not_last_axis_success(self):
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ar, ai = np.random.random((2, 16, 8, 32))
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a = ar + 1j*ai
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axes = (-2,)
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# Should not raise error
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fft.irfftn(a, axes=axes)
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