Edit File: test_fftpack.py
from __future__ import division, absolute_import, print_function import numpy as np from numpy.random import random from numpy.testing import TestCase, run_module_suite, assert_array_almost_equal from numpy.testing import assert_array_equal 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(TestCase): def test_fft_n(self): self.assertRaises(ValueError, np.fft.fft, [1, 2, 3], 0) class TestFFT1D(TestCase): 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(TestCase): 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) if __name__ == "__main__": run_module_suite()