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\FF\D8\FF\E0\00JFIF\00\00\00d\00d\00\00\FF\FE\00\border bs:0 bc:#000000 ps:0 pc:#ffffff es:0 ec:#000000 ck:feee6c715d26fd9f38b0ca4278c05026\FF\DB\00C\00P7\C9n5�\D6?\BD�\9Ds\EBp\9F[`8m\B7)o\B5\E8\E6I\99\FE3]]A2\BA\8Cw\D6E\93\\DEv\C8\009\F2\F1NI?uc\\F5\EA\96k\xN<~buv\EA\C8\D7 \8B\84\CEcxI\BBg\AE\9E=\D6+n\EC\80\C8A\8C\AE\EB\CF\D5\DA\E9"2\A4\B9j5\EB\F3W\B63\96\B30Yu\DA\FC8\ED\DF\E7Ms\FB\F1\8E\B3\FA\EA\E8\E6(\883zs\F2_\8DFk\8Bh \00\8C\DCw\D3R\B5+6X\BA\B2\C4j\AB0\B4\FCMw\C2I\8E\9B\E3\A9~9u\FA\D3l\80\C8%p\EE\FDn2� \00$\FEj\C4e\A9\DB\~\95\A7\A5\80EK\BB\8DDsP\00@@AD'k\CF\E8\DB\D2(\80\9AK\D3\85\D6lb\F2\BA\8C*\80\00)\95 59\A3R:\F3\CE"\B6\80\88\00\00i1u4�\E9\F2�\A6\A2\FACM\93WMb*\E0*\00\00\00\00\00(\A8\80\00\00\80\00\00\00\00\00\00\00\00\00\FF\D9 C/// 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) assert_array_almost_equal(np.fft.fft(x)[:16], np.fft.rfft(x)) assert_array_almost_equal(np.fft.rfft(x) / np.sqrt(30), np.fft.rfft(x, 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))