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test_helper.py
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"""Test functions for fftpack.helper module Copied from fftpack.helper by Pearu Peterson, October 2005 """ import numpy as np from numpy.testing import assert_array_almost_equal from numpy import fft, pi class TestFFTShift: def test_definition(self): x = [0, 1, 2, 3, 4, -4, -3, -2, -1] y = [-4, -3, -2, -1, 0, 1, 2, 3, 4] assert_array_almost_equal(fft.fftshift(x), y) assert_array_almost_equal(fft.ifftshift(y), x) x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1] y = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4] assert_array_almost_equal(fft.fftshift(x), y) assert_array_almost_equal(fft.ifftshift(y), x) def test_inverse(self): for n in [1, 4, 9, 100, 211]: x = np.random.random((n,)) assert_array_almost_equal(fft.ifftshift(fft.fftshift(x)), x) def test_axes_keyword(self): freqs = [[0, 1, 2], [3, 4, -4], [-3, -2, -1]] shifted = [[-1, -3, -2], [2, 0, 1], [-4, 3, 4]] assert_array_almost_equal(fft.fftshift(freqs, axes=(0, 1)), shifted) assert_array_almost_equal(fft.fftshift(freqs, axes=0), fft.fftshift(freqs, axes=(0,))) assert_array_almost_equal(fft.ifftshift(shifted, axes=(0, 1)), freqs) assert_array_almost_equal(fft.ifftshift(shifted, axes=0), fft.ifftshift(shifted, axes=(0,))) assert_array_almost_equal(fft.fftshift(freqs), shifted) assert_array_almost_equal(fft.ifftshift(shifted), freqs) def test_uneven_dims(self): """ Test 2D input, which has uneven dimension sizes """ freqs = [ [0, 1], [2, 3], [4, 5] ] # shift in dimension 0 shift_dim0 = [ [4, 5], [0, 1], [2, 3] ] assert_array_almost_equal(fft.fftshift(freqs, axes=0), shift_dim0) assert_array_almost_equal(fft.ifftshift(shift_dim0, axes=0), freqs) assert_array_almost_equal(fft.fftshift(freqs, axes=(0,)), shift_dim0) assert_array_almost_equal(fft.ifftshift(shift_dim0, axes=[0]), freqs) # shift in dimension 1 shift_dim1 = [ [1, 0], [3, 2], [5, 4] ] assert_array_almost_equal(fft.fftshift(freqs, axes=1), shift_dim1) assert_array_almost_equal(fft.ifftshift(shift_dim1, axes=1), freqs) # shift in both dimensions shift_dim_both = [ [5, 4], [1, 0], [3, 2] ] assert_array_almost_equal(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both) assert_array_almost_equal(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs) assert_array_almost_equal(fft.fftshift(freqs, axes=[0, 1]), shift_dim_both) assert_array_almost_equal(fft.ifftshift(shift_dim_both, axes=[0, 1]), freqs) # axes=None (default) shift in all dimensions assert_array_almost_equal(fft.fftshift(freqs, axes=None), shift_dim_both) assert_array_almost_equal(fft.ifftshift(shift_dim_both, axes=None), freqs) assert_array_almost_equal(fft.fftshift(freqs), shift_dim_both) assert_array_almost_equal(fft.ifftshift(shift_dim_both), freqs) def test_equal_to_original(self): """ Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """ from numpy.core import asarray, concatenate, arange, take def original_fftshift(x, axes=None): """ How fftshift was implemented in v1.14""" tmp = asarray(x) ndim = tmp.ndim if axes is None: axes = list(range(ndim)) elif isinstance(axes, int): axes = (axes,) y = tmp for k in axes: n = tmp.shape[k] p2 = (n + 1) // 2 mylist = concatenate((arange(p2, n), arange(p2))) y = take(y, mylist, k) return y def original_ifftshift(x, axes=None): """ How ifftshift was implemented in v1.14 """ tmp = asarray(x) ndim = tmp.ndim if axes is None: axes = list(range(ndim)) elif isinstance(axes, int): axes = (axes,) y = tmp for k in axes: n = tmp.shape[k] p2 = n - (n + 1) // 2 mylist = concatenate((arange(p2, n), arange(p2))) y = take(y, mylist, k) return y # create possible 2d array combinations and try all possible keywords # compare output to original functions for i in range(16): for j in range(16): for axes_keyword in [0, 1, None, (0,), (0, 1)]: inp = np.random.rand(i, j) assert_array_almost_equal(fft.fftshift(inp, axes_keyword), original_fftshift(inp, axes_keyword)) assert_array_almost_equal(fft.ifftshift(inp, axes_keyword), original_ifftshift(inp, axes_keyword)) class TestFFTFreq: def test_definition(self): x = [0, 1, 2, 3, 4, -4, -3, -2, -1] assert_array_almost_equal(9*fft.fftfreq(9), x) assert_array_almost_equal(9*pi*fft.fftfreq(9, pi), x) x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1] assert_array_almost_equal(10*fft.fftfreq(10), x) assert_array_almost_equal(10*pi*fft.fftfreq(10, pi), x) class TestRFFTFreq: def test_definition(self): x = [0, 1, 2, 3, 4] assert_array_almost_equal(9*fft.rfftfreq(9), x) assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x) x = [0, 1, 2, 3, 4, 5] assert_array_almost_equal(10*fft.rfftfreq(10), x) assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x) class TestIRFFTN: def test_not_last_axis_success(self): ar, ai = np.random.random((2, 16, 8, 32)) a = ar + 1j*ai axes = (-2,) # Should not raise error fft.irfftn(a, axes=axes)