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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)
|
|
