| """Test functions for fftpack.helper module |
| |
| Copied from fftpack.helper by Pearu Peterson, October 2005 |
| |
| """ |
| import numpy as np |
| from numpy import fft, pi |
| from numpy.testing import assert_array_almost_equal |
|
|
|
|
| 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_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_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_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) |
|
|
| |
| 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 the new (>=v1.15) and old implementations are equal (see #10073) """ |
| from numpy._core import arange, asarray, concatenate, 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 |
|
|
| |
| |
| 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,) |
|
|
| |
| fft.irfftn(a, axes=axes) |
|
|
