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+import queue
+import threading
+
+import pytest
+
+import numpy as np
+from numpy.random import random
+from numpy.testing import IS_WASM, assert_allclose, assert_array_equal, assert_raises
+
+
+def fft1(x):
+ L = len(x)
+ phase = -2j * np.pi * (np.arange(L) / L)
+ phase = np.arange(L).reshape(-1, 1) * phase
+ return np.sum(x * np.exp(phase), axis=1)
+
+
+class TestFFTShift:
+
+ def test_fft_n(self):
+ assert_raises(ValueError, np.fft.fft, [1, 2, 3], 0)
+
+
+class TestFFT1D:
+
+ def test_identity(self):
+ maxlen = 512
+ x = random(maxlen) + 1j * random(maxlen)
+ xr = random(maxlen)
+ for i in range(1, maxlen):
+ assert_allclose(np.fft.ifft(np.fft.fft(x[0:i])), x[0:i],
+ atol=1e-12)
+ assert_allclose(np.fft.irfft(np.fft.rfft(xr[0:i]), i),
+ xr[0:i], atol=1e-12)
+
+ @pytest.mark.parametrize("dtype", [np.single, np.double, np.longdouble])
+ def test_identity_long_short(self, dtype):
+ # Test with explicitly given number of points, both for n
+ # smaller and for n larger than the input size.
+ maxlen = 16
+ atol = 5 * np.spacing(np.array(1., dtype=dtype))
+ x = random(maxlen).astype(dtype) + 1j * random(maxlen).astype(dtype)
+ xx = np.concatenate([x, np.zeros_like(x)])
+ xr = random(maxlen).astype(dtype)
+ xxr = np.concatenate([xr, np.zeros_like(xr)])
+ for i in range(1, maxlen * 2):
+ check_c = np.fft.ifft(np.fft.fft(x, n=i), n=i)
+ assert check_c.real.dtype == dtype
+ assert_allclose(check_c, xx[0:i], atol=atol, rtol=0)
+ check_r = np.fft.irfft(np.fft.rfft(xr, n=i), n=i)
+ assert check_r.dtype == dtype
+ assert_allclose(check_r, xxr[0:i], atol=atol, rtol=0)
+
+ @pytest.mark.parametrize("dtype", [np.single, np.double, np.longdouble])
+ def test_identity_long_short_reversed(self, dtype):
+ # Also test explicitly given number of points in reversed order.
+ maxlen = 16
+ atol = 5 * np.spacing(np.array(1., dtype=dtype))
+ x = random(maxlen).astype(dtype) + 1j * random(maxlen).astype(dtype)
+ xx = np.concatenate([x, np.zeros_like(x)])
+ for i in range(1, maxlen * 2):
+ check_via_c = np.fft.fft(np.fft.ifft(x, n=i), n=i)
+ assert check_via_c.dtype == x.dtype
+ assert_allclose(check_via_c, xx[0:i], atol=atol, rtol=0)
+ # For irfft, we can neither recover the imaginary part of
+ # the first element, nor the imaginary part of the last
+ # element if npts is even. So, set to 0 for the comparison.
+ y = x.copy()
+ n = i // 2 + 1
+ y.imag[0] = 0
+ if i % 2 == 0:
+ y.imag[n - 1:] = 0
+ yy = np.concatenate([y, np.zeros_like(y)])
+ check_via_r = np.fft.rfft(np.fft.irfft(x, n=i), n=i)
+ assert check_via_r.dtype == x.dtype
+ assert_allclose(check_via_r, yy[0:n], atol=atol, rtol=0)
+
+ def test_fft(self):
+ x = random(30) + 1j * random(30)
+ assert_allclose(fft1(x), np.fft.fft(x), atol=1e-6)
+ assert_allclose(fft1(x), np.fft.fft(x, norm="backward"), atol=1e-6)
+ assert_allclose(fft1(x) / np.sqrt(30),
+ np.fft.fft(x, norm="ortho"), atol=1e-6)
+ assert_allclose(fft1(x) / 30.,
+ np.fft.fft(x, norm="forward"), atol=1e-6)
+
+ @pytest.mark.parametrize("axis", (0, 1))
+ @pytest.mark.parametrize("dtype", (complex, float))
+ @pytest.mark.parametrize("transpose", (True, False))
+ def test_fft_out_argument(self, dtype, transpose, axis):
+ def zeros_like(x):
+ if transpose:
+ return np.zeros_like(x.T).T
+ else:
+ return np.zeros_like(x)
+
+ # tests below only test the out parameter
+ if dtype is complex:
+ y = random((10, 20)) + 1j * random((10, 20))
+ fft, ifft = np.fft.fft, np.fft.ifft
+ else:
+ y = random((10, 20))
+ fft, ifft = np.fft.rfft, np.fft.irfft
+
+ expected = fft(y, axis=axis)
+ out = zeros_like(expected)
+ result = fft(y, out=out, axis=axis)
+ assert result is out
+ assert_array_equal(result, expected)
+
+ expected2 = ifft(expected, axis=axis)
+ out2 = out if dtype is complex else zeros_like(expected2)
+ result2 = ifft(out, out=out2, axis=axis)
+ assert result2 is out2
+ assert_array_equal(result2, expected2)
+
+ @pytest.mark.parametrize("axis", [0, 1])
+ def test_fft_inplace_out(self, axis):
+ # Test some weirder in-place combinations
+ y = random((20, 20)) + 1j * random((20, 20))
+ # Fully in-place.
+ y1 = y.copy()
+ expected1 = np.fft.fft(y1, axis=axis)
+ result1 = np.fft.fft(y1, axis=axis, out=y1)
+ assert result1 is y1
+ assert_array_equal(result1, expected1)
+ # In-place of part of the array; rest should be unchanged.
+ y2 = y.copy()
+ out2 = y2[:10] if axis == 0 else y2[:, :10]
+ expected2 = np.fft.fft(y2, n=10, axis=axis)
+ result2 = np.fft.fft(y2, n=10, axis=axis, out=out2)
+ assert result2 is out2
+ assert_array_equal(result2, expected2)
+ if axis == 0:
+ assert_array_equal(y2[10:], y[10:])
+ else:
+ assert_array_equal(y2[:, 10:], y[:, 10:])
+ # In-place of another part of the array.
+ y3 = y.copy()
+ y3_sel = y3[5:] if axis == 0 else y3[:, 5:]
+ out3 = y3[5:15] if axis == 0 else y3[:, 5:15]
+ expected3 = np.fft.fft(y3_sel, n=10, axis=axis)
+ result3 = np.fft.fft(y3_sel, n=10, axis=axis, out=out3)
+ assert result3 is out3
+ assert_array_equal(result3, expected3)
+ if axis == 0:
+ assert_array_equal(y3[:5], y[:5])
+ assert_array_equal(y3[15:], y[15:])
+ else:
+ assert_array_equal(y3[:, :5], y[:, :5])
+ assert_array_equal(y3[:, 15:], y[:, 15:])
+ # In-place with n > nin; rest should be unchanged.
+ y4 = y.copy()
+ y4_sel = y4[:10] if axis == 0 else y4[:, :10]
+ out4 = y4[:15] if axis == 0 else y4[:, :15]
+ expected4 = np.fft.fft(y4_sel, n=15, axis=axis)
+ result4 = np.fft.fft(y4_sel, n=15, axis=axis, out=out4)
+ assert result4 is out4
+ assert_array_equal(result4, expected4)
+ if axis == 0:
+ assert_array_equal(y4[15:], y[15:])
+ else:
+ assert_array_equal(y4[:, 15:], y[:, 15:])
+ # Overwrite in a transpose.
+ y5 = y.copy()
+ out5 = y5.T
+ result5 = np.fft.fft(y5, axis=axis, out=out5)
+ assert result5 is out5
+ assert_array_equal(result5, expected1)
+ # Reverse strides.
+ y6 = y.copy()
+ out6 = y6[::-1] if axis == 0 else y6[:, ::-1]
+ result6 = np.fft.fft(y6, axis=axis, out=out6)
+ assert result6 is out6
+ assert_array_equal(result6, expected1)
+
+ def test_fft_bad_out(self):
+ x = np.arange(30.)
+ with pytest.raises(TypeError, match="must be of ArrayType"):
+ np.fft.fft(x, out="")
+ with pytest.raises(ValueError, match="has wrong shape"):
+ np.fft.fft(x, out=np.zeros_like(x).reshape(5, -1))
+ with pytest.raises(TypeError, match="Cannot cast"):
+ np.fft.fft(x, out=np.zeros_like(x, dtype=float))
+
+ @pytest.mark.parametrize('norm', (None, 'backward', 'ortho', 'forward'))
+ def test_ifft(self, norm):
+ x = random(30) + 1j * random(30)
+ assert_allclose(
+ x, np.fft.ifft(np.fft.fft(x, norm=norm), norm=norm),
+ atol=1e-6)
+ # Ensure we get the correct error message
+ with pytest.raises(ValueError,
+ match='Invalid number of FFT data points'):
+ np.fft.ifft([], norm=norm)
+
+ def test_fft2(self):
+ x = random((30, 20)) + 1j * random((30, 20))
+ assert_allclose(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
+ np.fft.fft2(x), atol=1e-6)
+ assert_allclose(np.fft.fft2(x),
+ np.fft.fft2(x, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.fft2(x) / np.sqrt(30 * 20),
+ np.fft.fft2(x, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.fft2(x) / (30. * 20.),
+ np.fft.fft2(x, norm="forward"), atol=1e-6)
+
+ def test_ifft2(self):
+ x = random((30, 20)) + 1j * random((30, 20))
+ assert_allclose(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
+ np.fft.ifft2(x), atol=1e-6)
+ assert_allclose(np.fft.ifft2(x),
+ np.fft.ifft2(x, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.ifft2(x) * np.sqrt(30 * 20),
+ np.fft.ifft2(x, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.ifft2(x) * (30. * 20.),
+ np.fft.ifft2(x, norm="forward"), atol=1e-6)
+
+ def test_fftn(self):
+ x = random((30, 20, 10)) + 1j * random((30, 20, 10))
+ assert_allclose(
+ np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1), axis=0),
+ np.fft.fftn(x), atol=1e-6)
+ assert_allclose(np.fft.fftn(x),
+ np.fft.fftn(x, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
+ np.fft.fftn(x, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.fftn(x) / (30. * 20. * 10.),
+ np.fft.fftn(x, norm="forward"), atol=1e-6)
+
+ def test_ifftn(self):
+ x = random((30, 20, 10)) + 1j * random((30, 20, 10))
+ assert_allclose(
+ np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
+ np.fft.ifftn(x), atol=1e-6)
+ assert_allclose(np.fft.ifftn(x),
+ np.fft.ifftn(x, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
+ np.fft.ifftn(x, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.ifftn(x) * (30. * 20. * 10.),
+ np.fft.ifftn(x, norm="forward"), atol=1e-6)
+
+ def test_rfft(self):
+ x = random(30)
+ for n in [x.size, 2 * x.size]:
+ for norm in [None, 'backward', 'ortho', 'forward']:
+ assert_allclose(
+ np.fft.fft(x, n=n, norm=norm)[:(n // 2 + 1)],
+ np.fft.rfft(x, n=n, norm=norm), atol=1e-6)
+ assert_allclose(
+ np.fft.rfft(x, n=n),
+ np.fft.rfft(x, n=n, norm="backward"), atol=1e-6)
+ assert_allclose(
+ np.fft.rfft(x, n=n) / np.sqrt(n),
+ np.fft.rfft(x, n=n, norm="ortho"), atol=1e-6)
+ assert_allclose(
+ np.fft.rfft(x, n=n) / n,
+ np.fft.rfft(x, n=n, norm="forward"), atol=1e-6)
+
+ def test_rfft_even(self):
+ x = np.arange(8)
+ n = 4
+ y = np.fft.rfft(x, n)
+ assert_allclose(y, np.fft.fft(x[:n])[:n // 2 + 1], rtol=1e-14)
+
+ def test_rfft_odd(self):
+ x = np.array([1, 0, 2, 3, -3])
+ y = np.fft.rfft(x)
+ assert_allclose(y, np.fft.fft(x)[:3], rtol=1e-14)
+
+ def test_irfft(self):
+ x = random(30)
+ assert_allclose(x, np.fft.irfft(np.fft.rfft(x)), atol=1e-6)
+ assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="backward"),
+ norm="backward"), atol=1e-6)
+ assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="ortho"),
+ norm="ortho"), atol=1e-6)
+ assert_allclose(x, np.fft.irfft(np.fft.rfft(x, norm="forward"),
+ norm="forward"), atol=1e-6)
+
+ def test_rfft2(self):
+ x = random((30, 20))
+ assert_allclose(np.fft.fft2(x)[:, :11], np.fft.rfft2(x), atol=1e-6)
+ assert_allclose(np.fft.rfft2(x),
+ np.fft.rfft2(x, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.rfft2(x) / np.sqrt(30 * 20),
+ np.fft.rfft2(x, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.rfft2(x) / (30. * 20.),
+ np.fft.rfft2(x, norm="forward"), atol=1e-6)
+
+ def test_irfft2(self):
+ x = random((30, 20))
+ assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x)), atol=1e-6)
+ assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="backward"),
+ norm="backward"), atol=1e-6)
+ assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"),
+ norm="ortho"), atol=1e-6)
+ assert_allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="forward"),
+ norm="forward"), atol=1e-6)
+
+ def test_rfftn(self):
+ x = random((30, 20, 10))
+ assert_allclose(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x), atol=1e-6)
+ assert_allclose(np.fft.rfftn(x),
+ np.fft.rfftn(x, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
+ np.fft.rfftn(x, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.rfftn(x) / (30. * 20. * 10.),
+ np.fft.rfftn(x, norm="forward"), atol=1e-6)
+ # Regression test for gh-27159
+ x = np.ones((2, 3))
+ result = np.fft.rfftn(x, axes=(0, 0, 1), s=(10, 20, 40))
+ assert result.shape == (10, 21)
+ expected = np.fft.fft(np.fft.fft(np.fft.rfft(x, axis=1, n=40),
+ axis=0, n=20), axis=0, n=10)
+ assert expected.shape == (10, 21)
+ assert_allclose(result, expected, atol=1e-6)
+
+ def test_irfftn(self):
+ x = random((30, 20, 10))
+ assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x)), atol=1e-6)
+ assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="backward"),
+ norm="backward"), atol=1e-6)
+ assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"),
+ norm="ortho"), atol=1e-6)
+ assert_allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="forward"),
+ norm="forward"), atol=1e-6)
+
+ 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_allclose(np.fft.fft(x), np.fft.hfft(x_herm), atol=1e-6)
+ assert_allclose(np.fft.hfft(x_herm),
+ np.fft.hfft(x_herm, norm="backward"), atol=1e-6)
+ assert_allclose(np.fft.hfft(x_herm) / np.sqrt(30),
+ np.fft.hfft(x_herm, norm="ortho"), atol=1e-6)
+ assert_allclose(np.fft.hfft(x_herm) / 30.,
+ np.fft.hfft(x_herm, norm="forward"), atol=1e-6)
+
+ def test_ihfft(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_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)), atol=1e-6)
+ assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
+ norm="backward"), norm="backward"), atol=1e-6)
+ assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
+ norm="ortho"), norm="ortho"), atol=1e-6)
+ assert_allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
+ norm="forward"), norm="forward"), atol=1e-6)
+
+ @pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
+ np.fft.rfftn, np.fft.irfftn])
+ def test_axes(self, op):
+ x = random((30, 20, 10))
+ axes = [(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)]
+ for a in axes:
+ op_tr = op(np.transpose(x, a))
+ tr_op = np.transpose(op(x, axes=a), a)
+ assert_allclose(op_tr, tr_op, atol=1e-6)
+
+ @pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
+ np.fft.fft2, np.fft.ifft2])
+ def test_s_negative_1(self, op):
+ x = np.arange(100).reshape(10, 10)
+ # should use the whole input array along the first axis
+ assert op(x, s=(-1, 5), axes=(0, 1)).shape == (10, 5)
+
+ @pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
+ np.fft.rfftn, np.fft.irfftn])
+ def test_s_axes_none(self, op):
+ x = np.arange(100).reshape(10, 10)
+ with pytest.warns(match='`axes` should not be `None` if `s`'):
+ op(x, s=(-1, 5))
+
+ @pytest.mark.parametrize("op", [np.fft.fft2, np.fft.ifft2])
+ def test_s_axes_none_2D(self, op):
+ x = np.arange(100).reshape(10, 10)
+ with pytest.warns(match='`axes` should not be `None` if `s`'):
+ op(x, s=(-1, 5), axes=None)
+
+ @pytest.mark.parametrize("op", [np.fft.fftn, np.fft.ifftn,
+ np.fft.rfftn, np.fft.irfftn,
+ np.fft.fft2, np.fft.ifft2])
+ def test_s_contains_none(self, op):
+ x = random((30, 20, 10))
+ with pytest.warns(match='array containing `None` values to `s`'):
+ op(x, s=(10, None, 10), axes=(0, 1, 2))
+
+ 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, 'backward', 'ortho', 'forward']:
+ tmp = forw(x, n=n, norm=norm)
+ tmp = back(tmp, n=n, norm=norm)
+ assert_allclose(x_norm,
+ np.linalg.norm(tmp), atol=1e-6)
+
+ @pytest.mark.parametrize("axes", [(0, 1), (0, 2), None])
+ @pytest.mark.parametrize("dtype", (complex, float))
+ @pytest.mark.parametrize("transpose", (True, False))
+ def test_fftn_out_argument(self, dtype, transpose, axes):
+ def zeros_like(x):
+ if transpose:
+ return np.zeros_like(x.T).T
+ else:
+ return np.zeros_like(x)
+
+ # tests below only test the out parameter
+ if dtype is complex:
+ x = random((10, 5, 6)) + 1j * random((10, 5, 6))
+ fft, ifft = np.fft.fftn, np.fft.ifftn
+ else:
+ x = random((10, 5, 6))
+ fft, ifft = np.fft.rfftn, np.fft.irfftn
+
+ expected = fft(x, axes=axes)
+ out = zeros_like(expected)
+ result = fft(x, out=out, axes=axes)
+ assert result is out
+ assert_array_equal(result, expected)
+
+ expected2 = ifft(expected, axes=axes)
+ out2 = out if dtype is complex else zeros_like(expected2)
+ result2 = ifft(out, out=out2, axes=axes)
+ assert result2 is out2
+ assert_array_equal(result2, expected2)
+
+ @pytest.mark.parametrize("fft", [np.fft.fftn, np.fft.ifftn, np.fft.rfftn])
+ def test_fftn_out_and_s_interaction(self, fft):
+ # With s, shape varies, so generally one cannot pass in out.
+ if fft is np.fft.rfftn:
+ x = random((10, 5, 6))
+ else:
+ x = random((10, 5, 6)) + 1j * random((10, 5, 6))
+ with pytest.raises(ValueError, match="has wrong shape"):
+ fft(x, out=np.zeros_like(x), s=(3, 3, 3), axes=(0, 1, 2))
+ # Except on the first axis done (which is the last of axes).
+ s = (10, 5, 5)
+ expected = fft(x, s=s, axes=(0, 1, 2))
+ out = np.zeros_like(expected)
+ result = fft(x, s=s, axes=(0, 1, 2), out=out)
+ assert result is out
+ assert_array_equal(result, expected)
+
+ @pytest.mark.parametrize("s", [(9, 5, 5), (3, 3, 3)])
+ def test_irfftn_out_and_s_interaction(self, s):
+ # Since for irfftn, the output is real and thus cannot be used for
+ # intermediate steps, it should always work.
+ x = random((9, 5, 6, 2)) + 1j * random((9, 5, 6, 2))
+ expected = np.fft.irfftn(x, s=s, axes=(0, 1, 2))
+ out = np.zeros_like(expected)
+ result = np.fft.irfftn(x, s=s, axes=(0, 1, 2), out=out)
+ assert result is out
+ assert_array_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+ "dtype",
+ [np.float32, np.float64, np.complex64, np.complex128])
+@pytest.mark.parametrize("order", ["F", 'non-contiguous'])
+@pytest.mark.parametrize(
+ "fft",
+ [np.fft.fft, np.fft.fft2, np.fft.fftn,
+ np.fft.ifft, np.fft.ifft2, np.fft.ifftn])
+def test_fft_with_order(dtype, order, fft):
+ # Check that FFT/IFFT produces identical results for C, Fortran and
+ # non contiguous arrays
+ rng = np.random.RandomState(42)
+ X = rng.rand(8, 7, 13).astype(dtype, copy=False)
+ # See discussion in pull/14178
+ _tol = 8.0 * np.sqrt(np.log2(X.size)) * np.finfo(X.dtype).eps
+ if order == 'F':
+ Y = np.asfortranarray(X)
+ else:
+ # Make a non contiguous array
+ Y = X[::-1]
+ X = np.ascontiguousarray(X[::-1])
+
+ if fft.__name__.endswith('fft'):
+ for axis in range(3):
+ X_res = fft(X, axis=axis)
+ Y_res = fft(Y, axis=axis)
+ assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
+ elif fft.__name__.endswith(('fft2', 'fftn')):
+ axes = [(0, 1), (1, 2), (0, 2)]
+ if fft.__name__.endswith('fftn'):
+ axes.extend([(0,), (1,), (2,), None])
+ for ax in axes:
+ X_res = fft(X, axes=ax)
+ Y_res = fft(Y, axes=ax)
+ assert_allclose(X_res, Y_res, atol=_tol, rtol=_tol)
+ else:
+ raise ValueError
+
+
+@pytest.mark.parametrize("order", ["F", "C"])
+@pytest.mark.parametrize("n", [None, 7, 12])
+def test_fft_output_order(order, n):
+ rng = np.random.RandomState(42)
+ x = rng.rand(10)
+ x = np.asarray(x, dtype=np.complex64, order=order)
+ res = np.fft.fft(x, n=n)
+ assert res.flags.c_contiguous == x.flags.c_contiguous
+ assert res.flags.f_contiguous == x.flags.f_contiguous
+
+@pytest.mark.skipif(IS_WASM, reason="Cannot start thread")
+class TestFFTThreadSafe:
+ 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)
+
+
+def test_irfft_with_n_1_regression():
+ # Regression test for gh-25661
+ x = np.arange(10)
+ np.fft.irfft(x, n=1)
+ np.fft.hfft(x, n=1)
+ np.fft.irfft(np.array([0], complex), n=10)
+
+
+def test_irfft_with_n_large_regression():
+ # Regression test for gh-25679
+ x = np.arange(5) * (1 + 1j)
+ result = np.fft.hfft(x, n=10)
+ expected = np.array([20., 9.91628173, -11.8819096, 7.1048486,
+ -6.62459848, 4., -3.37540152, -0.16057669,
+ 1.8819096, -20.86055364])
+ assert_allclose(result, expected)
+
+
+@pytest.mark.parametrize("fft", [
+ np.fft.fft, np.fft.ifft, np.fft.rfft, np.fft.irfft
+])
+@pytest.mark.parametrize("data", [
+ np.array([False, True, False]),
+ np.arange(10, dtype=np.uint8),
+ np.arange(5, dtype=np.int16),
+])
+def test_fft_with_integer_or_bool_input(data, fft):
+ # Regression test for gh-25819
+ result = fft(data)
+ float_data = data.astype(np.result_type(data, 1.))
+ expected = fft(float_data)
+ assert_array_equal(result, expected)