2.0

6 files changed, 756 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/tests/__init__.py b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__init__.py
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+++ b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__init__.py
diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/__init__.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/__init__.cpython-312.pyc
new file mode 100644
index 0000000..f2fb847
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+++ b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/__init__.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/test_helper.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/test_helper.cpython-312.pyc
new file mode 100644
index 0000000..a1e4182
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+++ b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/test_helper.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/test_pocketfft.cpython-312.pyc b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/test_pocketfft.cpython-312.pyc
new file mode 100644
index 0000000..853bb4e
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+++ b/.venv/lib/python3.12/site-packages/numpy/fft/tests/__pycache__/test_pocketfft.cpython-312.pyc
diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/tests/test_helper.py b/.venv/lib/python3.12/site-packages/numpy/fft/tests/test_helper.py
new file mode 100644
index 0000000..c02a736
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+++ b/.venv/lib/python3.12/site-packages/numpy/fft/tests/test_helper.py
@@ -0,0 +1,167 @@
+"""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 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 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
+
+        # 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)
diff --git a/.venv/lib/python3.12/site-packages/numpy/fft/tests/test_pocketfft.py b/.venv/lib/python3.12/site-packages/numpy/fft/tests/test_pocketfft.py
new file mode 100644
index 0000000..0211818
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/numpy/fft/tests/test_pocketfft.py
@@ -0,0 +1,589 @@
+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)