mirror of https://github.com/exaloop/codon.git
786 lines
28 KiB
Python
786 lines
28 KiB
Python
import numpy as np
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import numpy.fft as fft
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import numpy.random as rnd
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def fft1(x):
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L = len(x)
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phase = np.pi * (np.arange(L) / L) * -2j
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phase = np.arange(L).reshape(-1, 1) * phase
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return np.sum(x*np.exp(phase), axis=1)
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@test
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def test_fft_n():
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try:
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fft.fft([1, 2, 3], 0)
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assert False
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except ValueError:
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pass
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@test
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def test_fft1d_identity():
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gen = rnd.default_rng(seed=0)
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maxlen = 512
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x = gen.random(maxlen) + gen.random(maxlen)*1j
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xr = gen.random(maxlen)
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for i in range(1, maxlen):
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assert np.allclose(np.fft.ifft(np.fft.fft(x[0:i])), x[0:i],
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atol=1e-12)
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assert np.allclose(np.fft.irfft(np.fft.rfft(xr[0:i]), i),
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xr[0:i], atol=1e-12)
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@test
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def test_fft1d_identity_long_short(dtype: type):
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# Test with explicitly given number of points, both for n
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# smaller and for n larger than the input size.
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gen = rnd.default_rng(seed=0)
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maxlen = 16
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atol = 4 * float(np.spacing(np.array(1., dtype=dtype)))
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x = gen.random(maxlen).astype(dtype) + gen.random(maxlen).astype(dtype)*1j
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xx = np.concatenate([x, np.zeros_like(x)])
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xr = gen.random(maxlen).astype(dtype)
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xxr = np.concatenate([xr, np.zeros_like(xr)])
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for i in range(1, maxlen*2):
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check_c = np.fft.ifft(np.fft.fft(x, n=i), n=i)
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assert check_c.real.dtype is dtype
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assert np.allclose(check_c, xx[0:i], atol=atol, rtol=0)
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check_r = np.fft.irfft(np.fft.rfft(xr, n=i), n=i)
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assert check_r.dtype is dtype
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assert np.allclose(check_r, xxr[0:i], atol=atol, rtol=0)
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@test
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def test_fft1d_identity_long_short_reversed(dtype: type):
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# Also test explicitly given number of points in reversed order.
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gen = rnd.default_rng(seed=1)
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maxlen = 16
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atol = 5 * float(np.spacing(np.array(1., dtype=dtype)))
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x = gen.random(maxlen).astype(dtype) + gen.random(maxlen).astype(dtype)*1j
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xx = np.concatenate([x, np.zeros_like(x)])
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for i in range(1, maxlen*2):
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check_via_c = np.fft.fft(np.fft.ifft(x, n=i), n=i)
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assert check_via_c.dtype is x.dtype
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assert np.allclose(check_via_c, xx[0:i], atol=atol, rtol=0)
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# For irfft, we can neither recover the imaginary part of
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# the first element, nor the imaginary part of the last
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# element if npts is even. So, set to 0 for the comparison.
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y = x.copy()
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n = i // 2 + 1
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y.imag[0] = 0
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if i % 2 == 0:
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y.imag[n-1:] = 0
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yy = np.concatenate([y, np.zeros_like(y)])
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check_via_r = np.fft.rfft(np.fft.irfft(x, n=i), n=i)
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assert check_via_r.dtype is x.dtype
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assert np.allclose(check_via_r, yy[0:n], atol=atol, rtol=0)
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@test
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def test_fft():
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gen = rnd.default_rng(seed=2)
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x = gen.random(30) + gen.random(30)*1j
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assert np.allclose(fft1(x), np.fft.fft(x), atol=1e-6)
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assert np.allclose(fft1(x), np.fft.fft(x, norm="backward"), atol=1e-6)
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assert np.allclose(fft1(x) / np.sqrt(30),
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np.fft.fft(x, norm="ortho"), atol=1e-6)
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assert np.allclose(fft1(x) / 30.,
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np.fft.fft(x, norm="forward"), atol=1e-6)
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@test
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def test_fft_out_argument(dtype: type, transpose: bool, axis: int):
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def zeros_like(x):
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if transpose:
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return np.zeros_like(x.T).T
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else:
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return np.zeros_like(x)
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gen = rnd.default_rng(seed=2)
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# tests below only test the out parameter
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if dtype is complex:
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y = gen.random((10, 20)) + gen.random((10, 20))*1j
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fft, ifft = np.fft.fft, np.fft.ifft
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else:
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y = gen.random((10, 20))
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fft, ifft = np.fft.rfft, np.fft.irfft
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expected = fft(y, axis=axis)
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out = zeros_like(expected)
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result = fft(y, out=out, axis=axis)
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assert result.data == out.data
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assert np.array_equal(result, expected)
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expected2 = ifft(expected, axis=axis)
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out2 = out if dtype is complex else zeros_like(expected2)
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result2 = ifft(out, out=out2, axis=axis)
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assert result2.data == out2.data
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assert np.array_equal(result2, expected2)
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@test
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def test_fft_inplace_out(axis: int):
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gen = rnd.default_rng(seed=3)
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# Test some weirder in-place combinations
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y = gen.random((20, 20)) + gen.random((20, 20))*1j
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# Fully in-place.
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y1 = y.copy()
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expected1 = np.fft.fft(y1, axis=axis)
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result1 = np.fft.fft(y1, axis=axis, out=y1)
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assert result1.data == y1.data
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assert np.array_equal(result1, expected1)
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# In-place of part of the array; rest should be unchanged.
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y2 = y.copy()
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out2 = y2[:10] if axis == 0 else y2[:, :10]
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expected2 = np.fft.fft(y2, n=10, axis=axis)
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result2 = np.fft.fft(y2, n=10, axis=axis, out=out2)
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assert result2.data == out2.data
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assert np.array_equal(result2, expected2)
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if axis == 0:
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assert np.array_equal(y2[10:], y[10:])
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else:
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assert np.array_equal(y2[:, 10:], y[:, 10:])
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# In-place of another part of the array.
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y3 = y.copy()
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y3_sel = y3[5:] if axis == 0 else y3[:, 5:]
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out3 = y3[5:15] if axis == 0 else y3[:, 5:15]
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expected3 = np.fft.fft(y3_sel, n=10, axis=axis)
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result3 = np.fft.fft(y3_sel, n=10, axis=axis, out=out3)
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assert result3.data == out3.data
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assert np.array_equal(result3, expected3)
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if axis == 0:
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assert np.array_equal(y3[:5], y[:5])
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assert np.array_equal(y3[15:], y[15:])
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else:
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assert np.array_equal(y3[:, :5], y[:, :5])
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assert np.array_equal(y3[:, 15:], y[:, 15:])
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# In-place with n > nin; rest should be unchanged.
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y4 = y.copy()
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y4_sel = y4[:10] if axis == 0 else y4[:, :10]
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out4 = y4[:15] if axis == 0 else y4[:, :15]
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expected4 = np.fft.fft(y4_sel, n=15, axis=axis)
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result4 = np.fft.fft(y4_sel, n=15, axis=axis, out=out4)
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assert result4.data == out4.data
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assert np.array_equal(result4, expected4)
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if axis == 0:
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assert np.array_equal(y4[15:], y[15:])
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else:
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assert np.array_equal(y4[:, 15:], y[:, 15:])
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# Overwrite in a transpose.
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y5 = y.copy()
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out5 = y5.T
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result5 = np.fft.fft(y5, axis=axis, out=out5)
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assert result5.data == out5.data
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# assert np.array_equal(result5, expected1) # TODO: we don't check for this
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# Reverse strides.
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y6 = y.copy()
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out6 = y6[::-1] if axis == 0 else y6[:, ::-1]
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result6 = np.fft.fft(y6, axis=axis, out=out6)
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assert result6.data == out6.data
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assert np.array_equal(result6, expected1)
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@test
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def test_fft_bad_out():
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x = np.arange(30.)
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try:
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np.fft.fft(x, out=np.zeros(5, complex))
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assert False
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except ValueError:
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pass
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@test
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def test_ifft(norm: Optional[str]):
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gen = rnd.default_rng(seed=4)
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x = gen.random(30) + gen.random(30)*1j
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assert np.allclose(
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x, np.fft.ifft(np.fft.fft(x, norm=norm), norm=norm),
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atol=1e-6)
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try:
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np.fft.ifft(x[0:0], norm=norm)
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assert False
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except ValueError:
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pass
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@test
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def test_fft2():
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gen = rnd.default_rng(seed=5)
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x = gen.random((30, 20)) + gen.random((30, 20))*1j
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assert np.allclose(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
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np.fft.fft2(x), atol=1e-6)
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assert np.allclose(np.fft.fft2(x),
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np.fft.fft2(x, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.fft2(x) / np.sqrt(30 * 20),
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np.fft.fft2(x, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.fft2(x) / (30. * 20.),
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np.fft.fft2(x, norm="forward"), atol=1e-6)
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@test
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def test_ifft2():
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gen = rnd.default_rng(seed=6)
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x = gen.random((30, 20)) + gen.random((30, 20))*1j
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assert np.allclose(np.fft.ifft(np.fft.ifft(x, axis=1), axis=0),
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np.fft.ifft2(x), atol=1e-6)
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assert np.allclose(np.fft.ifft2(x),
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np.fft.ifft2(x, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.ifft2(x) * np.sqrt(30 * 20),
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np.fft.ifft2(x, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.ifft2(x) * (30. * 20.),
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np.fft.ifft2(x, norm="forward"), atol=1e-6)
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@test
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def test_fftn():
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gen = rnd.default_rng(seed=7)
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x = gen.random((30, 20, 10)) + gen.random((30, 20, 10))*1j
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assert np.allclose(
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np.fft.fft(np.fft.fft(np.fft.fft(x, axis=2), axis=1), axis=0),
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np.fft.fftn(x), atol=1e-6)
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assert np.allclose(np.fft.fftn(x),
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np.fft.fftn(x, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.fftn(x) / np.sqrt(30 * 20 * 10),
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np.fft.fftn(x, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.fftn(x) / (30. * 20. * 10.),
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np.fft.fftn(x, norm="forward"), atol=1e-6)
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@test
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def test_ifftn():
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gen = rnd.default_rng(seed=8)
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x = gen.random((30, 20, 10)) + gen.random((30, 20, 10))*1j
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assert np.allclose(
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np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
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np.fft.ifftn(x), atol=1e-6)
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assert np.allclose(np.fft.ifftn(x),
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np.fft.ifftn(x, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
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np.fft.ifftn(x, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.ifftn(x) * (30. * 20. * 10.),
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np.fft.ifftn(x, norm="forward"), atol=1e-6)
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@test
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def test_rfft():
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gen = rnd.default_rng(seed=9)
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x = gen.random(30)
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for n in [x.size, 2*x.size]:
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for norm in [None, 'backward', 'ortho', 'forward']:
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assert np.allclose(
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np.fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
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np.fft.rfft(x, n=n, norm=norm), atol=1e-6)
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assert np.allclose(
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np.fft.rfft(x, n=n),
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np.fft.rfft(x, n=n, norm="backward"), atol=1e-6)
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assert np.allclose(
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np.fft.rfft(x, n=n) / np.sqrt(n),
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np.fft.rfft(x, n=n, norm="ortho"), atol=1e-6)
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assert np.allclose(
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np.fft.rfft(x, n=n) / n,
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np.fft.rfft(x, n=n, norm="forward"), atol=1e-6)
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@test
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def test_rfft_even():
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x = np.arange(8)
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n = 4
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y = np.fft.rfft(x, n)
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assert np.allclose(y, np.fft.fft(x[:n])[:n//2 + 1], rtol=1e-14)
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@test
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def test_rfft_odd():
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x = np.array([1, 0, 2, 3, -3])
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y = np.fft.rfft(x)
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assert np.allclose(y, np.fft.fft(x)[:3], rtol=1e-14)
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@test
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def test_irfft():
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gen = rnd.default_rng(seed=10)
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x = gen.random(30)
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assert np.allclose(x, np.fft.irfft(np.fft.rfft(x)), atol=1e-6)
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assert np.allclose(x, np.fft.irfft(np.fft.rfft(x, norm="backward"),
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norm="backward"), atol=1e-6)
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assert np.allclose(x, np.fft.irfft(np.fft.rfft(x, norm="ortho"),
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norm="ortho"), atol=1e-6)
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assert np.allclose(x, np.fft.irfft(np.fft.rfft(x, norm="forward"),
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norm="forward"), atol=1e-6)
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@test
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def test_rfft2():
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gen = rnd.default_rng(seed=11)
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x = gen.random((30, 20))
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assert np.allclose(np.fft.fft2(x)[:, :11], np.fft.rfft2(x), atol=1e-6)
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assert np.allclose(np.fft.rfft2(x),
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np.fft.rfft2(x, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.rfft2(x) / np.sqrt(30 * 20),
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np.fft.rfft2(x, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.rfft2(x) / (30. * 20.),
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np.fft.rfft2(x, norm="forward"), atol=1e-6)
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@test
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def test_irfft2():
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gen = rnd.default_rng(seed=12)
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x = gen.random((30, 20))
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assert np.allclose(x, np.fft.irfft2(np.fft.rfft2(x)), atol=1e-6)
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assert np.allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="backward"),
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norm="backward"), atol=1e-6)
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assert np.allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"),
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norm="ortho"), atol=1e-6)
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assert np.allclose(x, np.fft.irfft2(np.fft.rfft2(x, norm="forward"),
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norm="forward"), atol=1e-6)
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@test
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def test_rfftn():
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gen = rnd.default_rng(seed=13)
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x = gen.random((30, 20, 10))
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assert np.allclose(np.fft.fftn(x)[:, :, :6], np.fft.rfftn(x), atol=1e-6)
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assert np.allclose(np.fft.rfftn(x),
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np.fft.rfftn(x, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.rfftn(x) / np.sqrt(30 * 20 * 10),
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np.fft.rfftn(x, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.rfftn(x) / (30. * 20. * 10.),
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np.fft.rfftn(x, norm="forward"), atol=1e-6)
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@test
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def test_irfftn():
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gen = rnd.default_rng(seed=14)
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x = gen.random((30, 20, 10))
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assert np.allclose(x, np.fft.irfftn(np.fft.rfftn(x)), atol=1e-6)
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assert np.allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="backward"),
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norm="backward"), atol=1e-6)
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assert np.allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="ortho"),
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norm="ortho"), atol=1e-6)
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assert np.allclose(x, np.fft.irfftn(np.fft.rfftn(x, norm="forward"),
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norm="forward"), atol=1e-6)
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@test
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def test_hfft():
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gen = rnd.default_rng(seed=15)
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x = gen.random(14) + gen.random(14)*1j
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x_herm = np.concatenate((gen.random(1), x, gen.random(1)))
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x = np.concatenate((x_herm, x[::-1].conj()))
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assert np.allclose(np.fft.fft(x), np.fft.hfft(x_herm), atol=1e-6)
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assert np.allclose(np.fft.hfft(x_herm),
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np.fft.hfft(x_herm, norm="backward"), atol=1e-6)
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assert np.allclose(np.fft.hfft(x_herm) / np.sqrt(30),
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np.fft.hfft(x_herm, norm="ortho"), atol=1e-6)
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assert np.allclose(np.fft.hfft(x_herm) / 30.,
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np.fft.hfft(x_herm, norm="forward"), atol=1e-6)
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@test
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def test_ihfft():
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gen = rnd.default_rng(seed=16)
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x = gen.random(14) + gen.random(14)*1j
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x_herm = np.concatenate((gen.random(1), x, gen.random(1)))
|
|
x = np.concatenate((x_herm, x[::-1].conj()))
|
|
assert np.allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm)), atol=1e-6)
|
|
assert np.allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
|
|
norm="backward"), norm="backward"), atol=1e-6)
|
|
assert np.allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
|
|
norm="ortho"), norm="ortho"), atol=1e-6)
|
|
assert np.allclose(x_herm, np.fft.ihfft(np.fft.hfft(x_herm,
|
|
norm="forward"), norm="forward"), atol=1e-6)
|
|
|
|
@test
|
|
def test_axes(op):
|
|
gen = rnd.default_rng(seed=17)
|
|
x = gen.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 np.allclose(op_tr, tr_op, atol=1e-6)
|
|
|
|
@test
|
|
def test_s_negative_1(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)
|
|
|
|
@test
|
|
def test_s_axes_none(op):
|
|
x = np.arange(100).reshape(10, 10)
|
|
# Should test warning here:
|
|
op(x, s=(-1, 5))
|
|
|
|
@test
|
|
def test_s_axes_none_2D(op):
|
|
x = np.arange(100).reshape(10, 10)
|
|
# Should test warning here:
|
|
op(x, s=(-1, 5), axes=None)
|
|
|
|
@test
|
|
def test_all_1d_norm_preserving():
|
|
gen = rnd.default_rng(seed=18)
|
|
# verify that round-trip transforms are norm-preserving
|
|
x = gen.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 np.allclose(x_norm,
|
|
np.linalg.norm(tmp), atol=1e-6)
|
|
|
|
@test
|
|
def test_fftn_out_argument(dtype: type, transpose: bool, axes):
|
|
def zeros_like(x):
|
|
if transpose:
|
|
return np.zeros_like(x.T).T
|
|
else:
|
|
return np.zeros_like(x)
|
|
|
|
gen = rnd.default_rng(seed=19)
|
|
# tests below only test the out parameter
|
|
if dtype is complex:
|
|
x = gen.random((10, 5, 6)) + gen.random((10, 5, 6))*1j
|
|
fft, ifft = np.fft.fftn, np.fft.ifftn
|
|
else:
|
|
x = gen.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.data == out.data
|
|
assert np.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.data == out2.data
|
|
assert np.array_equal(result2, expected2)
|
|
|
|
@test
|
|
def test_fftn_out_and_s_interaction(fft, rfftn: Static[int]):
|
|
# With s, shape varies, so generally one cannot pass in out.
|
|
gen = rnd.default_rng(seed=20)
|
|
if rfftn:
|
|
x = gen.random((10, 5, 6))
|
|
else:
|
|
x = gen.random((10, 5, 6)) + gen.random((10, 5, 6))*1j
|
|
try:
|
|
fft(x, out=np.zeros_like(x, dtype=complex), s=(3, 3, 3), axes=(0, 1, 2))
|
|
assert False
|
|
except ValueError:
|
|
pass
|
|
# 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.data == out.data
|
|
assert np.array_equal(result, expected)
|
|
|
|
@test
|
|
def test_irfftn_out_and_s_interaction(s):
|
|
gen = rnd.default_rng(seed=21)
|
|
# Since for irfftn, the output is real and thus cannot be used for
|
|
# intermediate steps, it should always work.
|
|
x = gen.random((9, 5, 6, 2)) + gen.random((9, 5, 6, 2))*1j
|
|
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.data == out.data
|
|
assert np.array_equal(result, expected)
|
|
|
|
@test
|
|
def test_fft_with_order(dtype: type, order: str, fft, fftname: Static[str]):
|
|
def eps(dtype: type):
|
|
if dtype is complex or dtype is float:
|
|
return 2.220446049250313e-16
|
|
elif dtype is complex64 or dtype is float32:
|
|
return 1.1920929e-07
|
|
else:
|
|
compile_error("unknown type for eps")
|
|
|
|
# Check that FFT/IFFT produces identical results for C, Fortran and
|
|
# non contiguous arrays
|
|
gen = rnd.default_rng(seed=22)
|
|
X = gen.random((8, 7, 13)).astype(dtype, copy=False)
|
|
# See discussion in pull/14178
|
|
_tol = 8.0 * np.sqrt(np.log2(X.size)) * eps(X.dtype)
|
|
if order == 'F':
|
|
Y = np.asfortranarray(X)
|
|
else:
|
|
# Make a non contiguous array
|
|
Y = X[::-1]
|
|
X = np.ascontiguousarray(X[::-1])
|
|
|
|
if fftname[-3:] == 'fft':
|
|
for axis in range(3):
|
|
X_res = fft(X, axis=axis)
|
|
Y_res = fft(Y, axis=axis)
|
|
assert np.allclose(X_res, Y_res, atol=_tol, rtol=_tol)
|
|
elif fftname[-4:] == 'fft2' or fftname[-4:] == 'fftn':
|
|
for ax in ((0, 1), (1, 2), (0, 2)):
|
|
X_res = fft(X, axes=ax)
|
|
Y_res = fft(Y, axes=ax)
|
|
assert np.allclose(X_res, Y_res, atol=_tol, rtol=_tol)
|
|
if fftname[-4:] == 'fftn':
|
|
for ax in ((0,), (1,), (2,), None):
|
|
X_res = fft(X, axes=ax)
|
|
Y_res = fft(Y, axes=ax)
|
|
assert np.allclose(X_res, Y_res, atol=_tol, rtol=_tol)
|
|
else:
|
|
raise ValueError()
|
|
|
|
@test
|
|
def test_fft_output_order(order: str, n):
|
|
gen = rnd.default_rng(seed=22)
|
|
x = gen.random(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
|
|
|
|
@test
|
|
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)
|
|
|
|
@test
|
|
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 np.allclose(result, expected)
|
|
|
|
@test
|
|
def test_fft_with_integer_or_bool_input(data, fft):
|
|
# Regression test for gh-25819
|
|
result = fft(data)
|
|
float_data = data.astype(float)
|
|
expected = fft(float_data)
|
|
assert np.array_equal(result, expected)
|
|
|
|
|
|
test_fft_n()
|
|
test_fft1d_identity()
|
|
test_fft1d_identity_long_short(np.float32)
|
|
test_fft1d_identity_long_short(np.float64)
|
|
test_fft1d_identity_long_short_reversed(np.float32)
|
|
test_fft1d_identity_long_short_reversed(np.float64)
|
|
test_fft()
|
|
|
|
for axis in (0, 1):
|
|
for transpose in (False, True):
|
|
test_fft_out_argument(complex, transpose, axis)
|
|
test_fft_out_argument(float, transpose, axis)
|
|
|
|
test_fft_inplace_out(0)
|
|
test_fft_inplace_out(1)
|
|
test_fft_bad_out()
|
|
test_ifft(None)
|
|
test_ifft('backward')
|
|
test_ifft('ortho')
|
|
test_ifft('forward')
|
|
test_fft2()
|
|
test_ifft2()
|
|
test_fftn()
|
|
test_ifftn()
|
|
test_rfft()
|
|
test_rfft_even()
|
|
test_rfft_odd()
|
|
test_irfft()
|
|
test_rfft2()
|
|
test_irfft2()
|
|
test_rfftn()
|
|
test_irfftn()
|
|
test_hfft()
|
|
test_ihfft()
|
|
|
|
for op in (np.fft.fftn, np.fft.ifftn,
|
|
np.fft.rfftn, np.fft.irfftn):
|
|
test_axes(op)
|
|
|
|
for op in (np.fft.fftn, np.fft.ifftn,
|
|
np.fft.fft2, np.fft.ifft2):
|
|
test_s_negative_1(op)
|
|
|
|
for op in (np.fft.fftn, np.fft.ifftn,
|
|
np.fft.rfftn, np.fft.irfftn):
|
|
test_s_axes_none(op)
|
|
|
|
for op in (np.fft.fft2, np.fft.ifft2):
|
|
test_s_axes_none_2D(op)
|
|
|
|
test_all_1d_norm_preserving()
|
|
|
|
for axes in ((0, 1), (0, 2), None):
|
|
for transpose in (False, True):
|
|
test_fftn_out_argument(complex, transpose, axes)
|
|
test_fftn_out_argument(float, transpose, axes)
|
|
|
|
test_fftn_out_and_s_interaction(np.fft.fftn, rfftn=False)
|
|
test_fftn_out_and_s_interaction(np.fft.ifftn, rfftn=False)
|
|
test_fftn_out_and_s_interaction(np.fft.rfftn, rfftn=True)
|
|
test_irfftn_out_and_s_interaction((9, 5, 5))
|
|
test_irfftn_out_and_s_interaction((3, 3, 3))
|
|
|
|
for order in ('F', 'non-contiguous'):
|
|
test_fft_with_order(np.float32, order, np.fft.fft, 'fft')
|
|
test_fft_with_order(np.float64, order, np.fft.fft, 'fft')
|
|
test_fft_with_order(np.complex64, order, np.fft.fft, 'fft')
|
|
test_fft_with_order(np.complex128, order, np.fft.fft, 'fft')
|
|
|
|
test_fft_with_order(np.float32, order, np.fft.fft2, 'fft2')
|
|
test_fft_with_order(np.float64, order, np.fft.fft2, 'fft2')
|
|
test_fft_with_order(np.complex64, order, np.fft.fft2, 'fft2')
|
|
test_fft_with_order(np.complex128, order, np.fft.fft2, 'fft2')
|
|
|
|
test_fft_with_order(np.float32, order, np.fft.fftn, 'fftn')
|
|
test_fft_with_order(np.float64, order, np.fft.fftn, 'fftn')
|
|
test_fft_with_order(np.complex64, order, np.fft.fftn, 'fftn')
|
|
test_fft_with_order(np.complex128, order, np.fft.fftn, 'fftn')
|
|
|
|
test_fft_with_order(np.float32, order, np.fft.ifft, 'ifft')
|
|
test_fft_with_order(np.float64, order, np.fft.ifft, 'ifft')
|
|
test_fft_with_order(np.complex64, order, np.fft.ifft, 'ifft')
|
|
test_fft_with_order(np.complex128, order, np.fft.ifft, 'ifft')
|
|
|
|
test_fft_with_order(np.float32, order, np.fft.ifft2, 'ifft2')
|
|
test_fft_with_order(np.float64, order, np.fft.ifft2, 'ifft2')
|
|
test_fft_with_order(np.complex64, order, np.fft.ifft2, 'ifft2')
|
|
test_fft_with_order(np.complex128, order, np.fft.ifft2, 'ifft2')
|
|
|
|
test_fft_with_order(np.float32, order, np.fft.ifftn, 'ifftn')
|
|
test_fft_with_order(np.float64, order, np.fft.ifftn, 'ifftn')
|
|
test_fft_with_order(np.complex64, order, np.fft.ifftn, 'ifftn')
|
|
test_fft_with_order(np.complex128, order, np.fft.ifftn, 'ifftn')
|
|
|
|
for order in ('F', 'C'):
|
|
for n in [None, 7, 12]:
|
|
test_fft_output_order(order, n)
|
|
|
|
test_irfft_with_n_1_regression()
|
|
test_irfft_with_n_large_regression()
|
|
|
|
for fft in (np.fft.fft, np.fft.ifft, np.fft.rfft, np.fft.irfft):
|
|
for data in (np.array([False, True, False]),
|
|
np.arange(10, dtype=np.uint8),
|
|
np.arange(5, dtype=np.int16)):
|
|
test_fft_with_integer_or_bool_input(data, fft)
|
|
|
|
|
|
# Helper Tests
|
|
|
|
import numpy.fft as fft
|
|
|
|
@test
|
|
def TestFFTShift_test_definition():
|
|
x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
|
|
y = [-4, -3, -2, -1, 0, 1, 2, 3, 4]
|
|
assert np.allclose(fft.fftshift(x), y)
|
|
assert np.allclose(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 np.allclose(fft.fftshift(x), y)
|
|
assert np.allclose(fft.ifftshift(y), x)
|
|
|
|
@test
|
|
def TestFFTShift_test_inverse():
|
|
for n in [1, 4, 9, 100, 211]:
|
|
x = np.random.random((n,))
|
|
assert np.allclose(fft.ifftshift(fft.fftshift(x)), x)
|
|
|
|
@test
|
|
def TestFFTShift_test_axes_keyword():
|
|
freqs = [[0, 1, 2], [3, 4, -4], [-3, -2, -1]]
|
|
shifted = [[-1, -3, -2], [2, 0, 1], [-4, 3, 4]]
|
|
assert np.allclose(fft.fftshift(freqs, axes=(0, 1)), shifted)
|
|
assert np.allclose(fft.fftshift(freqs, axes=0),
|
|
fft.fftshift(freqs, axes=(0,)))
|
|
assert np.allclose(fft.ifftshift(shifted, axes=(0, 1)), freqs)
|
|
assert np.allclose(fft.ifftshift(shifted, axes=0),
|
|
fft.ifftshift(shifted, axes=(0,)))
|
|
|
|
assert np.allclose(fft.fftshift(freqs), shifted)
|
|
assert np.allclose(fft.ifftshift(shifted), freqs)
|
|
|
|
@test
|
|
def TestFFTShift_test_uneven_dims():
|
|
""" 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 np.allclose(fft.fftshift(freqs, axes=0), shift_dim0)
|
|
assert np.allclose(fft.ifftshift(shift_dim0, axes=0), freqs)
|
|
assert np.allclose(fft.fftshift(freqs, axes=(0,)), shift_dim0)
|
|
assert np.allclose(fft.ifftshift(shift_dim0, axes=(0,)), freqs)
|
|
|
|
# shift in dimension 1
|
|
shift_dim1 = [
|
|
[1, 0],
|
|
[3, 2],
|
|
[5, 4]
|
|
]
|
|
assert np.allclose(fft.fftshift(freqs, axes=1), shift_dim1)
|
|
assert np.allclose(fft.ifftshift(shift_dim1, axes=1), freqs)
|
|
|
|
# shift in both dimensions
|
|
shift_dim_both = [
|
|
[5, 4],
|
|
[1, 0],
|
|
[3, 2]
|
|
]
|
|
assert np.allclose(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
|
|
assert np.allclose(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
|
|
assert np.allclose(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
|
|
assert np.allclose(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
|
|
|
|
# axes=None (default) shift in all dimensions
|
|
assert np.allclose(fft.fftshift(freqs, axes=None), shift_dim_both)
|
|
assert np.allclose(fft.ifftshift(shift_dim_both, axes=None), freqs)
|
|
assert np.allclose(fft.fftshift(freqs), shift_dim_both)
|
|
assert np.allclose(fft.ifftshift(shift_dim_both), freqs)
|
|
|
|
@test
|
|
def TestFFTFreq_test_definition():
|
|
x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
|
|
assert np.allclose(9*fft.fftfreq(9), x)
|
|
assert np.allclose(9*np.pi*fft.fftfreq(9, np.pi), x)
|
|
x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
|
|
assert np.allclose(10*fft.fftfreq(10), x)
|
|
assert np.allclose(10*np.pi*fft.fftfreq(10, np.pi), x)
|
|
|
|
@test
|
|
def TestRFFTFreq_test_definition():
|
|
x = [0, 1, 2, 3, 4]
|
|
assert np.allclose(9*fft.rfftfreq(9), x)
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assert np.allclose(9*np.pi*fft.rfftfreq(9, np.pi), x)
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x = [0, 1, 2, 3, 4, 5]
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assert np.allclose(10*fft.rfftfreq(10), x)
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assert np.allclose(10*np.pi*fft.rfftfreq(10, np.pi), x)
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|
@test
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def TestIRFFTN_test_not_last_axis_success():
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ar, ai = np.random.random((2, 16, 8, 32))
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a = ar + ai*1j
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|
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axes = (-2,)
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|
|
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# Should not raise error
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|
fft.irfftn(a, axes=axes)
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|
|
|
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TestFFTShift_test_definition()
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TestFFTShift_test_inverse()
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|
TestFFTShift_test_axes_keyword()
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|
TestFFTShift_test_uneven_dims()
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|
TestFFTFreq_test_definition()
|
|
TestRFFTFreq_test_definition()
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|
TestIRFFTN_test_not_last_axis_success()
|