ai-content-maker/.venv/Lib/site-packages/scipy/fftpack/tests/test_basic.py

874 lines
30 KiB
Python

# Created by Pearu Peterson, September 2002
from numpy.testing import (assert_, assert_equal, assert_array_almost_equal,
assert_array_almost_equal_nulp, assert_array_less)
import pytest
from pytest import raises as assert_raises
from scipy.fftpack import ifft, fft, fftn, ifftn, rfft, irfft, fft2
from numpy import (arange, array, asarray, zeros, dot, exp, pi,
swapaxes, double, cdouble)
import numpy as np
import numpy.fft
from numpy.random import rand
# "large" composite numbers supported by FFTPACK
LARGE_COMPOSITE_SIZES = [
2**13,
2**5 * 3**5,
2**3 * 3**3 * 5**2,
]
SMALL_COMPOSITE_SIZES = [
2,
2*3*5,
2*2*3*3,
]
# prime
LARGE_PRIME_SIZES = [
2011
]
SMALL_PRIME_SIZES = [
29
]
def _assert_close_in_norm(x, y, rtol, size, rdt):
# helper function for testing
err_msg = f"size: {size} rdt: {rdt}"
assert_array_less(np.linalg.norm(x - y), rtol*np.linalg.norm(x), err_msg)
def random(size):
return rand(*size)
def direct_dft(x):
x = asarray(x)
n = len(x)
y = zeros(n, dtype=cdouble)
w = -arange(n)*(2j*pi/n)
for i in range(n):
y[i] = dot(exp(i*w), x)
return y
def direct_idft(x):
x = asarray(x)
n = len(x)
y = zeros(n, dtype=cdouble)
w = arange(n)*(2j*pi/n)
for i in range(n):
y[i] = dot(exp(i*w), x)/n
return y
def direct_dftn(x):
x = asarray(x)
for axis in range(len(x.shape)):
x = fft(x, axis=axis)
return x
def direct_idftn(x):
x = asarray(x)
for axis in range(len(x.shape)):
x = ifft(x, axis=axis)
return x
def direct_rdft(x):
x = asarray(x)
n = len(x)
w = -arange(n)*(2j*pi/n)
r = zeros(n, dtype=double)
for i in range(n//2+1):
y = dot(exp(i*w), x)
if i:
r[2*i-1] = y.real
if 2*i < n:
r[2*i] = y.imag
else:
r[0] = y.real
return r
def direct_irdft(x):
x = asarray(x)
n = len(x)
x1 = zeros(n, dtype=cdouble)
for i in range(n//2+1):
if i:
if 2*i < n:
x1[i] = x[2*i-1] + 1j*x[2*i]
x1[n-i] = x[2*i-1] - 1j*x[2*i]
else:
x1[i] = x[2*i-1]
else:
x1[0] = x[0]
return direct_idft(x1).real
class _TestFFTBase:
def setup_method(self):
self.cdt = None
self.rdt = None
np.random.seed(1234)
def test_definition(self):
x = np.array([1,2,3,4+1j,1,2,3,4+2j], dtype=self.cdt)
y = fft(x)
assert_equal(y.dtype, self.cdt)
y1 = direct_dft(x)
assert_array_almost_equal(y,y1)
x = np.array([1,2,3,4+0j,5], dtype=self.cdt)
assert_array_almost_equal(fft(x),direct_dft(x))
def test_n_argument_real(self):
x1 = np.array([1,2,3,4], dtype=self.rdt)
x2 = np.array([1,2,3,4], dtype=self.rdt)
y = fft([x1,x2],n=4)
assert_equal(y.dtype, self.cdt)
assert_equal(y.shape,(2,4))
assert_array_almost_equal(y[0],direct_dft(x1))
assert_array_almost_equal(y[1],direct_dft(x2))
def _test_n_argument_complex(self):
x1 = np.array([1,2,3,4+1j], dtype=self.cdt)
x2 = np.array([1,2,3,4+1j], dtype=self.cdt)
y = fft([x1,x2],n=4)
assert_equal(y.dtype, self.cdt)
assert_equal(y.shape,(2,4))
assert_array_almost_equal(y[0],direct_dft(x1))
assert_array_almost_equal(y[1],direct_dft(x2))
def test_invalid_sizes(self):
assert_raises(ValueError, fft, [])
assert_raises(ValueError, fft, [[1,1],[2,2]], -5)
class TestDoubleFFT(_TestFFTBase):
def setup_method(self):
self.cdt = np.complex128
self.rdt = np.float64
class TestSingleFFT(_TestFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
reason = ("single-precision FFT implementation is partially disabled, "
"until accuracy issues with large prime powers are resolved")
@pytest.mark.xfail(run=False, reason=reason)
def test_notice(self):
pass
class TestFloat16FFT:
def test_1_argument_real(self):
x1 = np.array([1, 2, 3, 4], dtype=np.float16)
y = fft(x1, n=4)
assert_equal(y.dtype, np.complex64)
assert_equal(y.shape, (4, ))
assert_array_almost_equal(y, direct_dft(x1.astype(np.float32)))
def test_n_argument_real(self):
x1 = np.array([1, 2, 3, 4], dtype=np.float16)
x2 = np.array([1, 2, 3, 4], dtype=np.float16)
y = fft([x1, x2], n=4)
assert_equal(y.dtype, np.complex64)
assert_equal(y.shape, (2, 4))
assert_array_almost_equal(y[0], direct_dft(x1.astype(np.float32)))
assert_array_almost_equal(y[1], direct_dft(x2.astype(np.float32)))
class _TestIFFTBase:
def setup_method(self):
np.random.seed(1234)
def test_definition(self):
x = np.array([1,2,3,4+1j,1,2,3,4+2j], self.cdt)
y = ifft(x)
y1 = direct_idft(x)
assert_equal(y.dtype, self.cdt)
assert_array_almost_equal(y,y1)
x = np.array([1,2,3,4+0j,5], self.cdt)
assert_array_almost_equal(ifft(x),direct_idft(x))
def test_definition_real(self):
x = np.array([1,2,3,4,1,2,3,4], self.rdt)
y = ifft(x)
assert_equal(y.dtype, self.cdt)
y1 = direct_idft(x)
assert_array_almost_equal(y,y1)
x = np.array([1,2,3,4,5], dtype=self.rdt)
assert_equal(y.dtype, self.cdt)
assert_array_almost_equal(ifft(x),direct_idft(x))
def test_random_complex(self):
for size in [1,51,111,100,200,64,128,256,1024]:
x = random([size]).astype(self.cdt)
x = random([size]).astype(self.cdt) + 1j*x
y1 = ifft(fft(x))
y2 = fft(ifft(x))
assert_equal(y1.dtype, self.cdt)
assert_equal(y2.dtype, self.cdt)
assert_array_almost_equal(y1, x)
assert_array_almost_equal(y2, x)
def test_random_real(self):
for size in [1,51,111,100,200,64,128,256,1024]:
x = random([size]).astype(self.rdt)
y1 = ifft(fft(x))
y2 = fft(ifft(x))
assert_equal(y1.dtype, self.cdt)
assert_equal(y2.dtype, self.cdt)
assert_array_almost_equal(y1, x)
assert_array_almost_equal(y2, x)
def test_size_accuracy(self):
# Sanity check for the accuracy for prime and non-prime sized inputs
if self.rdt == np.float32:
rtol = 1e-5
elif self.rdt == np.float64:
rtol = 1e-10
for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
np.random.seed(1234)
x = np.random.rand(size).astype(self.rdt)
y = ifft(fft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
y = fft(ifft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
x = (x + 1j*np.random.rand(size)).astype(self.cdt)
y = ifft(fft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
y = fft(ifft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
def test_invalid_sizes(self):
assert_raises(ValueError, ifft, [])
assert_raises(ValueError, ifft, [[1,1],[2,2]], -5)
class TestDoubleIFFT(_TestIFFTBase):
def setup_method(self):
self.cdt = np.complex128
self.rdt = np.float64
class TestSingleIFFT(_TestIFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
class _TestRFFTBase:
def setup_method(self):
np.random.seed(1234)
def test_definition(self):
for t in [[1, 2, 3, 4, 1, 2, 3, 4], [1, 2, 3, 4, 1, 2, 3, 4, 5]]:
x = np.array(t, dtype=self.rdt)
y = rfft(x)
y1 = direct_rdft(x)
assert_array_almost_equal(y,y1)
assert_equal(y.dtype, self.rdt)
def test_invalid_sizes(self):
assert_raises(ValueError, rfft, [])
assert_raises(ValueError, rfft, [[1,1],[2,2]], -5)
# See gh-5790
class MockSeries:
def __init__(self, data):
self.data = np.asarray(data)
def __getattr__(self, item):
try:
return getattr(self.data, item)
except AttributeError as e:
raise AttributeError("'MockSeries' object "
f"has no attribute '{item}'") from e
def test_non_ndarray_with_dtype(self):
x = np.array([1., 2., 3., 4., 5.])
xs = _TestRFFTBase.MockSeries(x)
expected = [1, 2, 3, 4, 5]
rfft(xs)
# Data should not have been overwritten
assert_equal(x, expected)
assert_equal(xs.data, expected)
def test_complex_input(self):
assert_raises(TypeError, rfft, np.arange(4, dtype=np.complex64))
class TestRFFTDouble(_TestRFFTBase):
def setup_method(self):
self.cdt = np.complex128
self.rdt = np.float64
class TestRFFTSingle(_TestRFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
class _TestIRFFTBase:
def setup_method(self):
np.random.seed(1234)
def test_definition(self):
x1 = [1,2,3,4,1,2,3,4]
x1_1 = [1,2+3j,4+1j,2+3j,4,2-3j,4-1j,2-3j]
x2 = [1,2,3,4,1,2,3,4,5]
x2_1 = [1,2+3j,4+1j,2+3j,4+5j,4-5j,2-3j,4-1j,2-3j]
def _test(x, xr):
y = irfft(np.array(x, dtype=self.rdt))
y1 = direct_irdft(x)
assert_equal(y.dtype, self.rdt)
assert_array_almost_equal(y,y1, decimal=self.ndec)
assert_array_almost_equal(y,ifft(xr), decimal=self.ndec)
_test(x1, x1_1)
_test(x2, x2_1)
def test_random_real(self):
for size in [1,51,111,100,200,64,128,256,1024]:
x = random([size]).astype(self.rdt)
y1 = irfft(rfft(x))
y2 = rfft(irfft(x))
assert_equal(y1.dtype, self.rdt)
assert_equal(y2.dtype, self.rdt)
assert_array_almost_equal(y1, x, decimal=self.ndec,
err_msg="size=%d" % size)
assert_array_almost_equal(y2, x, decimal=self.ndec,
err_msg="size=%d" % size)
def test_size_accuracy(self):
# Sanity check for the accuracy for prime and non-prime sized inputs
if self.rdt == np.float32:
rtol = 1e-5
elif self.rdt == np.float64:
rtol = 1e-10
for size in LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES:
np.random.seed(1234)
x = np.random.rand(size).astype(self.rdt)
y = irfft(rfft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
y = rfft(irfft(x))
_assert_close_in_norm(x, y, rtol, size, self.rdt)
def test_invalid_sizes(self):
assert_raises(ValueError, irfft, [])
assert_raises(ValueError, irfft, [[1,1],[2,2]], -5)
def test_complex_input(self):
assert_raises(TypeError, irfft, np.arange(4, dtype=np.complex64))
# self.ndec is bogus; we should have a assert_array_approx_equal for number of
# significant digits
class TestIRFFTDouble(_TestIRFFTBase):
def setup_method(self):
self.cdt = np.complex128
self.rdt = np.float64
self.ndec = 14
class TestIRFFTSingle(_TestIRFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
self.ndec = 5
class Testfft2:
def setup_method(self):
np.random.seed(1234)
def test_regression_244(self):
"""FFT returns wrong result with axes parameter."""
# fftn (and hence fft2) used to break when both axes and shape were
# used
x = numpy.ones((4, 4, 2))
y = fft2(x, shape=(8, 8), axes=(-3, -2))
y_r = numpy.fft.fftn(x, s=(8, 8), axes=(-3, -2))
assert_array_almost_equal(y, y_r)
def test_invalid_sizes(self):
assert_raises(ValueError, fft2, [[]])
assert_raises(ValueError, fft2, [[1, 1], [2, 2]], (4, -3))
class TestFftnSingle:
def setup_method(self):
np.random.seed(1234)
def test_definition(self):
x = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
y = fftn(np.array(x, np.float32))
assert_(y.dtype == np.complex64,
msg="double precision output with single precision")
y_r = np.array(fftn(x), np.complex64)
assert_array_almost_equal_nulp(y, y_r)
@pytest.mark.parametrize('size', SMALL_COMPOSITE_SIZES + SMALL_PRIME_SIZES)
def test_size_accuracy_small(self, size):
x = np.random.rand(size, size) + 1j*np.random.rand(size, size)
y1 = fftn(x.real.astype(np.float32))
y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
assert_equal(y1.dtype, np.complex64)
assert_array_almost_equal_nulp(y1, y2, 2000)
@pytest.mark.parametrize('size', LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES)
def test_size_accuracy_large(self, size):
x = np.random.rand(size, 3) + 1j*np.random.rand(size, 3)
y1 = fftn(x.real.astype(np.float32))
y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
assert_equal(y1.dtype, np.complex64)
assert_array_almost_equal_nulp(y1, y2, 2000)
def test_definition_float16(self):
x = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
y = fftn(np.array(x, np.float16))
assert_equal(y.dtype, np.complex64)
y_r = np.array(fftn(x), np.complex64)
assert_array_almost_equal_nulp(y, y_r)
@pytest.mark.parametrize('size', SMALL_COMPOSITE_SIZES + SMALL_PRIME_SIZES)
def test_float16_input_small(self, size):
x = np.random.rand(size, size) + 1j*np.random.rand(size, size)
y1 = fftn(x.real.astype(np.float16))
y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
assert_equal(y1.dtype, np.complex64)
assert_array_almost_equal_nulp(y1, y2, 5e5)
@pytest.mark.parametrize('size', LARGE_COMPOSITE_SIZES + LARGE_PRIME_SIZES)
def test_float16_input_large(self, size):
x = np.random.rand(size, 3) + 1j*np.random.rand(size, 3)
y1 = fftn(x.real.astype(np.float16))
y2 = fftn(x.real.astype(np.float64)).astype(np.complex64)
assert_equal(y1.dtype, np.complex64)
assert_array_almost_equal_nulp(y1, y2, 2e6)
class TestFftn:
def setup_method(self):
np.random.seed(1234)
def test_definition(self):
x = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
y = fftn(x)
assert_array_almost_equal(y, direct_dftn(x))
x = random((20, 26))
assert_array_almost_equal(fftn(x), direct_dftn(x))
x = random((5, 4, 3, 20))
assert_array_almost_equal(fftn(x), direct_dftn(x))
def test_axes_argument(self):
# plane == ji_plane, x== kji_space
plane1 = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
plane2 = [[10, 11, 12],
[13, 14, 15],
[16, 17, 18]]
plane3 = [[19, 20, 21],
[22, 23, 24],
[25, 26, 27]]
ki_plane1 = [[1, 2, 3],
[10, 11, 12],
[19, 20, 21]]
ki_plane2 = [[4, 5, 6],
[13, 14, 15],
[22, 23, 24]]
ki_plane3 = [[7, 8, 9],
[16, 17, 18],
[25, 26, 27]]
jk_plane1 = [[1, 10, 19],
[4, 13, 22],
[7, 16, 25]]
jk_plane2 = [[2, 11, 20],
[5, 14, 23],
[8, 17, 26]]
jk_plane3 = [[3, 12, 21],
[6, 15, 24],
[9, 18, 27]]
kj_plane1 = [[1, 4, 7],
[10, 13, 16], [19, 22, 25]]
kj_plane2 = [[2, 5, 8],
[11, 14, 17], [20, 23, 26]]
kj_plane3 = [[3, 6, 9],
[12, 15, 18], [21, 24, 27]]
ij_plane1 = [[1, 4, 7],
[2, 5, 8],
[3, 6, 9]]
ij_plane2 = [[10, 13, 16],
[11, 14, 17],
[12, 15, 18]]
ij_plane3 = [[19, 22, 25],
[20, 23, 26],
[21, 24, 27]]
ik_plane1 = [[1, 10, 19],
[2, 11, 20],
[3, 12, 21]]
ik_plane2 = [[4, 13, 22],
[5, 14, 23],
[6, 15, 24]]
ik_plane3 = [[7, 16, 25],
[8, 17, 26],
[9, 18, 27]]
ijk_space = [jk_plane1, jk_plane2, jk_plane3]
ikj_space = [kj_plane1, kj_plane2, kj_plane3]
jik_space = [ik_plane1, ik_plane2, ik_plane3]
jki_space = [ki_plane1, ki_plane2, ki_plane3]
kij_space = [ij_plane1, ij_plane2, ij_plane3]
x = array([plane1, plane2, plane3])
assert_array_almost_equal(fftn(x),
fftn(x, axes=(-3, -2, -1))) # kji_space
assert_array_almost_equal(fftn(x), fftn(x, axes=(0, 1, 2)))
assert_array_almost_equal(fftn(x, axes=(0, 2)), fftn(x, axes=(0, -1)))
y = fftn(x, axes=(2, 1, 0)) # ijk_space
assert_array_almost_equal(swapaxes(y, -1, -3), fftn(ijk_space))
y = fftn(x, axes=(2, 0, 1)) # ikj_space
assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -1, -2),
fftn(ikj_space))
y = fftn(x, axes=(1, 2, 0)) # jik_space
assert_array_almost_equal(swapaxes(swapaxes(y, -1, -3), -3, -2),
fftn(jik_space))
y = fftn(x, axes=(1, 0, 2)) # jki_space
assert_array_almost_equal(swapaxes(y, -2, -3), fftn(jki_space))
y = fftn(x, axes=(0, 2, 1)) # kij_space
assert_array_almost_equal(swapaxes(y, -2, -1), fftn(kij_space))
y = fftn(x, axes=(-2, -1)) # ji_plane
assert_array_almost_equal(fftn(plane1), y[0])
assert_array_almost_equal(fftn(plane2), y[1])
assert_array_almost_equal(fftn(plane3), y[2])
y = fftn(x, axes=(1, 2)) # ji_plane
assert_array_almost_equal(fftn(plane1), y[0])
assert_array_almost_equal(fftn(plane2), y[1])
assert_array_almost_equal(fftn(plane3), y[2])
y = fftn(x, axes=(-3, -2)) # kj_plane
assert_array_almost_equal(fftn(x[:, :, 0]), y[:, :, 0])
assert_array_almost_equal(fftn(x[:, :, 1]), y[:, :, 1])
assert_array_almost_equal(fftn(x[:, :, 2]), y[:, :, 2])
y = fftn(x, axes=(-3, -1)) # ki_plane
assert_array_almost_equal(fftn(x[:, 0, :]), y[:, 0, :])
assert_array_almost_equal(fftn(x[:, 1, :]), y[:, 1, :])
assert_array_almost_equal(fftn(x[:, 2, :]), y[:, 2, :])
y = fftn(x, axes=(-1, -2)) # ij_plane
assert_array_almost_equal(fftn(ij_plane1), swapaxes(y[0], -2, -1))
assert_array_almost_equal(fftn(ij_plane2), swapaxes(y[1], -2, -1))
assert_array_almost_equal(fftn(ij_plane3), swapaxes(y[2], -2, -1))
y = fftn(x, axes=(-1, -3)) # ik_plane
assert_array_almost_equal(fftn(ik_plane1),
swapaxes(y[:, 0, :], -1, -2))
assert_array_almost_equal(fftn(ik_plane2),
swapaxes(y[:, 1, :], -1, -2))
assert_array_almost_equal(fftn(ik_plane3),
swapaxes(y[:, 2, :], -1, -2))
y = fftn(x, axes=(-2, -3)) # jk_plane
assert_array_almost_equal(fftn(jk_plane1),
swapaxes(y[:, :, 0], -1, -2))
assert_array_almost_equal(fftn(jk_plane2),
swapaxes(y[:, :, 1], -1, -2))
assert_array_almost_equal(fftn(jk_plane3),
swapaxes(y[:, :, 2], -1, -2))
y = fftn(x, axes=(-1,)) # i_line
for i in range(3):
for j in range(3):
assert_array_almost_equal(fft(x[i, j, :]), y[i, j, :])
y = fftn(x, axes=(-2,)) # j_line
for i in range(3):
for j in range(3):
assert_array_almost_equal(fft(x[i, :, j]), y[i, :, j])
y = fftn(x, axes=(0,)) # k_line
for i in range(3):
for j in range(3):
assert_array_almost_equal(fft(x[:, i, j]), y[:, i, j])
y = fftn(x, axes=()) # point
assert_array_almost_equal(y, x)
def test_shape_argument(self):
small_x = [[1, 2, 3],
[4, 5, 6]]
large_x1 = [[1, 2, 3, 0],
[4, 5, 6, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]
y = fftn(small_x, shape=(4, 4))
assert_array_almost_equal(y, fftn(large_x1))
y = fftn(small_x, shape=(3, 4))
assert_array_almost_equal(y, fftn(large_x1[:-1]))
def test_shape_axes_argument(self):
small_x = [[1, 2, 3],
[4, 5, 6],
[7, 8, 9]]
large_x1 = array([[1, 2, 3, 0],
[4, 5, 6, 0],
[7, 8, 9, 0],
[0, 0, 0, 0]])
y = fftn(small_x, shape=(4, 4), axes=(-2, -1))
assert_array_almost_equal(y, fftn(large_x1))
y = fftn(small_x, shape=(4, 4), axes=(-1, -2))
assert_array_almost_equal(y, swapaxes(
fftn(swapaxes(large_x1, -1, -2)), -1, -2))
def test_shape_axes_argument2(self):
# Change shape of the last axis
x = numpy.random.random((10, 5, 3, 7))
y = fftn(x, axes=(-1,), shape=(8,))
assert_array_almost_equal(y, fft(x, axis=-1, n=8))
# Change shape of an arbitrary axis which is not the last one
x = numpy.random.random((10, 5, 3, 7))
y = fftn(x, axes=(-2,), shape=(8,))
assert_array_almost_equal(y, fft(x, axis=-2, n=8))
# Change shape of axes: cf #244, where shape and axes were mixed up
x = numpy.random.random((4, 4, 2))
y = fftn(x, axes=(-3, -2), shape=(8, 8))
assert_array_almost_equal(y,
numpy.fft.fftn(x, axes=(-3, -2), s=(8, 8)))
def test_shape_argument_more(self):
x = zeros((4, 4, 2))
with assert_raises(ValueError,
match="when given, axes and shape arguments"
" have to be of the same length"):
fftn(x, shape=(8, 8, 2, 1))
def test_invalid_sizes(self):
with assert_raises(ValueError,
match="invalid number of data points"
r" \(\[1, 0\]\) specified"):
fftn([[]])
with assert_raises(ValueError,
match="invalid number of data points"
r" \(\[4, -3\]\) specified"):
fftn([[1, 1], [2, 2]], (4, -3))
class TestIfftn:
dtype = None
cdtype = None
def setup_method(self):
np.random.seed(1234)
@pytest.mark.parametrize('dtype,cdtype,maxnlp',
[(np.float64, np.complex128, 2000),
(np.float32, np.complex64, 3500)])
def test_definition(self, dtype, cdtype, maxnlp):
x = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]], dtype=dtype)
y = ifftn(x)
assert_equal(y.dtype, cdtype)
assert_array_almost_equal_nulp(y, direct_idftn(x), maxnlp)
x = random((20, 26))
assert_array_almost_equal_nulp(ifftn(x), direct_idftn(x), maxnlp)
x = random((5, 4, 3, 20))
assert_array_almost_equal_nulp(ifftn(x), direct_idftn(x), maxnlp)
@pytest.mark.parametrize('maxnlp', [2000, 3500])
@pytest.mark.parametrize('size', [1, 2, 51, 32, 64, 92])
def test_random_complex(self, maxnlp, size):
x = random([size, size]) + 1j*random([size, size])
assert_array_almost_equal_nulp(ifftn(fftn(x)), x, maxnlp)
assert_array_almost_equal_nulp(fftn(ifftn(x)), x, maxnlp)
def test_invalid_sizes(self):
with assert_raises(ValueError,
match="invalid number of data points"
r" \(\[1, 0\]\) specified"):
ifftn([[]])
with assert_raises(ValueError,
match="invalid number of data points"
r" \(\[4, -3\]\) specified"):
ifftn([[1, 1], [2, 2]], (4, -3))
class FakeArray:
def __init__(self, data):
self._data = data
self.__array_interface__ = data.__array_interface__
class FakeArray2:
def __init__(self, data):
self._data = data
def __array__(self, dtype=None, copy=None):
return self._data
class TestOverwrite:
"""Check input overwrite behavior of the FFT functions."""
real_dtypes = (np.float32, np.float64)
dtypes = real_dtypes + (np.complex64, np.complex128)
fftsizes = [8, 16, 32]
def _check(self, x, routine, fftsize, axis, overwrite_x):
x2 = x.copy()
for fake in [lambda x: x, FakeArray, FakeArray2]:
routine(fake(x2), fftsize, axis, overwrite_x=overwrite_x)
sig = "{}({}{!r}, {!r}, axis={!r}, overwrite_x={!r})".format(
routine.__name__, x.dtype, x.shape, fftsize, axis, overwrite_x)
if not overwrite_x:
assert_equal(x2, x, err_msg="spurious overwrite in %s" % sig)
def _check_1d(self, routine, dtype, shape, axis, overwritable_dtypes,
fftsize, overwrite_x):
np.random.seed(1234)
if np.issubdtype(dtype, np.complexfloating):
data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
else:
data = np.random.randn(*shape)
data = data.astype(dtype)
self._check(data, routine, fftsize, axis,
overwrite_x=overwrite_x)
@pytest.mark.parametrize('dtype', dtypes)
@pytest.mark.parametrize('fftsize', fftsizes)
@pytest.mark.parametrize('overwrite_x', [True, False])
@pytest.mark.parametrize('shape,axes', [((16,), -1),
((16, 2), 0),
((2, 16), 1)])
def test_fft_ifft(self, dtype, fftsize, overwrite_x, shape, axes):
overwritable = (np.complex128, np.complex64)
self._check_1d(fft, dtype, shape, axes, overwritable,
fftsize, overwrite_x)
self._check_1d(ifft, dtype, shape, axes, overwritable,
fftsize, overwrite_x)
@pytest.mark.parametrize('dtype', real_dtypes)
@pytest.mark.parametrize('fftsize', fftsizes)
@pytest.mark.parametrize('overwrite_x', [True, False])
@pytest.mark.parametrize('shape,axes', [((16,), -1),
((16, 2), 0),
((2, 16), 1)])
def test_rfft_irfft(self, dtype, fftsize, overwrite_x, shape, axes):
overwritable = self.real_dtypes
self._check_1d(irfft, dtype, shape, axes, overwritable,
fftsize, overwrite_x)
self._check_1d(rfft, dtype, shape, axes, overwritable,
fftsize, overwrite_x)
def _check_nd_one(self, routine, dtype, shape, axes, overwritable_dtypes,
overwrite_x):
np.random.seed(1234)
if np.issubdtype(dtype, np.complexfloating):
data = np.random.randn(*shape) + 1j*np.random.randn(*shape)
else:
data = np.random.randn(*shape)
data = data.astype(dtype)
def fftshape_iter(shp):
if len(shp) <= 0:
yield ()
else:
for j in (shp[0]//2, shp[0], shp[0]*2):
for rest in fftshape_iter(shp[1:]):
yield (j,) + rest
if axes is None:
part_shape = shape
else:
part_shape = tuple(np.take(shape, axes))
for fftshape in fftshape_iter(part_shape):
self._check(data, routine, fftshape, axes,
overwrite_x=overwrite_x)
if data.ndim > 1:
self._check(data.T, routine, fftshape, axes,
overwrite_x=overwrite_x)
@pytest.mark.parametrize('dtype', dtypes)
@pytest.mark.parametrize('overwrite_x', [True, False])
@pytest.mark.parametrize('shape,axes', [((16,), None),
((16,), (0,)),
((16, 2), (0,)),
((2, 16), (1,)),
((8, 16), None),
((8, 16), (0, 1)),
((8, 16, 2), (0, 1)),
((8, 16, 2), (1, 2)),
((8, 16, 2), (0,)),
((8, 16, 2), (1,)),
((8, 16, 2), (2,)),
((8, 16, 2), None),
((8, 16, 2), (0, 1, 2))])
def test_fftn_ifftn(self, dtype, overwrite_x, shape, axes):
overwritable = (np.complex128, np.complex64)
self._check_nd_one(fftn, dtype, shape, axes, overwritable,
overwrite_x)
self._check_nd_one(ifftn, dtype, shape, axes, overwritable,
overwrite_x)
@pytest.mark.parametrize('func', [fftn, ifftn, fft2])
def test_shape_axes_ndarray(func):
# Test fftn and ifftn work with NumPy arrays for shape and axes arguments
# Regression test for gh-13342
a = np.random.rand(10, 10)
expect = func(a, shape=(5, 5))
actual = func(a, shape=np.array([5, 5]))
assert_equal(expect, actual)
expect = func(a, axes=(-1,))
actual = func(a, axes=np.array([-1,]))
assert_equal(expect, actual)
expect = func(a, shape=(4, 7), axes=(1, 0))
actual = func(a, shape=np.array([4, 7]), axes=np.array([1, 0]))
assert_equal(expect, actual)