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Python

# Created by Pearu Peterson, September 2002
from __future__ import division, print_function, absolute_import
__usage__ = """
Build fftpack:
python setup_fftpack.py build
Run tests if scipy is installed:
python -c 'import scipy;scipy.fftpack.test()'
Run tests if fftpack is not installed:
python tests/test_basic.py
"""
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 scipy.fftpack import _fftpack as fftpack
from scipy.fftpack.basic import _is_safe_size
from numpy import (arange, add, 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 = "size: %s rdt: %s" % (size, rdt)
assert_array_less(np.linalg.norm(x - y), rtol*np.linalg.norm(x), err_msg)
def random(size):
return rand(*size)
def get_mat(n):
data = arange(n)
data = add.outer(data, data)
return data
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(object):
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_djbfft(self):
for i in range(2,14):
n = 2**i
x = list(range(n))
y = fftpack.zfft(x)
y2 = numpy.fft.fft(x)
assert_array_almost_equal(y,y2)
y = fftpack.zrfft(x)
assert_array_almost_equal(y,y2)
def test_invalid_sizes(self):
assert_raises(ValueError, fft, [])
assert_raises(ValueError, fft, [[1,1],[2,2]], -5)
def test__is_safe_size(self):
vals = [(0, True), (1, True), (2, True), (3, True), (4, True), (5, True), (6, True), (7, False),
(15, True), (16, True), (17, False), (18, True), (21, False), (25, True), (50, True),
(120, True), (210, False)]
for n, is_safe in vals:
assert_equal(_is_safe_size(n), is_safe)
class TestDoubleFFT(_TestFFTBase):
def setup_method(self):
self.cdt = np.cdouble
self.rdt = np.double
class TestSingleFFT(_TestFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
@pytest.mark.xfail(run=False, reason="single-precision FFT implementation is partially disabled, until accuracy issues with large prime powers are resolved")
def test_notice(self):
pass
class TestFloat16FFT(object):
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(object):
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_djbfft(self):
for i in range(2,14):
n = 2**i
x = list(range(n))
y = fftpack.zfft(x,direction=-1)
y2 = numpy.fft.ifft(x)
assert_array_almost_equal(y,y2)
y = fftpack.zrfft(x,direction=-1)
assert_array_almost_equal(y,y2)
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.cdouble
self.rdt = np.double
class TestSingleIFFT(_TestIFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
class _TestRFFTBase(object):
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_djbfft(self):
from numpy.fft import fft as numpy_fft
for i in range(2,14):
n = 2**i
x = list(range(n))
y2 = numpy_fft(x)
y1 = zeros((n,),dtype=double)
y1[0] = y2[0].real
y1[-1] = y2[n//2].real
for k in range(1, n//2):
y1[2*k-1] = y2[k].real
y1[2*k] = y2[k].imag
y = fftpack.drfft(x)
assert_array_almost_equal(y,y1)
def test_invalid_sizes(self):
assert_raises(ValueError, rfft, [])
assert_raises(ValueError, rfft, [[1,1],[2,2]], -5)
# See gh-5790
class MockSeries(object):
def __init__(self, data):
self.data = np.asarray(data)
def __getattr__(self, item):
try:
return getattr(self.data, item)
except AttributeError:
raise AttributeError(("'MockSeries' object "
"has no attribute '{attr}'".
format(attr=item)))
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]
out = rfft(xs)
# Data should not have been overwritten
assert_equal(x, expected)
assert_equal(xs.data, expected)
class TestRFFTDouble(_TestRFFTBase):
def setup_method(self):
self.cdt = np.cdouble
self.rdt = np.double
class TestRFFTSingle(_TestRFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
class _TestIRFFTBase(object):
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_djbfft(self):
from numpy.fft import ifft as numpy_ifft
for i in range(2,14):
n = 2**i
x = list(range(n))
x1 = zeros((n,),dtype=cdouble)
x1[0] = x[0]
for k in range(1, n//2):
x1[k] = x[2*k-1]+1j*x[2*k]
x1[n-k] = x[2*k-1]-1j*x[2*k]
x1[n//2] = x[-1]
y1 = numpy_ifft(x1)
y = fftpack.drfft(x,direction=-1)
assert_array_almost_equal(y,y1)
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)
# 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.cdouble
self.rdt = np.double
self.ndec = 14
class TestIRFFTSingle(_TestIRFFTBase):
def setup_method(self):
self.cdt = np.complex64
self.rdt = np.float32
self.ndec = 5
class Testfft2(object):
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(object):
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(object):
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(object):
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 TestLongDoubleFailure(object):
def setup_method(self):
np.random.seed(1234)
def test_complex(self):
if np.dtype(np.longcomplex).itemsize == np.dtype(complex).itemsize:
# longdouble == double; so fft is supported
return
x = np.random.randn(10).astype(np.longdouble) + \
1j * np.random.randn(10).astype(np.longdouble)
for f in [fft, ifft]:
try:
f(x)
raise AssertionError("Type {0} not supported but does not fail" %
np.longcomplex)
except ValueError:
pass
def test_real(self):
if np.dtype(np.longdouble).itemsize == np.dtype(np.double).itemsize:
# longdouble == double; so fft is supported
return
x = np.random.randn(10).astype(np.longcomplex)
for f in [fft, ifft]:
try:
f(x)
raise AssertionError("Type %r not supported but does not fail" %
np.longcomplex)
except ValueError:
pass
class FakeArray(object):
def __init__(self, data):
self._data = data
self.__array_interface__ = data.__array_interface__
class FakeArray2(object):
def __init__(self, data):
self._data = data
def __array__(self):
return self._data
class TestOverwrite(object):
"""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, should_overwrite):
x2 = x.copy()
for fake in [lambda x: x, FakeArray, FakeArray2]:
routine(fake(x2), fftsize, axis, overwrite_x=overwrite_x)
sig = "%s(%s%r, %r, axis=%r, overwrite_x=%r)" % (
routine.__name__, x.dtype, x.shape, fftsize, axis, overwrite_x)
if not should_overwrite:
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)
should_overwrite = (overwrite_x
and dtype in overwritable_dtypes
and fftsize <= shape[axis]
and (len(shape) == 1 or
(axis % len(shape) == len(shape)-1
and fftsize == shape[axis])))
self._check(data, routine, fftsize, axis,
overwrite_x=overwrite_x,
should_overwrite=should_overwrite)
@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):
should_overwrite = (overwrite_x
and data.ndim == 1
and np.all([x < y for x, y in zip(fftshape,
part_shape)])
and dtype in overwritable_dtypes)
self._check(data, routine, fftshape, axes,
overwrite_x=overwrite_x,
should_overwrite=should_overwrite)
if data.ndim > 1:
# check fortran order: it never overwrites
self._check(data.T, routine, fftshape, axes,
overwrite_x=overwrite_x,
should_overwrite=False)
@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)