170 lines
6.2 KiB
Python
170 lines
6.2 KiB
Python
|
"""Test functions for fftpack.helper module
|
||
|
|
|
||
|
|
Copied from fftpack.helper by Pearu Peterson, October 2005
|
||
|
|
|
||
|
|
"""
|
||
|
|
from __future__ import division, absolute_import, print_function
|
||
|
|
import numpy as np
|
||
|
|
from numpy.testing import assert_array_almost_equal, assert_equal
|
||
|
|
from numpy import fft, pi
|
||
|
|
|
||
|
|
|
||
|
|
class TestFFTShift(object):
|
||
|
|
|
||
|
|
def test_definition(self):
|
||
|
|
x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
|
||
|
|
y = [-4, -3, -2, -1, 0, 1, 2, 3, 4]
|
||
|
|
assert_array_almost_equal(fft.fftshift(x), y)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(y), x)
|
||
|
|
x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
|
||
|
|
y = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4]
|
||
|
|
assert_array_almost_equal(fft.fftshift(x), y)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(y), x)
|
||
|
|
|
||
|
|
def test_inverse(self):
|
||
|
|
for n in [1, 4, 9, 100, 211]:
|
||
|
|
x = np.random.random((n,))
|
||
|
|
assert_array_almost_equal(fft.ifftshift(fft.fftshift(x)), x)
|
||
|
|
|
||
|
|
def test_axes_keyword(self):
|
||
|
|
freqs = [[0, 1, 2], [3, 4, -4], [-3, -2, -1]]
|
||
|
|
shifted = [[-1, -3, -2], [2, 0, 1], [-4, 3, 4]]
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=(0, 1)), shifted)
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=0),
|
||
|
|
fft.fftshift(freqs, axes=(0,)))
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shifted, axes=(0, 1)), freqs)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shifted, axes=0),
|
||
|
|
fft.ifftshift(shifted, axes=(0,)))
|
||
|
|
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs), shifted)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shifted), freqs)
|
||
|
|
|
||
|
|
def test_uneven_dims(self):
|
||
|
|
""" Test 2D input, which has uneven dimension sizes """
|
||
|
|
freqs = [
|
||
|
|
[0, 1],
|
||
|
|
[2, 3],
|
||
|
|
[4, 5]
|
||
|
|
]
|
||
|
|
|
||
|
|
# shift in dimension 0
|
||
|
|
shift_dim0 = [
|
||
|
|
[4, 5],
|
||
|
|
[0, 1],
|
||
|
|
[2, 3]
|
||
|
|
]
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=0), shift_dim0)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim0, axes=0), freqs)
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=(0,)), shift_dim0)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim0, axes=[0]), freqs)
|
||
|
|
|
||
|
|
# shift in dimension 1
|
||
|
|
shift_dim1 = [
|
||
|
|
[1, 0],
|
||
|
|
[3, 2],
|
||
|
|
[5, 4]
|
||
|
|
]
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=1), shift_dim1)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim1, axes=1), freqs)
|
||
|
|
|
||
|
|
# shift in both dimensions
|
||
|
|
shift_dim_both = [
|
||
|
|
[5, 4],
|
||
|
|
[1, 0],
|
||
|
|
[3, 2]
|
||
|
|
]
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=(0, 1)), shift_dim_both)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim_both, axes=(0, 1)), freqs)
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=[0, 1]), shift_dim_both)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim_both, axes=[0, 1]), freqs)
|
||
|
|
|
||
|
|
# axes=None (default) shift in all dimensions
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs, axes=None), shift_dim_both)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim_both, axes=None), freqs)
|
||
|
|
assert_array_almost_equal(fft.fftshift(freqs), shift_dim_both)
|
||
|
|
assert_array_almost_equal(fft.ifftshift(shift_dim_both), freqs)
|
||
|
|
|
||
|
|
def test_equal_to_original(self):
|
||
|
|
""" Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
|
||
|
|
from numpy.compat import integer_types
|
||
|
|
from numpy.core import asarray, concatenate, arange, take
|
||
|
|
|
||
|
|
def original_fftshift(x, axes=None):
|
||
|
|
""" How fftshift was implemented in v1.14"""
|
||
|
|
tmp = asarray(x)
|
||
|
|
ndim = tmp.ndim
|
||
|
|
if axes is None:
|
||
|
|
axes = list(range(ndim))
|
||
|
|
elif isinstance(axes, integer_types):
|
||
|
|
axes = (axes,)
|
||
|
|
y = tmp
|
||
|
|
for k in axes:
|
||
|
|
n = tmp.shape[k]
|
||
|
|
p2 = (n + 1) // 2
|
||
|
|
mylist = concatenate((arange(p2, n), arange(p2)))
|
||
|
|
y = take(y, mylist, k)
|
||
|
|
return y
|
||
|
|
|
||
|
|
def original_ifftshift(x, axes=None):
|
||
|
|
""" How ifftshift was implemented in v1.14 """
|
||
|
|
tmp = asarray(x)
|
||
|
|
ndim = tmp.ndim
|
||
|
|
if axes is None:
|
||
|
|
axes = list(range(ndim))
|
||
|
|
elif isinstance(axes, integer_types):
|
||
|
|
axes = (axes,)
|
||
|
|
y = tmp
|
||
|
|
for k in axes:
|
||
|
|
n = tmp.shape[k]
|
||
|
|
p2 = n - (n + 1) // 2
|
||
|
|
mylist = concatenate((arange(p2, n), arange(p2)))
|
||
|
|
y = take(y, mylist, k)
|
||
|
|
return y
|
||
|
|
|
||
|
|
# create possible 2d array combinations and try all possible keywords
|
||
|
|
# compare output to original functions
|
||
|
|
for i in range(16):
|
||
|
|
for j in range(16):
|
||
|
|
for axes_keyword in [0, 1, None, (0,), (0, 1)]:
|
||
|
|
inp = np.random.rand(i, j)
|
||
|
|
|
||
|
|
assert_array_almost_equal(fft.fftshift(inp, axes_keyword),
|
||
|
|
original_fftshift(inp, axes_keyword))
|
||
|
|
|
||
|
|
assert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
|
||
|
|
original_ifftshift(inp, axes_keyword))
|
||
|
|
|
||
|
|
|
||
|
|
class TestFFTFreq(object):
|
||
|
|
|
||
|
|
def test_definition(self):
|
||
|
|
x = [0, 1, 2, 3, 4, -4, -3, -2, -1]
|
||
|
|
assert_array_almost_equal(9*fft.fftfreq(9), x)
|
||
|
|
assert_array_almost_equal(9*pi*fft.fftfreq(9, pi), x)
|
||
|
|
x = [0, 1, 2, 3, 4, -5, -4, -3, -2, -1]
|
||
|
|
assert_array_almost_equal(10*fft.fftfreq(10), x)
|
||
|
|
assert_array_almost_equal(10*pi*fft.fftfreq(10, pi), x)
|
||
|
|
|
||
|
|
|
||
|
|
class TestRFFTFreq(object):
|
||
|
|
|
||
|
|
def test_definition(self):
|
||
|
|
x = [0, 1, 2, 3, 4]
|
||
|
|
assert_array_almost_equal(9*fft.rfftfreq(9), x)
|
||
|
|
assert_array_almost_equal(9*pi*fft.rfftfreq(9, pi), x)
|
||
|
|
x = [0, 1, 2, 3, 4, 5]
|
||
|
|
assert_array_almost_equal(10*fft.rfftfreq(10), x)
|
||
|
|
assert_array_almost_equal(10*pi*fft.rfftfreq(10, pi), x)
|
||
|
|
|
||
|
|
|
||
|
|
class TestIRFFTN(object):
|
||
|
|
|
||
|
|
def test_not_last_axis_success(self):
|
||
|
|
ar, ai = np.random.random((2, 16, 8, 32))
|
||
|
|
a = ar + 1j*ai
|
||
|
|
|
||
|
|
axes = (-2,)
|
||
|
|
|
||
|
|
# Should not raise error
|
||
|
|
fft.irfftn(a, axes=axes)
|