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"""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
from numpy.fft.helper import _FFTCache
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)
class TestFFTCache(object):
def test_basic_behaviour(self):
c = _FFTCache(max_size_in_mb=1, max_item_count=4)
# Put
c.put_twiddle_factors(1, np.ones(2, dtype=np.float32))
c.put_twiddle_factors(2, np.zeros(2, dtype=np.float32))
# Get
assert_array_almost_equal(c.pop_twiddle_factors(1),
np.ones(2, dtype=np.float32))
assert_array_almost_equal(c.pop_twiddle_factors(2),
np.zeros(2, dtype=np.float32))
# Nothing should be left.
assert_equal(len(c._dict), 0)
# Now put everything in twice so it can be retrieved once and each will
# still have one item left.
for _ in range(2):
c.put_twiddle_factors(1, np.ones(2, dtype=np.float32))
c.put_twiddle_factors(2, np.zeros(2, dtype=np.float32))
assert_array_almost_equal(c.pop_twiddle_factors(1),
np.ones(2, dtype=np.float32))
assert_array_almost_equal(c.pop_twiddle_factors(2),
np.zeros(2, dtype=np.float32))
assert_equal(len(c._dict), 2)
def test_automatic_pruning(self):
# That's around 2600 single precision samples.
c = _FFTCache(max_size_in_mb=0.01, max_item_count=4)
c.put_twiddle_factors(1, np.ones(200, dtype=np.float32))
c.put_twiddle_factors(2, np.ones(200, dtype=np.float32))
assert_equal(list(c._dict.keys()), [1, 2])
# This is larger than the limit but should still be kept.
c.put_twiddle_factors(3, np.ones(3000, dtype=np.float32))
assert_equal(list(c._dict.keys()), [1, 2, 3])
# Add one more.
c.put_twiddle_factors(4, np.ones(3000, dtype=np.float32))
# The other three should no longer exist.
assert_equal(list(c._dict.keys()), [4])
# Now test the max item count pruning.
c = _FFTCache(max_size_in_mb=0.01, max_item_count=2)
c.put_twiddle_factors(2, np.empty(2))
c.put_twiddle_factors(1, np.empty(2))
# Can still be accessed.
assert_equal(list(c._dict.keys()), [2, 1])
c.put_twiddle_factors(3, np.empty(2))
# 1 and 3 can still be accessed - c[2] has been touched least recently
# and is thus evicted.
assert_equal(list(c._dict.keys()), [1, 3])
# One last test. We will add a single large item that is slightly
# bigger then the cache size. Some small items can still be added.
c = _FFTCache(max_size_in_mb=0.01, max_item_count=5)
c.put_twiddle_factors(1, np.ones(3000, dtype=np.float32))
c.put_twiddle_factors(2, np.ones(2, dtype=np.float32))
c.put_twiddle_factors(3, np.ones(2, dtype=np.float32))
c.put_twiddle_factors(4, np.ones(2, dtype=np.float32))
assert_equal(list(c._dict.keys()), [1, 2, 3, 4])
# One more big item. This time it is 6 smaller ones but they are
# counted as one big item.
for _ in range(6):
c.put_twiddle_factors(5, np.ones(500, dtype=np.float32))
# '1' no longer in the cache. Rest still in the cache.
assert_equal(list(c._dict.keys()), [2, 3, 4, 5])
# Another big item - should now be the only item in the cache.
c.put_twiddle_factors(6, np.ones(4000, dtype=np.float32))
assert_equal(list(c._dict.keys()), [6])