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"""
Discrete Fourier Transforms - helper.py
"""
from __future__ import division, absolute_import, print_function
import collections
import threading
from numpy.compat import integer_types
from numpy.core import (
asarray, concatenate, arange, take, integer, empty
)
# Created by Pearu Peterson, September 2002
__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq']
integer_types = integer_types + (integer,)
def fftshift(x, axes=None):
"""
Shift the zero-frequency component to the center of the spectrum.
This function swaps half-spaces for all axes listed (defaults to all).
Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
Parameters
----------
x : array_like
Input array.
axes : int or shape tuple, optional
Axes over which to shift. Default is None, which shifts all axes.
Returns
-------
y : ndarray
The shifted array.
See Also
--------
ifftshift : The inverse of `fftshift`.
Examples
--------
>>> freqs = np.fft.fftfreq(10, 0.1)
>>> freqs
array([ 0., 1., 2., 3., 4., -5., -4., -3., -2., -1.])
>>> np.fft.fftshift(freqs)
array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.])
Shift the zero-frequency component only along the second axis:
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.fftshift(freqs, axes=(1,))
array([[ 2., 0., 1.],
[-4., 3., 4.],
[-1., -3., -2.]])
"""
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 ifftshift(x, axes=None):
"""
The inverse of `fftshift`. Although identical for even-length `x`, the
functions differ by one sample for odd-length `x`.
Parameters
----------
x : array_like
Input array.
axes : int or shape tuple, optional
Axes over which to calculate. Defaults to None, which shifts all axes.
Returns
-------
y : ndarray
The shifted array.
See Also
--------
fftshift : Shift zero-frequency component to the center of the spectrum.
Examples
--------
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.ifftshift(np.fft.fftshift(freqs))
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
"""
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
def fftfreq(n, d=1.0):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
-------
f : ndarray
Array of length `n` containing the sample frequencies.
Examples
--------
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
>>> fourier = np.fft.fft(signal)
>>> n = signal.size
>>> timestep = 0.1
>>> freq = np.fft.fftfreq(n, d=timestep)
>>> freq
array([ 0. , 1.25, 2.5 , 3.75, -5. , -3.75, -2.5 , -1.25])
"""
if not isinstance(n, integer_types):
raise ValueError("n should be an integer")
val = 1.0 / (n * d)
results = empty(n, int)
N = (n-1)//2 + 1
p1 = arange(0, N, dtype=int)
results[:N] = p1
p2 = arange(-(n//2), 0, dtype=int)
results[N:] = p2
return results * val
#return hstack((arange(0,(n-1)/2 + 1), arange(-(n/2),0))) / (n*d)
def rfftfreq(n, d=1.0):
"""
Return the Discrete Fourier Transform sample frequencies
(for usage with rfft, irfft).
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd
Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
the Nyquist frequency component is considered to be positive.
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
-------
f : ndarray
Array of length ``n//2 + 1`` containing the sample frequencies.
Examples
--------
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
>>> fourier = np.fft.rfft(signal)
>>> n = signal.size
>>> sample_rate = 100
>>> freq = np.fft.fftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., -50., -40., -30., -20., -10.])
>>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., 50.])
"""
if not isinstance(n, integer_types):
raise ValueError("n should be an integer")
val = 1.0/(n*d)
N = n//2 + 1
results = arange(0, N, dtype=int)
return results * val
class _FFTCache(object):
"""
Cache for the FFT twiddle factors as an LRU (least recently used) cache.
Parameters
----------
max_size_in_mb : int
Maximum memory usage of the cache before items are being evicted.
max_item_count : int
Maximum item count of the cache before items are being evicted.
Notes
-----
Items will be evicted if either limit has been reached upon getting and
setting. The maximum memory usages is not strictly the given
``max_size_in_mb`` but rather
``max(max_size_in_mb, 1.5 * size_of_largest_item)``. Thus the cache will
never be completely cleared - at least one item will remain and a single
large item can cause the cache to retain several smaller items even if the
given maximum cache size has been exceeded.
"""
def __init__(self, max_size_in_mb, max_item_count):
self._max_size_in_bytes = max_size_in_mb * 1024 ** 2
self._max_item_count = max_item_count
self._dict = collections.OrderedDict()
self._lock = threading.Lock()
def put_twiddle_factors(self, n, factors):
"""
Store twiddle factors for an FFT of length n in the cache.
Putting multiple twiddle factors for a certain n will store it multiple
times.
Parameters
----------
n : int
Data length for the FFT.
factors : ndarray
The actual twiddle values.
"""
with self._lock:
# Pop + later add to move it to the end for LRU behavior.
# Internally everything is stored in a dictionary whose values are
# lists.
try:
value = self._dict.pop(n)
except KeyError:
value = []
value.append(factors)
self._dict[n] = value
self._prune_cache()
def pop_twiddle_factors(self, n):
"""
Pop twiddle factors for an FFT of length n from the cache.
Will return None if the requested twiddle factors are not available in
the cache.
Parameters
----------
n : int
Data length for the FFT.
Returns
-------
out : ndarray or None
The retrieved twiddle factors if available, else None.
"""
with self._lock:
if n not in self._dict or not self._dict[n]:
return None
# Pop + later add to move it to the end for LRU behavior.
all_values = self._dict.pop(n)
value = all_values.pop()
# Only put pack if there are still some arrays left in the list.
if all_values:
self._dict[n] = all_values
return value
def _prune_cache(self):
# Always keep at least one item.
while len(self._dict) > 1 and (
len(self._dict) > self._max_item_count or self._check_size()):
self._dict.popitem(last=False)
def _check_size(self):
item_sizes = [sum(_j.nbytes for _j in _i)
for _i in self._dict.values() if _i]
if not item_sizes:
return False
max_size = max(self._max_size_in_bytes, 1.5 * max(item_sizes))
return sum(item_sizes) > max_size
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