_helper.py
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from functools import update_wrapper, lru_cache
import numpy as np
from . import _pocketfft
from ._pocketfft import helper as _helper
def next_fast_len(target, real=False):
"""Find the next fast size of input data to ``fft``, for zero-padding, etc.
SciPy's FFT algorithms gain their speed by a recursive divide and conquer
strategy. This relies on efficient functions for small prime factors of the
input length. Thus, the transforms are fastest when using composites of the
prime factors handled by the fft implementation. If there are efficient
functions for all radices <= `n` then the result will be a number `x`
>= ``target`` with only prime factors < `n`. (Also known as `n`-smooth
numbers)
Parameters
----------
target : int
Length to start searching from. Must be a positive integer.
real : bool, optional
True if the FFT involves real input or output (e.g. `rfft` or `hfft` but
not `fft`). Defaults to False.
Returns
-------
out : int
The smallest fast length greater than or equal to ``target``.
Notes
-----
The result of this function may change in future as performance
considerations change, for example if new prime factors are added.
Calling `fft` or `ifft` with real input data performs an ``'R2C'``
transform internally.
Examples
--------
On a particular machine, an FFT of prime length takes 17 ms:
>>> from scipy import fft
>>> min_len = 93059 # prime length is worst case for speed
>>> a = np.random.randn(min_len)
>>> b = fft.fft(a)
Zero-padding to the next regular length reduces computation time to
1.3 ms, a speedup of 13 times:
>>> fft.next_fast_len(min_len)
93312
>>> b = fft.fft(a, 93312)
Rounding up to the next power of 2 is not optimal, taking 1.9 ms to
compute; 1.3 times longer than the size given by ``next_fast_len``:
>>> b = fft.fft(a, 131072)
"""
pass
# Directly wrap the c-function good_size but take the docstring etc. from the
# next_fast_len function above
next_fast_len = update_wrapper(lru_cache()(_helper.good_size), next_fast_len)
next_fast_len.__wrapped__ = _helper.good_size
def _init_nd_shape_and_axes(x, shape, axes):
"""Handle shape and axes arguments for n-dimensional transforms.
Returns the shape and axes in a standard form, taking into account negative
values and checking for various potential errors.
Parameters
----------
x : array_like
The input array.
shape : int or array_like of ints or None
The shape of the result. If both `shape` and `axes` (see below) are
None, `shape` is ``x.shape``; if `shape` is None but `axes` is
not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``.
If `shape` is -1, the size of the corresponding dimension of `x` is
used.
axes : int or array_like of ints or None
Axes along which the calculation is computed.
The default is over all axes.
Negative indices are automatically converted to their positive
counterpart.
Returns
-------
shape : array
The shape of the result. It is a 1D integer array.
axes : array
The shape of the result. It is a 1D integer array.
"""
return _helper._init_nd_shape_and_axes(x, shape, axes)