102 lines
3.3 KiB
Python
102 lines
3.3 KiB
Python
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from functools import update_wrapper, lru_cache
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from ._pocketfft import helper as _helper
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def next_fast_len(target, real=False):
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"""Find the next fast size of input data to ``fft``, for zero-padding, etc.
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SciPy's FFT algorithms gain their speed by a recursive divide and conquer
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strategy. This relies on efficient functions for small prime factors of the
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input length. Thus, the transforms are fastest when using composites of the
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prime factors handled by the fft implementation. If there are efficient
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functions for all radices <= `n`, then the result will be a number `x`
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>= ``target`` with only prime factors < `n`. (Also known as `n`-smooth
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numbers)
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Parameters
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----------
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target : int
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Length to start searching from. Must be a positive integer.
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real : bool, optional
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True if the FFT involves real input or output (e.g., `rfft` or `hfft`
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but not `fft`). Defaults to False.
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Returns
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-------
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out : int
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The smallest fast length greater than or equal to ``target``.
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Notes
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-----
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The result of this function may change in future as performance
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considerations change, for example, if new prime factors are added.
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Calling `fft` or `ifft` with real input data performs an ``'R2C'``
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transform internally.
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Examples
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--------
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On a particular machine, an FFT of prime length takes 11.4 ms:
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>>> from scipy import fft
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>>> import numpy as np
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>>> rng = np.random.default_rng()
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>>> min_len = 93059 # prime length is worst case for speed
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>>> a = rng.standard_normal(min_len)
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>>> b = fft.fft(a)
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Zero-padding to the next regular length reduces computation time to
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1.6 ms, a speedup of 7.3 times:
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>>> fft.next_fast_len(min_len, real=True)
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93312
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>>> b = fft.fft(a, 93312)
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Rounding up to the next power of 2 is not optimal, taking 3.0 ms to
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compute; 1.9 times longer than the size given by ``next_fast_len``:
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>>> b = fft.fft(a, 131072)
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"""
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pass
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# Directly wrap the c-function good_size but take the docstring etc., from the
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# next_fast_len function above
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next_fast_len = update_wrapper(lru_cache()(_helper.good_size), next_fast_len)
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next_fast_len.__wrapped__ = _helper.good_size
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def _init_nd_shape_and_axes(x, shape, axes):
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"""Handle shape and axes arguments for N-D transforms.
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Returns the shape and axes in a standard form, taking into account negative
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values and checking for various potential errors.
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Parameters
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----------
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x : array_like
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The input array.
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shape : int or array_like of ints or None
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The shape of the result. If both `shape` and `axes` (see below) are
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None, `shape` is ``x.shape``; if `shape` is None but `axes` is
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not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
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If `shape` is -1, the size of the corresponding dimension of `x` is
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used.
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axes : int or array_like of ints or None
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Axes along which the calculation is computed.
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The default is over all axes.
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Negative indices are automatically converted to their positive
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counterparts.
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Returns
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-------
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shape : array
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The shape of the result. It is a 1-D integer array.
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axes : array
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The shape of the result. It is a 1-D integer array.
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"""
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return _helper._init_nd_shape_and_axes(x, shape, axes)
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