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import operator |
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import numpy as np |
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from numpy.fft import fftshift, ifftshift, fftfreq |
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import scipy.fft._pocketfft.helper as _helper |
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__all__ = ['fftshift', 'ifftshift', 'fftfreq', 'rfftfreq', 'next_fast_len'] |
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def rfftfreq(n, d=1.0): |
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"""DFT sample frequencies (for usage with rfft, irfft). |
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The returned float array contains the frequency bins in |
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cycles/unit (with zero at the start) given a window length `n` and a |
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sample spacing `d`:: |
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f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2]/(d*n) if n is even |
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f = [0,1,1,2,2,...,n/2-1,n/2-1,n/2,n/2]/(d*n) if n is odd |
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Parameters |
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---------- |
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n : int |
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Window length. |
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d : scalar, optional |
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Sample spacing. Default is 1. |
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Returns |
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------- |
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out : ndarray |
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The array of length `n`, containing the sample frequencies. |
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Examples |
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-------- |
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>>> import numpy as np |
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>>> from scipy import fftpack |
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>>> sig = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float) |
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>>> sig_fft = fftpack.rfft(sig) |
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>>> n = sig_fft.size |
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>>> timestep = 0.1 |
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>>> freq = fftpack.rfftfreq(n, d=timestep) |
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>>> freq |
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array([ 0. , 1.25, 1.25, 2.5 , 2.5 , 3.75, 3.75, 5. ]) |
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""" |
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n = operator.index(n) |
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if n < 0: |
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raise ValueError(f"n = {n} is not valid. " |
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"n must be a nonnegative integer.") |
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return (np.arange(1, n + 1, dtype=int) // 2) / float(n * d) |
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def next_fast_len(target): |
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""" |
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Find the next fast size of input data to `fft`, for zero-padding, etc. |
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SciPy's FFTPACK has efficient functions for radix {2, 3, 4, 5}, so this |
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returns the next composite of the prime factors 2, 3, and 5 which is |
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greater than or equal to `target`. (These are also known as 5-smooth |
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numbers, regular numbers, or Hamming 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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Returns |
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------- |
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out : int |
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The first 5-smooth number greater than or equal to `target`. |
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Notes |
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----- |
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.. versionadded:: 0.18.0 |
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Examples |
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-------- |
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On a particular machine, an FFT of prime length takes 133 ms: |
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>>> from scipy import fftpack |
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>>> import numpy as np |
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>>> rng = np.random.default_rng() |
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>>> min_len = 10007 # prime length is worst case for speed |
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>>> a = rng.standard_normal(min_len) |
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>>> b = fftpack.fft(a) |
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Zero-padding to the next 5-smooth length reduces computation time to |
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211 us, a speedup of 630 times: |
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>>> fftpack.next_fast_len(min_len) |
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10125 |
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>>> b = fftpack.fft(a, 10125) |
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Rounding up to the next power of 2 is not optimal, taking 367 us to |
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compute, 1.7 times as long as the 5-smooth size: |
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>>> b = fftpack.fft(a, 16384) |
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""" |
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return _helper.good_size(target, True) |
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def _good_shape(x, shape, axes): |
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"""Ensure that shape argument is valid for scipy.fftpack |
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scipy.fftpack does not support len(shape) < x.ndim when axes is not given. |
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""" |
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if shape is not None and axes is None: |
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shape = _helper._iterable_of_int(shape, 'shape') |
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if len(shape) != np.ndim(x): |
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raise ValueError("when given, axes and shape arguments" |
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" have to be of the same length") |
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return shape |
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