`scipy.fft._helper:prev_fast_len`

Signature

def prev_fast_len ( target , real = False )

Summary

Find the previous fast size of input data to fft. Useful for discarding a minimal number of samples before FFT.

Extended Summary

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: Maximum length to search until. 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 largest fast length less 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.

In the current implementation, prev_fast_len assumes radices of 2,3,5,7,11 for complex FFT and 2,3,5 for real FFT.

Array API Standard Support

prev_fast_len is not in-scope for support of Python Array API Standard compatible backends other than NumPy.

See dev-arrayapi for more information.

Examples

On a particular machine, an FFT of prime length takes 16.2 ms:

from scipy import fft
import numpy as np
rng = np.random.default_rng()
max_len = 93059  # prime length is worst case for speed
a = rng.standard_normal(max_len)
b = fft.fft(a)

✓

Performing FFT on the maximum fast length less than max_len reduces the computation time to 1.5 ms, a speedup of 10.5 times:

fft.prev_fast_len(max_len, real=True)
c = fft.fft(a[:92160]) # discard last 899 samples