scipy.fftpack.

next_fast_len#

scipy.fftpack.next_fast_len(target)[source]#

Find the next fast size of input data to `fft`, for zero-padding, etc.

SciPy’s FFTPACK has efficient functions for radix {2, 3, 4, 5}, so this returns the next composite of the prime factors 2, 3, and 5 which is greater than or equal to target. (These are also known as 5-smooth numbers, regular numbers, or Hamming numbers.)

Parameters:
targetint

Length to start searching from. Must be a positive integer.

Returns:
outint

The first 5-smooth number greater than or equal to target.

Notes

Examples

On a particular machine, an FFT of prime length takes 133 ms:

```>>> from scipy import fftpack
>>> import numpy as np
>>> rng = np.random.default_rng()
>>> min_len = 10007  # prime length is worst case for speed
>>> a = rng.standard_normal(min_len)
>>> b = fftpack.fft(a)
```

Zero-padding to the next 5-smooth length reduces computation time to 211 us, a speedup of 630 times:

```>>> fftpack.next_fast_len(min_len)
10125
>>> b = fftpack.fft(a, 10125)
```

Rounding up to the next power of 2 is not optimal, taking 367 us to compute, 1.7 times as long as the 5-smooth size:

```>>> b = fftpack.fft(a, 16384)
```