Cumulative cross addition/multiplication in NumPy

Question

a = [1,2,3]
b = [2,4,6]

c = [1*2, 1*4 + 2*2, 1*6 + 2*4 + 3*2]

I have done using dot product by creating Toeplitz matrix but I am looking for a much faster version since I am dealing with a huge dataset. Using loop will also slow down computation.

3

Show your code that works? – Divakar Mar 25 '18 at 18:45

user2357112 · Accepted Answer · 2018-03-25T19:04:16.927

4

This output is the first half of a convolution of a and b:

numpy.convolve(a, b)[:len(a)]

If your arrays are big enough, you may be able to save time with an FFT-based convolution:

scipy.signal.fftconvolve(a, b)[:len(a)]

An FFT convolution has runtime O(n log n) where n is the length of the input arrays, in contrast to the O(n^2) runtime of a straightforward nested-loop convolution. However, it has a worse constant factor, and it requires floating-point arithmetic, so results may have a small amount of numerical error.

On a sufficiently recent version of SciPy (at least 0.19.0, released March 09, 2017), you can use scipy.signal.convolve to automatically pick between a direct or FFT convolution based on an estimate of which would be faster. Prior to 0.19.0, scipy.signal.convolve would always use a direct computation.

edited Mar 25 '18 at 19:04

answered Mar 25 '18 at 18:46

user2357112

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Oh, sorry. I used `b = [4,5,6]` instead of `[2,4,6]`. – chepner Mar 25 '18 at 18:56
`scipy.signal.convolve` by default _"Automatically chooses direct or Fourier method based on an estimate of which is faster"_ – Paul Panzer Mar 25 '18 at 18:58
@PaulPanzer: It does?.. ah, I see, "New in version 0.19.0." – user2357112 Mar 25 '18 at 19:00
@PradeepTummala: If you have a new question, post a new question. Don't keep asking for more in an existing question. – user2357112 Mar 25 '18 at 19:31

Cumulative cross addition/multiplication in NumPy

1 Answers1