Every Nth Element In Convolution-CodePudding

Is there a faster way to do np.convolve(A, B)[::N] using Numpy? It feels wasteful to compute all the convolutions and then throw N - 1 of N away... I could do a for loop or list comprehension, but I thought it would be faster to use only native Numpy methods.

EDIT

Or does Numpy do lazy evaluation? I just saw this from a JS library, would be awesome for Numpy as well:

// Get first 3 unique values
const arr = [1, 2, 2, 3, 3, 4, 5, 6];

const result = R.pipe(
  arr,
  R.map(x => {
    console.log('iterate', x);
    return x;
  }),
  R.uniq(),
  R.take(3)
); // => [1, 2, 3]
  
/**
 * Console output:
 * iterate 1
 * iterate 2
 * iterate 2
 * iterate 3
 * /

CodePudding user response：

A convolution is a product of your kernel and a window on your array, then the sum. You can achieve the same manually using a rolling window:

First let's see a dummy example

A = np.arange(30)
B = np.ones(6)
N = 3

out = np.convolve(A, B)[::N]
print(out)

output: [ 0. 6. 21. 39. 57. 75. 93. 111. 129. 147. 135. 57.]

Now we do the same with a rolling view, padding, and slicing:

from numpy.lib.stride_tricks import sliding_window_view as swv

out = (swv(np.pad(A, B.shape[0]-1), B.shape[0])[::N]*B).sum(axis=1)
print(out)

output: [ 0. 6. 21. 39. 57. 75. 93. 111. 129. 147. 135. 57.]

Intermediate sliding view:

swv(np.pad(A, B.shape[0]-1), B.shape[0])

array([[ 0,  0,  0,  0,  0,  0],
       [ 0,  0,  0,  0,  0,  1],
       [ 0,  0,  0,  0,  1,  2],
       [ 0,  0,  0,  1,  2,  3],
       [ 0,  0,  1,  2,  3,  4],
       [ 0,  1,  2,  3,  4,  5],
       [ 1,  2,  3,  4,  5,  6],
       [ 2,  3,  4,  5,  6,  7],
       ...
       [24, 25, 26, 27, 28, 29],
       [25, 26, 27, 28, 29,  0],
       [26, 27, 28, 29,  0,  0],
       [27, 28, 29,  0,  0,  0],
       [28, 29,  0,  0,  0,  0],
       [29,  0,  0,  0,  0,  0]])


# with slicing
swv(np.pad(A, B.shape[0]-1), B.shape[0])[::N]

array([[ 0,  0,  0,  0,  0,  0],
       [ 0,  0,  0,  1,  2,  3],
       [ 1,  2,  3,  4,  5,  6],
       [ 4,  5,  6,  7,  8,  9],
       [ 7,  8,  9, 10, 11, 12],
       [10, 11, 12, 13, 14, 15],
       [13, 14, 15, 16, 17, 18],
       [16, 17, 18, 19, 20, 21],
       [19, 20, 21, 22, 23, 24],
       [22, 23, 24, 25, 26, 27],
       [25, 26, 27, 28, 29,  0],
       [28, 29,  0,  0,  0,  0]])