Adding the previous n rows as columns to a NumPy array

Question

I want to add the previous n rows as columns to a NumPy array.

For example, if n=2 , the array below...

[[ 1, 2]
 [ 3, 4]
 [ 5, 6]
 [ 7, 8]
 [ 9, 10]
 [11, 12]]

...should be turned into the following one:

[[ 1, 2, 0, 0, 0, 0]
 [ 3, 4, 1, 2, 0, 0]
 [ 5, 6, 3, 4, 1, 2]
 [ 7, 8, 5, 6, 3, 4]
 [ 9, 10, 7, 8, 5, 6]
 [11, 12, 9, 10, 7, 8]]

Any ideas how I could do that without going over the entire array in a for loop?

Answer 1

Here's a vectorized approach -

def vectorized_app(a,n):   
    M,N = a.shape
    idx = np.arange(a.shape[0])[:,None] - np.arange(n+1)
    out = a[idx.ravel(),:].reshape(-1,N*(n+1))
    out[N*(np.arange(1,M+1))[:,None] <= np.arange(N*(n+1))] = 0
    return out

Sample run -

In [255]: a
Out[255]: 
array([[ 1,  2,  3],
       [ 4,  5,  6],
       [ 7,  8,  9],
       [10, 11, 12],
       [13, 14, 15],
       [16, 17, 18]])

In [256]: vectorized_app(a,3)
Out[256]: 
array([[ 1,  2,  3,  0,  0,  0,  0,  0,  0,  0,  0,  0],
       [ 4,  5,  6,  1,  2,  3,  0,  0,  0,  0,  0,  0],
       [ 7,  8,  9,  4,  5,  6,  1,  2,  3,  0,  0,  0],
       [10, 11, 12,  7,  8,  9,  4,  5,  6,  1,  2,  3],
       [13, 14, 15, 10, 11, 12,  7,  8,  9,  4,  5,  6],
       [16, 17, 18, 13, 14, 15, 10, 11, 12,  7,  8,  9]])

Runtime test -

I am timing @Psidom's loop-comprehension based method and the vectorized method listed in this post on a 100x scaled up version (in terms of size) of the sample posted in the question :

In [246]: a = np.random.randint(0,9,(600,200))

In [247]: n = 200

In [248]: %timeit np.column_stack(mypad(a, i) for i in range(n + 1))
1 loops, best of 3: 748 ms per loop

In [249]: %timeit vectorized_app(a,n)
1 loops, best of 3: 224 ms per loop

Answer 2

Here is a way to pad 0 in the beginning of the array and then column stack them:

import numpy as np
n = 2
def mypad(myArr, n):
    if n == 0:
        return myArr
    else:
        return np.pad(myArr, ((n,0), (0,0)), mode = "constant")[:-n]

np.column_stack(mypad(arr, i) for i in range(n + 1))

# array([[ 1,  2,  0,  0,  0,  0],
#        [ 3,  4,  1,  2,  0,  0],
#        [ 5,  6,  3,  4,  1,  2],
#        [ 7,  8,  5,  6,  3,  4],
#        [ 9, 10,  7,  8,  5,  6],
#        [11, 12,  9, 10,  7,  8]])