How to extract elements from a matrix using a vector of indices?

Question

Suppose I have a matrix A of order m×n and a vector of order m×1. I would like to extract elements from each row of the matrix A by using the elements of the vector as an offset in each row.

For example,

A = [[3, 0, 0, 8, 3],
     [9, 3, 2, 2, 6],
     [5, 5, 4, 2, 8],
     [3, 8, 7, 1, 2],
     [3, 9, 1, 5, 5]]

and a vector

y = [4, 2, 1, 3, 2]

What I want to achieve is a way to extract the elements of A such that each element of the vector indexes an element in the corresponding row of A, i.e., implementing

for i in range(len(y)):
    A[i, y[i]] = #perform operations here

without the use of any explicit loops.

The expected output is,

[3, 2, 5, 1, 1]

I am using Python and the NumPy library.

Answer 1

You should start by converting list A into a NumPy array:

In [270]: import numpy as np

In [271]: A = np.array([[3, 0, 0, 8, 3],
     ...:               [9, 3, 2, 2, 6],
     ...:               [5, 5, 4, 2, 8],
     ...:               [3, 8, 7, 1, 2],
     ...:               [3, 9, 1, 5, 5]])

In [272]: cols = [4, 2, 1, 3, 2]

And after that, nothing prevents you from using advanced indexing:

In [273]: rows = np.arange(A.shape[0])

In [274]: rows
Out[274]: array([0, 1, 2, 3, 4])

In [275]: A[rows, cols]
Out[275]: array([3, 2, 5, 1, 1])

In [276]: A[rows, cols] = -99

In [277]: A
Out[277]: 
array([[  3,   0,   0,   8, -99],
       [  9,   3, -99,   2,   6],
       [  5, -99,   4,   2,   8],
       [  3,   8,   7, -99,   2],
       [  3,   9, -99,   5,   5]])

Answer 2

The following adheres to conventional python style, but is not optimized for speed. Try it and see if it works for your use case.

A = [[1, 0, 0, 6, 1],
    [8, 2, 1, 1, 5],
    [1, 1, 0, 0, 4],
    [3, 8, 7, 1, 2],
    [3, 9, 1, 5, 5]]

b = [0, 1, 2, 3, 4]

result = [A[i][b_i] for i, b_i in enumerate(b)]
# -> [1, 2, 0, 1, 5]