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.

Solution

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

>>> import numpy as np
>>> 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]])
...
>>> y = [4, 2, 1, 3, 2]

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

>>> A[np.arange(A.shape[0]), y]
array([3, 2, 5, 1, 1])
>>> A[np.arange(A.shape[0]), y] = -99
>>> A
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]])