Sort rows and columns of a matrix by another list with numpy

Sort rows and columns of a matrix by another list with numpy

I have a square NxN matrix. This matrix is often quite large (N around
5000), and I want to aggregate parts of this matrix to make a smaller
matrix.
Therefore, I have a list with N elements, and these elemenets denote which
rows/columns should be grouped together in the new matrix.
To make the algorithm a bit easier and faster, I want to sort the rows and
columns based on the above list.
Example:
Input 5x5 matrix:
row/col | 1 | 2 | 3 | 4 | 5 |
1 | 5 | 4 | 3 | 2 | 1 |
2 | 10 | 9 | 8 | 7 | 6 |
3 | 15 | 14 | 13 | 12 | 11 |
4 | 20 | 19 | 18 | 17 | 16 |
5 | 25 | 24 | 23 | 22 | 21 |
To be clear: the first row is [5 4 3 2 1] and the first column is [5, 10,
15, 20, 25].
The list containing the 'labels' which denote which rows and columns
should be grouped together in the new matrix:
[2 2 1 3 3]
This means the new matrix will be 3x3 (we have 3 distinct values).
The matrix with the labels:
labels 2 1 3
--------- ---- ---------
row/col | 1 | 2 | 3 | 4 | 5 |
2 | 1 | 5 | 4 | 3 | 2 | 1 |
2 | 2 | 10 | 9 | 8 | 7 | 6 |
1 | 3 | 15 | 14 | 13 | 12 | 11 |
3 | 4 | 20 | 19 | 18 | 17 | 16 |
3 | 5 | 25 | 24 | 23 | 22 | 21 |
Expected sorted matrix:
row/col | 3 | 1 | 2 | 4 | 5 |
3 | 13 |15 | 14 | 12 | 11 |
1 | 3 | 5 | 4 | 2 | 1 |
2 | 8 |10 | 9 | 7 | 6 |
4 | 18 |20 | 19 | 17 | 16 |
5 | 23 |25 | 24 | 22 | 21 |
And with this matrix I can easily sum the grouped elements to form a new
element in the 3x3 matrix.
The question: how to sort a matrix in this way with numpy? I've searched
other questions and found lexsort, record arrays and other things, but as
someone with not a lot of experience with numpy, I found it hard to
accomplish the sorting I wanted.
Thanks in advance!