Replace all the subdiagonals of a matrix for a given k in Python

Question

I would like to replace all values of the subdiagonals under the k-diagonal.

For example :

We first import the numpy library :

import numpy as np

Then we create the matrix :

In [14]: matrix = np.matrix('1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1')

We are then getting :

In [15]: print(matrix)

Out[16]: 
    [[1 1 1 1 1 1]
     [1 1 1 1 1 1]
     [1 1 1 1 1 1]
     [1 1 1 1 1 1]
     [1 1 1 1 1 1]]

We then get the diagonals under the k-diagonal for k = 1 for example :

In [17]: lowerdiags = [np.diag(matrix, k=e+1).tolist() for e in range(-len(matrix), k)]

In [18]: print(lowerdiags)

Out[19]: [[1], [1, 1], [1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, 1, 1]]

And, I'm stuck there, what should I add for it to be for k = 1 and replace all values per 0, like that: (Knowing that we just found the subdiagonals)

[[0 1 1 1 1 1]
 [0 0 1 1 1 1]
 [0 0 0 1 1 1]
 [0 0 0 0 1 1]
 [0 0 0 0 0 1]]

or even for k = 0 :

[[1 1 1 1 1 1]
 [0 1 1 1 1 1]
 [0 0 1 1 1 1]
 [0 0 0 1 1 1]
 [0 0 0 0 1 1]]

Thank you for your help and your patience.

Answer 1

I found a way by using the numpy method : fill_diagonal and by moving around the different k :

# Import numpy library
import numpy as np

def Exercise_3(matrix, k):
    # print initial matrix
    print(matrix)
    
    for k in range(-len(matrix)+1, k):
        if k < 0:
            # Smart slicing when filling diagonals with "np.fill_diagonal" on our matrix for lower diagonals
            np.fill_diagonal(matrix[-k:, :k], 0)
        if k > 0:
            # Smart slicing when filling diagonals with "np.fill_diagonal" on our matrix for upper diagonals
            np.fill_diagonal(matrix[:-k, k:], 0)
        if k == 0:
            # Just replace the main diagonal by 0
            np.fill_diagonal(matrix, 0)
        # print to see each change on the matrix    
        #print(matrix)
        
        #print(k)

    return matrix

def main():
    k = 0
    # an another way of creating a matrix
    #matrix = np.matrix('1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1; 1 1 1 1 1 1')
    # matrix of 5 rows and 5 columns filled by 1
    matrix = np.array(([1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1],[1,1,1,1,1]))
    
    NewMatrix = Exercise_3(matrix, k)
    print(NewMatrix)

main()