How to obtain bottom diagonals of a matrix according to an index?-CodePudding

I would like to know how it is possible to obtain the diagonals that point downwards (left and right) with respect to a specific index of the matrix.

To be more graphic I will give the following example of an expected output:

matrix = np.array([[2, 0, 0, 2],
                  [3, 9, 8, 3],
                  [3, 0, 0, 2],
                  [0, 0, 0, 0]])

Expected output results for position: matrix[1][2]

matrix[1][2]
8

diag_right = [2]
diag_left  = [0, 0]

Same example but using the matrix in matrix[1][2]

matrix = np.array([[x, x, x, x],
                   [x, x, 8, x],
                   [x, 0, x, 2],
                   [0, x, x, x]])

CodePudding user response：

An easy way using numpy would be: (i've changed the matrix to make more clear some results in test_ij)

import numpy as np

def get_right_left_diags(matrix,i,j):
    n = len(matrix)
    left_diag  = np.diag(matrix[i 1:n,j 1:n])
    right_diag = np.diag( matrix[i 1:n, j-1::-1])
    return right_diag,left_diag

%lets check some results
matrix = np.array([[2, 0, 0, 2],
                  [3, 9, 8, 3],
                  [3, 0, 0, 2],
                  [1, 2, 3, 4]])

n = len(matrix)

cases = [[0,0],[0,3],[1,1],[1,2],[2,1]]
for i,j in cases:
    right_diag,left_diag = get_right_left_diags(matrix,i,j)
    print(f"i={i}, j={j}, left_diag: {left_diag} \t right_diag: {right_diag}")

this will output:

#i=0, j=0, left_diag: [9 0 4]    right_diag: [3 0 2]
#i=0, j=3, left_diag: []     right_diag: [8 0 1]
#i=1, j=1, left_diag: [0 4]      right_diag: [3]
#i=1, j=2, left_diag: [2]    right_diag: [0 1]
#i=2, j=1, left_diag: [3]    right_diag: [1]

for me it has total sense.

CodePudding user response：

matrix = np.array([[2, 0, 0, 2],
                  [3, 9, 8, 3],
                  [3, 0, 0, 2],
                  [0, 0, 0, 0]])

i = 1; j = 2
diag_right = []; diag_left = []

for k in range(1, len(matrix) - i):
    if(j k < len(matrix[0])):
        diag_right.append(matrix[i k][j k])
    if(j-k >= 0):
        diag_left.append(matrix[i k][j-k])

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