How to find elements loactions is numpy array [closed]

Question

I have a 2D array, from which I want to get the indices of every element that is in the top 2 values both in it's row and in it's column. For example, given the following array -

r = np.random.rand(5,5)
>>> r
array([[ 0.89771084,  0.84415435,  0.81601728,  0.42322215,  0.78240944],
       [ 0.84490939,  0.53644975,  0.3506268 ,  0.98212093,  0.76426087],
       [ 0.254155  ,  0.12818165,  0.82656036,  0.97441244,  0.58597015],
       [ 0.50566688,  0.67774518,  0.58434845,  0.5204808 ,  0.9225643 ],
       [ 0.73930611,  0.31890204,  0.47691016,  0.28034347,  0.57832287]])

The required output is -

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

Notice [0,2] is left out, because although it is the second largest element of it's columns, it is the third largest element of it's row.

Answer 1

As suggested in the comments, argsort is the key. It gives you the indices of the sorted elements. Performing argsort twice gives you the rank. (There is a more efficient way to obtain the ranks, which I evilly leave as an exercise.)

Then use the ranks along rows and columns to identify elements that are in the top 2 for both, ranks and columns.

Example implementation:

import numpy as np

r = np.array([[ 0.89771084,  0.84415435,  0.81601728,  0.42322215,  0.78240944],
              [ 0.84490939,  0.53644975,  0.3506268 ,  0.98212093,  0.76426087],
              [ 0.254155  ,  0.12818165,  0.82656036,  0.97441244,  0.58597015],
              [ 0.50566688,  0.67774518,  0.58434845,  0.5204808 ,  0.9225643 ],
              [ 0.73930611,  0.31890204,  0.47691016,  0.28034347,  0.57832287]])

# indices of elements in descending order
col_order = np.argsort(r, axis=0)[::-1, :]
row_order = np.argsort(r, axis=1)[:, ::-1]

# sorting the indices gives the rank (0=highest element, 4=lowest element)
col_rank = np.argsort(col_order, axis=0)
row_rank = np.argsort(row_order, axis=1)

# mark top n elements in each row and column
n = 2
col_top_n = col_rank < n
row_top_n = row_rank < n

# mark elements that are in the nop n of BOTH, a row and a column
both_top_n = np.logical_and(row_top_n, col_top_n)

# get indices of marked elements
row_indices, col_indices = np.nonzero(both_top_n)

print('The following elements are in the top {} of both their rows and columns:'.format(n))
for row, column in zip(row_indices, col_indices):
    print('row: {}, column: {}, value: {}'.format(row, column, r[row, column]))