I had to change the order of the rows and columns of a matrix to force the diagonal to be ordered. One possibility was to use the sort function on the diagonal,

I had to change the order of the rows and columns of a matrix to force the diagonal to be ordered. One possibility was to use the sort function on the diagonal, somehow get the permutation, and then apply the permutation to all the rows and columns. How had can it be? There is a 50% chance of apply the permutation in the wrong direction, and other possible tricky details. Since the worst case was N=20, I used bubble sort that is as quick and dirty, but it's also obvious and well known.