Need help understanding the following MATLAB operations for Gaussian Elimination with Partial Pivoting?

Question

MATLAB code for Guassian Elimination with Partial Pivoting

I'm having trouble understanding the following segment:

for j = 1:n-1

  [m,k] = max (abs(A(j:n,j))

  k = k+j-1

  if k ~= j

    A([k,j],j:n+1) = A([j,k],j:n+1)

  end

I'm uncertain about why k is set to be equal to k+j-1. I don't see how that helps to determine if the rows below the pivot element need to be swapped.

Answer 1

The first two lines are the search of the pivot, absolute maximum of the first rows.

$k$ is the pivot.

The two last lines swap $k$-th and $j$-th lines as part of the Gaussian elimination algorithm.