how to get this code to work for non square matrix

Can some1 pls help me modify this code and give me tips on how to get other codes of this nature to run for non square Matrix Function [L, U, P, Q] = gecp(A)

%GECP calculate Gauss elimination with complete pivoting
%
% (G)aussian (E)limination (C)omplete (P)ivoting
% Input : A nxn matrix
% Output
% L = Lower triangular matrix with ones as diagonals 
% U = Upper triangular matrix
% P and Q permutations matrices so that P*A*Q = L*U 
% 
% See also LU
%
% written by : Cheilakos Nick 
[n, n] = size(A);
p = 1:n; 
q = 1:n;
for k = 1:n-1
    [maxc, rowindices] = max( abs(A(k:n, k:n)) );
    [maxm, colindex] = max(maxc);
    row = rowindices(colindex)+k-1; col = colindex+k-1;
    A( [k, row], : ) = A( [row, k], : );
    A( :, [k, col] ) = A( :, [col, k] );
    p( [k, row] ) = p( [row, k] ); q( [k, col] ) = q( [col, k] );
    if A(k,k) == 0
      break
    end
    A(k+1:n,k) = A(k+1:n,k)/A(k,k);
    i = k+1:n;
    A(i,i) = A(i,i) - A(i,k) * A(k,i);
end
L = tril(A,-1) + eye(n);
U = triu(A);
   P = eye(n);
   P = P(p,:);
   Q = eye(n);
   Q = Q(:,q);

Answer 1

[Star Strider]

The rref function does a Gauss-Jordan elimination on non-square matrices. (If you ask it nicely, it will even do a matrix inverse for you.)

Answer 2

[Matt J]

This File Exchange submission appears to accommodate non-square matrices

http://www.mathworks.com/matlabcentral/fileexchange/27249-lu-factorization-with-complete-pivoting

though I haven't used it myself.