lutx function can be found here : https://www.mathworks.com/matlabcentral/fileexchange/37976-numerical-computing-with-matlab

click 'function' tab and click lutx(A) on the left side.

or just copy and paste below :

function [L,U,p] = lutx(A) %LUTX Triangular factorization, textbook version % [L,U,p] = lutx(A) produces a unit lower triangular matrix L, % an upper triangular matrix U, and a permutation vector p, % so that L*U = A(p,:) % Copyright 2014 Cleve Moler % Copyright 2014 The MathWorks, Inc. [n,n] = size(A); p = (1:n)'; for k = 1:n-1 % Find index of largest element below diagonal in k-th column [r,m] = max(abs(A(k:n,k))); m = m+k-1; % Skip elimination if column is zero if (A(m,k) ~= 0) % Swap pivot row if (m ~= k) A([k m],:) = A([m k],:); p([k m]) = p([m k]); end % Compute multipliers i = k+1:n; A(i,k) = A(i,k)/A(k,k); % Update the remainder of the matrix j = k+1:n; A(i,j) = A(i,j) - A(i,k)*A(k,j); end end % Separate result L = tril(A,-1) + eye(n,n); U = triu(A); 

2.12. If the built-in MATLAB lu function is called with only two output arguments [L, U] = lu (A) the permutations are incorporated into the output matrix L. The help entry for lu describes L as "psychologically lower triangular. Modify lutx so that it does the same thing. You can use if nargout == 2