function A = nluFactor(A)
% nlu Naive LU factoriztion of A
% Syntax: A = nluFactor(A)
% A is the n by n matrix returned in LU form

[m,n] = size(A);
if m ~= n
   error('Matrix is not square');
end

% forward elimination

% loop over pivot positions (diagonal elements)
for k = 1 : n-1
   
   % loop down pivot column k beginning below pivot
   for i = k+1 : n
      
      % calculate multiplier for row i
      % and subtract multiple of row k from row i
      mult = A(i,k) / A(k,k);
      for j = k+1 : n % We begin at j=k+1 here
         A(i,j) = A(i,j) - mult*A(k,j);
      end
         A(i,k) = mult; % store where 0 would go
   end
end
end % nluFactor