function x = nopvt(A,b)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Solution of Ax = b with no-pivoting.
% 
x = b; n = length(b);
% %%%%%%%%%%%%%%%%%%%%%
% Forward elimination %
% %%%%%%%%%%%%%%%%%%%%%
for k = 1:n-1
% 
% Eliminate x_k from equations k+1 to n
% 
% Compute the multipliers, overwriting A(k+1:n,k)
% 
  A(k+1:n,k) = A(k+1:n,k)/A(k,k);
% 
%   Subtract m(k+1:n) times equation k from equations k+1:n
% 
  A(k+1:n,k+1:n) = A(k+1:n,k+1:n) - A(k+1:n,k)*A(k,k+1:n);
  x(k+1:n)       = x(k+1:n)       - A(k+1:n,k)*x(k);
end
% %%%%%%%%%%%%%%%%%%%
% Back substitution %
% %%%%%%%%%%%%%%%%%%%
L = eye(n) + tril(A,-1); L, U=triu(A)
x(n) = x(n)/A(n,n);
for k = n-1:-1:1,
% 
% Substitute x(k+1) to x(n) (now known) 
% into equation k, then solve for x(k).
% 
  x(k) = (x(k) - A(k,k+1:n)*x(k+1:n))/A(k,k);
end