function x=mnhf_naiveGauss(A,b)
%MNHF_NAIVEGAUSS implements Gaussian elimination 
% without pivoting.
%
% A - n-by-n matrix
% b - RHS column vector of length n.
%
% Usage  mnhf_naiveGauss(A,b);

[rA,cA] = size(A);  % Compute the size of A.
[rb,cb] = size(b);  % Compute the size of b.
if cb==1
 if rA==cA
  if rA==rb
   % Step 1: form n-by-n+1 augmented matrix.
   A(:,rA+1) = b;
   
   for i=1:rA
    % Step 2: Make diagonal elements unity.
    A(i,i+1:rA+1) = A(i,i+1:rA+1)/A(i,i);
    
    % Step 3: Make elements below diagonal 0. 
    for j=i+1:rA
     A(j,i+1:rA+1) = A(j,i+1:rA+1)-A(j,i)*A(i,i+1:rA+1);
    end
   end
   
   % Step 4: Back substitution.
   for j=rA-1:-1:1
    A(j,rA+1) = A(j,rA+1)-A(j,j+1:rA)*A(j+1:rA,rA+1);
   end
   x = A(:,rA+1);
  
  else
   fprintf('Rows of A ~= rows of b.') 
  end
 else
  fprintf('A is not a square matrix.')
 end
else
 fprintf('b is not a column vector.')
end