function x = GE3(A,b)
%  Input:  a square matrix A  and a vector b
%  Output:  the approximate solution to Ax=b
%  Gaussian elimination, w/o pivoting
%  JG for Math 436,  October 2008
[m, n] = size(A);
[mb , nb] = size(b);

% A few checks, make sure that the input meets our expectations
if m ~= mb
    error('you screwed up, b must have as many rows as A')
end
if nb ~= 1, error('b must be a column vector'), end
if m ~= n, error('A must be s square matrix'), end


A = eliminationstep(A,b);
x = backsub(A);

% -----------------------------------------
function AA = eliminationstep(A,b)
%  this is the old GE1 as a subfunction
%  modified for partial pivoting

warn = 0;  % no warnings yet
AA = [A , b];
[m, n] = size(A);
for p = 1:m-1        
    for k=p+1:m
        mult = AA(k,p)/AA(p,p);
        AA(k,:) = AA(k,:) - mult*AA(p,:);
    end
end



% -----------------------------------------
function x = backsub(A)
% Backsubstitution 
[m n] = size(A);
x = zeros(m, 1);
x(m) = A(m,n)/A(m,n-1);
for j=(m-1):-1:1
    S = A(j,n);
    for i=j+1:m
        S = S - A(j,i)*x(i);
    end
    x(j) = S/A(j,j);
end