function G=cholesky(A)
n=length(A);
G=zeros(n);
G(1,1)=sqrt(A(1,1));
G(1,2:n)=A(1,2:n)/G(1,1);
for i=2:n
    G(i,i)=sqrt(A(i,i)-G(1:(i-1),i)'*G(1:(i-1),i));
    for j=i+1:n
        t=G(1:(i-1),i)'*G(1:(i-1),j);
        G(i,j)=(A(i,j)-t)/G(i,i);
    end
end
end