%CHOLESKY

clear all
clc
A=[2 1 3;1 4 0; 3 0 10];
b=sum(A,2);

[S] = CHOLESKYY(A)
y=S\b;
x=S'\y;

function [S] = CHOLESKYY(A)
n=length(A);
S=zeros(n);
S(1,1)=sqrt(A(1,1));

for i=2:n
    for j=1:i-1
        S(i,j)=(A(i,j) - S(i,1:j-1)*S(j,1:j-1)')/S(j,j);
        S(i,i)=sqrt(A(i,i)-S(i,1:i-1)*S(i,1:i-1)');
    end
end

end