function [F]=cholesky(A,option)
%Function to find the Cholesky factor of a Positive Definite matrix A
 
%Author Mathuranathan for http://www.gaussianwaves.com
 
%Licensed under Creative Commons: CC-NC-BY-SA 3.0
 
%A = positive definite matrix
 
%Option can be one of the following 'Lower','Upper'
 
%L = Cholesky factorizaton of A such that A=LL^T
 
%If option ='Lower', then it returns the Cholesky factored matrix L in
 
%lower triangular form
 
%If option ='Upper', then it returns the Cholesky factored matrix L in
 
%upper triangular form    
 
 
    %Test for positive definiteness
    if isPositiveDefinite(A),
        [m,n]=size(A);
        L=zeros(m,m);%Initialize to all zeros
        row=1;
        col=1;
        j=1;
        for i=1:m,
            a11=sqrt(A(1,1));
            L(row,col)=a11;
            if(m~=1) %Reached the last partition                
                L21=A(j+1:m,1)/a11;
                L(row+1:end,col)=L21;
                A=(A(j+1:m,j+1:m)-L21*L21');
                [m,n]=size(A);
                row=row+1;
                col=col+1;  
            end
        end
        if strcmpi(option,'upper'),F=L';
        else if strcmpi(option,'lower'),F=L;
            else error('Opção inválida');end
        end
    else
        error('A Matriz A dada NÃO é definida positiva');
    end;
end