trying to find main diagonal of a matrix for cholesky method

my goal is to find the main diagonal of a matrix G, through the cholesky method. For this I'm using a summation, however there is no success follow the code so far and the sum of interest.

clear;

clc;

%cholesky

n= input ("dimension of system:"); %dimension of system for the matrix

A= input("enter matrix A "); %initial matrix A for the cholesky method

disp (A);

i=1;

j=1;

for i=j

if i==1

g(1,1)=sqrt (A(1,1));

fprintf ("first element: \n"); %first element of the diagonal g(1,1)

disp (g(1,1))

end

%diagonal

k=1;

for i=2:n

for i=i-1

g(i,i)= g(i,i) + sqrt(A(i,i) - g(i,k)^2); % summation for the remaining diagonals dependent on the dimension of the system

end

end

end

disp(g(i,i))

the sum of interest below:

the entries are respectively:

3 -> dimension of system

[ 1 1 0; 1 2 -1; 0 -1 3] -> matrix A

the error is:

Answer 1

[Dyuman Joshi]

%Random data
n = 5; %input ("dimensão do sistema:"); %dimension of system for the matrix
A = magic(5); %input("entre com a matriz "); %initial matrix A for the cholesky method
disp(A);

    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

%Pre-allocate g array
g = zeros(n);

for i=1:n
    if i==1
        g(i,i) = sqrt(A(i,i));
        fprintf("primeiro elemento: %f\n", g(1,1)); %first element of the diagonal g(1,1)
    else
        k=1:i-1;
        %summation for the remaining diagonals dependent on the dimension of the system
        g(i,i) = sqrt(A(i,i) - sum(g(i,k).^2));
    end
end

primeiro elemento: 4.123106

disp(g)

    4.1231         0         0         0         0
         0    2.2361         0         0         0
         0         0    3.6056         0         0
         0         0         0    4.5826         0
         0         0         0         0    3.0000

[Gabriel]

maybe I got it wrong somewhere, but the results don't match the table test, you could test with n = 3 and A = [ 1 1 0; 1 2 -1; 0 -1 3] please?

[Dyuman Joshi]

FYI, You can make a function and test for any inputs -

n = 3;
A = [1 1 0; 1 2 -1; 0 -1 3];
disp(A);

     1     1     0
     1     2    -1
     0    -1     3

g = choleskymethod(A,n)

primeiro elemento: 1.000000

g = 3×3

1.0000 0 0 0 1.4142 0 0 0 1.7321

function g = choleskymethod(A,n)

%Pre-allocate g array
g = zeros(n);

for i=1:n
    if i==1
        g(i,i) = sqrt(A(i,i));
        fprintf("primeiro elemento: %f\n", g(1,1)); %first element of the diagonal g(1,1)
    else
        k=1:i-1;
        %summation for the remaining diagonals dependent on the dimension of the system
        g(i,i) = sqrt(A(i,i) - sum(g(i,k).^2));
    end
end
end