Index in position 1 exceeds array bounds (must not exceed 2 )

Hi!

I'm trying to create a script that will manually find the LU factorization of a given matrix. This code seems to work for a 3x3 matrix, but once I increase the size to a 4x4 matrix, it seizes up and tells me that the index in the first position exceeds its bounds of 2. Here is the code:

clear all;
n = 4;
% Set up the 4x4 A matrix & b = column vector
disp(' n=4 ... Setting up 4x4 A matrix  &  b column vector  ...')
n_rows = n ;
n_cols = n ;

A = [  1    -2    -3   4  ;
      -5    6    7    -8  ;
       9  -10   11   -12  ;
     -13   14  -15    16  ]  ;
%
%  Remember to transpose (') from row matrix to column matrix
b = [  1   2   3   4 ]' ;
disp(' and initial L = U = A  ...')
disp(' Warning: Up to you to reassign L and U  ...') 
L(:,1)=A(:,1)
U(1,:)=A(1,:)/L(1,1)   

for k=2:size(A,2)
    for j=2:size(A,2)
        for i = j:size(A,2)
            L(i,j) = A(i,j) - sum ( L(i,1:j-1)*U(1:j-1,j) )
            
        end
        U(k,j) = ( A(k,j) - sum( L(k,1:k-1)*U(1:k-1,j) ))/L(k,k)
    end
end

It seizes up during the line "L(i,j) = A(i,j) - sum ( L(i,1:j-1)*U(1:j-1,j) )" and displays "Index in position 1 exceeds array bounds (must not exceed 2).

Error in set_Ab4 (line 24)

L(i,j) = A(i,j) - sum ( L(i,1:j-1)*U(1:j-1,j) )"

I've tried everything I can think up and find on here but nothing seems to make it want to finish. Any ideas?

[Walter Roberson]

You are growing U as you go. The number of rows of U does not exceed k. But j can exceed k+1 and you have not created the full diagonal U(j-1,j) to be able to access it.

[FuManchuToo]

Oh darn! Thinking about this, I went ahead and created L and U to be 4x4 matrices filled with zeros at the beginning of the script, and that did the trick! Thanks!

Answer 1

[Asad (Mehrzad) Khoddam]

try this

for i = j:size(A,1)