MATLAB: LU decomposition code, don’t know what it’s doing. Can someone explain what this code is doing line-by-line

computational methodsfor loopslinear algebralu decompositionmathematicsMATLAB

Hi,
I'm trying to modify this code that performs an LU decompositon for a matrix A via column operations. The default code is written for row operations.
I don't understand what the code is doing though for the row operations. Does anyone mind explaining what is going on line-by-line? I know how to do LU decomposition by hand, but I don't have a really good idea what the script is doing.
I'll include the programme for you.
Thank You! 
function [L,U] = mylu(A)
n = size(A,1);
for k = 1:n
    if A(k,k)==0
        warning('LU factorization fails');
        L = []; U = []; return; 
    end
    i = k+1:n;
    A(i,k) = A(i,k)/A(k,k);
    A(i,i) = A(i,i)-A(i,k)*A(k,i);
end
L = tril(A,-1)+eye(n); U = triu(A);

Best Answer

Hi, In LU Decomposition method we try to convert A matrix to echleon form by using gauss elimination method. The code starts from the first row, tries to find the factor by which we need to multiply the current row and subtract it from the rows below it, to make the elements in the Lower Triangular Matrix as zeros.
 i = k+1:n; %To access rows below the current row
 A(i,k) = A(i,k)/A(k,k); % To get the factor by which we need to multiply the current row and subtract it from row present below
 A(i,i) = A(i,i)-A(i,k)*A(k,i); % To subtract from each row elementwise
The above code iterates till all the elements in Lower Triangular matrix becomes zero. Later we get the tril and triu of A, which gives L and U matrices.
I suggest using breakpoints, and work on this program. To know the updation of A for each iteration.
Hope this helps!
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