LU Factorization for MATLAB

user_18174947 0
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How do you write MATLAB code for LU factorization when U is the unit matrix instead of L. The upper triangular matrix will have the diagonal of 1s instead of the lower triangular matrix.

matrix matlab
2 Answers

Here's one way to do this. If M is your matrix,

[P,Q] = lu(M');
L = Q'; U = P';

Alternatively, assuming that M has an LU decomposition, we could do the following:

[L,U,P,Q,D] = lu(M);
L = L*P'*D*Q';

This should yield a lower triangular L and upper triangular U where U has 1's on the diagonal whenever M has an LU decomposition.

user_24769770

You are looking for Crout's Method for LU decomposition.

The Wikipedia article has the following code

function [L, U] = LUdecompCrout(A)
        
        [R, C] = size(A);
        for i = 1:R
            L(i, 1) = A(i, 1);
            U(i, i) = 1;
        end
        for j = 2:R
            U(1, j) = A(1, j) / L(1, 1);
        end
        for i = 2:R
            for j = 2:i
                L(i, j) = A(i, j) - L(i, 1:j - 1) * U(1:j - 1, j);
            end
            
            for j = i + 1:R
                U(i, j) = (A(i, j) - L(i, 1:i - 1) * U(1:i - 1, j)) / L(i,i);

            end
        end
   end
user_3803840
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