Finding D matrix in LDU in matlab

Question

I have been searching the web for nearly 3 hours about a MatLab function that can take matrix A and give me back L, D, and U. Does such function exist in MatLab?

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Answer 1

This can be performed in Matlab as follows:

Given matrix A.

[L,U,P] = lu(A); % calculate partial-pivoted LU decomposition of A

D = diag(diag(U)); % get diagonal matrix

U = D\U; % the 'U' that is needed is really inv(D)*U

This allows you to write $LDU = PA$, where $P$ is a permutation matrix.

Answer 2

Matlab's lu function will find a LU decomposition of $A=LU$, then you can always write $U$ as $U=D\cdot \tilde U$ so $\tilde U$ has ones on the diagonal and $D$ is diagonal.