LDL does not support complex symmetric matrices
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Christine Tobler on 7 Jan 2022
Largely the reason LDL doesn't support this is that it's less commonly requested for complex symmetric matrices than for complex Hermitian ones, so LDL only supports the more common variant. We would also need some option to indicate which of the two modes is meant to be used.
There is a LAPACK function ZSYTRF that you can call from a mex-file to get the complex symmetric LDL decomposition.
More Answers (1)
David Goodmanson on 6 Jan 2022
Edited: David Goodmanson on 7 Jan 2022
the LDL decomposition works for hermitian matrices. In LDL the D matrix is hermitian, so
if A = L*D*L', then A' = L*D' *L' = L*D*L' = A, and A has to be hermitian.
But a symmetric complex matrix is not hermitian, so LDL won't work.