User`s guide

LDL Inverse
5-257
5LDL Inverse
Purpose Compute the inverse of a Hermitian positive definite matrix using LDL
factorization.
Library Math Functions / Matrices and Linear Algebra / Matrix Inverses
Description The LDL Inverse block computes the inverse of the Hermitian positive definite
input matrix S by performing an LDL factorization.
L is a lower triangular square matrix with unity diagonal elements, D is a
diagonal matrix, and L
*
is the Hermitian (complex conjugate) transpose of L.
Only the diagonal and lower triangle of the input matrix are used, and any
imaginary component of the diagonal entries is disregarded. The output is
always sample-based.
LDL factorization requires half the computation of Gaussian elimination
(LU decomposition), and is always stable. It is more efficient than Cholesky
factorization because it avoids computing the square roots of the diagonal
elements.
The algorithm requires that the input be Hermitian positive definite. When the
input is not positive definite, the block reacts with the behavior specified by the
Non-positive definite input parameter. The following options are available:
•
Ignore – Proceed with the computation and do not issue an alert. The output
is not a valid inverse.
•
Warning – Display a warning message in the MATLAB command window,
and continue the simulation. The output is not a valid inverse.
•
Error – Display an error dialog box and terminate the simulation.
Dialog Box
S
1–
LDL
*
()
1–
=