User`s guide

LDL Solver
5-259
5LDL Solver
Purpose Solve the equation SX=B for X when S is a square Hermitian positive definite
matrix.
Library Math Functions / Matrices and Linear Algebra / Linear System Solvers
Description The LDL Solver block solves the linear system SX=B by applying LDL
factorization to the matrix at the
S port, which must be square (M-by-M) and
Hermitian positive definite. Only the diagonal and lower triangle of the matrix
are used, and any imaginary component of the diagonal entries is disregarded.
The input to the
B port is the right-hand side M-by-N matrix, B. The output is
the unique solution of the equations, M-by-N matrix X, and is always
sample-based.
A length-M 1-D vector input for right-hand side B is treated as an M-by-1
matrix.
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 solution.
•
Warning – Proceed with the computation and display a warning message in
the MATLAB command window. The output is not a valid solution.
•
Error – Display an error dialog box and terminate the simulation.
Algorithm The LDL algorithm uniquely factors the Hermitian positive definite input
matrix S as
where 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.
The equation
is solved for X by the following steps:
S LDL
*
=
LDL
*
XB=