Signal Processing Blockset™

LDL Solver - Solve SX=B for X when S is square Hermitian positive definite matrix

Library

Math Functions / Matrices and Linear Algebra / Linear System Solvers

dspsolvers

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 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 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 and terminate the simulation.

Note   The Non-positive definite input parameter is a diagnostic parameter. Like all diagnostic parameters on the Configuration Parameters dialog, it is set to Ignore in the code generated for this block by Real-Time Workshop code generation software.

Algorithm

The LDL algorithm uniquely factors the Hermitian positive definite input matrix S as

S = LDL^*

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

LDL^*X = B

is solved for X by the following steps:

1. Substitute

   Y = DL^*X

2. Substitute

   Z = L^*X

3. Solve one diagonal and two triangular systems.

   LY = B

   DZ = Y

   L^*X = Z

Dialog Box

Non-positive definite input

Response to nonpositive definite matrix inputs.

Supported Data Types

• Double-precision floating point

• Single-precision floating point

See Also

See Linear System Solvers for related information.

LDL Inverse

Least Squares FIR Filter Design (Obsolete)