DSP Blockset

LDL Solver

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:

1. Substitute

2. Substitute

3. Solve one diagonal and two triangular systems.

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

See Also

Autocorrelation LPC	DSP Blockset
Cholesky Solver	DSP Blockset
LDL Factorization	DSP Blockset
LDL Inverse	DSP Blockset
Levinson-Durbin	DSP Blockset
LU Solver	DSP Blockset
QR Solver	DSP Blockset

See Solving Linear Systems for related information.

LDL Inverse

Least Squares FIR Filter Design