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.

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

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. Also see Linear System Solvers for a list of all the blocks in the Linear System Solvers library.

LDL Inverse

Least Squares Polynomial Fit