Signal Processing Blockset™

Cholesky 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 Cholesky Solver block solves the linear system SX=B by applying Cholesky factorization to input matrix at the S port, which must be square (M-by-M) and Hermitian positive definite. Only the diagonal and upper 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.

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.

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

A length-M vector input for right side B is treated as an M-by-1 matrix.

Algorithm

Cholesky factorization uniquely factors the Hermitian positive definite input matrix S as

where L is a lower triangular square matrix with positive diagonal elements.

The equation SX=B then becomes

which is solved for X by making the substitution , and solving the following two triangular systems by forward and backward substitution, respectively.

Dialog Box

Non-positive definite input: Response to nonpositive definite matrix inputs.

Supported Data Types

Double-precision floating point
Single-precision floating point