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 M-by-N output matrix X is the unique solution
of the equations.
A length-M vector input for right side B is treated as an M-by-1 matrix.
Response to Nonpositive Definite Input
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 Simulink®
Coder™ code generation software.
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.
Parameters
- Non-positive definite input
Response to nonpositive definite matrix inputs:
Ignore,Warning, orError. See Response to Nonpositive Definite Input.
Supported Data Types
Double-precision floating point
Single-precision floating point
See Also
| Autocorrelation LPC | DSP System Toolbox |
| Cholesky Factorization | DSP System Toolbox |
| Cholesky Inverse | DSP System Toolbox |
| LDL Solver | DSP System Toolbox |
| LU Solver | DSP System Toolbox |
| QR Solver | DSP System Toolbox |
chol | MATLAB |
See Linear System Solvers for related information.