Solve SX=B for X when S is square Hermitian positive definite matrix
Math Functions / Matrices and Linear Algebra / Linear System Solvers
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.
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
Error — Display an error dialog box and
terminate the simulation.
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.
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.
Response to nonpositive definite matrix inputs:
Error. See Response to Nonpositive Definite Input.
Double-precision floating point
Single-precision floating point
|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|
See Linear System Solvers for related information.
Generated code relies on
memset functions (string.h) under certain conditions.