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Solve SX=B for X when S is square Hermitian positive definite matrix
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 solution.
Error — Display an error dialog box and terminate the simulation.
Cholesky factorization uniquely factors the Hermitian positive definite input matrix S as
$$S=L{L}^{\ast}$$
where L is a lower triangular square matrix with positive diagonal elements.
The equation SX=B then becomes
$$L{L}^{\ast}X=B$$
which is solved for X by making the substitution $$Y={L}^{\ast}X$$, and solving the following two triangular systems by forward and backward substitution, respectively.
$$LY=B$$
$${L}^{\ast}X=Y$$
Response to nonpositive definite matrix inputs: Ignore, Warning, or Error. See Response to Nonpositive Definite Input.
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.