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
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: Ignore, Warning, or Error. See Response to Nonpositive Definite Input.