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
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
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.
The Non-positive definite input parameter
is a diagnostic parameter. Like all diagnostic parameters on the Configuration
Parameters dialog box, it is set to
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