Solve SX=B for X when S is square Hermitian positive definite matrix
Math Functions / Matrices and Linear Algebra / Linear System Solvers
dspsolvers
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.
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 |
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.
Double-precision floating point
Single-precision floating point
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See Linear System Solvers for related information.