Cholesky Solver (DSP Blockset)

Solve the equation Sx=b for Hermitian positive definite matrix S.

Library

Linear Algebra, in Math Functions

Description

The Cholesky Solver block solves the linear system Sx=b by applying Cholesky factorization to matrix S (top input), which must be square and Hermitian positive definite. The bottom input is the right-hand-side of the equation, b. The output is the unique solution of the equations, x.

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 y = L^Hx, and solving the following two triangular systems by forward and backward substitution, respectively:

The algorithm requires that the input be square and Hermitian positive definite. When the input is not positive definite, the block reacts with the behavior specified by the Invalid input matrix 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.
Error - Display an error dialog box and terminate the simulation.

The block may generate NaN or Inf for underdetermined or inconsistent (overdetermined) systems.

Dialog Box

Invalid input matrix: Response to non-positive definite matrix inputs.