Cholesky Inverse

Compute inverse of Hermitian positive definite matrix using Cholesky factorization

• 

Libraries:
DSP System Toolbox / Math Functions / Matrices and Linear Algebra / Matrix Inverses

Description

The Cholesky Inverse block computes the inverse of the Hermitian positive definite input matrix S by performing Cholesky factorization.

$$S^{-1}={(L{L}^{\ast })}^{-1}$$

L is a lower triangular square matrix with positive diagonal elements and L^* is the Hermitian (complex conjugate) transpose of L. The block uses only the diagonal and upper triangle of the input matrix and disregards any imaginary component of the diagonal entries. Cholesky factorization requires half the computation of Gaussian elimination (LU decomposition) and is always stable.

Ports

Input

Input — Input matrix

square matrix

Specify the input as a square matrix S that is Hermitian positive definite. When the input is not positive definite, the block behaves as specified by the Non-positive definite input parameter. For more details, see the description of the Non-positive definite input parameter.

Data Types: single | double
Complex Number Support: Yes

Output

Output — Matrix inverse

square matrix

Inverse of the Hermitian positive definite input matrix S, returned as a square matrix. This is the equation for Cholesky factorization.

$$S^{-1}={(L{L}^{\ast })}^{-1}$$

L is a lower triangular square matrix with positive diagonal elements and L^* is the Hermitian (complex conjugate) transpose of L. The block uses only the diagonal and upper triangle of the input matrix and disregards any imaginary component of the diagonal entries. Cholesky factorization requires half the computation of Gaussian elimination (LU decomposition) and is always stable.

Data Types: single | double
Complex Number Support: Yes

Parameters

Non-positive definite input — Non-positive definite input

Warning (default) | Ignore | Error

Specify the response to non-positive definite matrix input as Ignore, Warning, or Error.

The algorithm requires that the input be Hermitian positive definite. When the input is not positive definite, the block behaves as specified by the Non-positive definite input parameter. When you set this parameter to:

• Ignore — The block proceeds with the computation and does not issue an alert. The output is not a valid inverse.

• Warning — The block displays a warning message in the MATLAB^® command window and continues the simulation. The output is not a valid inverse.

• Error — The block displays an error dialog box and terminates the simulation.

Note

The Non-positive definite input parameter is a diagnostic parameter. Like all diagnostic parameters in the Configuration Parameters dialog box, it is set to Ignore in the code generated for this block by Simulink^® Coder™ code generation software.

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

References

[1] Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Version History

Introduced before R2006a