DSP Blockset

Cholesky Factorization

Factor a square Hermitian positive definite matrix into triangular components.

Library

Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description

The Cholesky Factorization block uniquely factors the square Hermitian positive definite input matrix S as

where L is a lower triangular square matrix with positive diagonal elements and L^* is the Hermitian (complex conjugate) transpose of L. Only the diagonal and upper triangle of the input matrix are used, and any imaginary component of the diagonal entries is disregarded.

The block's output is a composite matrix with lower triangle elements from L and upper triangle elements from L^*, and is always sample-based.

Note that L and L^* share the same diagonal in the output matrix. Cholesky factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable.

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 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 factorization. A partial factorization will be present in the upper left corner of the output.
• Warning - Display a warning message in the MATLAB command window, and continue the simulation. The output is not a valid factorization. A partial factorization will be present in the upper left corner of the output.
• Error - Display an error dialog box and terminate the simulation.

Dialog Box

Non-positive definite input

Response to non-positive definite matrix inputs. Tunable.

References

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

See Also

Autocorrelation LPC	DSP Blockset
Cholesky Inverse	DSP Blockset
Cholesky Solver	DSP Blockset
LDL Factorization	DSP Blockset
LU Factorization	DSP Blockset
QR Factorization	DSP Blockset
chol	MATLAB

See Factoring Matrices for related information.

Chirp

Cholesky Inverse