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胆固醇esky Factorization

Factor square Hermitian positive definite matrix into triangular components

Library

Math Functions / Matrices and Linear Algebra / Matrix Factorizations

dspfactors

  • 胆固醇esky Factorization block

Description

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

S = L L *

whereLis a lower triangular square matrix with positive diagonal elements andL*is the Hermitian (complex conjugate) transpose ofL. The block outputs a matrix with lower triangle elements fromLand upper triangle elements fromL*. The output is not in the same form as the output of the MATLAB®cholfunction. In order to convert the output of the Cholesky Factorization block to the MATLAB form, use the following equation:

R = triu(LL');

In order to extract theLmatrix exclusively, pass the output of the Cholesky Factorization block,LL', to theExtract Triangular Matrixblock. Setting theExtractparameter of theExtract Triangular MatrixtoLowerextracts theLmatrix. Setting theExtractparameter toUpperextracts theL'matrix.

Here,LL'is the output of the Cholesky Factorization block. Due to roundoff error, these equations do not produce a result that is exactly the same as the MATLAB result.

Block Output Composed of L and L*

Input Requirements for Valid Output

The block output is valid only when its input has the following characteristics:

  • Hermitian — The block doesnotcheck whether the input is Hermitian; it uses only the diagonal and upper triangle of the input to compute the output.

  • Real-valued diagonal entries — The block disregards any imaginary component of the input's diagonal entries.

  • Positive definite — Set the block to notify you when the input is not positive definite as described inResponse to Nonpositive Definite Input.

Response to Nonpositive Definite Input

To generate a valid output, the block algorithm requires a positive definite input (seeInput Requirements for Valid Output). Set the没有n-positive definite inputparameter to determine how the block responds to a nonpositive definite input:

  • Ignore— Proceed with the computation anddo notissue an alert. The output isnota 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 isnota valid factorization. A partial factorization will be present in the upper left corner of the output.

  • Error— Display an error dialog and terminate the simulation.

没有te

The没有n-positive definite inputparameter is a diagnostic parameter. Like all diagnostic parameters on the Configuration Parameters dialog box, it is set toIgnorein the code generated for this block by万博1manbetx®Coder™code generation software.

Performance Comparisons with Other Blocks

没有te thatLandL*共享相同的输出矩阵中对角线。胆固醇esky factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable.

Parameters

没有n-positive definite input

应对负的定矩阵输入:Ignore,Warning, orError. SeeResponse to Nonpositive Definite Input.

References

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

Supported Data Types

Port Supported Data Types

S

  • Double-precision floating point

  • Single-precision floating point

LL'

  • Double-precision floating point

  • Single-precision floating point

See Also

Autocorrelation LPC DSP System Toolbox
胆固醇esky Inverse DSP System Toolbox
胆固醇esky Solver DSP System Toolbox
LDL Factorization DSP System Toolbox
LU Factorization DSP System Toolbox
QR Factorization DSP System Toolbox

chol

 MATLAB

SeeMatrix Factorizationsfor related information.

Extended Capabilities

Version History

Introduced before R2006a