Factor square Hermitian positive definite matrix into triangular components
Math Functions / Matrices and Linear Algebra / Matrix Factorizations
dspfactors
The Cholesky Factorization block uniquely factors the square Hermitian positive definite input matrix S as
$$S=L{L}^{*}$$
where L is a lower triangular square matrix
with positive diagonal elements and L^{*} is
the Hermitian (complex conjugate) transpose of L.
The block outputs a matrix with lower triangle elements from L and
upper triangle elements from L^{*}.
The output is not in the same form as the output of the MATLAB^{®} chol
function.
In order to convert the output of the Cholesky Factorization block
to the MATLAB form, use the following equation:
R = triu(LL');
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^{*}
The block output is valid only when its input has the following characteristics:
Hermitian — The block does not check whether the input is Hermitian; it uses only the diagonal and upper triangle of the input to compute the output.
Realvalued 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 in Response to Nonpositive Definite Input.
To generate a valid output, the block algorithm requires a positive definite input (see Input Requirements for Valid Output). Set the Nonpositive definite input parameter to determine how the block responds to a nonpositive definite input:
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 and terminate the simulation.
Note
The Nonpositive definite input parameter
is a diagnostic parameter. Like all diagnostic parameters on the Configuration
Parameters dialog box, it is set to 
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.
Response to nonpositive definite matrix inputs: Ignore
, Warning
,
or Error
. See Response to Nonpositive Definite Input.
Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.
Port  Supported Data Types 

S 

LL 

Autocorrelation LPC  DSP System Toolbox 
Cholesky Inverse  DSP System Toolbox 
Cholesky Solver  DSP System Toolbox 
LDL Factorization  DSP System Toolbox 
LU Factorization  DSP System Toolbox 
QR Factorization  DSP System Toolbox 
MATLAB 
See Matrix Factorizations for related information.