Factor square Hermitian positive definite matrices into lower, upper, and diagonal components
Math Functions / Matrices and Linear Algebra / Matrix Factorizations
dspfactors
The LDL Factorization block uniquely factors the square Hermitian positive definite input matrix S as
$$S=LD{L}^{*}$$
where L is a lower triangular square matrix with unity diagonal elements, D is a diagonal matrix, and L^{*} is the Hermitian (complex conjugate) transpose of L. Only the diagonal and lower 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 l_{ij} from L, diagonal elements d_{ij} from D, and upper triangle elements u_{ij} from L^{*}. The output format is shown below for a 5by5 matrix.
LDL factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable. It is more efficient than Cholesky factorization because it avoids computing the square roots of the diagonal elements.
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 Nonpositive definite input parameter.
The following diagram shows the data types used within the LDL Factorization block for fixedpoint signals.
You can set the intermediate product, product output, accumulator, and output data types in the block dialog as discussed below.
The output of the second multiplier is in the product output data type when the input is real. When the input is complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types.
LDL decomposition of a 3by3 Hermitian positive definite matrix:
Main Tab
Specify the action when nonpositive definite matrix inputs occur:
Ignore
— Proceed with the
computation and do not issue an alert. The output is not a valid
factorization. A partial factorization is 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 is
present in the upper left corner of the output.
Error
— Display an error
dialog and terminate the simulation.
Data Types Tab
Specify the rounding mode for fixedpoint operations as one of the following:
Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero
For more details, see rounding mode.
When you select this parameter, the block saturates the result of its
fixedpoint operation. When you clear this parameter, the block wraps the
result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint operations.
Specify the intermediate product data type. As shown in FixedPoint Data Types, the output of the multiplier is cast to the intermediate product data type before the next element of the input is multiplied into it. You can set it to:
A rule that inherits a data type, for example,
Inherit: Same as input
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the product output data type. See FixedPoint Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
.
For more information on this rule, see Inherit via Internal Rule.
A rule that inherits a data type, for example,
Inherit: Same as input
.
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the accumulator data type. See FixedPoint Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
.
For more information on this rule, see Inherit via Internal Rule.
A rule that inherits a data type, for example,
Inherit: Same as input
.
A rule that inherits a data type, for example,
Inherit: Same as product
output
.
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the output data type. See FixedPoint Data Types for illustrations depicting the use of the output data type in this block. You can set it to:
A rule that inherits a data type, for example,
Inherit: Same as input
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.
See Control Signal Data Types (Simulink) for more information.
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.
Port  Supported Data Types 

S 

LDL 

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