LDL Factorization
Decomposition of a square Hermite positively definite matrix into lower, upper and diagonal components.
Description
Block LDL Factorization uniquely decomposes the Hermite positively defined input matrix as
where:
-
- lower triangular matrix with unit diagonal elements (unitriangular matrix).
-
- diagonal matrix.
-
- Hermite (complex-conjugate) transposed matrix L.
Only the diagonal and lower triangle of the input matrix are used. Any imaginary component of the diagonal elements is ignored.
The LDL decomposition requires half the computation of the LU decomposition and is always stable. It is more efficient than the Choletsky decomposition because it avoids the computation of square roots of diagonal elements.
Ports
Input
Port_1 - initial matrix S
`matrix M by M
The input signal is in the form of a square matrix.
The algorithm requires the input matrix to be square and Hermite positively defined. When the input is not positively defined, the block responds as specified by the input parameter Non-positive Definity.
Data types: Float64
Support for complex numbers: yes
Output
Port_1 - output matrix
`matrix M by M
The output is a composite matrix with elements below the main diagonal of , diagonal elements of and elements above the main diagonal of ,
where:
-
- lower triangular matrix with unit diagonal elements (unitriangular matrix).
-
- diagonal matrix.
-
- Hermite (complex-conjugate) transposed matrix L.
The output format is shown below for a 5 by 5 matrix.
Data types: Float64
Parameters
Main
Non-positive definite input - response to non-positive definite input matrix
Ignore (by default) | Warning | Error
Sets the action when non-positive definite input matrix parameters occur:
-
Ignore- the simulation continues and no warning is issued. The result is not a valid decomposition. A partial decomposition will be present in the upper left corner of the output matrix. -
Warning- the simulation continues, but a warning message is displayed in the Engee command window. The result is not a valid decomposition. A partial decomposition will be present in the upper left corner of the output matrix. -
Error- an error dialogue box is displayed and the simulation stops.