Solve SX=B for X when S is square Hermitian positive definite matrix
Math Functions / Matrices and Linear Algebra / Linear System Solvers
The LDL Solver block solves the linear system SX=B by applying LDL factorization to the matrix at the S port, which must be square (M-by-M) and Hermitian positive definite. Only the diagonal and lower triangle of the matrix are used, and any imaginary component of the diagonal entries is disregarded. The input to the B port is the right side M-by-N matrix, B. The M-by-N output matrix X is the unique solution of the equations.
A length-M unoriented vector input for right side B is treated as an M-by-1 matrix.
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 solution.
Warning — Proceed
with the computation and display a warning message in the MATLAB® Command
Window. The output is not a valid solution.
Error — Display
an error dialog and terminate the simulation.
The Non-positive definite input parameter
is a diagnostic parameter. Like all diagnostic parameters on the Configuration
Parameters dialog, it is set to
The LDL algorithm uniquely factors the Hermitian positive definite input matrix S as
S = LDL*
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.
LDL*X = B
is solved for X by the following steps:
Y = DL*X
Z = L*X
Solve one diagonal and two triangular systems.
LY = B
DZ = Y
L*X = Z
Response to nonpositive definite matrix inputs.
Double-precision floating point
Single-precision floating point
|Autocorrelation LPC||DSP System Toolbox|
|Cholesky Solver||DSP System Toolbox|
|LDL Factorization||DSP System Toolbox|
|LDL Inverse||DSP System Toolbox|
|Levinson-Durbin||DSP System Toolbox|
|LU Solver||DSP System Toolbox|
|QR Solver||DSP System Toolbox|
See Linear System Solvers for related information.