Solve SX=B for X when S is square Hermitian positive definite matrix
Math Functions / Matrices and Linear Algebra / Linear System Solvers
dspsolvers
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.
Note
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.
The equation
LDL^{*}X = B
is solved for X by the following steps:
Substitute
Y = DL^{*}X
Substitute
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
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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.