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LDL Solver

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 Ignore in the code generated for this block by Simulink® Coder™ code generation software.


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


is solved for X by the following steps:

  1. Substitute

    Y = DL*X

  2. Substitute

    Z = L*X

  3. Solve one diagonal and two triangular systems.

    LY = B

    DZ = Y

    L*X = Z


Non-positive definite input

Response to nonpositive definite matrix inputs.

Supported Data Types

  • Double-precision floating point

  • Single-precision floating point

See Also

Autocorrelation LPCDSP System Toolbox
Cholesky SolverDSP System Toolbox
LDL FactorizationDSP System Toolbox
LDL InverseDSP System Toolbox
Levinson-DurbinDSP System Toolbox
LU SolverDSP System Toolbox
QR SolverDSP System Toolbox

See Linear System Solvers for related information.

Extended Capabilities

Introduced before R2006a