DSP Blockset

LU Factorization

Factor a square matrix into lower and upper triangular components

Library

Math Functions / Matrices and Linear Algebra / Matrix Factorizations

Description

The LU Factorization block factors a row permutation of the square input matrix A as

where L is a lower-triangular square matrix with unity diagonal elements, and U is an upper-triangular square matrix. The row-pivoted matrix A_p contains the rows of A permuted as indicated by the permutation index vector P.

• Ap = A(P,:)          % Equivalent MATLAB code
  

The output at the LU port is a composite matrix with lower subtriangle elements from L and upper triangle elements from U, and is always sample based.

Examples

The row-pivoted matrix A_p and permutation index vector P computed by the block are shown below for 3-by-3 input matrix A.

The LU output is a composite matrix whose lower subtriangle forms L and whose upper triangle forms U.

Dialog Box

.

Show singularity status

When selected, the block indicates the singularity of the input at a third output port labeled S, which outputs Boolean data type values of 1 or 0. An output of 1 indicates that the current input is singular, and an output of 0 indicates the current input is nonsingular.

References

Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

Supported Data Types

• Double-precision floating point
• Single-precision floating point
• Boolean -- Supported only by the optional output port that appears when you select the Show singularity status check box.

To learn how to convert your data types to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Autocorrelation LPC	DSP Blockset
Cholesky Factorization	DSP Blockset
LDL Factorization	DSP Blockset
LU Inverse	DSP Blockset
LU Solver	DSP Blockset
Permute Matrix	DSP Blockset
QR Factorization	DSP Blockset
lu	MATLAB

See Factoring Matrices for related information.

LPC/RC to Autocorrelation

LU Inverse