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 Ap contains the rows of A permuted as indicated by the permutation index vector P.

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.

Example

The row-pivoted matrix Ap 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

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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

To learn how to convert 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. Also see Matrix Factorizations for a list of all the blocks in the Matrix Factorizations library.


  LSF/LSP to LPC Conversion LU Inverse