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.

Example

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.

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References

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

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.

LMS Adaptive Filter

LU Inverse