User`s guide

LU Factorization
5-272
5LU Factorization
Purpose 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.
A
p
LU=
A
1– 85–
91– 2
25– 7
= A
p
91– 2
1– 85–
25– 7
=
P=(213)
1– 85–
91– 2
25– 7
9.00 1.00– 2.00
0.11– 7.89 4.78–
0.22 0.61– 3.66
L
100
0.11– 10
0.22 0.61– 1
= U
9.00 1.00– 2.00
07.894.78–
0 0 3.66
=
(213)