LU Factorization
LU decomposition of a square matrix.
Description
Block LU Factorization decomposes a row-rearranged version of the square input matrix A into the following upper and lower triangular matrices:
where:
-
- lower triangular matrix with unit diagonal elements (unitriangular matrix);
-
- upper triangular matrix;
-
- matrix A with rows rearranged as shown by the rearrangement vector P.
The block uses the matrix , obtained by row permutation, instead of the exact input matrix A, as this improves the numerical accuracy of the computation.
Ports
Output
LU - lower and upper triangular matrices
`matrix M by M
A composite matrix containing both lower elements , and upper elements . Usage of a composite matrix increases the efficiency of the block.
Data types: Float64
P is a permutation vector
vector
A permutation vector of length M. The block rearranges the rows of the input square matrix A as specified in the permutation vector P, and decomposes the rearranged matrix into a unitriangular matrix and an upper triangular matrix .
Consider the following input matrix:
With the permutation vector P equal to , then the matrix obtained after permutation takes the form:
The block divides this matrix into upper and lower triangular matrices.
Data types: Float64
Parameters
Main
Show singularity status - show singularity status
off (by default) | on
Specifies whether to output the input matrix singularities to port S, which outputs values of logical data type 1 or 0. An output of 1 indicates that the input matrix is singular and vice versa.
Rounding mode - rounding mode
Floor (By default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero
Set the rounding mode:
-
Floor. -
Ceiling -
Convergent -
`Nearest
-
`Round
-
`Simplest
-
`Zero