Sparse LU decomposition of a square sparse matrix

Description

Objects of this class contain the components of the LU decomposition of a sparse square matrix.

Objects from the Class

Objects can be created by calls of the form new("sparseLU", ...) but are more commonly created by function lu() applied to a sparse matrix, such as a matrix of class dgCMatrix.

Slots

L:

Object of class "dtCMatrix", the lower triangular factor from the left.

U:

Object of class "dtCMatrix", the upper triangular factor from the right.

p:

Object of class "integer", permutation applied from the left.

q:

Object of class "integer", permutation applied from the right.

Dim:

the dimension of the original matrix; inherited from class MatrixFactorization.

Extends

Class "LU", directly. Class "MatrixFactorization", by class "LU".

Methods

expand

signature(x = "sparseLU") Returns a list with components P, L, U, and Q, where P and Q represent fill-reducing permutations, and L, and U the lower and upper triangular matrices of the decomposition. The original matrix corresponds to the product PLUQ.

Note

The decomposition is of the form

A = PLUQ

where all matrices are sparse and of size n by n. The matrices P and Q are permutation matrices, L is lower triangular and U is upper triangular.

See Also

lu, solve, dgCMatrix

Examples

  ## see  examples(lu)