LU (dense) Matrix Decompositions

Description

The "LU" class is the virtual class of LU decompositions of real matrices. "denseLU" the class of LU decompositions of dense real matrices.

Objects from the Class

Objects can be created by calls of the form new("denseLU", ...). More commonly the objects are created explicitly from calls of the form lu(mm) where mm is an object that inherits from the "dgeMatrix" class or as a side-effect of other functions applied to "dgeMatrix" objects.

Extends

"LU" directly extends the virtual class "MatrixFactorization".

"denseLU" directly extends "LU".

Slots

x:

object of class "numeric". The "L" (unit lower triangular) and "U" (upper triangular) factors of the original matrix. These are stored in a packed format described in the Lapack manual.

perm:

Object of class "integer" - a vector of length min(Dim) that describes the permutation applied to the rows of the original matrix. The contents of this vector are described in the Lapack manual.

Dim:

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

Methods

expand

signature(x = "denseLU"): Produce the "L" and "U" (and "P") factors as a named list of matrices, see also the example below.

solve

signature(a = "denseLU", b = "missing"): ComputeProduce the "L" and "U" (and "P") factors as a named list of matrices, see also the example below.

See Also

class sparseLU for LU decompositions of sparse matrices; further, class dgeMatrix and functions lu, expand.

Examples

set.seed(1)
mm <- Matrix(round(rnorm(9),2), nrow = 3)
mm
str(lum <- lu(mm))
elu <- expand(lum)
elu # three components: "L", "U", and "P", the permutation
elu$L %*% elu$U
(m2 <- with(elu, P %*% L %*% U)) # the same as 'mm'
stopifnot(all.equal(as(mm, "matrix"),
                    as(m2, "matrix")))