MatrixFactorization-class: Virtual Class "MatrixFactorization" of Matrix Factorizations
In Matrix: Sparse and Dense Matrix Classes and Methods

MatrixFactorization-class

R Documentation

Virtual Class "MatrixFactorization" of Matrix Factorizations

Description

MatrixFactorization is the virtual class of factorizations of m \times n matrices A, having the general form

P_{1} A P_{2} = A_{1} \cdots A_{p}

or (equivalently)

A = P_{1}' A_{1} \cdots A_{p} P_{2}'

where P_{1} and P_{2} are permutation matrices. Factorizations requiring symmetric A have the constraint P_{2} = P_{1}', and factorizations without row or column pivoting have the constraints P_{1} = I_{m} and P_{2} = I_{n}, where I_{m} and I_{n} are the m \times m and n \times n identity matrices.

CholeskyFactorization, BunchKaufmanFactorization, SchurFactorization, LU, and QR are the virtual subclasses of MatrixFactorization containing all Cholesky, Bunch-Kaufman, Schur, LU, and QR factorizations, respectively.

Slots

Dim: an integer vector of length 2 giving the dimensions of the factorized matrix.
Dimnames: a list of length 2 preserving the dimnames of the factorized matrix. Each element must be NULL or a character vector of length equal to the corresponding element of Dim.

Methods

determinant: signature(x = "MatrixFactorization", logarithm = "missing"): sets logarithm = TRUE and recalls the generic function.
dim: signature(x = "MatrixFactorization"): returns x@Dim.
dimnames: signature(x = "MatrixFactorization"): returns x@Dimnames.
dimnames<-: signature(x = "MatrixFactorization", value = "NULL"): returns x with x@Dimnames set to list(NULL, NULL).
dimnames<-: signature(x = "MatrixFactorization", value = "list"): returns x with x@Dimnames set to value.
length: signature(x = "MatrixFactorization"): returns prod(x@Dim).
show: signature(object = "MatrixFactorization"): prints the internal representation of the factorization using str.
solve: signature(a = "MatrixFactorization", b = .): see solve-methods.
unname: signature(obj = "MatrixFactorization"): returns obj with obj@Dimnames set to list(NULL, NULL).