Matrix (version 1.2-7.1)

Cholesky-class: Cholesky and Bunch-Kaufman Decompositions

Description

The "Cholesky" class is the class of Cholesky decompositions of positive-semidefinite, real dense matrices. The "BunchKaufman" class is the class of Bunch-Kaufman decompositions of symmetric, real matrices. The "pCholesky" and "pBunchKaufman" classes are their packed storage versions.

Objects from the Class

Objects can be created by calls of the form new("Cholesky", ...) or new("BunchKaufman", ...), etc, or rather by calls of the form chol(pm) or BunchKaufman(pm) where pm inherits from the "dpoMatrix" or "dsyMatrix" class or as a side-effect of other functions applied to "dpoMatrix" objects (see dpoMatrix).

Slots

A Cholesky decomposition extends class MatrixFactorization but is basically a triangular matrix extending the "dtrMatrix" class.

A Bunch-Kaufman decomposition also extends the "dtrMatrix" class and has a perm slot representing a permutation matrix. The packed versions extend the "dtpMatrix" class.

Extends

Class "MatrixFactorization" and "dtrMatrix", directly. Class "dgeMatrix", by class "dtrMatrix". Class "Matrix", by class "dtrMatrix".

Methods

Both these factorizations can directly be treated as (triangular) matrices, as they extend "dtrMatrix", see above. There are currently no further explicit methods defined with class "Cholesky" or "BunchKaufman" in the signature.

See Also

Classes dtrMatrix, dpoMatrix; function chol.

Function Cholesky resulting in class CHMfactor objects, not class "Cholesky" ones, see the section ‘Note’.

Examples

(sm <- as(as(Matrix(diag(5) + 1), "dsyMatrix"), "dspMatrix"))
signif(csm <- chol(sm), 4)

(pm <- crossprod(Matrix(rnorm(18), nrow = 6, ncol = 3)))
(ch <- chol(pm))
if (toupper(ch@uplo) == "U") # which is TRUE
   crossprod(ch)
stopifnot(all.equal(as(crossprod(ch), "matrix"),
                    as(pm, "matrix"), tolerance=1e-14))