gchol-class {bdsmatrix}R Documentation

Class "gchol"

Description

The result of a generalized Cholesky decomposition A=LDL' where A is a symmetric matrix, L is lower triangular with 1s on the diagonal, and D is a diagonal matrix.

Objects from the Class

These objects are created by the gchol function.

Slots

.Data:
A numeric vector containing the results of the decompostion
Dim:
An integer vector of length 2, the dimension of the matrix
Dimnames:
A list of length 2 containing the dimnames. These default to the dimnames of the matrix A
rank:
The rank of the matrix

Methods

coerce
signature(from = "gchol", to = "matrix"): Use of the as.matrix function will return L
diag
signature(x = "gchol"): Use of the diag function will return D
dim
signature(x = "gchol"): returns the dimension of the matrix
dimnames
signature(x = "gchol"): returns the dimnames
show
signature(object = "gchol"): By default a triangular matrix is printed showing D on the diagonal and L off the diagonal
gchol
signature(x= "matrix"): create a generalized Cholesky decompostion of the matrix

Note

The primary advantages of the genearlized decomposition, as compared to the standard chol function, has to do with redundant columns and generalized inverses (g-inverse). The lower triangular matrix L is always of full rank. The diagonal matrix D has a 0 element at position j if and only if the jth column of A is linearly dependent on columns 1 to j-1 preceding it. The g-inverse of A involves the inverse of L and a g-inverse of D. The g-inverse of D retains the zeros and inverts non-zero elements of D. All this makes manipulation of the result particularly convenient.

Author(s)

Terry Therneau

See Also

gchol

Examples

showClass("gchol")

[Package bdsmatrix version 1.0 Index]