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

- %*%
`signature(x = "gchol", y = "matrix")`

: multiply
the cholesky decomposition by a matrix. That is, if A=LDL' is the
decomposition, then `gchol(A) %*% B`

will return L D^.5 B.

- %*%
`signature(x = "matrix", y = "gchol")`

: multiply
by a matrix on the left

- [
`signature(x = "gchol")`

: if a square portion from the
upper left corner is selected, then the result will be a gchol
object, otherwise an ordinary matrix is returned. The latter most
often occurs when printing part of the matrix at the command line.

- 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.
This is very useful inside modeling functions such as `coxph`

,
since the X matrix can often contain a redundant column.

### Author(s)

Terry Therneau

### See Also

`gchol`

### Examples

showClass("gchol")

[Package

*bdsmatrix* version 1.3-4

Index]