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

`gchol`
```showClass("gchol")