pdFactor {nlme} | R Documentation |

## Square-Root Factor of a Positive-Definite Matrix

### Description

A square-root factor of the positive-definite matrix represented by
`object`

is obtained. Letting *S* denote a
positive-definite matrix, a square-root factor of *S* is
any square matrix *L* such that *S =
L'L*. This function extracts *L*.

### Usage

pdFactor(object)

### Arguments

`object` |
an object inheriting from class `pdMat` , representing
a positive definite matrix, which must have been initialized
(i.e. `length(coef(object)) > 0` ). |

### Value

a vector with a square-root factor of the positive-definite matrix
associated with `object`

stacked column-wise.

### Note

This function is used intensively in optimization
algorithms and its value is returned as a vector for efficiency
reasons. The `pdMatrix`

function can be used to obtain
square-root factors in matrix form.

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

### References

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models
in S and S-PLUS", Springer.

### See Also

`pdMatrix`

### Examples

pd1 <- pdCompSymm(4 * diag(3) + 1)
pdFactor(pd1)

[Package

*nlme* version 3.1-80

Index]