R: Square-Root Factor of a Positive-Definite Matrix

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 3.1-86 Index]