nlme (version 3.1-131)

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

Description

A square-root factor of the positive-definite matrix represented by object is obtained. Letting $\mathrm{\Sigma }$ denote a positive-definite matrix, a square-root factor of $\mathrm{\Sigma }$ is any square matrix $L$ such that $\mathrm{\Sigma }=L^{\prime }L$. 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.

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)