nlme: pdFactor – R documentation

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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 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)

José Pinheiro 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.

Examples

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

nlme

Linear and Nonlinear Mixed Effects Models

v3.1-152

GPL (>= 2) | file LICENCE

Authors

José Pinheiro [aut] (S version), Douglas Bates [aut] (up to 2007), Saikat DebRoy [ctb] (up to 2002), Deepayan Sarkar [ctb] (up to 2005), EISPACK authors [ctb] (src/rs.f), Siem Heisterkamp [ctb] (Author fixed sigma), Bert Van Willigen [ctb] (Programmer fixed sigma), Johannes Ranke [ctb] (varConstProp()), R-core [aut, cre]

Initial release

2021-02-03