pdFactor                package: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)

