Positive-Definite Matrix Classes

Standard classes of positive-definite matrices (pdMat) available in the nlme package.

Value

Available standard classes:

pdSymm

general positive-definite matrix, with no additional structure

pdLogChol

general positive-definite matrix, with no additional structure, using a log-Cholesky parameterization

pdDiag

diagonal

pdIdent

multiple of an identity

pdCompSymm

compound symmetry structure (constant diagonal and constant off-diagonal elements)

pdBlocked

block-diagonal matrix, with diagonal blocks of any "atomic" pdMat class

pdNatural

general positive-definite matrix in natural parametrization (i.e. parametrized in terms of standard deviations and correlations). The underlying coefficients are not unrestricted, so this class should NOT be used for optimization.

References

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

Author

José Pinheiro and Douglas Bates bates@stat.wisc.edu

Note

Users may define their own pdMat classes by specifying a constructor function and, at a minimum, methods for the functions pdConstruct, pdMatrix, and coef. For examples of these functions, see the methods for classes pdSymm and pdDiag.