R: Positive-Definite Matrix Classes

pdClasses {nlme} | R Documentation

## Positive-Definite Matrix Classes

### Description

Standard classes of positive-definite matrices (`pdMat`) structures 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.

### 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`.

### 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.

### See Also

`pdBlocked`, `pdCompSymm`, `pdDiag`, `pdFactor`, `pdIdent`, `pdMat`, `pdMatrix`, `pdNatural`, `pdSymm`, `pdLogChol`

[Package nlme version 3.1-118 Index]