pdSymm                 package:nlme                 R Documentation

General Positive-Definite Matrix

Description:

     This function is a constructor for the 'pdSymm' class,
     representing a general positive-definite matrix. If the matrix
     associated with 'object' is of dimension n, it is represented by
     n*(n+1)/2 unrestricted parameters, using the matrix-logarithm
     parametrization described in Pinheiro and Bates (1996). When
     'value' is 'numeric(0)', an uninitialized 'pdMat' object, a
     one-sided formula, or a vector of character strings, 'object' is
     returned as an uninitialized 'pdSymm' object (with just some of
     its attributes and its class defined) and needs to have its
     coefficients assigned later, generally using the 'coef' or
     'matrix' replacement functions. If 'value' is an initialized
     'pdMat' object, 'object' will be constructed from
     'as.matrix(value)'. Finally, if 'value' is a numeric vector, it is
     assumed to represent the unrestricted coefficients of the
     matrix-logarithm parametrization of the underlying
     positive-definite matrix.

Usage:

     pdSymm(value, form, nam, data)

Arguments:

   value: an optional initialization value, which can be any of the
          following: a 'pdMat' object, a positive-definite matrix, a
          one-sided linear formula (with variables separated by '+'), a
          vector of character strings, or a numeric vector. Defaults to
          'numeric(0)', corresponding to an uninitialized object.

    form: an optional one-sided linear formula specifying the
          row/column names for the matrix represented by 'object'.
          Because factors may be present in 'form', the formula needs
          to be evaluated on a data.frame to resolve the names it
          defines. This argument is ignored when 'value' is a one-sided
          formula. Defaults to 'NULL'.

     nam: an optional vector of character strings specifying the
          row/column names for the matrix represented by object. It
          must have  length equal to the dimension of the underlying
          positive-definite matrix and unreplicated elements. This
          argument is ignored when 'value' is a vector of character
          strings. Defaults to 'NULL'.

    data: an optional data frame in which to evaluate the variables
          named in 'value' and 'form'. It is used to obtain the levels
          for 'factors', which affect the dimensions and the row/column
          names of the underlying matrix. If 'NULL', no attempt is made
          to obtain information on  'factors' appearing in the
          formulas. Defaults to the parent frame from which the
          function was called.

Value:

     a 'pdSymm' object representing a general positive-definite matrix,
     also inheriting from class 'pdMat'.

Author(s):

     Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates
     bates@stat.wisc.edu

References:

     Pinheiro, J.C. and Bates., D.M.  (1996) "Unconstrained
     Parametrizations for Variance-Covariance Matrices", Statistics and
     Computing, 6, 289-296.

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

See Also:

     'as.matrix.pdMat', 'coef.pdMat', 'pdClasses', 'matrix<-.pdMat'

Examples:

     pd1 <- pdSymm(diag(1:3), nam = c("A","B","C"))
     pd1

