pdLogChol {nlme}  R Documentation 
This function is a constructor for the pdLogChol
class,
representing a general positivedefinite matrix. If the matrix
associated with object
is of dimension n
, it is
represented by n(n+1)/2
unrestricted parameters,
using the logCholesky parametrization described in Pinheiro and
Bates (1996).
When value
is numeric(0)
, an uninitialized pdMat
object, a onesided formula, or a character vector, object
is
returned as an uninitialized pdLogChol
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 matrixlogarithm
parametrization of the underlying positivedefinite matrix.
pdLogChol(value, form, nam, data)
value 
an optional initialization value, which can be any of the
following: a 
form 
an optional onesided linear formula specifying the
row/column names for the matrix represented by 
nam 
an optional character vector specifying the row/column names
for the matrix represented by object. It must have length equal to
the dimension of the underlying positivedefinite matrix and
unreplicated elements. This argument is ignored when

data 
an optional data frame in which to evaluate the variables
named in 
Internally, the pdLogChol
representation of a symmetric
positive definite matrix is a vector starting with the logarithms of
the diagonal of the Choleski factorization of that matrix followed by
its upper triangular portion.
a pdLogChol
object representing a general positivedefinite
matrix, also inheriting from class pdMat
.
JosÃ© Pinheiro and Douglas Bates bates@stat.wisc.edu
Pinheiro, J.C. and Bates., D.M. (1996) Unconstrained Parametrizations for VarianceCovariance Matrices, Statistics and Computing 6, 289–296.
Pinheiro, J.C., and Bates, D.M. (2000) MixedEffects Models in S and SPLUS, Springer.
as.matrix.pdMat
,
coef.pdMat
,
pdClasses
,
matrix<.pdMat
(pd1 < pdLogChol(diag(1:3), nam = c("A","B","C")))
(pd4 < pdLogChol(1:6))
(pd4c < chol(pd4)) # > uppertri matrix with offdiagonals 4 5 6
pd4c[upper.tri(pd4c)]
log(diag(pd4c)) # 1 2 3