https://github.com/cran/fda
Tip revision: 4c1575a5f8d26f0a3bf07ad7bf318206f89f7c1d authored by J. O. Ramsay on 03 October 2008, 00:00:00 UTC
version 2.1.1
version 2.1.1
Tip revision: 4c1575a
powerpen.Rd
\name{powerpen}
\alias{powerpen}
\title{
Power Penalty Matrix
}
\description{
Computes the matrix defining the roughness penalty for functions
expressed in terms of a power basis.
}
\usage{
powerpen(basisobj, Lfdobj=int2Lfd(2))
}
\arguments{
\item{basisobj}{
a power basis object.
}
\item{Lfdobj}{
either a nonnegative integer or a linear differential operator object.
}
}
\value{
a symmetric matrix of order equal to the number of basis functions
defined by the power basis object. Each element is the inner product
of two power basis functions after applying the derivative or linear
differential operator defined by \code{Lfdobj}.
}
\details{
A roughness penalty for a function $ x(t) $ is defined by
integrating the square of either the derivative of $ x(t) $ or,
more generally, the result of applying a linear differential operator
$ L $ to it. The most common roughness penalty is the integral of
the square of the second derivative, and
this is the default. To apply this roughness penalty, the matrix of
inner products produced by this function is necessary.
}
\seealso{
\code{\link{create.power.basis}},
\code{\link{powerbasis}}
}
\examples{
# set up an power basis with 3 basis functions.
# the powers are 0, 1, and 2.
basisobj <- create.power.basis(c(0,1),3,c(0,1,2))
# compute the 3 by 3 matrix of inner products of second derivatives
#FIXME
#penmat <- powerpen(basisobj, 2)
}
% docclass is function
\keyword{smooth}