https://github.com/cran/fda
Tip revision: 2fc4de4b372bbc86c6cea004c617ad4a41b06b81 authored by J. O. Ramsay on 03 May 2014, 00:00:00 UTC
version 2.4.3
version 2.4.3
Tip revision: 2fc4de4
ppBspline.Rd
\name{ppBspline}
\alias{ppBspline}
\title{Convert a B-spline function to piece-wise polynomial form}
\description{
The B-spline basis functions of order \code{k = length(t) - 1}
defined by the knot sequence in argument \code{t} each consist of polynomial
segments with the same order joined end-to-end over the successive gaps in the
knot sequence. This function computes the \code{k} coefficients of these polynomial
segments in the rows of the output matrix \code{coeff}, with each row corresponding
to a B-spline basis function that is positive over the interval spanned by the
values in \code{t}. The elements of the output vector \code{index} indicate where
in the sequence \code{t} we find the knots. Note that we assume
\code{t[1] < t[k+1]}, i.e. \code{t} is not a sequence of the same knot.
}
\usage{
ppBspline(t)
}
\arguments{
\item{t}{
numeric vector = knot sequence of length norder+1 where norder =
the order of the B-spline. The knot sequence must contain at least one gap.
}
}
\value{
a list object containing components
\item{Coeff}{
a matrix with rows corresponding to B-spline basis functions positive
over the interval spanned by \code{t} and columns corresponding to the
terms \code{1, x, x^2, ...} in the polynomial representation.
}
\item{index}{
indices indicating where in the sequence \code{t} the knots are to be found
}
}
\seealso{
\code{\link{bsplineS}}
}
\examples{
ppBspline(1:5)
}
\keyword{smooth}