% fields, Tools for spatial data
% Copyright 2004-2011, Institute for Mathematics Applied Geosciences
% University Corporation for Atmospheric Research
% Licensed under the GPL -- www.gpl.org/licenses/gpl.html

\name{splint}
\alias{splint}
\title{
  Cubic spline interpolation 
}
\description{
A fast, FORTRAN based function for cubic spline interpolation. 
}
\usage{
splint(x, y, xgrid, wt=NULL, derivative=0,lam=0, df=NA, lambda=NULL)
}
\arguments{
\item{x}{
The x values that define the curve or a two column matrix of  
x and y values. 
}
\item{y}{
The y values that are paired with the x's. 
}
\item{xgrid}{
The grid to evaluate the fitted cubic interpolating curve. 
}
\item{derivative}{
Indicates whether the function or a a first or second derivative 
should be evaluated. 
}
\item{wt}{Weights for different obsrevations in the scale of reciprocal 
variance.}
\item{lam}{ Value for smoothing parameter. Default value is zero giving 
interpolation.}
\item{lambda}{Same as \code{lam} just to make this easier to remember.}
\item{df}{ Effective degrees of freedom. Default is to use lambda =0 or a  
df equal to the number of observations.}

}
\value{
A vector consisting of the spline evaluated at the grid values in \code{xgrid}. 
}
\details{
Fits a piecewise interpolating or smoothing cubic 
polynomial to the x and y values. 
This code is designed to be fast but does not many options in  
\code{sreg} or other more statistical implementations.  
To make the solution well posed the
the second and third derivatives are set to zero at the limits of the  x 
values. Extrapolation outside the range of the x 
values will be a linear function. 

It is assumed that there are no repeated x values; use sreg followed by
predict if you do have replicated data. 

}
\section{References}{
See Additive Models by Hastie and Tibshriani. 
}
\seealso{
sreg,  Tps  
}
\examples{
x<- seq( 0, 120,,200)

# an interpolation
splint(rat.diet$t, rat.diet$trt,x )-> y

plot( rat.diet$t, rat.diet$trt)
lines( x,y)
#( this is weird and not appropriate!)

# the following two smooths should be the same

splint( rat.diet$t, rat.diet$con,x, df= 7)-> y1

# sreg function has more flexibility than splint but will
# be slower for larger data sets. 

sreg( rat.diet$t, rat.diet$con, df= 7)-> obj
predict(obj, x)-> y2 

# in fact predict.sreg interpolates the predicted values using splint!

# the two predicted lines (should) coincide
lines( x,y1, col="red",lwd=2)
lines(x,y2, col="blue", lty=2,lwd=2)
 
}
\keyword{smooth}
% docclass is function
% Converted by Sd2Rd version 1.21.