\name{whittaker}
\alias{whittaker}
\title{
  Whittaker Smoothing
}
\description{
  Smoothing of time series using the Whittaker-Henderson approach.
}
\usage{
whittaker(y, lambda = 1600, d = 2)
}
\arguments{
  \item{y}{signal to be smoothed.}
  \item{lambda}{smoothing parameter (rough 50..1e4 smooth); the default
                value of 1600 has been recommended in the literature.}
  \item{d}{order of differences in penalty (generally 2)}
}
\details{
  The Whittaker smoother family was first presented by Whittaker in 1923
  for life tables, based on penalized least squares. These ideas were
  revived by Paul Eilers, Leiden University, in 2003. This approach is
  also known as Whittaker-Henderson smoothing.

  The smoother attempts to both fit a curve that represents the raw data,
  but is penalized if subsequent points vary too much. Mathematically it
  is a large, but sparse optimization problem that can be expressed in a
  few lines of Matlab or R code.
}
\value{
  A smoothed time series.
}
\note{
  *** The function is not yet fully implemented ***

  See the example in `savgol' for working code. This R implementation
  requires the SparseM package. It will stop if this package cannot be loaded.
}
\author{
  An R version, based on Matlab code by P. Eilers in 2002, has been published
  by Nicholas Lewin-Koh on the R-help mailing list in February 2004, and in
  private communication to the author of this package.
}
\references{
  P. H. C. Eilers (2003). A Perfect Smoother. Analytical Chemistry, Vol. 75,
  No. 14, pp. 3631--3636.

  Wilson, D. I. (2006). The Black Art of Smoothing. Electrical and Automation
  Technology, June/July issue.
}
\seealso{
  \code{\link{savgol}}, \code{ptw::whit2}
}
\examples{
\dontrun{
# *** Sinosoid test function ***
ts <- sin(2*pi*(1:1000)/200)
t1 <- ts + rnorm(1000)/10
t3 <- whittaker(t1, lambda = 1000)
plot(1:1000, t1, col = "grey")
lines(1:1000, ts, col="blue")
lines(1:1000, t3, col="red")
}

}
\keyword{ timeseries }