\HeaderA{backSpline}{Monotone Inverse Spline}{backSpline}
\keyword{models}{backSpline}
\begin{Description}\relax
Create a monotone inverse of a monotone natural spline.
\end{Description}
\begin{Usage}
\begin{verbatim}
backSpline(object)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{object}] an object that inherits from class \code{nbSpline} or
\code{npolySpline}.  That is, the object must represent a natural
interpolation spline but it can be either in the B-spline
representation or the piecewise polynomial one.  The spline is
checked to see if it represents a monotone function.

\end{ldescription}
\end{Arguments}
\begin{Value}
An object of class \code{polySpline} that contains the piecewise
polynomial representation of a function that has the appropriate
values and derivatives at the knot positions to be an inverse of the
spline represented by \code{object}.  Technically this object is not a
spline because the second derivative is not constrained to be
continuous at the knot positions.  However, it is often a much better
approximation to the inverse than fitting an interpolation spline to
the y/x pairs.
\end{Value}
\begin{Author}\relax
Douglas Bates and Bill Venables
\end{Author}
\begin{SeeAlso}\relax
\code{\LinkA{interpSpline}{interpSpline}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
require(graphics)
ispl <- interpSpline( women$height, women$weight )
bspl <- backSpline( ispl )
plot( bspl )                   # plots over the range of the knots
points( women$weight, women$height )
\end{ExampleCode}
\end{Examples}

