\name{warpArea}
\alias{warpArea}
\title{Compute Warping Path Area}
\description{
  Compute the area between the warping function and the
  diagonal (no-warping) path, in unit steps.
}
\usage{
warpArea(d)
}
\arguments{
\item{d}{an object of class \code{dtw}}
}
\value{
  The area, not normalized by path length or else.
}
\details{
  
 Above- and below- diagonal unit areas all count \emph{plus} one (they
 do not cancel with each other).  The "diagonal" goes from one corner to
 the other of the possibly rectangular cost matrix, therefore having a
 slope of \code{M/N}, not 1, as in \code{\link{slantedBandWindow}}.

 The computation is approximate: points having multiple correspondences
 are averaged, and points without a match are interpolated. Therefore,
 the area can be fractionary.
 
}

\note{ There could be alternative definitions to the area, including
  considering the envelope of the path.  }


\examples{
  ds<-dtw(1:4,1:8);

  plot(ds);lines(seq(1,8,len=4),col="red");

  warpArea(ds)

  ## Result: 6
  ##  index 2 is 2 while diag is 3.3  (+1.3)
  ##        3    3               5.7  (+2.7)
  ##        4   4:8 (avg to 6)    8   (+2  )
  ##                                 --------
  ##                                     6

}


\author{Toni Giorgino}
\concept{Warping Function Area}
\keyword{ts}