\name{dtwDistanceFunctions}
\alias{dtwDistanceFunctions}
\alias{euclideanSquared}
\alias{euclideanDistance}
%- Also NEED an '\alias' for EACH other topic documented here.
\title{Distance functions for DTW}
\description{
  Compute Euclidean squared distance between two given vectors
  (default function for \code{dtw}).
}
\usage{
euclideanSquared(a, b)
euclideanDistance(a, b)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{a,b}{ floating point values }
}

\details{
  These distance functions are supplied as an example of what can be
  passed to the \code{distance.function} argument in \code{\link{dtw}}.
  
  Although it makes sense for \code{a} and \code{b} to be \emph{vectors}
  rather than numbers, direct alignment of two multivariate time series
  is currently not supported natively by \code{dtw} (this may change in
  the future).  The user should instead build a local distance matrix,
  e.g. via a custom function or \code{\link[pkg:analogue]{distance}} in
  package \code{analogue}, and feed the result into \code{dtw} as a
  matrix first argument.

}

\value{
  Local distance (float).
}
\references{Euclid's Elements, T.L. Heath (translator), Dover (1956).}
\author{Toni Giorgino }


\seealso{  \code{\link[pkg:analogue]{distance}} can build a distance
  matrix according to several distance definitions.}
\examples{

# A constant vector
z<-numeric(10);     

# dtw between two constant vectors with a squared euclidean distance
# this should be 2^2 times 10 elements = 40
d2<-dtw(z,z+2);
stopifnot(d2$distance==40);

# dtw between two constant vectors with a root squared euclidean distance
# this should be 2 times 10 elements = 20
d1<-dtw(z,z+2,
 	distance.function=function(a,b){return(abs(a-b));})
stopifnot(d1$distance==20);


}


\keyword{ internal }