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\name{L2metric}
\alias{L2metric}
\title{Fast Computation of the \eqn{L^2} Metric for Sets of Functional Data}
\usage{
L2metric(A, B)
}
\arguments{
\item{A}{Functions of the first set, represented by a matrix of their functional values of
size \code{m*d}. \code{m} stands for the number of functions, \code{d}
is the number of the equi-distant points {1,...,d} in the domain of the data [1,d] at which the functional
values of the \code{m} functions are evaluated.}
\item{B}{Functions of the second set, represented by a matrix of their functional values of
size \code{n*d}. \code{n} stands for the number of functions, \code{d}
is the number of the equi-distant points {1,...,d} in the domain of the data [1,d] at which the functional
values of the \code{n} functions are evaluated. The grid of observation points for the
functions \code{A} and \code{B} must be the same.}
}
\value{
A symmetric matrix of the distances of the functions of size \code{m*n}.
}
\description{
Returns the matrix of \eqn{L^2} distances between two sets of functional data.
}
\details{
For two sets of functional data of sizes \code{m} and \code{n}
represented by matrices of their functional values on the common domain {1,...,d},
this function returns the symmetric matrix of size \code{m*n} whose entry in the
\code{i}-th row and \code{j}-th column is the approximated \eqn{L^2} distance of the
\code{i}-th function from the first set, and the \code{j}-th function from the second set.
This function is utilized in the computation of the h-mode depth.
}
\examples{
datapop = dataf2rawfd(dataf.population()$dataf,range=c(1950,2015),d=66)
A = datapop[1:20,]
B = datapop[21:50,]
L2metric(A,B)
}
\seealso{
\code{\link{depthf.hM}}
\code{\link{dataf2rawfd}}
}
\author{
Stanislav Nagy, \email{nagy at karlin.mff.cuni.cz}
}
\keyword{functional}
\keyword{metric}
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