text: \name{Lcross}
  \alias{Lcross}
  \title{Multitype L-function (cross-type)}
  \description{
    Calculates an estimate of the cross-type L-function
    for a multitype point pattern.
  }
  \usage{
    Lcross(X, i, j, ..., from, to, correction)
  }
  \arguments{
    \item{X}{The observed point pattern, 
      from which an estimate of the cross-type \eqn{L} function
      \eqn{L_{ij}(r)}{Lij(r)} will be computed.
      It must be a multitype point pattern (a marked point pattern
      whose marks are a factor). See under Details.
    }
    \item{i}{The type (mark value)
      of the points in \code{X} from which distances are measured.
      A character string (or something that will be converted to a
      character string).
      Defaults to the first level of \code{marks(X)}.
    }
    \item{j}{The type (mark value)
      of the points in \code{X} to which distances are measured.
      A character string (or something that will be
      converted to a character string).
      Defaults to the second level of \code{marks(X)}.
    }
    \item{correction,\dots}{
      Arguments passed to \code{\link{Kcross}}.
    }
    \item{from,to}{
      An alternative way to specify \code{i} and \code{j} respectively.
    }
  }
  \details{
    The cross-type L-function is a transformation of the cross-type K-function,
    \deqn{L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}}{Lij(r) = sqrt(Kij(r)/pi)}
    where \eqn{K_{ij}(r)}{Kij(r)} is the cross-type K-function
    from type \code{i} to type \code{j}.
    See \code{\link{Kcross}} for information
    about the cross-type K-function.
  
    The command \code{Lcross} first calls
    \code{\link{Kcross}} to compute the estimate of the cross-type K-function,
    and then applies the square root transformation.
  
    For a marked point pattern in which the points of type \code{i}
    are independent of the points of type \code{j},
    the theoretical value of the L-function is
    \eqn{L_{ij}(r) = r}{Lij(r) = r}.
    The square root also has the effect of stabilising
    the variance of the estimator, so that \eqn{L_{ij}}{Lij} is more appropriate
    for use in simulation envelopes and hypothesis tests.
  }
  
  \value{
    An object of class \code{"fv"}, see \code{\link{fv.object}},
    which can be plotted directly using \code{\link{plot.fv}}.
  
    Essentially a data frame containing columns
    \item{r}{the vector of values of the argument \eqn{r} 
      at which the function \eqn{L_{ij}}{Lij} has been  estimated
    }
    \item{theo}{the theoretical value \eqn{L_{ij}(r) = r}{Lij(r) = r}
      for a stationary Poisson process
    }
    together with columns named 
    \code{"border"}, \code{"bord.modif"},
    \code{"iso"} and/or \code{"trans"},
    according to the selected edge corrections. These columns contain
    estimates of the function \eqn{L_{ij}}{Lij} obtained by the edge corrections
    named.
  }
  \seealso{
    \code{\link{Kcross}},
    \code{\link{Ldot}},
    \code{\link{Lest}}
  }
  \examples{
   data(amacrine)
   L <- Lcross(amacrine, "off", "on")
   plot(L)
  }
  \author{\adrian
    
    
    and \rolf
    
  }
  \keyword{spatial}
  \keyword{nonparametric}
  