\name{intensity.ppm}  
\alias{intensity.ppm}
\title{
  Intensity of Fitted Point Process Model
}
\description{
  Computes the intensity of a fitted point process model.
}
\usage{
\method{intensity}{ppm}(X, \dots)
}
\arguments{
  \item{X}{
    A fitted point process model (object of class \code{"ppm"}).
  }
  \item{\dots}{
    Arguments passed to \code{\link{predict.ppm}} in some cases.
    See Details.
  }
}
\details{
  This is a method for the generic function \code{\link{intensity}}
  for fitted point process models (class \code{"ppm"}).

  The intensity of a point process model is the expected
  number of random points per unit area. 

  If \code{X} is a Poisson point process model, the intensity of the
  process is computed exactly.
  The result is a numerical value if \code{X}
  is a stationary Poisson point process, and a pixel image if \code{X}
  is non-stationary. (In the latter case, the resolution of the pixel
  image is controlled by the arguments \code{\dots} which are passed
  to \code{\link{predict.ppm}}.)

  If \code{X} is another Gibbs point process model, the intensity is
  computed approximately using the Poisson-saddlepoint approximation
  (Baddeley and Nair, 2012a, 2012b, 2016; Anderssen et al, 2014). 
  The approximation is currently available for pairwise-interaction
  models (Baddeley and Nair, 2012a, 2012b)
  and for the area-interaction model and Geyer saturation model
  (Baddeley and Nair, 2016).

  For a non-stationary Gibbs model, the 
  pseudostationary solution (Baddeley and Nair, 2012b;
  Anderssen et al, 2014) is used. The result is a pixel image,
  whose resolution is controlled by the arguments \code{\dots} which are passed
  to \code{\link{predict.ppm}}.
}
\value{
  A numeric value (if the model is stationary)
  or a pixel image.
}
\references{
  Anderssen, R.S., Baddeley, A., DeHoog, F.R. and Nair, G.M. (2014)
  Solution of an integral equation arising in spatial point process theory.
  \emph{Journal of Integral Equations and Applications} 
  \bold{26} (4) 437--453.

  Baddeley, A. and Nair, G. (2012a) 
  Fast approximation of the intensity of Gibbs point processes.
  \emph{Electronic Journal of Statistics} \bold{6} 1155--1169.

  Baddeley, A. and Nair, G. (2012b)
  Approximating the moments of a spatial point process.
  \emph{Stat} \bold{1}, 1, 18--30.
  doi: 10.1002/sta4.5

  Baddeley, A. and Nair, G. (2016)
  Poisson-saddlepoint approximation for spatial point processes
  with infinite order interaction.
  Submitted for publication.
}
\seealso{
  \code{\link{intensity}},
  \code{\link{intensity.ppp}}
}
\examples{
  fitP <- ppm(swedishpines ~ 1)
  intensity(fitP)
  fitS <- ppm(swedishpines ~ 1, Strauss(9))
  intensity(fitS)
  fitSx <- ppm(swedishpines ~ x, Strauss(9))
  lamSx <- intensity(fitSx)
  fitG <- ppm(swedishpines ~ 1, Geyer(9, 1))
  lamG <- intensity(fitG)
  fitA <- ppm(swedishpines ~ 1, AreaInter(7))
  lamA <- intensity(fitA)
}
\author{
  \adrian
  and Gopalan Nair.
}
\keyword{spatial}
\keyword{models}