https://github.com/cran/spatstat
Tip revision: 7c29845cd80606f8ceb6cc1904f98fc86bf77b7e authored by Adrian Baddeley on 05 February 2008, 04:20:32 UTC
version 1.12-6
version 1.12-6
Tip revision: 7c29845
quadratcount.Rd
\name{quadratcount}
\alias{quadratcount}
\title{Quadrat counting for a point pattern}
\description{
Divides window into quadrats and
counts the numbers of points in each quadrat.
}
\usage{
quadratcount(X, nx=5, ny=nx, xbreaks, ybreaks)
}
\arguments{
\item{X}{
A point pattern
(object of class \code{"ppp"}).
}
\item{nx,ny}{
Numbers of quadrats in the \eqn{x} and \eqn{y} directions.
Incompatible with \code{xbreaks} and \code{ybreaks}.
}
\item{xbreaks}{
Numeric vector giving the \eqn{x} coordinates of the
boundaries of the quadrats. Incompatible with \code{nx}.
}
\item{ybreaks}{
Numeric vector giving the \eqn{y} coordinates of the
boundaries of the quadrats. Incompatible with \code{ny}.
}
}
\value{
A contingency table containing the number of points in each
quadrat.
The table is also an object of the special class \code{"quadratcount"}
and there is a plot method for this class.
}
\details{
Quadrat counting is an elementary technique for analysing spatial
point patterns. See Diggle (2003).
The window containing the point pattern \code{X} is divided into
an \code{nx * ny} grid of rectangular tiles or `quadrats'.
The number of points of \code{X} falling in each quadrat is
counted. These numbers are returned as a contingency table.
If \code{xbreaks} is given, it should be a numeric vector
giving the \eqn{x} coordinates of the quadrat boundaries.
If it is not given, it defaults to a
sequence of \code{nx+1} values equally spaced
over the range of \eqn{x} coordinates in the window \code{X$window}.
Similarly if \code{ybreaks} is given, it should be a numeric
vector giving the \eqn{y} coordinates of the quadrat boundaries.
It defaults to a vector of \code{ny+1} values
equally spaced over the range of \eqn{y} coordinates in the window.
The lengths of \code{xbreaks} and \code{ybreaks} may be different.
The algorithm counts the number of points of \code{X}
falling in each quadrat, and returns these counts as a
contingency table. The \code{[i,j]} entry in the contingency table
is the point count for the quadrat with coordinates
\code{(xbreaks[i],xbreaks[i+1])} by \code{(ybreaks[i], ybreaks[i+1])}.
The return value is a \code{table} which can be printed neatly.
The return value is also a member of the special class
\code{"quadratcount"}. Plotting the object will display the
quadrats, annotated by their counts. See the examples.
To perform a chi-squared test based on the quadrat counts,
use \code{\link{quadrat.test}}.
}
\seealso{
\code{\link{quadrat.test}}
}
\references{
Diggle, P.J. \emph{Statistical analysis of spatial point patterns}.
Academic Press, 2003.
Stoyan, D. and Stoyan, H. (1994)
Fractals, random shapes and point fields:
methods of geometrical statistics.
John Wiley and Sons.
}
\examples{
X <- runifpoint(50)
quadratcount(X)
quadratcount(X, 4, 5)
quadratcount(X, xbreaks=c(0, 0.3, 1), ybreaks=c(0, 0.4, 0.8, 1))
qX <- quadratcount(X, 4, 5)
# plotting:
plot(X, pch="+")
plot(qX, add=TRUE, col="red", cex=1.5, lty=2)
}
\author{Adrian Baddeley
\email{adrian@maths.uwa.edu.au}
\url{http://www.maths.uwa.edu.au/~adrian/}
and Rolf Turner
\email{rolf@math.unb.ca}
\url{http://www.math.unb.ca/~rolf}
}
\keyword{spatial}
\keyword{math}