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dval: Multiscale local density of a spatial point pattern

Description

Computes local density estimates of a spatial point pattern, i.e. the number of points per unit area, within sample circles of regularly increasing radii $r$, centred at the nodes of a grid covering a simple (rectangular or circular) or complex sampling window (see Details).

Usage

dval(p, upto, by, nx, ny)

Arguments

p

a "spp" object defining a spatial point pattern in a given sampling window (see spp).

upto

maximum radius of the sample circles (see Details).

by

interval length between successive sample circles radii (see Details).

nx,ny

number of sample circles regularly spaced out in $x$ and $y$ directions.

Value

• A list of class c("vads","dval") with essentially the following components:
• r
  a vector of regularly spaced out distances (seq(by,upto,by)).
• xy
  a data frame of $(nx*ny)$ observations giving $(x,y)$ coordinates of the centers of the sample circles (the grid nodes).
• cval
  a matrix of size $(nx*ny,length(r))$ giving the estimated number of points of the pattern per sample circle with radius $r$.
• dval
  a matrix of size $(nx*ny,length(r))$ giving the estimated number of points of the pattern per unit area per sample circle with radius $r$.

encoding

latin1

Warning

In its current version, function dval ignores the marks of multivariate and marked point patterns (they are all considered to be univariate patterns).

Details

The local density is estimated for a regular sequence of sample circles radii given by seq(by,upto,by) (see seq). The sample circles are centred at the nodes of a regular grid with size $nx$ by $ny$. Ripley's edge effect correction is applied when the sample circles overlap boundary of the sampling window (see Ripley (1977) or Goreaud & P�lissier (1999) for an extension to circular and complex sampling windows). Due to edge effect correction, upto, the maximum radius of the sample circles, is half the longer side for a rectangle sampling window (i.e. $0.5*max((xmax-xmin),(ymax-ymin))$) and the radius $r0$ for a circular sampling window (see swin).

References

Goreaud, F. and P�lissier, R. 1999. On explicit formula of edge effect correction for Ripley's K-function. Journal of Vegetation Science, 10:433-438. P�lissier, R. and Goreaud, F. 2001. A practical approach to the study of spatial structure in simple cases of heterogeneous vegetation. Journal of Vegetation Science, 12:99-108. Ripley, B.D. 1977. Modelling spatial patterns. Journal of the Royal Statistical Society B, 39:172-212.

See Also

plot.vads, spp.

Examples

data(BPoirier)
  BP <- BPoirier
  # spatial point pattern in a rectangle sampling window of size [0,110] x [0,90]
  swr <- spp(BP$trees, win=BP$rect)
  dswr <- dval(swr,25,1,11,9)
  summary(dswr)
  plot(dswr)
  
  # spatial point pattern in a circle with radius 50 centred on (55,45)
  swc <- spp(BP$trees, win=c(55,45,45))
  dswc <- dval(swc,25,1,9,9)
  summary(dswc)
  plot(dswc)
  
  # spatial point pattern in a complex sampling window
  swrt <- spp(BP$trees, win=BP$rect, tri=BP$tri1)
  dswrt <- dval(swrt,25,1,11,9)
  summary(dswrt)
  plot(dswrt)