kernel2d: Kernel smoothing of a point pattern

In splancs: Spatial and Space-Time Point Pattern Analysis

Kernel smoothing of a point pattern

Description

Perform kernel smoothing of a point pattern

Usage

kernel2d(pts,poly,h0,nx=20,ny=20,kernel='quartic',quiet=FALSE)
spkernel2d(pts, poly, h0, grd, kernel = "quartic")

Arguments

pts	A points data set, or in function spkernel2d an object with a coordinates method from the sp package
poly	A splancs polygon data set
h0	The kernel width parameter
nx	Number of points along the x-axis of the returned grid.
ny	Number of points along the y-axis of the returned grid.
kernel	Type of kernel function to use. Currently only the quartic kernel is implemented.
quiet	If TRUE, no debugging output is printed.
grd	a GridTopology object from the sp package

Details

The kernel estimate, with a correction for edge effects, is computed for a grid of points that span the input polygon. The kernel function for points in the grid that are outside the polygon are returned as NA's. The output list is in a format that can be read into image() directly, for display and superposition onto other plots.

Value

kernel2d returns a list with the following components:

x	List of x-coordinates at which the kernel function has been evaluated.
y	List of y-coordinates at which the kernel function has been evaluated.
z	A matrix of dimension nx by ny containing the value of the kernel function.
h0, kernel	containing the values input to kernel2d

spkernel2d returns a numeric vector with the value of the kernel function stored in the order required by sp package SpatialGridDataFrame objects

References

Berman M. and Diggle P.J. (1989) Estimating Weighted Integrals of the Second-Order Intensity of Spatial Point Patterns. J. R. Statist Soc B51 81-92; Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655, (Barry Rowlingson ); the original sources can be accessed at: https://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.

Examples

data(bodmin)
plot(bodmin$poly, asp=1, type="n")
image(kernel2d(as.points(bodmin), bodmin$poly, h0=2, nx=100, ny=100), 
add=TRUE, col=terrain.colors(20))
pointmap(as.points(bodmin), add=TRUE)
polymap(bodmin$poly, add=TRUE)
bodmin.xy <- coordinates(bodmin[1:2])
apply(bodmin$poly, 2, range)
grd1 <- GridTopology(cellcentre.offset=c(-5.2, -11.5), cellsize=c(0.2, 0.2), cells.dim=c(75,100))
k100 <- spkernel2d(bodmin.xy, bodmin$poly, h0=1, grd1)
k150 <- spkernel2d(bodmin.xy, bodmin$poly, h0=1.5, grd1)
k200 <- spkernel2d(bodmin.xy, bodmin$poly, h0=2, grd1)
k250 <- spkernel2d(bodmin.xy, bodmin$poly, h0=2.5, grd1)
df <- data.frame(k100=k100, k150=k150, k200=k200, k250=k250)
kernels <- SpatialGridDataFrame(grd1, data=df)
spplot(kernels, checkEmptyRC=FALSE, col.regions=terrain.colors(16), cuts=15)

splancs documentation built on May 29, 2024, 6:22 a.m.