Introducing another core to estimate the density of a two-dimensional core in R

Question

I'm looking for some help to figure out how to implement a two-dimensional kernel density method with isotropic dispersion and a two-dimensional normal core, sort of, but instead of the usual distance, since the data is on the surface of the earth, I need to use a big circle.

I would like to reproduce this in R, but I cannot figure out how to use a distance metric other than a simple Euclidean distance for any of the built-in estimates, and since it uses a sophisticated convolution method, add kernels. Does anyone have a way to program an arbitrary kernel?

Answer 1

kde2d MASS. , . , , . (rdist.earth() , h - , , n - . rdist.earth "", )

2d, . ( , .)

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kde2d_mod <- function (data, h, n = 200, lims = c(range(data$lat), range(data$lon))) {
#Data is a matrix: lon,lat for each source. (lon,lat to match rdist.earth format.)
print(Sys.time()) #for timing

nx <- dim(data)[1]
if (dim(data)[2] != 2) 
stop("data vectors have only lat-long data")
if (any(!is.finite(data))) 
stop("missing or infinite values in the data are not allowed")
if (any(!is.finite(lims))) 
stop("only finite values are allowed in 'lims'")
#Grid:
g<-grid(n,lims) #Function to create grid.

#The distance matrix gets large... Can we work around it? YES WE CAN!
sets<-ceiling(dim(g)[1]/10000)
#Allocate our output:
z<-rep(as.double(0),dim(g)[1])

for (i in (1:sets)-1) {
   g_subset=g[(i*10000+1):(min((i+1)*10000,dim(g)[1])),]
   a_matrix<-rdist.earth(g_subset,data,miles=FALSE)

   z[(i*10000+1):(min((i+1)*10000,dim(g)[1]))]<- apply( #Here is my kernel...
    a_matrix,1,FUN=function(X)
    {sum(exp(-X^2/(2*(h^2))))/(2*pi*nx)}
   )
rm(a_matrix)
}

print(Sys.time())
#Un-transpose the final data.
z<-t(matrix(z,n,n))
dim(z)<-c(n^2,1)
z<-as.vector(z)
return(z)
}

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:

grid<- function(n,lims) {
num <- rep(n, length.out = 2L)
gx <- seq.int(lims[1L], lims[2L], length.out = num[1L])
gy <- seq.int(lims[3L], lims[4L], length.out = num[2L])

v1=rep(gy,length(gx))
v2=rep(gx,length(gy))
v1<-matrix(v1, nrow=length(gy), ncol=length(gx))
v2<-t(matrix(v2, nrow=length(gx), ncol=length(gy)))
grid_out<-c(unlist(v1),unlist(v2))

grid_out<-aperm(array(grid_out,dim=c(n,n,2)),c(3,2,1) ) #reshape
grid_out<-unlist(as.list(grid_out))
dim(grid_out)<-c(2,n^2)
grid_out<-t(grid_out)
return(grid_out)
}

image.plot, v1 v2 x, y :

kde2d_mod_plot<-function(kde2d_mod_output,n,lims) ){
 num <- rep(n, length.out = 2L)
 gx <- seq.int(lims[1L], lims[2L], length.out = num[1L])
 gy <- seq.int(lims[3L], lims[4L], length.out = num[2L])

 v1=rep(gy,length(gx))
 v2=rep(gx,length(gy))
 v1<-matrix(v1, nrow=length(gy), ncol=length(gx))
 v2<-t(matrix(v2, nrow=length(gx), ncol=length(gy)))

 image.plot(v1,v2,matrix(kde2d_mod_output,n,n))
 map('world', fill = FALSE,add=TRUE)
}