Nothing

```
# fields is a package for analysis of spatial data written for
# the R software environment .
# Copyright (C) 2018
# University Corporation for Atmospheric Research (UCAR)
# Contact: Douglas Nychka, nychka@ucar.edu,
# National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307-3000
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with the R software environment if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
# or see http://www.r-project.org/Licenses/GPL-2
wendland.image.cov <- function(ind1, ind2, Y, cov.obj = NULL,
setup = FALSE, grid, M = NULL, N = NULL, cov.args=NULL, ...) {
#
# if cov object is missing then create
# basically need to enlarge domain and find the FFT of the
# covariance
#
cov.args<-c( cov.args, list(...))
#
# theta has been deopreciated.
if( !is.null(cov.args$theta )){
cov.args$aRange <- cov.args$theta
}
#
delta<- cov.args$aRange
if (is.null(cov.obj)) {
dx <- grid$x[2] - grid$x[1]
dy <- grid$y[2] - grid$y[1]
m <- length(grid$x)
n <- length(grid$y)
#
# determine size of padding
# default is twice domain and will then yeild exact results
# delta indicates that covariance is zero beyond a distance delta
# so using a smaller grid than twice domain will still give exact results.
if(!is.null(delta)){
M<- ceiling(m + 2*delta/dx)
N<- ceiling(n + 2*delta/dy)
}
if (is.null(M))
M <- (2 * m)
if (is.null(N))
N <- (2 * n)
# make sure M and N are even.
# (not sure what it means if this is not the case!)
if( M%%2 !=0) {
M<- M+1}
if( N%%2 !=0) {
N<- N+1}
#
# print( c(m,n, M,N))
xGrid<- (1:M) * dx - (dx * M)/2
yGrid<- (1:N) * dy - (dy * N)/2
bigDistance<-
sqrt(
matrix( xGrid^2, M,N, byrow=FALSE) + matrix( yGrid^2, M,N, byrow=TRUE))
# cat("Wendland", fill=TRUE)
out<- Wendland( bigDistance / cov.args$aRange, dimension=2, k=cov.args$k )
temp <- matrix(0, nrow = M, ncol = N)
#
# a simple way to normalize. This could be avoided by
# translating image from the center ...
#
temp[M/2, N/2] <- 1
wght <- fft(out)/(fft(temp) * M * N)
#
# wght is the discrete FFT for the covariance suitable for fast
# multiplication by convolution.
#
cov.obj <- list(m = m, n = n, grid = grid, N = N, M = M,
wght = wght, call = match.call())
if (setup) {
return(cov.obj)
}
}
temp <- matrix(0, nrow = cov.obj$M, ncol = cov.obj$N)
if (missing(ind1)) {
temp[1:cov.obj$m, 1:cov.obj$n] <- Y
Re(fft(fft(temp) * cov.obj$wght, inverse = TRUE)[1:cov.obj$m,
1:cov.obj$n])
}
else {
if (missing(ind2)) {
temp[ind1] <- Y
}
else {
temp[ind2] <- Y
}
#
# as promised this is a single clean step
#
Re(fft(fft(temp) * cov.obj$wght, inverse = TRUE)[ind1])
}
}
```

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