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
matern.image.cov <- function(ind1, ind2, Y, cov.obj = NULL,
setup = FALSE, grid, M = NULL, N = NULL,
aRange=1, smoothness=.5,theta=NULL ) {
# theta argument has been depreciated.
if( !is.null( theta)){
aRange<- theta
}
#
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)
if (is.null(M))
M <- ceiling2(2 * m)
if (is.null(N))
N <- ceiling2(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}
# need to evaluate the covariance between the center of the grid and
# every grid point do this using several simple steps for efficiency.
xGrid<- (1:M) * dx - (dx * M)/2
yGrid<- (1:N) * dy - (dy * N)/2
# a matrix the same size as the grid that has the distance between every
# grid point and the center point.
bigDistance<-
sqrt(
matrix( xGrid^2, M,N, byrow=FALSE) +
matrix( yGrid^2, M,N, byrow=TRUE) )
# this should make for a nice image plot of the covariance w/r to the center point #
out<- Matern( bigDistance /aRange, smoothness=smoothness)
temp <- matrix(0, nrow = M, ncol = N)
temp[M/2, N/2] <- 1
wght <- fft(out)/(fft(temp) * M * N)
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$n])
}
else {
if (missing(ind2)) {
temp[ind1] <- Y
}
else {
temp[ind2] <- Y
}
Re(fft(fft(temp) * cov.obj$wght, inverse = TRUE)[ind1])
}
}
```

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