R/wendland.image.cov.R

In fields: Tools for Spatial Data

#
# fields  is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2022 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka,  douglasnychka@gmail.edu,
#
# 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
##END HEADER
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])                        
    }
}