# fields, Tools for spatial data
# Copyright 2004-2011, Institute for Mathematics Applied Geosciences
# University Corporation for Atmospheric Research
# Licensed under the GPL -- www.gpl.org/licenses/gpl.html
stationary.image.cov <- function(ind1, ind2, Y, cov.obj = NULL, 
    setup = FALSE, grid, M = NULL, N = NULL, Covariance = "Matern", 
    Distance = "rdist", ...) {
    #
    # if cov object is missing then create
    # basically need to enlarge domain and find the FFT of the
    # covariance
    #
    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
        #
        if (is.null(M)) 
            M <- (2 * m)
        if (is.null(N)) 
            N <- (2 * n)
        xg <- make.surface.grid(list((1:M) * dx, (1:N) * dy))
        center <- matrix(c((dx * M)/2, (dy * N)/2), nrow = 1, 
            ncol = 2)
        #
        # here is where the actual covarinace form is used
        # note passed arguments from call for parameters etc.
        #
        out <- stationary.cov(xg, center, Covariance = Covariance, 
            Distance = Distance, ...)
        # coerce to a matrix (image)
        out <- matrix(c(out), nrow = M, ncol = N)
        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])
    }
}