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#
# 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
"image.smooth" <- function(x, wght = NULL, dx = 1,
dy = 1, kernel.function = double.exp, aRange = 1, grid = NULL,
tol = 1e-08, xwidth = NULL, ywidth = NULL, weights = NULL, theta=NULL,
...) {
# theta argument has been depreciated.
if( !is.null( theta)){
aRange<- theta
}
# first part of this function is figuring what has been passed and
# what to do
if (is.list(x)) {
# assume that an image list format has been passed as x
Y <- x$z
grid <- list(x = x$x, y = x$y)
}
else {
Y <- x
}
if (!is.matrix(Y)) {
stop("Requires a matrix")
}
m <- nrow(Y)
n <- ncol(Y)
# use information in previous setup kernel function from a
# a call to setup.image.smooth and in the process override any
# passed arguments
if (!is.null(wght)) {
dx <- wght$dx
dy <- wght$dy
xwidth <- wght$xwidth
ywidth <- wght$ywidth
}
# set up grid if it is missing
if (is.null(grid)) {
grid <- list(x = (1:m) * dx, y = (1:n) * dy)
}
else {
dx <- grid$x[2] - grid$x[1]
dy <- grid$y[2] - grid$y[1]
}
# padding of zeroes around actual image
# if less than m and n there may be spurious effects due to
# the periodicity from the fft.
# make sure that the span of the kernel is less than xwidth and ywidth.
# there will be substantial speedup if the kernel has a small support,
# Y is big (e.g. 512X512) and Mwidth and N widht are adjusted to suit.
if (is.null(xwidth)) {
xwidth <- dx * m
}
if (is.null(ywidth)) {
ywidth <- dy * n
}
# kernel wght function as fft
# reusing this saves an fft for each image smooth.
if (is.null(wght)) {
wght <- setup.image.smooth(nrow = m, ncol = n, xwidth = xwidth,
ywidth = ywidth, dx = dx, dy = dy, kernel.function = kernel.function,
aRange = aRange,...)
}
M <- nrow(wght$W)
N <- ncol(wght$W)
temp <- matrix(0, nrow = M, ncol = N)
temp2 <- matrix(0, nrow = M, ncol = N)
# pad with zeroes
if (!is.null(weights)) {
temp[1:m, 1:n] <- Y * weights
temp[is.na(temp)] <- 0
temp2[1:m, 1:n] <- ifelse(!is.na(Y), weights, 0)
}
else {
temp[1:m, 1:n] <- Y
temp[is.na(temp)] <- 0
temp2[1:m, 1:n] <- ifelse(!is.na(Y), 1, 0)
}
# temp and temp2 are numerator and denominator of Nadarya-Watson estimator.
temp <- Re(fft(fft(temp) * wght$W, inverse = TRUE))[1:m,
1:n]
temp2 <- Re(fft(fft(temp2) * wght$W, inverse = TRUE))[1:m,
1:n]
# try not to divide by zero!
temp <- ifelse((temp2 > tol), (temp/temp2), NA)
list(x = grid$x, y = grid$y, z = temp)
}
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