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#
# fields is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2024 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka, douglasnychka@gmail.com,
#
# 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
"cover.design" <- function(R, nd, nruns = 1, nn = TRUE,
num.nn = 100, fixed = NULL, scale.type = "unscaled", R.center,
R.scale, P = -20, Q = 20, start = NULL, DIST = NULL, return.grid = TRUE,
return.transform = TRUE, max.loop = 20, verbose = FALSE) {
if (!is.null(start) && is.matrix(start)) {
if (any(duplicated(start)))
stop("Error: start must not have duplicate rows")
test <- duplicated(start, R)
if (sum(test) < nrow(start))
stop("Error: Starting design must be a subset of R")
}
R.orig <- R
R <- as.matrix(R)
# some checks on inputs
if (nd >= nrow(R)) {
stop(" number of design points >= the number of candidates")
}
if (any(duplicated.array(R)))
stop("Error: R must not have duplicate rows")
if (num.nn >= (nrow(R) - nd)) {
nn <- FALSE
warning("Number of nearst neighbors (nn) reduced to the actual number of candidates")
}
if (is.null(DIST))
DIST <- function(x, y) {
rdist(x, y)
}
id <- 1:nrow(R)
if (!is.null(start))
nd <- length(start)
if (is.null(fixed))
n <- nd
else {
n <- nd + length(fixed)
}
R <- transformx(R, scale.type, R.center, R.scale)
transform <- attributes(R)
saved.crit <- rep(NA, nruns)
saved.designs <- matrix(NA, nrow = nruns, ncol = n)
saved.hist <- list(1:nruns)
if (verbose) {
cat(dim(R), fill = TRUE)
}
#
# do nruns with initial desing drawn at random
#
# in this code Dset are the indices of the design
# Cset are the complement set of indices indicating the candidate points
# no used in the design
#
for (RUNS in 1:nruns) {
if (is.null(start)) {
if (!is.null(fixed)) {
Dset <- sample((1:nrow(R))[-fixed], nd)
Dset <- c(Dset, fixed)
}
else Dset <- sample(1:nrow(R), nd)
}
else {
if (length(start) > nd)
stop("Error: the start matrix must have nd rows")
Dset <- start
if (!is.null(fixed))
Dset <- c(Dset, fixed)
}
design.original <- R.orig[Dset, ]
Dset.orginal <- Dset
Cset <- id[-Dset]
dist.mat <- DIST(R[Cset, ], R[Dset, ])
rs <- dist.mat^P %*% rep(1, n)
crit.i <- crit.original <- sum(rs^(Q/P))^(1/Q)
CRIT <- rep(NA, length(Cset))
CRIT.temp <- rep(NA, length(Cset))
hist <- matrix(c(0, 0, crit.i), ncol = 3, nrow = 1)
loop.counter <- 1
repeat {
for (i in 1:nd) {
# loop over current design points looking for a productive swap
Dset.i <- matrix(R[Dset[i], ], nrow = 1)
if (verbose) {
cat("design point", i, Dset.i, fill = TRUE)
}
partial.newrow <- sum(DIST(Dset.i, R[Dset[-i],
])^P)
rs.without.i <- rs - c(DIST(Dset.i, R[-Dset,
])^P)
if (nn)
vec <- (1:length(Cset))[order(dist.mat[, i])[1:num.nn]]
else vec <- 1:length(Cset)
for (j in vec) {
# loop over possible candidates to swap with design point
Cset.j <- matrix(R[Cset[j], ], nrow = 1)
newcol <- c(DIST(Cset.j, R[c(-Dset, -Cset[j]),
])^P)
CRIT[j] <- (sum((rs.without.i[-j] + newcol)^(Q/P)) +
(DIST(Cset.j, Dset.i)^P + partial.newrow)^(Q/P))^(1/Q)
if (verbose) {
cat(j, " ")
}
}
best <- min(CRIT[!is.na(CRIT)])
best.spot <- Cset[CRIT == best][!is.na(Cset[CRIT ==
best])][1]
if (verbose) {
cat(i, "best found ", best, " at", best.spot,
fill = TRUE)
}
crit.old <- crit.i
# check if the best swap is really better thatn what you already have.
if (best < crit.i) {
if (verbose) {
cat(i, "best swapped ", fill = TRUE)
}
crit.i <- best
hist <- rbind(hist, c(Dset[i], best.spot, crit.i))
Dset[i] <- best.spot
Cset <- id[-Dset]
dist.mat <- DIST(R[Cset, ], R[Dset, ])
rs <- (dist.mat^P) %*% rep(1, n)
}
}
if ((crit.i == crit.old) | (loop.counter >= max.loop))
break
loop.counter <- loop.counter + 1
}
saved.crit[RUNS] <- crit.i
saved.designs[RUNS, ] <- Dset
saved.hist[[RUNS]] <- hist
}
ret <- (1:nruns)[saved.crit == min(saved.crit)]
if (length(ret) > 1) {
print("Greater than 1 optimal design; keeping first one......")
ret <- ret[1]
}
crit.i <- saved.crit[ret]
hist <- saved.hist[[ret]]
nhist <- nrow(hist)
nloop <- nruns
hist <- cbind(c(0:(nrow(hist) - 1)), hist)
dimnames(hist) <- list(NULL, c("step", "swap.out", "swap.in",
"new.crit"))
out.des <- R[saved.designs[ret, ], ]
out.des <- unscale(out.des, transform$x.center, transform$x.scale)
out <- list(design = out.des, call = match.call(), best.id = c(saved.designs[ret,
]), fixed = fixed, opt.crit = crit.i, start.design = design.original,
start.crit = crit.original, history = hist, other.designs = saved.designs,
other.crit = saved.crit, DIST = DIST, nn = nn, num.nn = num.nn,
P = P, Q = Q, nhist = nhist - 1, nloop = (nloop - 1)/n)
if (return.grid)
out$grid <- R.orig
if (return.transform)
out$transform <- transform
class(out) <- "spatialDesign"
out
}
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