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#' distsuml2min at orloca package
#'
#' \code{distsuml2min} is the \code{distsummin} function for the Euclidean norm (\eqn{l_2}).
#' This function returns the solution of the minimization problem.
#' Mainly for internal use.
#'
#' @name distsuml2min
#' @aliases distsuml2min distsuml2min,loca.p-method
#' @keywords internal classes optimize
#' @inherit distsummin
setGeneric("distsuml2min",
function (o, x = 0, y = 0, max.iter = 100, eps = 1.e-3, verbose = FALSE, algorithm = "Weiszfeld", ...) standardGeneric("distsuml2min")
)
## General distsuml2min function
## L-BFGS-B seems to be the best similar to Weiszfeld
## Take into account that Weiszfeld is completely implemented in R
#' @export
setMethod("distsuml2min", "loca.p",
function (o, x = 0, y = 0, max.iter = 100, eps = 1.e-3, verbose = FALSE, algorithm = "Weiszfeld", control = list(maxit = max.iter), ...) {
algorithm <- match.arg(algorithm, c('Weiszfeld', 'gradient', 'ucminf', 'Nelder-Mead', 'BFGS', 'CG', 'L-BFGS-B', 'SANN'))
if (algorithm == "gradient") distsuml2mingradient.loca.p(o, x, y, max.iter, eps, verbose)
else if (algorithm == "Weiszfeld") distsuml2minWeiszfeld.loca.p(o, x, y, max.iter, eps, verbose, ...)
else if (algorithm == "ucminf") distsuml2minucminf.loca.p(o, x, y, max.iter, eps, verbose)
else {
zdistsummin <- function(x) distsum(o, x[1], x[2])
par <- c(sum(o@x*o@w)/sum(o@w), sum(o@y*o@w)/sum(o@w))
optim(par, zdistsummin, method = algorithm, control = list(maxit = max.iter))$par
}
}
)
## Optimization by ucminf function from ucminf package
distsuml2minucminf.loca.p <- function (o, x = 0, y = 0, max.iter = 100, eps = 1.e-3, verbose = FALSE) {
zdistsum <- function(xx) distsum(o, xx[1], xx[2])
sol <- ucminf(par = c(x, y), fn = zdistsum, control = list(maxeval = max.iter, trace = verbose))
if (verbose) cat(gettext(sol$message))
return(sol$par)
}
## Gradient Method
distsuml2mingradient.loca.p <- function (o, x = 0, y = 0, max.iter = 100, eps = 1.e-3, verbose = FALSE) {
lambda <- 1;
eps2 <- eps^2
u<-c(x,y)
z <- distsum(o, u[1], u[2])
for (i in 0:max.iter) {
if (verbose) cat(paste(gettext("Iter"), ".", i, ": (", u[1], ",", u[2], ") ", z, "\n", sep = ""))
g<-distsumgra(o, u[1], u[2])
mg <- sum(g^2)
## Check stop rule
if (is.na(mg)) {
## A demand point stop rule
g<-distsumgra(o, u[1], u[2], partial = T)
mg <- sum(g^2)
ii <- which.min((o@x-u[1])^2+(o@y-u[2])^2)
if (mg < sum(o@w[ii]^2)) {
if(verbose) cat(gettext("Optimality condition reached at demand point."));
break
}
} else if (mg < eps2) {
if(verbose) cat(gettext("Optimality condition reached."));
break;
}
nu <- u - lambda*g
nz <- distsum(o, nu[1], nu[2])
if (nz < z) {
u<-nu
z<-nz
lambda <- lambda*2.2
} else {
lambda <- lambda/2
}
}
if (i == max.iter) warning.max.iter(max.iter)
u
}
distsuml2minWeiszfeld.loca.p <- function (o, x = 0, y = 0, max.iter = 100, eps = 1.e-3, verbose = FALSE, csmooth = .9) {
## Check smooth value
if (!identical(csmooth >= 0 && csmooth < 1, TRUE)) {
warning(paste(gettext("Value for smooth parameter non valid:"), smooth, gettext("Reseting to its default value.")))
csmooth <- .5
}
eps2 <- eps^2
u<-c(x,y)
## Begin iterations in non smooth mode
.smooth = 0
i.i = 0
i.s = round(max.iter*.5)
for (j in 1:2) {
for (i in i.i:i.s) {
if (verbose) cat(paste(gettext("Iter"), ". ", i, ": (", u[1], ",", u[2], ") ", distsum(o, u[1], u[2]), "\n", sep = ""))
## Compute the distances to demand points
n <- sqrt((u[1]-o@x)^2+(u[2]-o@y)^2)
## Check for demand point proximities
ii <- (n > eps)
## Compute the numerator of iteration
n <- o@w/n;
## Compute the gradient
g <- c(sum((u[1]-o@x[ii])*n[ii]), sum((u[2]-o@y[ii])*n[ii]))
mg <- sum(g^2)
## Check stop rule
if (!all(ii)) {
## A demand point stop rule
if (mg < sum(o@w[!ii]^2) || mg < eps2) {
if(verbose) cat(gettext("Optimality condition reached at demand point."));
break
}
} else if (mg <eps2) { ## Generic stop rule
if(verbose) cat(gettext("Optimality condition reached."));
break
}
s <- sum(n[ii])
nx <- n*o@x
ny <- n*o@y
u <- .smooth * u + (1-.smooth) * c(sum(nx[ii]), sum(ny[ii]))/s
}
## Check if optimality condition had been reached
if (i != i.s) break
## Changing to smooth version
.smooth = csmooth
if (j == 1) warning(gettext("The algorithm seems converges very slowly. Trying now with the smooth version."))
i.i = i.s
i.s = max.iter
}
if (i == max.iter) warning.max.iter(max.iter)
u
}
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