Nothing
R/variofit.R
In geoR: Analysis of Geostatistical Data
.geoR.env <- new.env()
"variofit" <-
function (vario, ini.cov.pars, cov.model,
fix.nugget = FALSE, nugget = 0,
fix.kappa = TRUE, kappa = 0.5,
simul.number = NULL, max.dist = vario$max.dist,
weights, minimisation.function,
limits = pars.limits(), messages, ...)
{
call.fc <- match.call()
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
if(length(class(vario)) == 0 || all(class(vario) != "variogram"))
warning("object vario should preferably be of the geoR's class \"variogram\"")
if(!missing(ini.cov.pars)){
if(any(class(ini.cov.pars) == "eyefit"))
cov.model <- ini.cov.pars[[1]]$cov.model
if(any(class(ini.cov.pars) == "variomodel"))
cov.model <- ini.cov.pars$cov.model
}
if(missing(cov.model)) cov.model <- "matern"
cov.model <- match.arg(cov.model, choices = .geoR.cov.models)
if(cov.model == "stable") cov.model <- "powered.exponential"
if(cov.model == "powered.exponential")
if(limits$kappa["upper"] > 2) limits$kappa["upper"] <- 2
## if(cov.model == "matern" | cov.model == " powered.exponential" |
## cov.model == "cauchy" | cov.model == "gneiting.matern")
## fix.kappa <- TRUE
if(missing(weights)){
if(vario$output.type == "cloud") weights <- "equal"
else weights <- "npairs"
}
else
weights <- match.arg(weights, choices = c("npairs", "equal", "cressie"))
if(messages.screen){
cat(paste("variofit: covariance model used is", cov.model, "\n"))
cat(paste("variofit: weights used:", weights, "\n"))
}
# if(missing(minimisation.function)){
# if(weights == "equal") minimisation.function <- "nls"
# else minimisation.function <- "optim"
# }
if(missing(minimisation.function))
minimisation.function <- "optim"
if(any(cov.model == c("linear", "power")) & minimisation.function == "nls"){
cat("warning: minimisation function nls can not be used with given cov.model.\n changing for \"optim\".\n")
minimisation.function <- "optim"
}
if(minimisation.function == "nls" & weights != "equal"){
warning("variofit: minimisation function nls can only be used with weights=\"equal\".\n changing for \"optim\".\n")
minimisation.function <- "optim"
}
if (is.matrix(vario$v) & is.null(simul.number))
stop("object in vario$v is a matrix. This function works for only 1 empirical variogram at once\n")
if (!is.null(simul.number))
vario$v <- vario$v[, simul.number]
##
## Setting maximum distance
##
if(mode(max.dist) != "numeric" || length(max.dist) > 1)
stop("a single numerical value must be provided in the argument max.dist")
if (max.dist == vario$max.dist)
XY <- list(u = vario$u, v = vario$v, n=vario$n)
else
XY <- list(u = vario$u[vario$u <= max.dist],
v = vario$v[vario$u <= max.dist],
n = vario$n[vario$u <= max.dist])
if(cov.model == "pure.nugget"){
##
## parameter estimation for model which does not require numerical minimisation
##
minimisation.function <- "not used"
message <- "correlation function does not require numerical minimisation"
if(weights == "equal") lm.wei <- rep(1, length(XY$u))
else lm.wei <- XY$n
if(cov.model == "pure.nugget"){
if(fix.nugget){
temp <- lm((XY$v-nugget) ~ 1, weights = lm.wei)
cov.pars <- c(temp$coef, 0)
}
else{
temp <- lm(XY$v ~ 1, weights = lm.wei)
nugget <- temp$coef
cov.pars <- c(0,0)
}
}
value <- sum((temp$residuals)^2)
}
else{
if(messages.screen)
cat(paste("variofit: minimisation function used:", minimisation.function, "\n"))
##
## setting things for numerical minimisation
##
## Checking initial values
##
umax <- max(vario$u)
vmax <- max(vario$v)
if(missing(ini.cov.pars)){
ini.cov.pars <- as.matrix(expand.grid(c(vmax/2, 3*vmax/4, vmax),
seq(0, 0.8*umax, len=6)))
if(!fix.nugget)
nugget <- unique(c(nugget, vmax/10, vmax/4, vmax/2))
if(!fix.kappa)
kappa <- unique(c(kappa, 0.25, 0.5, 1, 1.5, 2))
if(messages.screen)
warning("initial values not provided - running the default search")
}
else{
if(any(class(ini.cov.pars) == "eyefit")){
init <- nugget <- kappa <- NULL
for(i in 1:length(ini.cov.pars)){
init <- drop(rbind(init, ini.cov.pars[[i]]$cov.pars))
nugget <- c(nugget, ini.cov.pars[[i]]$nugget)
if(cov.model == "gneiting.matern")
kappa <- drop(rbind(kappa, ini.cov.pars[[i]]$kappa))
else
kappa <- c(kappa, ini.cov.pars[[i]]$kappa)
}
ini.cov.pars <- init
}
if(any(class(ini.cov.pars) == "variomodel")){
nugget <- ini.cov.pars$nugget
kappa <- ini.cov.pars$kappa
ini.cov.pars <- ini.cov.pars$cov.pars
}
}
if(is.matrix(ini.cov.pars) | is.data.frame(ini.cov.pars)){
ini.cov.pars <- as.matrix(ini.cov.pars)
if(nrow(ini.cov.pars) == 1)
ini.cov.pars <- as.vector(ini.cov.pars)
else{
if(ncol(ini.cov.pars) != 2)
stop("\nini.cov.pars must be a matrix or data.frame with 2 components: \ninitial values for sigmasq (partial sill) and phi (range parameter)\n")
}
}
else
if(length(ini.cov.pars) > 2)
stop("\nini.cov.pars must provide initial values for sigmasq and phi\n")
##
## Preparing grid of initial values and choosing the best
##
if(is.matrix(ini.cov.pars) | (length(nugget) > 1) | (length(kappa) > 1)) {
if(messages.screen)
cat("variofit: searching for best initial value ...")
ini.temp <- matrix(ini.cov.pars, ncol=2)
grid.ini <- as.matrix(expand.grid(sigmasq=unique(ini.temp[,1]),
phi=unique(ini.temp[,2]),
tausq=unique(nugget), kappa=unique(kappa)))
## loss function:
v.loss <- function(parms, u, v, n, cov.model, weights){
sigmasq <- parms[1]
phi <- parms[2]
if(cov.model == "power") phi <- 2 * exp(phi)/(1+exp(phi))
tausq <- parms[3]
kappa <- parms[4]
if(cov.model == "power")
v.mod <- tausq +
cov.spatial(u, cov.pars=c(sigmasq, phi), cov.model="power", kappa=kappa)
else
v.mod <- (sigmasq + tausq) -
cov.spatial(u, cov.pars=c(sigmasq, phi), cov.model = cov.model,
kappa = kappa)
if(weights == "equal")
loss <- sum((v - v.mod)^2)
if (weights == "npairs")
loss <- sum(n * (v - v.mod)^2)
if (weights == "cressie")
loss <- sum((n/(v.mod^2)) * (v - v.mod)^2)
return(loss)
}
grid.loss <- apply(grid.ini, 1, v.loss, u=XY$u, v=XY$v, n=XY$n, cov.model = cov.model, weights = weights)
ini.temp <- grid.ini[which(grid.loss == min(grid.loss))[1],, drop=FALSE]
rownames(ini.temp) <- "initial.value"
if(messages.screen){
cat(" selected values:\n")
print(rbind(round(ini.temp, digits=2), status=ifelse(c(FALSE, FALSE, fix.nugget, fix.kappa), "fix", "est")))
cat(paste("loss value:", min(grid.loss), "\n"))
}
names(ini.temp) <- NULL
ini.cov.pars <- ini.temp[1:2]
nugget <- ini.temp[3]
kappa <- ini.temp[4]
grid.ini <- NULL
}
##
## checking for unreasonable initial values
##
if(ini.cov.pars[1] > 2*vmax)
warning("unreasonable initial value for sigmasq (too high)")
if(ini.cov.pars[1] + nugget > 3*vmax)
warning("unreasonable initial value for sigmasq + nugget (too high)")
if(vario$output.type != "cloud"){
if(ini.cov.pars[1] + nugget < 0.3*vmax)
warning("unreasonable initial value for sigmasq + nugget (too low)")
}
if(nugget > 2*vmax)
warning("unreasonable initial value for nugget (too high)")
if(ini.cov.pars[2] > 1.5*umax)
warning("unreasonable initial value for phi (too high)")
##
## transforming kappa for constraint minimisation
##
if(!fix.kappa){
if(cov.model == "powered.exponential")
Tkappa.ini <- log(kappa/(2-kappa))
else
Tkappa.ini <- log(kappa)
}
##
## minimisation using "nls"
##
if (minimisation.function == "nls") {
if(ini.cov.pars[2] == 0) ini.cov.pars <- max(XY$u)/10
if(kappa == 0) kappa <- 0.5
if(cov.model == "power")
Tphi.ini <- log(ini.cov.pars[2]/(2-ini.cov.pars[2]))
else Tphi.ini <- log(ini.cov.pars[2])
XY$cov.model <- cov.model
##
if (fix.nugget) {
XY$nugget <- as.vector(nugget)
if(fix.kappa){
XY$kappa <- as.vector(kappa)
res <- nls((v-nugget) ~ matrix((1-cov.spatial(u,cov.pars=c(1,exp(Tphi)),
cov.model=cov.model, kappa=kappa)),
ncol=1),
start=list(Tphi=Tphi.ini), data=XY, algorithm="plinear", ...)
}
else{
if(cov.model == "powered.exponential")
res <- nls((v-nugget) ~ matrix((1-cov.spatial(u,cov.pars=c(1,exp(Tphi)),
cov.model=cov.model,
kappa=(2*exp(Tkappa)/(1+exp(Tkappa))))),
ncol=1),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
data=XY, algorithm="plinear", ...)
else
res <- nls((v-nugget) ~ matrix((1-cov.spatial(u,cov.pars=c(1,exp(Tphi)),
cov.model=cov.model,
kappa=exp(Tkappa))), ncol=1),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
data=XY, algorithm="plinear", ...)
kappa <- exp(coef(res)["Tkappa"])
names(kappa) <- NULL
}
cov.pars <- coef(res)[c(".lin", "Tphi")]
names(cov.pars) <- NULL
}
else{
if(fix.kappa){
XY$kappa <- kappa
res <- nls(v ~ cbind(1,(1- cov.spatial(u, cov.pars=c(1,exp(Tphi)),
cov.model = cov.model, kappa=kappa))),
start=list(Tphi=Tphi.ini), algorithm="plinear", data=XY, ...)
}
else{
if(cov.model == "powered.exponential")
res <- nls(v ~ cbind(1, (1-cov.spatial(u, cov.pars=c(1, exp(Tphi)),
cov.model = cov.model,
kappa=(2*exp(Tkappa)/(1+exp(Tkappa)))))),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
algorithm="plinear", data=XY, ...)
else
res <- nls(v ~ cbind(1, (1-cov.spatial(u, cov.pars=c(1, exp(Tphi)),
cov.model = cov.model,
kappa=exp(Tkappa)))),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
algorithm="plinear", data=XY, ...)
kappa <- exp(coef(res)["Tkappa"]);names(kappa) <- NULL
}
nugget <- coef(res)[".lin1"];names(nugget) <- NULL
cov.pars <- coef(res)[c(".lin2", "Tphi")]
names(cov.pars) <- NULL
}
if(cov.model == "power")
cov.pars[2] <- 2 * exp(cov.pars[2])/(1+exp(cov.pars[2]))
else cov.pars[2] <- exp(cov.pars[2])
if(nugget < 0 | cov.pars[1] < 0){
warning("\nvariofit: negative variance parameter found using the default option \"nls\".\n Try another minimisation function and/or fix some of the parameters.\n")
temp <- c(sigmasq=cov.pars[1], phi=cov.pars[2], tausq=nugget, kappa=kappa)
print(rbind(round(temp, digits=4),
status=ifelse(c(FALSE, FALSE, fix.nugget, fix.kappa), "fix", "est")))
return(invisible())
}
value <- sum(resid(res)^2)
message <- "nls does not provides convergence message"
}
##
## minimisation using "optim" or "nlm"
##
if (minimisation.function == "nlm" | minimisation.function == "optim") {
##
## Preparing lists for the minimiser
##
.global.list <- list(u = XY$u, v = XY$v, n=XY$n, fix.nugget = fix.nugget,
nugget = nugget, fix.kappa = fix.kappa, kappa = kappa,
cov.model = cov.model, m.f = minimisation.function,
weights = weights)
##
## Preparing initial value
##
ini <- ini.cov.pars
if(cov.model == "power") ini[2] <- log(ini[2]/(2-ini[2]))
if(cov.model == "linear") ini <- ini[1]
if(fix.nugget == FALSE) ini <- c(ini, nugget)
## setting kappa > 0 for both methods
if(!fix.kappa) ini <- c(ini, Tkappa.ini)
names(ini) <- NULL
if(minimisation.function == "nlm"){
result <- nlm(.loss.vario, ini, g.l = .global.list, ...)
result$par <- result$estimate
result$value <- result$minimum
result$convergence <- result$code
if(!is.null(get(".temp.theta", pos=.geoR.env)))
result$par <- get(".temp.theta", pos=.geoR.env)
}
else{
# if(fix.kappa == FALSE) ini <- c(ini, kappa)
# names(ini) <- NULL
lower.l <- sapply(limits, function(x) x[1])
upper.l <- sapply(limits, function(x) x[2])
if(fix.kappa == FALSE){
if(fix.nugget){
lower <- lower.l[c("sigmasq.lower", "phi.lower","kappa.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper","kappa.upper")]
}
else{
lower <- lower.l[c("sigmasq.lower", "phi.lower",
"tausq.rel.lower", "kappa.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper",
"tausq.rel.upper", "kappa.upper")]
}
}
else{
if(cov.model == "power"){
if(fix.nugget){
lower <- lower.l[c("sigmasq.lower", "phi.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper")]
}
else{
lower <- lower.l[c("sigmasq.lower", "phi.lower", "tausq.rel.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper", "tausq.rel.upper")]
}
}
else{
lower <- lower.l["phi.lower"]
upper <- upper.l["phi.upper"]
}
}
result <- optim(ini, .loss.vario, method = "L-BFGS-B",
hessian = TRUE, lower = lower,
upper = upper, g.l = .global.list, ...)
# require(methods)
# if(exists("trySilent"))
# hess <- trySilent(solve(as.matrix(result$hessian)))
# else{
# op.sem <- options()$show.error.messages
# options(show.error.messages = FALSE)
# hess <- try(solve(as.matrix(result$hessian)))
# options(show.error.messages = op.sem)
# }
# if(!inherits(hess, "try-error")) hess <- sqrt(diag(hess))
# else print("WARNING: unable to compute the hessian")
}
value <- result$value
message <- paste(minimisation.function, "convergence code:", result$convergence)
if(cov.model == "linear")
result$par <- c(result$par[1],1,result$par[-1])
cov.pars <- as.vector(result$par[1:2])
if(cov.model == "power")
cov.pars[2] <- 2 * exp(cov.pars[2])/(1+exp(cov.pars[2]))
if(!fix.kappa){
if (fix.nugget)
kappa <- result$par[3]
else{
nugget <- result$par[3]
kappa <- result$par[4]
}
## kappa now > 0 for both nlm() and optim()
## if(minimisation.function == "nlm"){
if(.global.list$cov.model == "powered.exponential")
kappa <- 2*(exp(kappa))/(1+exp(kappa))
else kappa <- exp(kappa)
## }
}
else
if(!fix.nugget)
nugget <- result$par[3]
}
}
##
## Estimating implicity beta
##
##
## Preparing output
##
estimation <- list(nugget = nugget, cov.pars = cov.pars,
cov.model = cov.model, kappa = kappa, value = value,
trend = vario$trend, beta.ols = vario$beta.ols,
practicalRange = practicalRange(cov.model=cov.model,
phi = cov.pars[2], kappa = kappa),
max.dist = max.dist,
minimisation.function = minimisation.function)
# if(exists("hess")) estimation$hessian <- hess
estimation$weights <- weights
if(weights == "equal") estimation$method <- "OLS"
else estimation$method <- "WLS"
estimation$fix.nugget <- fix.nugget
estimation$fix.kappa <- fix.kappa
estimation$lambda <- vario$lambda
estimation$message <- message
estimation$call <- call.fc
oldClass(estimation) <- c("variomodel", "variofit")
return(estimation)
}
".loss.vario" <-
function (theta, g.l)
{
if(g.l$cov.model == "linear")
theta <- c(theta[1], 1, theta[-1])
##
## Imposing constraints for nlm
##
if(g.l$m.f == "nlm"){
## assign(".temp.theta", NULL, pos=1)
assign(".temp.theta", NULL, pos=.geoR.env)
if(!g.l$fix.kappa){
if(g.l$fix.nugget){
if(g.l$cov.model == "power")
theta.minimiser <- theta[1]
else
theta.minimiser <- theta[1:2]
Tkappa <- theta[3]
}
else{
if(g.l$cov.model == "power")
theta.minimiser <- theta[c(1:3)]
else
theta.minimiser <- theta[1:3]
Tkappa <- theta[4]
}
}
else theta.minimiser <- theta
penalty <- 10000 * sum(0 - pmin(theta.minimiser, 0))
theta <- pmax(theta.minimiser, 0)
if(!g.l$fix.kappa) theta <- c(theta.minimiser, Tkappa)
if (any(theta.minimiser < 0)){
##assign(".temp.theta", theta, pos=1)
assign(".temp.theta", theta, pos=.geoR.env)
}
else penalty <- 0
}
else penalty <- 0
##
## reading parameters
##
if(!g.l$fix.kappa){
if (g.l$fix.nugget){
tausq <- g.l$nugget
Tkappa <- theta[3]
}
else{
tausq <- theta[3]
Tkappa <- theta[4]
}
## kappa now > 0 for both nlm() and optim()
##if(g.l$m.f == "nlm"){
if(g.l$cov.model == "powered.exponential")
kappa <- 2*(exp(Tkappa))/(1+exp(Tkappa))
else kappa <- exp(Tkappa)
##}
##else kappa <- Tkappa
}
else{
kappa <- g.l$kappa
if (g.l$fix.nugget) tausq <- g.l$nugget
else tausq <- theta[3]
}
##
sigmasq <- theta[1]
phi <- theta[2]
if(g.l$cov.model == "power") phi <- 2 * exp(phi)/(1+exp(phi))
sill.total <- sigmasq + tausq
##
## Computing values for the theoretical variogram
##
if(any(g.l$cov.model == c("linear", "power")))
gammaU <- tausq + sigmasq * (g.l$u^phi)
else
gammaU <- sill.total - cov.spatial(g.l$u, cov.model = g.l$cov.model,
kappa = kappa, cov.pars = c(sigmasq, phi))
##
## Computing loss function
##
if(g.l$weight == "equal")
loss <- sum((g.l$v - gammaU)^2)
if (g.l$weights == "npairs")
loss <- sum(g.l$n * (g.l$v - gammaU)^2)
if (g.l$weights == "cressie")
loss <- sum((g.l$n/(gammaU^2)) * (g.l$v - gammaU)^2)
if(loss > (.Machine$double.xmax^0.5) | loss == Inf | loss == -Inf | is.nan(loss))
loss <- .Machine$double.xmax^0.5
return(loss + penalty)
}
"print.variofit" <-
function(x, digits = "default", ...)
{
if(digits == "default") digits <- max(3, getOption("digits") - 3)
if(x$fix.nugget){
est.pars <- c(sigmasq = x$cov.pars[1], phi=x$cov.pars[2])
if(x$fix.kappa == FALSE)
est.pars <- c(est.pars, kappa = x$kappa)
}
else{
est.pars <- c(tausq = x$nugget, sigmasq = x$cov.pars[1], phi=x$cov.pars[2])
if(x$fix.kappa == FALSE)
est.pars <- c(est.pars, kappa = x$kappa)
}
if(x$weights == "equal")
cat("variofit: model parameters estimated by OLS (ordinary least squares):\n")
else
cat("variofit: model parameters estimated by WLS (weighted least squares):\n")
cat(paste("covariance model is:", x$cov.model))
if(any(x$cov.model == c("matern", "powered.exponential",
"cauchy", "gencauchy", "gneiting.matern")))
if(x$fix.kappa) cat(paste(" with fixed kappa =", x$kappa))
if(x$cov.model == "matern" & x$fix.kappa & x$kappa == 0.5)
cat(" (exponential)")
cat("\n")
if(x$fix.nugget)
cat(paste("fixed value for tausq = ", x$nugget,"\n"))
cat("parameter estimates:\n")
print(round(est.pars, digits=digits))
cat(paste("Practical Range with cor=0.05 for asymptotic range:", format(x$practicalRange, ...)))
cat("\n")
if(x$weights == "equal") cat("\nvariofit: minimised sum of squares = ")
else cat("\nvariofit: minimised weighted sum of squares = ")
cat(round(x$value, digits=digits))
cat("\n")
return(invisible())
}
"summary.variofit" <-
function(object, ...)
{
## o problema disto eh no reconhecer a classe variofit...
# if(all(lapply(lapply(object, class), function(x) any(x ==
# "variofit")))){
# summa <- lapply(object, summary.variofit)
# }
# if (length(list(object, ...)) > 1){
# }
##
summ.lik <- list()
if(object$weights == "equal")
summ.lik$pmethod <- "OLS (ordinary least squares)"
else
summ.lik$pmethod <- "WLS (weighted least squares)"
summ.lik$cov.model <- object$cov.model
summ.lik$spatial.component <- c(sigmasq = object$cov.pars[1], phi=object$cov.pars[2])
summ.lik$spatial.component.extra <- c(kappa = object$kappa)
summ.lik$nugget.component <- c(tausq = object$nugget)
summ.lik$fix.nugget <- object$fix.nugget
summ.lik$fix.kappa <- object$fix.kappa
summ.lik$practicalRange <- object$practicalRange
summ.lik$sum.of.squares <- c(value = object$value)
if(object$fix.nugget){
summ.lik$estimated.pars <- c(sigmasq = object$cov.pars[1], phi=object$cov.pars[2])
if(object$fix.kappa == FALSE)
summ.lik$estimated.pars <- c(summ.lik$estimated.pars, kappa = object$kappa)
}
else{
summ.lik$estimated.pars <- c(tausq = object$nugget, sigmasq = object$cov.pars[1], phi=object$cov.pars[2])
if(object$fix.kappa == FALSE)
summ.lik$estimated.pars <- c(summ.lik$estimated.pars, kappa = object$kappa)
}
summ.lik$weights <- object$weights
summ.lik$call <- object$call
oldClass(summ.lik) <- "summary.variomodel"
return(summ.lik)
}
"print.summary.variofit" <-
function(x, digits = "default", ...)
{
if(length(class(x)) == 0 || all(class(x) != "summary.variomodel"))
stop("object is not of the class \"summary.variomodel\"")
if(digits == "default") digits <- max(3, getOption("digits") - 3)
cat("Summary of the parameter estimation\n")
cat("-----------------------------------\n")
cat(paste("Estimation method:", x$pmethod, "\n"))
cat("\n")
##
## Estimates of the model components
## Model: Y(x) = X\beta + S(x) + e
##
# cat("Parameters of the mean component (trend):")
# cat("\n")
# print(round(x$mean.component, digits=digits))
# cat("\n")
##
cat("Parameters of the spatial component:")
cat("\n")
cat(paste(" correlation function:", x$cov.model))
if(x$cov.model == "matern" & x$fix.kappa & x$spatial.component.extra == 0.5)
cat(" (exponential)")
if(any(x$cov.model == c("matern", "powered.exponential",
"cauchy", "gencauchy", "gneiting.matern"))){
if(x$fix.kappa)
cat(paste("\n (fixed) extra parameter kappa = ", round(x$spatial.component.extra, digits=digits)))
else
cat(paste("\n (estimated) extra parameter kappa = ", round(x$spatial.component.extra, digits=digits)))
}
cat(paste("\n (estimated) variance parameter sigmasq (partial sill) = ", round(x$spatial.component[1], digits=digits)))
cat(paste("\n (estimated) cor. fct. parameter phi (range parameter) = ", round(x$spatial.component[2], digits=digits)))
cat("\n")
##
cat("\n")
cat("Parameter of the error component:")
if(x$fix.nugget)
cat(paste("\n (fixed) nugget =", round(x$nugget.component, digits = digits)))
else
cat(paste("\n (estimated) nugget = ", round(x$nugget.component, digits=digits)))
cat("\n")
cat("\n")
cat("Practical Range with cor=0.05 for asymptotic range:",
format(x$practicalRange, ...))
cat("\n")
cat("\n")
names(x$sum.of.squares) <- NULL
if(x$weights == "equal") cat("Minimised sum of squares: ")
else cat("Minimised weighted sum of squares: ")
cat(round(x$sum.of.squares, digits=digits))
cat("\n")
cat("\n")
cat("Call:")
cat("\n")
print(x$call)
cat("\n")
invisible(x)
}
"variog.model.env" <-
function(geodata, coords = geodata$coords, obj.variog,
model.pars, nsim = 99, save.sim = FALSE, messages)
{
call.fc <- match.call()
obj.variog$v <- NULL
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
##
## reading input
##
if(any(class(model.pars) == "eyefit")){
if(length(model.pars) == 1L)
model.pars <- model.pars[[1]]
else
stop(paste("variog.model.env: more than one variograma model in the object",
deparse(substitute(model.pars)), "\n specify which i_th model in the list to be used using [[i]]"))
}
if(!is.null(model.pars$beta)) beta <- model.pars$beta
else beta <- 0
if(!is.null(model.pars$cov.model))
cov.model <- model.pars$cov.model
else cov.model <- "exponential"
if(!is.null(model.pars$kappa)) kappa <- model.pars$kappa
else kappa <- 0.5
#if(!is.null(model.pars$lambda)) lambda <- model.pars$lambda
#else lambda <- 0.5
if(!is.null(model.pars$nugget)) nugget <- model.pars$nugget
else nugget <- 0
cov.pars <- model.pars$cov.pars
if(!is.null(obj.variog$estimator.type))
estimator.type <- obj.variog$estimator.type
else estimator.type <- "classical"
if (obj.variog$output.type != "bin")
stop("envelops can be computed only for binned variogram")
##
## generating simulations from the model with parameters provided
##
if (messages.screen)
cat(paste("variog.env: generating", nsim, "simulations (with ",
obj.variog$n.data,
"points each) using the function grf\n"))
# simula <- grf(obj.variog$n.data, grid = as.matrix(coords),
# cov.model = cov.model, cov.pars = cov.pars,
# nugget = nugget, kappa = kappa, nsim = nsim,
# messages = FALSE, lambda = obj.variog$lambda)
simula <- grf(obj.variog$n.data, grid = as.matrix(coords),
cov.model = cov.model, cov.pars = cov.pars,
nugget = nugget, kappa = kappa, nsim = nsim,
messages = FALSE)
##
## add the mean
##
if(messages.screen)
cat("variog.env: adding the mean or trend\n")
x.mat <- unclass(trend.spatial(trend=obj.variog$trend, geodata = geodata))
if(ncol(x.mat) != length(beta))
stop("incompatible sizes of trend matrix and beta parameter vector. Check whether the trend specification are the same in the objects passed to the arguments \"obj.vario\" and \"model.pars\"")
simula$data <- as.vector(x.mat %*% beta) + simula$data
##
## computing empirical variograms for the simulations
##
if (messages.screen)
cat(paste("variog.env: computing the empirical variogram for the",
nsim, "simulations\n"))
nbins <- length(obj.variog$bins.lim) - 1
bin.f <- function(sim){
cbin <- vbin <- sdbin <- rep(0, nbins)
temp <- .C("binit",
as.integer(obj.variog$n.data),
as.double(as.vector(coords[,1])),
as.double(as.vector(coords[,2])),
as.double(as.vector(sim)),
as.integer(nbins),
as.double(as.vector(obj.variog$bins.lim)),
as.integer(estimator.type == "modulus"),
as.double(max(obj.variog$u)),
as.double(cbin),
vbin = as.double(vbin),
as.integer(FALSE),
as.double(sdbin),
PACKAGE = "geoR")$vbin
return(temp)
}
simula.bins <- apply(simula$data, 2, bin.f)
simula.bins <- simula.bins[obj.variog$ind.bin,]
# if(exists(".IND.geoR.variog.model.env", where=1))
if(exists(".IND.geoR.variog.model.env"))
return(simula.bins)
if(save.sim == FALSE) simula$data <- NULL
##
## computing envelops
##
if (messages.screen)
cat("variog.env: computing the envelops\n")
limits <- apply(simula.bins, 1, range)
res.env <- list(u = obj.variog$u, v.lower = limits[1, ],
v.upper = limits[2,])
if(save.sim)
res.env$simulated.data <- simula$data
res.env$call <- call.fc
oldClass(res.env) <- "variogram.envelope"
return(res.env)
}
"boot.variofit" <-
function(geodata, coords = geodata$coords, obj.variog,
model.pars, nsim = 99, trace = FALSE, messages)
{
call.fc <- match.call()
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
##
if(messages.screen)
cat("Computing empirical variograms for simulations\n")
## assign(".IND.geoR.variog.model.env", TRUE, pos =1)
geoR.env <- new.env()
assign(".IND.geoR.variog.model.env", TRUE, pos=geoR.env)
environment(variog.model.env) <- geoR.env
vmat <- variog.model.env(geodata=geodata, coords=coords,
obj.variog=obj.variog, model.pars=model.pars,
nsim=nsim, messages = FALSE)
## rm(".IND.geoR.variog.model.env", pos=1)
##
if(messages.screen){
cat("Fitting models (variofit) for the simulated variograms\n")
cat("be patient - this can take a while to run\n")
}
geoR.count <- new.env()
assign(".geoR.count", 1, envir=geoR.count)
.vf <- function(v){
obj.variog$v <- v
pars <- summary(variofit(obj.variog, messages=FALSE))$estimated.pars
## pars <- summary(variofit(obj.variog, ini = model.pars$cov.pars,
## nugget = model.pars$nugget,
## messages=FALSE))$estimated.pars
if(trace){
cat(paste("simulation", get(".geoR.count", envir=geoR.count),
"out of", nsim, "\n"))
print(pars)
assign(".geoR.count", get(".geoR.count", envir=geoR.count)+1,
envir=geoR.count)
}
return(pars)
}
res <- as.data.frame(t(apply(vmat, 2, .vf)))
class(res) <- "boot.variofit"
return(res)
}
##"beta.variofit" <-
## function(geodata, coords = geodata$coords, data=geodata$data,
## obj.variofit)
## {
##
## }
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.geoR.env <- new.env()
"variofit" <-
function (vario, ini.cov.pars, cov.model,
fix.nugget = FALSE, nugget = 0,
fix.kappa = TRUE, kappa = 0.5,
simul.number = NULL, max.dist = vario$max.dist,
weights, minimisation.function,
limits = pars.limits(), messages, ...)
{
call.fc <- match.call()
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
if(length(class(vario)) == 0 || all(class(vario) != "variogram"))
warning("object vario should preferably be of the geoR's class \"variogram\"")
if(!missing(ini.cov.pars)){
if(any(class(ini.cov.pars) == "eyefit"))
cov.model <- ini.cov.pars[[1]]$cov.model
if(any(class(ini.cov.pars) == "variomodel"))
cov.model <- ini.cov.pars$cov.model
}
if(missing(cov.model)) cov.model <- "matern"
cov.model <- match.arg(cov.model, choices = .geoR.cov.models)
if(cov.model == "stable") cov.model <- "powered.exponential"
if(cov.model == "powered.exponential")
if(limits$kappa["upper"] > 2) limits$kappa["upper"] <- 2
## if(cov.model == "matern" | cov.model == " powered.exponential" |
## cov.model == "cauchy" | cov.model == "gneiting.matern")
## fix.kappa <- TRUE
if(missing(weights)){
if(vario$output.type == "cloud") weights <- "equal"
else weights <- "npairs"
}
else
weights <- match.arg(weights, choices = c("npairs", "equal", "cressie"))
if(messages.screen){
cat(paste("variofit: covariance model used is", cov.model, "\n"))
cat(paste("variofit: weights used:", weights, "\n"))
}
# if(missing(minimisation.function)){
# if(weights == "equal") minimisation.function <- "nls"
# else minimisation.function <- "optim"
# }
if(missing(minimisation.function))
minimisation.function <- "optim"
if(any(cov.model == c("linear", "power")) & minimisation.function == "nls"){
cat("warning: minimisation function nls can not be used with given cov.model.\n changing for \"optim\".\n")
minimisation.function <- "optim"
}
if(minimisation.function == "nls" & weights != "equal"){
warning("variofit: minimisation function nls can only be used with weights=\"equal\".\n changing for \"optim\".\n")
minimisation.function <- "optim"
}
if (is.matrix(vario$v) & is.null(simul.number))
stop("object in vario$v is a matrix. This function works for only 1 empirical variogram at once\n")
if (!is.null(simul.number))
vario$v <- vario$v[, simul.number]
##
## Setting maximum distance
##
if(mode(max.dist) != "numeric" || length(max.dist) > 1)
stop("a single numerical value must be provided in the argument max.dist")
if (max.dist == vario$max.dist)
XY <- list(u = vario$u, v = vario$v, n=vario$n)
else
XY <- list(u = vario$u[vario$u <= max.dist],
v = vario$v[vario$u <= max.dist],
n = vario$n[vario$u <= max.dist])
if(cov.model == "pure.nugget"){
##
## parameter estimation for model which does not require numerical minimisation
##
minimisation.function <- "not used"
message <- "correlation function does not require numerical minimisation"
if(weights == "equal") lm.wei <- rep(1, length(XY$u))
else lm.wei <- XY$n
if(cov.model == "pure.nugget"){
if(fix.nugget){
temp <- lm((XY$v-nugget) ~ 1, weights = lm.wei)
cov.pars <- c(temp$coef, 0)
}
else{
temp <- lm(XY$v ~ 1, weights = lm.wei)
nugget <- temp$coef
cov.pars <- c(0,0)
}
}
value <- sum((temp$residuals)^2)
}
else{
if(messages.screen)
cat(paste("variofit: minimisation function used:", minimisation.function, "\n"))
##
## setting things for numerical minimisation
##
## Checking initial values
##
umax <- max(vario$u)
vmax <- max(vario$v)
if(missing(ini.cov.pars)){
ini.cov.pars <- as.matrix(expand.grid(c(vmax/2, 3*vmax/4, vmax),
seq(0, 0.8*umax, len=6)))
if(!fix.nugget)
nugget <- unique(c(nugget, vmax/10, vmax/4, vmax/2))
if(!fix.kappa)
kappa <- unique(c(kappa, 0.25, 0.5, 1, 1.5, 2))
if(messages.screen)
warning("initial values not provided - running the default search")
}
else{
if(any(class(ini.cov.pars) == "eyefit")){
init <- nugget <- kappa <- NULL
for(i in 1:length(ini.cov.pars)){
init <- drop(rbind(init, ini.cov.pars[[i]]$cov.pars))
nugget <- c(nugget, ini.cov.pars[[i]]$nugget)
if(cov.model == "gneiting.matern")
kappa <- drop(rbind(kappa, ini.cov.pars[[i]]$kappa))
else
kappa <- c(kappa, ini.cov.pars[[i]]$kappa)
}
ini.cov.pars <- init
}
if(any(class(ini.cov.pars) == "variomodel")){
nugget <- ini.cov.pars$nugget
kappa <- ini.cov.pars$kappa
ini.cov.pars <- ini.cov.pars$cov.pars
}
}
if(is.matrix(ini.cov.pars) | is.data.frame(ini.cov.pars)){
ini.cov.pars <- as.matrix(ini.cov.pars)
if(nrow(ini.cov.pars) == 1)
ini.cov.pars <- as.vector(ini.cov.pars)
else{
if(ncol(ini.cov.pars) != 2)
stop("\nini.cov.pars must be a matrix or data.frame with 2 components: \ninitial values for sigmasq (partial sill) and phi (range parameter)\n")
}
}
else
if(length(ini.cov.pars) > 2)
stop("\nini.cov.pars must provide initial values for sigmasq and phi\n")
##
## Preparing grid of initial values and choosing the best
##
if(is.matrix(ini.cov.pars) | (length(nugget) > 1) | (length(kappa) > 1)) {
if(messages.screen)
cat("variofit: searching for best initial value ...")
ini.temp <- matrix(ini.cov.pars, ncol=2)
grid.ini <- as.matrix(expand.grid(sigmasq=unique(ini.temp[,1]),
phi=unique(ini.temp[,2]),
tausq=unique(nugget), kappa=unique(kappa)))
## loss function:
v.loss <- function(parms, u, v, n, cov.model, weights){
sigmasq <- parms[1]
phi <- parms[2]
if(cov.model == "power") phi <- 2 * exp(phi)/(1+exp(phi))
tausq <- parms[3]
kappa <- parms[4]
if(cov.model == "power")
v.mod <- tausq +
cov.spatial(u, cov.pars=c(sigmasq, phi), cov.model="power", kappa=kappa)
else
v.mod <- (sigmasq + tausq) -
cov.spatial(u, cov.pars=c(sigmasq, phi), cov.model = cov.model,
kappa = kappa)
if(weights == "equal")
loss <- sum((v - v.mod)^2)
if (weights == "npairs")
loss <- sum(n * (v - v.mod)^2)
if (weights == "cressie")
loss <- sum((n/(v.mod^2)) * (v - v.mod)^2)
return(loss)
}
grid.loss <- apply(grid.ini, 1, v.loss, u=XY$u, v=XY$v, n=XY$n, cov.model = cov.model, weights = weights)
ini.temp <- grid.ini[which(grid.loss == min(grid.loss))[1],, drop=FALSE]
rownames(ini.temp) <- "initial.value"
if(messages.screen){
cat(" selected values:\n")
print(rbind(round(ini.temp, digits=2), status=ifelse(c(FALSE, FALSE, fix.nugget, fix.kappa), "fix", "est")))
cat(paste("loss value:", min(grid.loss), "\n"))
}
names(ini.temp) <- NULL
ini.cov.pars <- ini.temp[1:2]
nugget <- ini.temp[3]
kappa <- ini.temp[4]
grid.ini <- NULL
}
##
## checking for unreasonable initial values
##
if(ini.cov.pars[1] > 2*vmax)
warning("unreasonable initial value for sigmasq (too high)")
if(ini.cov.pars[1] + nugget > 3*vmax)
warning("unreasonable initial value for sigmasq + nugget (too high)")
if(vario$output.type != "cloud"){
if(ini.cov.pars[1] + nugget < 0.3*vmax)
warning("unreasonable initial value for sigmasq + nugget (too low)")
}
if(nugget > 2*vmax)
warning("unreasonable initial value for nugget (too high)")
if(ini.cov.pars[2] > 1.5*umax)
warning("unreasonable initial value for phi (too high)")
##
## transforming kappa for constraint minimisation
##
if(!fix.kappa){
if(cov.model == "powered.exponential")
Tkappa.ini <- log(kappa/(2-kappa))
else
Tkappa.ini <- log(kappa)
}
##
## minimisation using "nls"
##
if (minimisation.function == "nls") {
if(ini.cov.pars[2] == 0) ini.cov.pars <- max(XY$u)/10
if(kappa == 0) kappa <- 0.5
if(cov.model == "power")
Tphi.ini <- log(ini.cov.pars[2]/(2-ini.cov.pars[2]))
else Tphi.ini <- log(ini.cov.pars[2])
XY$cov.model <- cov.model
##
if (fix.nugget) {
XY$nugget <- as.vector(nugget)
if(fix.kappa){
XY$kappa <- as.vector(kappa)
res <- nls((v-nugget) ~ matrix((1-cov.spatial(u,cov.pars=c(1,exp(Tphi)),
cov.model=cov.model, kappa=kappa)),
ncol=1),
start=list(Tphi=Tphi.ini), data=XY, algorithm="plinear", ...)
}
else{
if(cov.model == "powered.exponential")
res <- nls((v-nugget) ~ matrix((1-cov.spatial(u,cov.pars=c(1,exp(Tphi)),
cov.model=cov.model,
kappa=(2*exp(Tkappa)/(1+exp(Tkappa))))),
ncol=1),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
data=XY, algorithm="plinear", ...)
else
res <- nls((v-nugget) ~ matrix((1-cov.spatial(u,cov.pars=c(1,exp(Tphi)),
cov.model=cov.model,
kappa=exp(Tkappa))), ncol=1),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
data=XY, algorithm="plinear", ...)
kappa <- exp(coef(res)["Tkappa"])
names(kappa) <- NULL
}
cov.pars <- coef(res)[c(".lin", "Tphi")]
names(cov.pars) <- NULL
}
else{
if(fix.kappa){
XY$kappa <- kappa
res <- nls(v ~ cbind(1,(1- cov.spatial(u, cov.pars=c(1,exp(Tphi)),
cov.model = cov.model, kappa=kappa))),
start=list(Tphi=Tphi.ini), algorithm="plinear", data=XY, ...)
}
else{
if(cov.model == "powered.exponential")
res <- nls(v ~ cbind(1, (1-cov.spatial(u, cov.pars=c(1, exp(Tphi)),
cov.model = cov.model,
kappa=(2*exp(Tkappa)/(1+exp(Tkappa)))))),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
algorithm="plinear", data=XY, ...)
else
res <- nls(v ~ cbind(1, (1-cov.spatial(u, cov.pars=c(1, exp(Tphi)),
cov.model = cov.model,
kappa=exp(Tkappa)))),
start=list(Tphi=Tphi.ini, Tkappa = Tkappa.ini),
algorithm="plinear", data=XY, ...)
kappa <- exp(coef(res)["Tkappa"]);names(kappa) <- NULL
}
nugget <- coef(res)[".lin1"];names(nugget) <- NULL
cov.pars <- coef(res)[c(".lin2", "Tphi")]
names(cov.pars) <- NULL
}
if(cov.model == "power")
cov.pars[2] <- 2 * exp(cov.pars[2])/(1+exp(cov.pars[2]))
else cov.pars[2] <- exp(cov.pars[2])
if(nugget < 0 | cov.pars[1] < 0){
warning("\nvariofit: negative variance parameter found using the default option \"nls\".\n Try another minimisation function and/or fix some of the parameters.\n")
temp <- c(sigmasq=cov.pars[1], phi=cov.pars[2], tausq=nugget, kappa=kappa)
print(rbind(round(temp, digits=4),
status=ifelse(c(FALSE, FALSE, fix.nugget, fix.kappa), "fix", "est")))
return(invisible())
}
value <- sum(resid(res)^2)
message <- "nls does not provides convergence message"
}
##
## minimisation using "optim" or "nlm"
##
if (minimisation.function == "nlm" | minimisation.function == "optim") {
##
## Preparing lists for the minimiser
##
.global.list <- list(u = XY$u, v = XY$v, n=XY$n, fix.nugget = fix.nugget,
nugget = nugget, fix.kappa = fix.kappa, kappa = kappa,
cov.model = cov.model, m.f = minimisation.function,
weights = weights)
##
## Preparing initial value
##
ini <- ini.cov.pars
if(cov.model == "power") ini[2] <- log(ini[2]/(2-ini[2]))
if(cov.model == "linear") ini <- ini[1]
if(fix.nugget == FALSE) ini <- c(ini, nugget)
## setting kappa > 0 for both methods
if(!fix.kappa) ini <- c(ini, Tkappa.ini)
names(ini) <- NULL
if(minimisation.function == "nlm"){
result <- nlm(.loss.vario, ini, g.l = .global.list, ...)
result$par <- result$estimate
result$value <- result$minimum
result$convergence <- result$code
if(!is.null(get(".temp.theta", pos=.geoR.env)))
result$par <- get(".temp.theta", pos=.geoR.env)
}
else{
# if(fix.kappa == FALSE) ini <- c(ini, kappa)
# names(ini) <- NULL
lower.l <- sapply(limits, function(x) x[1])
upper.l <- sapply(limits, function(x) x[2])
if(fix.kappa == FALSE){
if(fix.nugget){
lower <- lower.l[c("sigmasq.lower", "phi.lower","kappa.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper","kappa.upper")]
}
else{
lower <- lower.l[c("sigmasq.lower", "phi.lower",
"tausq.rel.lower", "kappa.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper",
"tausq.rel.upper", "kappa.upper")]
}
}
else{
if(cov.model == "power"){
if(fix.nugget){
lower <- lower.l[c("sigmasq.lower", "phi.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper")]
}
else{
lower <- lower.l[c("sigmasq.lower", "phi.lower", "tausq.rel.lower")]
upper <- upper.l[c("sigmasq.upper", "phi.upper", "tausq.rel.upper")]
}
}
else{
lower <- lower.l["phi.lower"]
upper <- upper.l["phi.upper"]
}
}
result <- optim(ini, .loss.vario, method = "L-BFGS-B",
hessian = TRUE, lower = lower,
upper = upper, g.l = .global.list, ...)
# require(methods)
# if(exists("trySilent"))
# hess <- trySilent(solve(as.matrix(result$hessian)))
# else{
# op.sem <- options()$show.error.messages
# options(show.error.messages = FALSE)
# hess <- try(solve(as.matrix(result$hessian)))
# options(show.error.messages = op.sem)
# }
# if(!inherits(hess, "try-error")) hess <- sqrt(diag(hess))
# else print("WARNING: unable to compute the hessian")
}
value <- result$value
message <- paste(minimisation.function, "convergence code:", result$convergence)
if(cov.model == "linear")
result$par <- c(result$par[1],1,result$par[-1])
cov.pars <- as.vector(result$par[1:2])
if(cov.model == "power")
cov.pars[2] <- 2 * exp(cov.pars[2])/(1+exp(cov.pars[2]))
if(!fix.kappa){
if (fix.nugget)
kappa <- result$par[3]
else{
nugget <- result$par[3]
kappa <- result$par[4]
}
## kappa now > 0 for both nlm() and optim()
## if(minimisation.function == "nlm"){
if(.global.list$cov.model == "powered.exponential")
kappa <- 2*(exp(kappa))/(1+exp(kappa))
else kappa <- exp(kappa)
## }
}
else
if(!fix.nugget)
nugget <- result$par[3]
}
}
##
## Estimating implicity beta
##
##
## Preparing output
##
estimation <- list(nugget = nugget, cov.pars = cov.pars,
cov.model = cov.model, kappa = kappa, value = value,
trend = vario$trend, beta.ols = vario$beta.ols,
practicalRange = practicalRange(cov.model=cov.model,
phi = cov.pars[2], kappa = kappa),
max.dist = max.dist,
minimisation.function = minimisation.function)
# if(exists("hess")) estimation$hessian <- hess
estimation$weights <- weights
if(weights == "equal") estimation$method <- "OLS"
else estimation$method <- "WLS"
estimation$fix.nugget <- fix.nugget
estimation$fix.kappa <- fix.kappa
estimation$lambda <- vario$lambda
estimation$message <- message
estimation$call <- call.fc
oldClass(estimation) <- c("variomodel", "variofit")
return(estimation)
}
".loss.vario" <-
function (theta, g.l)
{
if(g.l$cov.model == "linear")
theta <- c(theta[1], 1, theta[-1])
##
## Imposing constraints for nlm
##
if(g.l$m.f == "nlm"){
## assign(".temp.theta", NULL, pos=1)
assign(".temp.theta", NULL, pos=.geoR.env)
if(!g.l$fix.kappa){
if(g.l$fix.nugget){
if(g.l$cov.model == "power")
theta.minimiser <- theta[1]
else
theta.minimiser <- theta[1:2]
Tkappa <- theta[3]
}
else{
if(g.l$cov.model == "power")
theta.minimiser <- theta[c(1:3)]
else
theta.minimiser <- theta[1:3]
Tkappa <- theta[4]
}
}
else theta.minimiser <- theta
penalty <- 10000 * sum(0 - pmin(theta.minimiser, 0))
theta <- pmax(theta.minimiser, 0)
if(!g.l$fix.kappa) theta <- c(theta.minimiser, Tkappa)
if (any(theta.minimiser < 0)){
##assign(".temp.theta", theta, pos=1)
assign(".temp.theta", theta, pos=.geoR.env)
}
else penalty <- 0
}
else penalty <- 0
##
## reading parameters
##
if(!g.l$fix.kappa){
if (g.l$fix.nugget){
tausq <- g.l$nugget
Tkappa <- theta[3]
}
else{
tausq <- theta[3]
Tkappa <- theta[4]
}
## kappa now > 0 for both nlm() and optim()
##if(g.l$m.f == "nlm"){
if(g.l$cov.model == "powered.exponential")
kappa <- 2*(exp(Tkappa))/(1+exp(Tkappa))
else kappa <- exp(Tkappa)
##}
##else kappa <- Tkappa
}
else{
kappa <- g.l$kappa
if (g.l$fix.nugget) tausq <- g.l$nugget
else tausq <- theta[3]
}
##
sigmasq <- theta[1]
phi <- theta[2]
if(g.l$cov.model == "power") phi <- 2 * exp(phi)/(1+exp(phi))
sill.total <- sigmasq + tausq
##
## Computing values for the theoretical variogram
##
if(any(g.l$cov.model == c("linear", "power")))
gammaU <- tausq + sigmasq * (g.l$u^phi)
else
gammaU <- sill.total - cov.spatial(g.l$u, cov.model = g.l$cov.model,
kappa = kappa, cov.pars = c(sigmasq, phi))
##
## Computing loss function
##
if(g.l$weight == "equal")
loss <- sum((g.l$v - gammaU)^2)
if (g.l$weights == "npairs")
loss <- sum(g.l$n * (g.l$v - gammaU)^2)
if (g.l$weights == "cressie")
loss <- sum((g.l$n/(gammaU^2)) * (g.l$v - gammaU)^2)
if(loss > (.Machine$double.xmax^0.5) | loss == Inf | loss == -Inf | is.nan(loss))
loss <- .Machine$double.xmax^0.5
return(loss + penalty)
}
"print.variofit" <-
function(x, digits = "default", ...)
{
if(digits == "default") digits <- max(3, getOption("digits") - 3)
if(x$fix.nugget){
est.pars <- c(sigmasq = x$cov.pars[1], phi=x$cov.pars[2])
if(x$fix.kappa == FALSE)
est.pars <- c(est.pars, kappa = x$kappa)
}
else{
est.pars <- c(tausq = x$nugget, sigmasq = x$cov.pars[1], phi=x$cov.pars[2])
if(x$fix.kappa == FALSE)
est.pars <- c(est.pars, kappa = x$kappa)
}
if(x$weights == "equal")
cat("variofit: model parameters estimated by OLS (ordinary least squares):\n")
else
cat("variofit: model parameters estimated by WLS (weighted least squares):\n")
cat(paste("covariance model is:", x$cov.model))
if(any(x$cov.model == c("matern", "powered.exponential",
"cauchy", "gencauchy", "gneiting.matern")))
if(x$fix.kappa) cat(paste(" with fixed kappa =", x$kappa))
if(x$cov.model == "matern" & x$fix.kappa & x$kappa == 0.5)
cat(" (exponential)")
cat("\n")
if(x$fix.nugget)
cat(paste("fixed value for tausq = ", x$nugget,"\n"))
cat("parameter estimates:\n")
print(round(est.pars, digits=digits))
cat(paste("Practical Range with cor=0.05 for asymptotic range:", format(x$practicalRange, ...)))
cat("\n")
if(x$weights == "equal") cat("\nvariofit: minimised sum of squares = ")
else cat("\nvariofit: minimised weighted sum of squares = ")
cat(round(x$value, digits=digits))
cat("\n")
return(invisible())
}
"summary.variofit" <-
function(object, ...)
{
## o problema disto eh no reconhecer a classe variofit...
# if(all(lapply(lapply(object, class), function(x) any(x ==
# "variofit")))){
# summa <- lapply(object, summary.variofit)
# }
# if (length(list(object, ...)) > 1){
# }
##
summ.lik <- list()
if(object$weights == "equal")
summ.lik$pmethod <- "OLS (ordinary least squares)"
else
summ.lik$pmethod <- "WLS (weighted least squares)"
summ.lik$cov.model <- object$cov.model
summ.lik$spatial.component <- c(sigmasq = object$cov.pars[1], phi=object$cov.pars[2])
summ.lik$spatial.component.extra <- c(kappa = object$kappa)
summ.lik$nugget.component <- c(tausq = object$nugget)
summ.lik$fix.nugget <- object$fix.nugget
summ.lik$fix.kappa <- object$fix.kappa
summ.lik$practicalRange <- object$practicalRange
summ.lik$sum.of.squares <- c(value = object$value)
if(object$fix.nugget){
summ.lik$estimated.pars <- c(sigmasq = object$cov.pars[1], phi=object$cov.pars[2])
if(object$fix.kappa == FALSE)
summ.lik$estimated.pars <- c(summ.lik$estimated.pars, kappa = object$kappa)
}
else{
summ.lik$estimated.pars <- c(tausq = object$nugget, sigmasq = object$cov.pars[1], phi=object$cov.pars[2])
if(object$fix.kappa == FALSE)
summ.lik$estimated.pars <- c(summ.lik$estimated.pars, kappa = object$kappa)
}
summ.lik$weights <- object$weights
summ.lik$call <- object$call
oldClass(summ.lik) <- "summary.variomodel"
return(summ.lik)
}
"print.summary.variofit" <-
function(x, digits = "default", ...)
{
if(length(class(x)) == 0 || all(class(x) != "summary.variomodel"))
stop("object is not of the class \"summary.variomodel\"")
if(digits == "default") digits <- max(3, getOption("digits") - 3)
cat("Summary of the parameter estimation\n")
cat("-----------------------------------\n")
cat(paste("Estimation method:", x$pmethod, "\n"))
cat("\n")
##
## Estimates of the model components
## Model: Y(x) = X\beta + S(x) + e
##
# cat("Parameters of the mean component (trend):")
# cat("\n")
# print(round(x$mean.component, digits=digits))
# cat("\n")
##
cat("Parameters of the spatial component:")
cat("\n")
cat(paste(" correlation function:", x$cov.model))
if(x$cov.model == "matern" & x$fix.kappa & x$spatial.component.extra == 0.5)
cat(" (exponential)")
if(any(x$cov.model == c("matern", "powered.exponential",
"cauchy", "gencauchy", "gneiting.matern"))){
if(x$fix.kappa)
cat(paste("\n (fixed) extra parameter kappa = ", round(x$spatial.component.extra, digits=digits)))
else
cat(paste("\n (estimated) extra parameter kappa = ", round(x$spatial.component.extra, digits=digits)))
}
cat(paste("\n (estimated) variance parameter sigmasq (partial sill) = ", round(x$spatial.component[1], digits=digits)))
cat(paste("\n (estimated) cor. fct. parameter phi (range parameter) = ", round(x$spatial.component[2], digits=digits)))
cat("\n")
##
cat("\n")
cat("Parameter of the error component:")
if(x$fix.nugget)
cat(paste("\n (fixed) nugget =", round(x$nugget.component, digits = digits)))
else
cat(paste("\n (estimated) nugget = ", round(x$nugget.component, digits=digits)))
cat("\n")
cat("\n")
cat("Practical Range with cor=0.05 for asymptotic range:",
format(x$practicalRange, ...))
cat("\n")
cat("\n")
names(x$sum.of.squares) <- NULL
if(x$weights == "equal") cat("Minimised sum of squares: ")
else cat("Minimised weighted sum of squares: ")
cat(round(x$sum.of.squares, digits=digits))
cat("\n")
cat("\n")
cat("Call:")
cat("\n")
print(x$call)
cat("\n")
invisible(x)
}
"variog.model.env" <-
function(geodata, coords = geodata$coords, obj.variog,
model.pars, nsim = 99, save.sim = FALSE, messages)
{
call.fc <- match.call()
obj.variog$v <- NULL
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
##
## reading input
##
if(any(class(model.pars) == "eyefit")){
if(length(model.pars) == 1L)
model.pars <- model.pars[[1]]
else
stop(paste("variog.model.env: more than one variograma model in the object",
deparse(substitute(model.pars)), "\n specify which i_th model in the list to be used using [[i]]"))
}
if(!is.null(model.pars$beta)) beta <- model.pars$beta
else beta <- 0
if(!is.null(model.pars$cov.model))
cov.model <- model.pars$cov.model
else cov.model <- "exponential"
if(!is.null(model.pars$kappa)) kappa <- model.pars$kappa
else kappa <- 0.5
#if(!is.null(model.pars$lambda)) lambda <- model.pars$lambda
#else lambda <- 0.5
if(!is.null(model.pars$nugget)) nugget <- model.pars$nugget
else nugget <- 0
cov.pars <- model.pars$cov.pars
if(!is.null(obj.variog$estimator.type))
estimator.type <- obj.variog$estimator.type
else estimator.type <- "classical"
if (obj.variog$output.type != "bin")
stop("envelops can be computed only for binned variogram")
##
## generating simulations from the model with parameters provided
##
if (messages.screen)
cat(paste("variog.env: generating", nsim, "simulations (with ",
obj.variog$n.data,
"points each) using the function grf\n"))
# simula <- grf(obj.variog$n.data, grid = as.matrix(coords),
# cov.model = cov.model, cov.pars = cov.pars,
# nugget = nugget, kappa = kappa, nsim = nsim,
# messages = FALSE, lambda = obj.variog$lambda)
simula <- grf(obj.variog$n.data, grid = as.matrix(coords),
cov.model = cov.model, cov.pars = cov.pars,
nugget = nugget, kappa = kappa, nsim = nsim,
messages = FALSE)
##
## add the mean
##
if(messages.screen)
cat("variog.env: adding the mean or trend\n")
x.mat <- unclass(trend.spatial(trend=obj.variog$trend, geodata = geodata))
if(ncol(x.mat) != length(beta))
stop("incompatible sizes of trend matrix and beta parameter vector. Check whether the trend specification are the same in the objects passed to the arguments \"obj.vario\" and \"model.pars\"")
simula$data <- as.vector(x.mat %*% beta) + simula$data
##
## computing empirical variograms for the simulations
##
if (messages.screen)
cat(paste("variog.env: computing the empirical variogram for the",
nsim, "simulations\n"))
nbins <- length(obj.variog$bins.lim) - 1
bin.f <- function(sim){
cbin <- vbin <- sdbin <- rep(0, nbins)
temp <- .C("binit",
as.integer(obj.variog$n.data),
as.double(as.vector(coords[,1])),
as.double(as.vector(coords[,2])),
as.double(as.vector(sim)),
as.integer(nbins),
as.double(as.vector(obj.variog$bins.lim)),
as.integer(estimator.type == "modulus"),
as.double(max(obj.variog$u)),
as.double(cbin),
vbin = as.double(vbin),
as.integer(FALSE),
as.double(sdbin),
PACKAGE = "geoR")$vbin
return(temp)
}
simula.bins <- apply(simula$data, 2, bin.f)
simula.bins <- simula.bins[obj.variog$ind.bin,]
# if(exists(".IND.geoR.variog.model.env", where=1))
if(exists(".IND.geoR.variog.model.env"))
return(simula.bins)
if(save.sim == FALSE) simula$data <- NULL
##
## computing envelops
##
if (messages.screen)
cat("variog.env: computing the envelops\n")
limits <- apply(simula.bins, 1, range)
res.env <- list(u = obj.variog$u, v.lower = limits[1, ],
v.upper = limits[2,])
if(save.sim)
res.env$simulated.data <- simula$data
res.env$call <- call.fc
oldClass(res.env) <- "variogram.envelope"
return(res.env)
}
"boot.variofit" <-
function(geodata, coords = geodata$coords, obj.variog,
model.pars, nsim = 99, trace = FALSE, messages)
{
call.fc <- match.call()
if(missing(messages))
messages.screen <- as.logical(ifelse(is.null(getOption("geoR.messages")), TRUE, getOption("geoR.messages")))
else messages.screen <- messages
##
if(messages.screen)
cat("Computing empirical variograms for simulations\n")
## assign(".IND.geoR.variog.model.env", TRUE, pos =1)
geoR.env <- new.env()
assign(".IND.geoR.variog.model.env", TRUE, pos=geoR.env)
environment(variog.model.env) <- geoR.env
vmat <- variog.model.env(geodata=geodata, coords=coords,
obj.variog=obj.variog, model.pars=model.pars,
nsim=nsim, messages = FALSE)
## rm(".IND.geoR.variog.model.env", pos=1)
##
if(messages.screen){
cat("Fitting models (variofit) for the simulated variograms\n")
cat("be patient - this can take a while to run\n")
}
geoR.count <- new.env()
assign(".geoR.count", 1, envir=geoR.count)
.vf <- function(v){
obj.variog$v <- v
pars <- summary(variofit(obj.variog, messages=FALSE))$estimated.pars
## pars <- summary(variofit(obj.variog, ini = model.pars$cov.pars,
## nugget = model.pars$nugget,
## messages=FALSE))$estimated.pars
if(trace){
cat(paste("simulation", get(".geoR.count", envir=geoR.count),
"out of", nsim, "\n"))
print(pars)
assign(".geoR.count", get(".geoR.count", envir=geoR.count)+1,
envir=geoR.count)
}
return(pars)
}
res <- as.data.frame(t(apply(vmat, 2, .vf)))
class(res) <- "boot.variofit"
return(res)
}
##"beta.variofit" <-
## function(geodata, coords = geodata$coords, data=geodata$data,
## obj.variofit)
## {
##
## }
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