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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
gcv.sreg<- function(out, lambda.grid = NA, cost = 1,
nstep.cv = 80, rmse = NA, offset = 0, trmin = NA, trmax = NA,
verbose = FALSE, tol = 1e-05,
give.warnings=TRUE) {
tauHat.pure.error <- out$tauHat.pure.error
pure.ss <- out$pure.ss
nt <- 2
np <- out$np
N <- out$N
out$cost <- cost
out$offset <- offset
# find good end points for lambda coarse grid.
if (is.na(trmin))
trmin <- 2.05
if (is.na(trmax))
trmax <- out$np * 0.95
if (is.na(lambda.grid[1])) {
l2 <- sreg.df.to.lambda(trmax, out$xM, out$weightsM)
l1 <- sreg.df.to.lambda(trmin, out$xM, out$weightsM)
lambda.grid <- exp(seq(log(l2), log(l1), , nstep.cv))
}
if (verbose) {
cat("endpoints of coarse lamdba grid", fill = TRUE)
cat(l1, l2, fill = TRUE)
}
# build up table of coarse grid serach results for lambda
# in the matrix gcv.grid
nl <- length(lambda.grid)
V <- V.model <- V.one <- trA <- MSE <- RSS.model <- rep(NA,
nl)
# loop through lambda's and compute various quantities related to
# lambda and the fitted spline.
for (k in 1:nl) {
temp <- sreg.fit(lambda.grid[k], out, verbose = verbose)
RSS.model[k] <- temp$rss
trA[k] <- temp$trace
V[k] <- temp$gcv
V.one[k] <- temp$gcv.one
V.model[k] <- temp$gcv.model
}
# adjustments to columns of gcv.grid
RSS <- RSS.model + pure.ss
tauHat <- sqrt(RSS/(N - trA))
gcv.grid <- cbind(lambda.grid, trA, V, V.one, V.model, tauHat)
dimnames(gcv.grid) <- list(NULL, c("lambda", "trA", "GCV",
"GCV.one", "GCV.model", "tauHat"))
gcv.grid<- as.data.frame( gcv.grid)
if (verbose) {
cat("Results of coarse grid search", fill = TRUE)
print(gcv.grid)
}
lambda.est <- matrix(NA, ncol = 5, nrow = 5,
dimnames = list(
c("GCV","GCV.model", "GCV.one", "RMSE", "pure error"),
c("lambda","trA", "GCV", "tauHat", "converge")))
# now do various refinements for different flavors of finding
# a good value for lambda the smoothing parameter
##### traditional leave-one-out
IMIN<- rep( NA, 5)
IMIN[1]<- which.min( gcv.grid$GCV )
IMIN[2]<- ifelse( is.na(tauHat.pure.error), NA,
which.min(gcv.grid$GCV.model) )
IMIN[3]<- which.min( gcv.grid$GCV.one)
if( is.na( rmse)){
IMIN[4] <- NA
}
else{
rangeShat<- range( gcv.grid$tauHat)
IUpcross<- max( (1:nl)[gcv.grid$tauHat< rmse] )
IMIN[4]<- ifelse( (rangeShat[1]<= rmse)&(rangeShat[2] >=rmse),
IUpcross, NA)
}
IMIN[5]<- ifelse( is.na(tauHat.pure.error), NA,
which.min(abs(gcv.grid$tauHat-tauHat.pure.error)) )
# NOTE IMIN indexes from smallest lambda to largest lambda in grid.
warningTable<- data.frame(
IMIN, IMIN == nl, IMIN==1,
gcv.grid$lambda[IMIN],
gcv.grid$trA[IMIN],
row.names = c("GCV","GCV.model", "GCV.one", "RMSE", "pure error") )
warning<- (warningTable[,2]|warningTable[,3])&
(!is.na(warningTable[,1]))
indRefine<- (!warningTable[,2]) & (!warningTable[,3]) &
(!is.na(warningTable[,1]))
warningTable<- cbind( warning, indRefine, warningTable )
names( warningTable)<- c("Warning","Refine","indexMIN", "leftEndpoint", "rightEndpoint",
"lambda","effdf")
if( verbose){
print(warningTable)
}
# fill in grid search estimates
for( k in 1:5){
if( !is.na(IMIN[k])){
lambda.est[k,1]<- gcv.grid$lambda[IMIN[k]]
}
}
# now optimze the search producing refined optima
#
# now step through the many different ways to find lambda
# This is the key to these choices:
# 1- the usual GCV proposed by Craven/Wahba
# 2- GCV where data fitting is collapsed to the mean for
# each location and each location is omitted
# 3- True leave-one-out even with replicated observations
# 4- Match estimate of tau to external value supplied (RMSE)
# 5- Match estimate of tau from the estimate based the
# pure error sum of squares obtained by the observations
# replicated at the same locations
#test<- sreg.fit(.1, out)
#print( test)
if(indRefine[1]){
starts <- lambda.grid[IMIN[1] + c(-1,0,1)]
outGs <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=sreg.fgcv, f.extra = out, tol = tol)
lambda.est[1,1]<- outGs$x
lambda.est[1,5]<- outGs$iter
}
if( indRefine[2]) {
starts <- lambda.grid[IMIN[2] + c(-1,0,1)]
outGs <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=sreg.fgcv.model, f.extra = out, tol = tol)
lambda.est[2,1]<- outGs$x
lambda.est[2,5]<- outGs$iter
}
if( indRefine[3]) {
starts <- lambda.grid[IMIN[3] + c(-1,0,1)]
outGs <- golden.section.search(ax=starts[1],bx=starts[2],cx=starts[3],
f=sreg.fgcv.one, f.extra = out, tol = tol)
lambda.est[3, 1] <-outGs$x
lambda.est[3,5]<- outGs$iter
}
if ( indRefine[4] ) {
guess<- gcv.grid$lambda[IMIN[4]]
lambda.rmse <- find.upcross(sreg.fs2hat, out,
upcross.level = rmse^2,
guess = guess, tol = tol * rmse^2)
lambda.est[4, 1] <- lambda.rmse
}
if ( indRefine[5] ) {
guess <- gcv.grid$lambda[IMIN[5]]
lambda.pure.error <- find.upcross(sreg.fs2hat, out,
upcross.level = tauHat.pure.error^2, guess = guess,
tol = tol * tauHat.pure.error^2)
lambda.est[5, 1] <- lambda.pure.error
}
if (verbose) {
cat("All forms of estimated lambdas so far", fill = TRUE)
print(lambda.est)
}
for (k in 1:5) {
lam <- lambda.est[k, 1]
if (!is.na(lam)) {
temp <- sreg.fit(lam, out)
lambda.est[k, 2] <- temp$trace
if ((k == 1) | (k > 3)) {
lambda.est[k, 3] <- temp$gcv
}
if (k == 2) {
lambda.est[k, 3] <- temp$gcv.model
}
if (k == 3) {
lambda.est[k, 3] <- temp$gcv.one
}
lambda.est[k, 4] <- temp$tauHat
}
}
if( give.warnings & any(warningTable$Warning)){
cat("Methods at endpoints of grid search:", fill=TRUE)
print(warningTable[warningTable$Warning,])
}
list(gcv.grid = gcv.grid, lambda.est = lambda.est,
warningTable=warningTable)
}
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