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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
"simLocal.spatialProcess" <- function(mKrigObject,
gridList = NULL,
M = 1,
nx = 80,
ny = 80,
delta = NULL,
fast = FALSE,
NNSize = 4,
NNSizePredict = 4,
#truncate = NULL,
giveWarnings = FALSE,
verbose = FALSE,
...)
#
# NOTE throughout $x is first dimension of the grid in a gridList object but also
# $x in mKrig object is the _matrix_ of locations
#
{
nObs<- nrow( mKrigObject$x)
sDimension<- ncol(mKrigObject$x)
if ( sDimension !=2) {
stop("conditional simulation using fast, local algorithm
only implemented for 2 dimensions")
}
# great circle distance is not a stationary model for a regular lon/lat
# grid
if( !is.null(mKrigObject$args$Distance)){
if( (mKrigObject$args$Distance!="rdist") & fast){
cat( mKrigObject$args$Distance, fill=TRUE)
stop("can not use fast predict option with nonEuclidean distance.")
}
}
#
# this is needed because of the fast simulation algorithm
gridInfo<- augmentPredictionGrid(
gridList = gridList,
s = mKrigObject$x,
nx = nx,
ny = ny,
NNSize = NNSize,
)
# this will fill in gridList from nx, ny if not passed.
gridList<- gridInfo$gridList
predictionGrid<- gridInfo$predictionGrid
indexSubset<- gridInfo$indexSubset
#
# core covariance parameters from spatial model
#
tau <- mKrigObject$summary["tau"]
sigma2 <- mKrigObject$summary["sigma2"]
aRange<- mKrigObject$summary["aRange"]
Covariance <- mKrigObject$args$Covariance
# just use mKrigObject for covariance info
#
# set up various arrays for reuse during the simulation
#
####### NOTE there are two and possibly (if fast ==TRUE ) three SETUP steps to
# make conditional simulation loops efficients by reusing some objects.
#
# SETUP weights for fast, local off grid simulation
# grid is expanded to include nearest neighbors.
#
timeOffGridSetup <- system.time(
localObject <- offGridWeights2D( s=mKrigObject$x,
gridList=predictionGrid,
NNSize=NNSize,
mKrigObject=mKrigObject,
Covariance=Covariance,
covArgs=NULL,
aRange=aRange,
sigma2=sigma2,
giveWarnings=giveWarnings,
debug=FALSE,
verbose=verbose)
)[3]
#
# SETUP object when fast==TRUE for rapid prediction
#
timefastSetup<- NA
fastObject<-NULL
if(fast){
if( verbose){
cat("covariance function info", fill=TRUE)
print(mKrigObject$cov.function.name)
print(mKrigObject$args)
}
timefastSetup<- system.time(
fastObject<- mKrigFastPredictSetup(
mKrigObject,
gridList = gridList,
NNSize = NNSizePredict,
giveWarnings = giveWarnings,
verbose = verbose) )[3]
}
#
# SETUP object for simulating on a grid using circulant embedding (CE)
#
timeCESetup<- system.time(
CEObject<- circulantEmbeddingSetup(predictionGrid,
cov.function = mKrigObject$cov.function,
cov.args = mKrigObject$args,
#truncate=truncate,
delta = delta
)
)[3]
if( verbose){
cat("info on circulant embedding", fill=TRUE)
cat( "ratioRMSE", CEObject$ratioRMSE, fill=TRUE)
cat("dim of full circulant matrix ", CEObject$M,
fill = TRUE)
}
#
# find conditional mean field from initial fit
#.
if( verbose){
print(mKrigObject$args)
}
hHat <- predictSurface.mKrig(mKrigObject,
gridList = gridList,
fast = fast,
setupObject = fastObject,
#setupObject = NULL,
# NNSize = NNSizePredict,
...)$z
sdNugget<- tau* sqrt(1/mKrigObject$weights)
#
# setup output array to hold ensemble
#
out <- array(NA, c( length(indexSubset$x),
length(indexSubset$y),
M))
t1<-t2<- t3<- rep( NA, M)
#outData<- matrix( NA,nObs,M )
##########################################################################################
### begin the big loop
##########################################################################################
for (k in 1:M) {
if( k%%10 ==0 ){
cat(k, " ")
}
# simulate full field
t1[k]<- system.time(
hTrue<- as.matrix(sqrt(sigma2) * circulantEmbedding(CEObject))
)[3]
# NOTE: linear, fixed part of model (null space) does not need to be simulated
# because the estimator is unbiased for this part.
# the variability is still captured because the fixed part
# is still estimated as part of the predict step below
#
# unroll hTrue from grid and do sparse matrix multiply
#
localError<- rnorm(nObs)
# sparse matrix multiplication of weights by process on grid
# and add in independent error
t2[k]<- system.time(
hData <- localObject$B%*%c(hTrue) +
(localObject$SE)%*%localError
)[3]
ySynthetic <- hData + sdNugget*rnorm(nObs)
#outData[,k] <- ySynthetic
#
# predict at grid using these data
# and subtract from synthetic 'true' value
#
t3[k]<-system.time(
spatialPrediction <- predictSurface.mKrig(mKrigObject,
gridList = gridList,
ynew = ySynthetic,
fast=fast,
NNSize= NNSizePredict,
setupObject= fastObject,
giveWarnings = TRUE,
...)$z
)[3]
# # add the error to the actual estimate (conditional mean)
# # subset hTrue to the prediction grid
# # note for 1D $y is 1.
# NOTE subset hTrue because it may be generated on a larger grid to include nearest neighbors
# for local simulation.
tmpError<- (spatialPrediction - hTrue[indexSubset$x,indexSubset$y])
# hHat is of course the conditional mean ...
out[,, k] <- (hHat + tmpError)
}
cat(" ", fill=TRUE)
timingTable<- c( CESetup = timeCESetup,
SetupSim = timeOffGridSetup,
SetupPredict = timefastSetup,
medCE = median(t1),
medOffGridSim = median(t2),
medPredict = median(t3)
)
return(list(x = predictionGrid$x[indexSubset$x],
y = predictionGrid$y[indexSubset$y],
z = out,
hHat= hHat,
timing=timingTable,
M= CEObject$M,
timingFull = cbind( t1, t2,t3),
#outData=outData,
#outhData = outhData,
call = match.call(),
CEObject = CEObject
)
)
}
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