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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\
offGridWeights1D<-function(s, gridList, np=2,
mKrigObject=NULL,
Covariance=NULL, covArgs=NULL,
aRange=NULL, sigma2=NULL,
giveWarnings=TRUE,
debug=FALSE
){
#
# function assumes the grid is
# integer locations and 1:m by 1:n
# grid and off grid locations need to be transformed to that scale
#
# also assumes the grid extends two cells beyond any off
# e.g. s coordinates should be between
# 2 and m-3 and 2 and n-3
#
# If mKrigObject (result of fitting model) is given
# extract all the covariance information from it.
# For the Matern family besides aRange and sigma2 is the
# smoothness
if( !is.null( mKrigObject)){
sigma2<- mKrigObject$summary["sigma2"]
aRange<- mKrigObject$summary["aRange"]
Covariance<- mKrigObject$args$Covariance
if( is.null(Covariance)){
Covariance<- "Exponential"
}
covArgs<-mKrigObject$args
# some R arcania -- strip out all arguments used by say stationary.cov
# but not used by the Covariance function
# Do not want to call the covariance function with these extra args.
if( !is.null( covArgs) ){
argNames<- names( as.list( get(Covariance)))
argNames<- argNames[ -length(argNames)]
ind<- match( names(covArgs), argNames)
covArgs[is.na( ind)] <- NULL
}
}
m<- length( gridList$x)
dx<- gridList$x[2]- gridList$x[1]
M<- nrow( s)
# lower left corner of grid box containing the points
s0<- cbind(
trunc( (s[,1]- gridList$x[1] )/dx) + 1
)
# index of locations when 2D array is unrolled
s0Index<- as.integer( s0[,1])
# check for more than one obs in a grid box
tableLoc<- table( s0Index)
allSingle<- all( tableLoc ==1 )
theShift<- (0:(2*np-1)) - (np-1)
xshift<- theShift
nnX<- cbind( xshift)
nnXCoords<- cbind( xshift*dx)
#
# sX
sX<- s0[,1] + matrix( rep( xshift,M),
nrow=M, ncol=(2*np), byrow=TRUE)
if( any( (sX < 1)| (sX>m)) ) {
stop( "sX outside range for grid")
}
# indices of all nearest neighbors for unrolled vector.
# this is an M by (2*np)^2 matrix where indices go from 1 to m*n
# these work for the unrolled 2D array
#
sIndex<- sX
# differences between nn and the off grid locations
# for both coordinates
# convert from integer grid to actual units.
differenceX<- (sX-1)*dx + gridList$x[1] - s[,1]
dAll<- abs(differenceX)
# pairwise distance among nearest neighbors.
dNN<- rdist(nnXCoords, nnXCoords)
# cross covariances
Sigma21Star<- sigma2* do.call(Covariance,
c(list(d = dAll/aRange),
covArgs))
# covariance among nearest neighbors
Sigma11 <- sigma2* do.call(Covariance,
c(list(d = dNN/aRange),
covArgs))
Sigma11Inv <- solve( Sigma11)
# each row of B are the weights used to predict off grid point
B <- Sigma21Star%*%Sigma11Inv
# create spind sparse matrix
# note need to use unrolled indices to refer to grid points
ind<- cbind( rep(1:M, each= (2*np) ), c( t( sIndex)))
ra<- c( t( B))
da<- c( M, m )
spindBigB<- list(ind=ind, ra=ra, da=da )
# now convert to the more efficient spam format
BigB<- spind2spam( spindBigB)
#
# prediction variances
# use cholesky for more stable numerics
cholSigma11Inv<- chol(Sigma11Inv)
# create spind sparse matrix of sqrt variances
# or covariances to simulate prediction error.
w <- Sigma21Star%*%t(cholSigma11Inv)
predictionVariance <- sigma2 - rowSums(w^2)
# easiest case of just one obs in each grid box
# sigma2 - diag(Sigma21Star%*%Sigma11Inv%*%t(Sigma21Star) )
spindObjSE<- list(ind=cbind( 1:M, 1:M),
ra=sqrt(predictionVariance),
da= c( M,M)
)
BigSE<- spind2spam( spindObjSE)
if(allSingle){
duplicateIndex<-NA
}
if( !allSingle){
indDuplicates<- (tableLoc > 1)
if( giveWarnings){
cat("Found", sum(indDuplicates),
"grid box(es) containing more than 1 obs location",
fill=TRUE)
}
duplicateIndex<-names( tableLoc) [indDuplicates]
duplicateIndex<- as.numeric(duplicateIndex)
# duplicateIndex is the unrolled indices for all grid boxes with
# 2 or more observations
# following code is written assuming there are not many of these.
nBox<- length( duplicateIndex)
indDupSE<-NULL
raDupSE<- NULL
for( k in 1:nBox){
theBox<- duplicateIndex[k]
# the obs that are in this box
indBox<- which(s0Index == theBox)
nDup<- length( indBox)
dDup<- rdist( s[indBox,], s[indBox,])
sigmaMarginal<- sigma2* do.call(Covariance,
c(list(d = dDup/aRange),
covArgs))
A<- w[indBox,]
localSE2<- sigmaMarginal - A%*%t(A)
localSE<- t(chol( localSE2 ))
# localSE %*% rnorm(nDup) will generate correct corrected
# prediction errors for obs in this grid box ("theBox")
indTmp<- cbind(rep( indBox, nDup), rep( indBox, each=nDup) )
raTmp<- c(localSE)
indDupSE<- rbind( indDupSE,indTmp)
raDupSE<- c( raDupSE, raTmp)
}
#print( dim(indDupSE ))
#print( length(raDupSE))
BigSE[indDupSE]<- raDupSE
}
if( debug){
return(
list( B= BigB, SE= BigSE,
predictionVariance = predictionVariance,
Sigma11Inv = Sigma11Inv,
Sigma21Star= Sigma21Star,
s0Index = s0Index,
s0 = s0,
gridX = t( (sX-1)*dx + gridList$x[1]),
gridList = gridList,
duplicateIndex= duplicateIndex
)
)
}
else{
return(
list( B = BigB,
SE = BigSE,
predictionVariance = predictionVariance )
)
}
}
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