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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
##END HEADER
suppressMessages(library(fields))
options( echo=FALSE)
test.for.zero.flag<- 1
#
#
# test of off diagonal weight matrix for obs
# Check against linear algebra
#
#cat("A very nasty case with off diagonal weights",fill=TRUE)
set.seed(123)
x<- matrix( runif( 30), 15,2)
y<- rnorm( 15)*.01 + x[,1]**2 + x[,2]**2
#weights<- rep( 1, 15)
weights<- runif(15)*10
# WBW
# double check that just diagonals work.
lambda.test<- .6
Krig( x,y,cov.function=Exp.cov,weights=weights)-> out
Krig( x,y,cov.function=Exp.cov,weights=weights, lambda=lambda.test)-> out2
Krig.coef( out, lambda=lambda.test)-> test
W<- diag( weights)
W2<- diag( sqrt(weights))
K<- Exp.cov(x,x)
M<- (lambda.test*solve(W) + K);T<- fields.mkpoly(x, 2)
temp.d<- c(solve( t(T) %*% solve( M)%*%T) %*% t(T)%*% solve( M) %*%y)
temp.c<- solve( M)%*% (y - T%*% temp.d)
#
# test for d coefficients
test.for.zero( test$d, out2$d, tag=" d coef diag W fixed lam")
test.for.zero( temp.d, out2$d, tag=" d coef diag W")
# test for c coefficents
test.for.zero( test$c, out2$c, tag="c coef diag W fixed lam" )
test.for.zero( temp.c, out2$c, tag="c coef diag W " )
# the full monty
temp.wght<- function(x, alpha=.1){
Exp.cov( x, aRange=alpha) }
Krig( x,y,
cov.function=Exp.cov,weights=weights, wght.function= temp.wght,
)-> out.new
W2<-out.new$W2
W<- out.new$W
test.for.zero( c( W2%*%W2), c( W), tag=" sqrt of W")
Krig( x,y, cov.function=Exp.cov,weights=weights, W= out.new$W)-> temp
test.for.zero( predict(temp, y= y), predict(out.new,y=y),
tag=" Test of passing W explicitly")
K<- Exp.cov(x,x); lambda.test<- .6;
M<- (lambda.test*solve(W) + K);T<- fields.mkpoly(x, 2)
temp.d<- c(solve( t(T) %*% solve( M)%*%T) %*% t(T)%*% solve( M) %*%y)
temp.c<- solve( M)%*% (y - T%*% temp.d)
#
Krig.coef( out.new,lambda=lambda.test )-> out2
test.for.zero( temp.d, out2$d, tag=" d coef full W")
# test for c coefficents
test.for.zero( temp.c, out2$c, tag="c coef full W" )
####
### testing the GCV function
lambda<- out.new$lambda
Krig.Amatrix( out.new, lambda=lambda)-> Alam
test.for.zero( Alam%*%y , predict(out.new), tag="A matrix")
N<- length( y)
test<- sum( diag( Alam))
# compare to
test2<- out.new$eff.df
test.for.zero( test,test2, tag=" check trace of A")
Krig.fgcv.one( lam=lambda, out.new)-> test
# compare to
test2<- (1/N)*sum(
(out.new$W2%*%(y - c(Alam%*% y) ))**2
) / (1- sum(diag( Alam))/N)**2
test.for.zero( test,test2,tol=.5e-7, tag="GCV one" )
cat( "all done testing off diag W case", fill=TRUE)
options( echo=TRUE)
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