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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))
#
#
# test of fixed lambda case
# Check against linear algebra
#
options( echo=FALSE)
test.for.zero.flag<-1
#cat("A very nasty case with knots and weights",fill=TRUE)
set.seed(123)
x<- matrix( runif( 30), 15,2)
Z<- matrix( rnorm(30), 15,2)
y<- rnorm( 15)*.01 + 5*(x[,1]**3 + (x[,2]-.5)**2) + (Z[,1] +Z[,2])*.001
#weights<- runif(15)*10
# first without knots compare default to fixed
out.new<- Krig( x,y,Z=Z, cov.function=Exp.cov, give.warnings=FALSE)-> out.new
out.new2<- Krig( x,y,Z=Z, cov.function=Exp.cov,
lambda=1)
##########
## compute test using linear algebra
K<- Exp.cov( x,x)
lambda<-1
M<- (lambda* diag(nrow( x)) + K)
T<- cbind( rep(1,15), x, Z)
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( out.new2$d, temp.d, tag=" d coef")
# test for c coefficents
test.for.zero( out.new2$c, temp.c, tag="c coef" )
####### testing predict function
hold2<- predict( out.new2, x=x, Z=Z, just.fixed=TRUE)
hold3<- predict( out.new2, x=x, Z=Z, drop.Z=TRUE)
hold4<- predict( out.new2, x=x, Z=Z, drop.Z=TRUE, just.fixed=TRUE)
hold<-T%*%temp.d
test.for.zero( hold, hold2, tag="predict for null fixed" )
hold<-T[,1:3]%*%temp.d[1:3] + K %*% temp.c
test.for.zero( hold, hold3, tag="predict for null spatial" )
hold<-T[,1:3]%*%temp.d[1:3]
test.for.zero( hold, hold4, tag="predict for null drift" )
######tests where coefficients are recomputed from object
hold2<- predict( out.new,y=y, lambda=1.0, x=x, Z=Z, just.fixed=TRUE)
hold3<- predict( out.new,y=y, lambda=1.0, x=x, Z=Z, drop.Z=TRUE)
hold4<- predict( out.new, y=y, lambda=1.0, x=x, Z=Z,
drop.Z=TRUE, just.fixed=TRUE)
hold<-T%*%temp.d
test.for.zero( hold, hold2, tag="predict for null fixed" )
hold<-T[,1:3]%*%temp.d[1:3] + K %*% temp.c
test.for.zero( hold, hold3, tag="predict for null spatial" )
hold<-T[,1:3]%*%temp.d[1:3]
test.for.zero( hold, hold4, tag="predict for null drift " )
#
####### tests using predict.se
x<- ChicagoO3$x
y<- ChicagoO3$y
Zcov<- x[,1]**3 + x[,2]**3
tps.fit<-Tps( x,y, scale.type="unscaled", Z= Zcov)
# here is lazy way to get a grid.list
gridList<- fields.x.to.grid( x, nx=20,ny=20)
xg<- make.surface.grid(gridList)
Zcov.grid<- xg[,1]**3 + xg[,2]**3
########### tests on just predict have been commented out to
########### indicate that they are redundant given
########### previous tests however, they could be useful for
########### future debugging ...
# full surface with covariate
# curv.mean1 <- predictSurface(tps.fit, gridlist, extrap = TRUE,
## Z =Zcov.grid, drop.Z = FALSE)$z
# just the spline surface
# curv.mean2 <- predictSurface(tps.fit, gridlist,
# extrap = TRUE,drop.Z=TRUE)$z
# explicitly here is the difference surface of curv.mean1 and curv.mean2
# curv.mean0<- as.surface( gridlist, Zcov.grid* tps.fit$d[4])$z
# test.for.zero( curv.mean1- curv.mean2, curv.mean0)
## new tests
predictSurfaceSE( tps.fit, gridList, extrap=TRUE,
drop.Z=TRUE)$z-> curv.var1
predictSE( tps.fit, xg, drop.Z=TRUE)-> curv.var2
test.for.zero( curv.var1, curv.var2)
# SE with covariates included
predictSE( tps.fit, xg, Z=Zcov.grid, drop.Z=FALSE)**2-> curv.var1
# as.surface( gridlist, curv.var1)$z-> curv.var1
# SE for just the spline part
predictSE( tps.fit, xg, drop.Z=TRUE)**2-> curv.var2
# as.surface( gridlist, curv.var2)$z-> curv.var2
# SE for just the fixed part
predictSE( tps.fit, xg,Z=Zcov.grid, drop.Z=FALSE,
just.fixed=TRUE )**2-> curv.var3
# as.surface( gridlist, curv.var3)$z-> curv.var3
# calculating from more basic functions
## these tests assume that Krig.Amatrix is working correctly!
out<- tps.fit
A<- Krig.Amatrix( tps.fit,x= xg, drop.Z=TRUE)
Sigma<- out$sigmahat*Rad.cov( out$x, out$x, p=2)
S0<- out$sigmahat*Rad.cov(xg, xg, p=2)
S1<- out$sigmahat*Rad.cov(out$x, xg, p=2)
#yhat= Ay
#var( f0 - yhat)= var( f0) - 2 cov( f0,yhat)+ cov( yhat)
look<- S0 - t(S1)%*% t(A) - A%*%S1 +
A%*% ( Sigma + diag(out$tauHat.MLE**2/out$weightsM))%*% t(A)
look<- diag( look)
test.for.zero(curv.var2 ,look,tag="SE w/o covariate")
A<- Krig.Amatrix( tps.fit,x= xg, drop.Z=FALSE,Z=Zcov.grid)
# see tps.fit$args for value of p
Sigma<- out$sigmahat*Rad.cov( out$x, out$x, p=2)
S0<- out$sigmahat*Rad.cov(xg, xg, p=2)
S1<- out$sigmahat*Rad.cov(out$x, xg, p=2)
#yhat= Ay
#var( f0 - yhat)= var( f0) - 2 cov( f0,yhat)+ cov( yhat)
look<- S0 - t(S1)%*% t(A) - A%*%S1 +
A%*% ( Sigma + diag(out$tauHat.MLE**2/out$weightsM))%*% t(A)
look<- diag( look)
test.for.zero(curv.var1 ,look,tag="SE with covariate")
A<- Krig.Amatrix( tps.fit,x= xg, drop.Z=FALSE,Z=Zcov.grid, just.fixed=TRUE)
# see tps.fit$args for value of p
Sigma<- out$sigmahat*Rad.cov( out$x, out$x, p=2)
S0<- out$sigmahat*Rad.cov(xg, xg, p=2)
S1<- out$sigmahat*Rad.cov(out$x, xg, p=2)
#yhat= Ay
#var( f0 - yhat)= var( f0) - 2 cov( f0,yhat)+ cov( yhat)
look<- S0 - t(S1)%*% t(A) - A%*%S1 +
A%*% ( Sigma + diag(out$tauHat.MLE**2/out$weightsM))%*% t(A)
look<- diag( look)
test.for.zero(curv.var3 ,look, tag="SE for fixed part")
cat("All done with Z tests and Krig/Tps including predict and predictSE !",
fill=TRUE)
options( echo=TRUE)
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