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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)
#options( echo=TRUE)
#
##### generate test data
#
data( ozone2)
# x is a two column matrix where each row is a location in lon/lat
# coordinates
x<- ozone2$lon.lat
# y is a vector of ozone measurements at day 16 a the locations.
y<- ozone2$y[16,]
#ind<- !is.na( y)
#x<- x[ind,]
#y<- y[ind]
x<-x[1:31,]
y<-y[1:31]
y[31]<-NA
################ test that optim results match the model evaluated
################ at the optimized parameters.
optim.args = list(method = "BFGS",
control = list(fnscale = -1, parscale = c(0.5, 0.5),
ndeps = c(0.05,0.05)))
MLEfit0 <- mKrigMLEJoint(x, y,
cov.params.start= list(lambda=.5, aRange=1.2),
cov.fun="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern", smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=1),
verbose=FALSE)
# check agreement with a fast return note cov.params.start and lambda.fixed
# are the switches to indicate this case
MLEfit0C <- mKrigMLEJoint(x, y,
cov.params.start = NULL,
cov.function = "stationary.cov",
cov.args = list(Covariance = "Matern",
lambda = MLEfit0$pars.MLE["lambda"],
smoothness = 1.0,
aRange = MLEfit0$pars.MLE["aRange"]),
na.rm = TRUE,
mKrig.args = list( m=1),
verbose = FALSE
)
test.for.zero( MLEfit0$summary["lnProfileLike.FULL"], MLEfit0C$summary["lnProfileLike.FULL"],
tag="Likelihood Values optim and the fast return")
test.for.zero( MLEfit0$summary["lnProfileLike.FULL"], MLEfit0$optimResults$value,
tag="Likelihood Values summary and optim")
obj0<- mKrig( x,y, cov.args = list(Covariance = "Matern",
smoothness = 1.0),
na.rm=TRUE, m=1,
lambda= MLEfit0$pars.MLE["lambda"],
aRange=MLEfit0$pars.MLE["aRange"])
test.for.zero( MLEfit0$summary["lnProfileLike.FULL"],
obj0$summary["lnProfileLike.FULL"],
tag="Likelihood Values summary and direct mKrig call")
test.for.zero( MLEfit0$summary["sigma2"],obj0$summary["sigma2"],
tag="... and sigma^2.MLE")
# test that grid seraching is correct
aRange.MLE<- MLEfit0$summary["aRange"]
par.grid<- list( aRange= c(.5, 1.0, 1.5)*aRange.MLE )
MLEfit1<- mKrigMLEGrid(x, y,
cov.fun = "stationary.cov",
cov.args = list(Covariance = "Matern",
smoothness = 1.0
),
par.grid = par.grid,
mKrig.args = list( m=1),
na.rm = TRUE,
verbose = FALSE,
cov.params.start = list( lambda = .2)
)
hold<- (MLEfit1$summary[1,"lnProfileLike.FULL"] < MLEfit1$summary[2,"lnProfileLike.FULL"]) &
(MLEfit1$summary[3,"lnProfileLike.FULL"] < MLEfit1$summary[2,"lnProfileLike.FULL"])
test.for.zero(as.numeric(hold), 1, relative=FALSE,
tag="consistency of Likelihood values")
##########################
### now evaluate on the "grid" of lambdas found by profiling
lambda.MLEs<- MLEfit1$summary[,"lambda"]
par.grid<- list( lambda = lambda.MLEs,
aRange = c(.5, 1.0, 1.5)*aRange.MLE )
MLEfit1B<- mKrigMLEGrid(x, y,
cov.function = "stationary.cov",
cov.args = list(Covariance = "Matern", smoothness = 1.0),
par.grid = par.grid,
mKrig.args = list( m=1),
na.rm = TRUE,
verbose = FALSE)
tempCol<- c( "lnProfileLike.FULL",
"lambda", "tau","sigma2")
test.for.zero( as.matrix(MLEfit1$summary[,tempCol]),
as.matrix(MLEfit1B$summary[,tempCol]),
tag="grid search with and w/o profile")
par.grid<- list( lambda = c(.999, 1.0, 1.001)*MLEfit0$summary["lambda"],
aRange = rep(MLEfit0$summary["aRange"] ,3 ) )
MLEfit2 <- mKrigMLEGrid(x, y,
cov.function = "stationary.cov",
cov.args = list(Covariance = "Matern",
smoothness = 1.0),
mKrig.args = list( m=1),
par.grid = par.grid,
verbose = FALSE)
hold<- (MLEfit2$summary[1,"lnProfileLike.FULL"] < MLEfit2$summary[2,"lnProfileLike.FULL"]) &
(MLEfit2$summary[3,"lnProfileLike.FULL"] < MLEfit2$summary[2,"lnProfileLike.FULL"])
test.for.zero(as.numeric(hold), 1, relative=FALSE, tag="crude test of maxmimum")
#MLEfit3<- MLESpatialProcess( x,y,
# cov.args = list(Covariance = "Matern",
# smoothness = 1.0),
# mKrig.args = list( m=1),
# cov.params.start = list( lambda =.2, aRange = NA)
# )
MLEfit3<- spatialProcess( x,y,
cov.args = list(Covariance = "Matern",
smoothness = 1.0),
mKrig.args = list( m=1),
cov.params.start = list( lambda =.2)
)
test.for.zero(MLEfit0$summary[1:2]/
(MLEfit3$summary[1:2]), 1, tol=1e-5,
tag="Testing MLE from spatialProcess ")
######### making sure spatialProcess uses parameter information correctly
obj<- spatialProcess( x, y, mKrig.args= list(m = 1),
lambda= MLEfit0$summary["lambda"],
aRange = MLEfit0$summary["aRange"]
)
obj1<- spatialProcess( x, y, mKrig.args= list(m = 1),
)
test.for.zero(MLEfit0$summary[1],
obj$summary["lnProfileLike.FULL"],
tag="spatialProcess finding MLE " )
test.for.zero(MLEfit0$summary[1],
obj1$summary["lnProfileLike.FULL"], tol=1e-5,
tag="spatialProcess given MLE "
)
# testing Krig function
#out1<- Krig( x,y, cov.fun="stationary.cov",
# cov.args = list(Covariance = "Matern",
# smoothness=1.0, aRange=.9),
# na.rm=TRUE,
# m=2)
#generate observation locations
set.seed( 22)
n=100
x = matrix(runif(2*n), nrow=n)
#generate observations at the locations
trueARange = .1
trueLambda = .1
distanceMatrix<- rdist(x,x)
Sigma<- Matern( distanceMatrix/trueARange, smoothness=1.0 )
U = chol(Sigma)
M<- 2e3 # lots of replicated fields.
set.seed( 332)
y = t(U)%*%matrix( rnorm(n*M), n,M) +
sqrt(trueLambda)*matrix( rnorm(n*M), n,M)
out<- mKrig( x,y, lambda=trueLambda, aRange=trueARange,
cov.function ="stationary.cov",cov.args = list(Covariance = "Matern",
smoothness=1.0)
)
optim.args = list(method = "BFGS",
control = list(fnscale = -1,
ndeps = c(0.09,0.09)))
MLEfitA <- mKrigMLEJoint(x, y,
cov.params.start= list(aRange=.2, lambda=.01),
cov.function="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
reltol = 1e-6,
mKrig.args = list( m=0),
verbose=FALSE)
cat("Testing mKrigMLEJoint against true values",
fill=TRUE)
test.for.zero( MLEfitA$summary["lambda"],.1, tol=.006)
test.for.zero( MLEfitA$summary["aRange"],.1, tol=.02)
test.for.zero( MLEfitA$summary["sigma2"], 1.0, tol=.02)
### now test REML fitting
MLEfitB <- mKrigMLEJoint(x, y,
cov.params.start= list(aRange=.12, lambda=.5),
cov.function="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=0),
REML=TRUE,
verbose=FALSE)
cat("Testing mKrigMLEJoint with REML against true values",
fill=TRUE)
test.for.zero( MLEfitB$summary["lambda"],.1, tol=.007)
test.for.zero( MLEfitB$summary["aRange"],.1, tol=.01)
test.for.zero( MLEfitB$summary["sigma2"], 1.0, tol=.01)
cat("Testing mKrigMLEJoint with REML FALSE against true values",
fill=TRUE)
MLEfitC <- mKrigMLEJoint(x, y,
cov.params.start= list(aRange=.12, lambda=.5),
cov.function ="stationary.cov",
optim.args=optim.args,
cov.args = list(Covariance = "Matern",
smoothness=1.0),
na.rm=TRUE,
mKrig.args = list( m=2),
REML=FALSE,
verbose=FALSE
)
test.for.zero( MLEfitC$summary["lambda"], .1, tol=.02)
test.for.zero( MLEfitC$summary[ "aRange"], .1, tol=.02)
test.for.zero( MLEfitC$summary["sigma2"], 1.0, tol=.01)
cat("all done with mKrigMLEGrid tests", fill=TRUE)
options( echo=TRUE)
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