R version 4.2.1 (2022-06-23) -- "Funny-Looking Kid"
Copyright (C) 2022 The R Foundation for Statistical Computing
Platform: x86_64-apple-darwin17.0 (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> #
> # 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))
> 
> # tests of predictSE
> # against direct linear algebra 
> 
> #options( echo=FALSE)
> 
> 
> 
> x0<- expand.grid( c(-8,-4,0,20,30), c(10,8,4,0))
> 
> 
> out<- Krig( ChicagoO3$x, ChicagoO3$y, cov.function = "Exp.cov", aRange=50)
> 
> 
> # direct calculation
> Krig.Amatrix( out, x=x0)-> A
> test.for.zero( A%*%ChicagoO3$y, predict( out, x0),tag="Amatrix vs. predict")
Testing:  Amatrix vs. predict
PASSED test at tolerance  1e-08
> 
> Sigma<- out$sigmahat*Exp.cov( ChicagoO3$x, ChicagoO3$x, aRange=50)
> S0<- out$sigmahat*c(Exp.cov( x0, x0, aRange=50))
> S1<- out$sigmahat*Exp.cov( out$x, x0, aRange=50)
> 
> #yhat= Ay
> #var( f0 - yhat)=    var( f0) - 2 cov( f0,yhat)+  cov( yhat)
> 
> look<- S0 - t(S1)%*% t(A) - A%*%S1 +  
+        A%*% ( Sigma + diag(out$tauHat.MLE**2/out$weightsM))%*% t(A)
> #
> #compare to 
> # diagonal elements
> 
> 
> test2<- predictSE( out, x= x0) 
> test.for.zero( sqrt(diag(  look)), test2,tag="Marginal predictSE")
Testing:  Marginal predictSE
PASSED test at tolerance  1e-08
> 
> out2<- Krig( ChicagoO3$x, ChicagoO3$y, cov.function = "Exp.cov", aRange=50,
+             lambda=out$lambda)
> 
> test2<- predictSE( out2, x= x0) 
> test.for.zero( sqrt(diag(  look)), test2,tag="Marginal predictSE fixed ")
Testing:  Marginal predictSE fixed 
PASSED test at tolerance  1e-08
> 
> test<- predictSE( out, x= x0, cov=TRUE)
> test.for.zero( look, test,tag="Full covariance predictSE")
Testing:  Full covariance predictSE
PASSED test at tolerance  1e-08
> 
> 
> # simulation based.
> 
> set.seed( 333)
> 
> sim.Krig( out, x0,M=4e3)-> test
>  # columns are the realizations rows are locations
> 
> var(t(test))-> look
> 
> predictSE( out, x=x0)-> test2
> mean( diag( look)/ test2**2)-> look2
> test.for.zero(look2, 1.0, tol=1.5e-2, tag="Marginal standard Cond. Sim.")
Testing:  Marginal standard Cond. Sim.
PASSED test at tolerance  0.015
> 
> predictSE( out, x=x0, cov=TRUE)-> test2
> 
> # multiply simulated values by inverse square root of covariance
> # to make them white
> 
> eigen( test2, symmetric=TRUE)-> hold
> hold$vectors%*% diag( 1/sqrt( hold$values))%*% t( hold$vectors)-> hold
> cor(t(test)%*% hold)-> hold2
> # off diagonal elements of correlations -- expected values are zero. 
> 
> abs(hold2[ col(hold2)> row( hold2)])-> hold3
> 
> test.for.zero(   mean(hold3), 0, relative=FALSE, tol=.02,
+           tag="Full covariance standard Cond. Sim.")
Testing:  Full covariance standard Cond. Sim.
PASSED test at tolerance  0.02
> 
> 
> # test of A matrix
> #
> # first create and check a gridded test case. 
> 
> 
> data( ozone2)
> as.image(ozone2$y[16,], x= ozone2$lon.lat, ny=24, nx=20, 
+           na.rm=TRUE)-> dtemp
> #
> # A useful disctrtized version of ozone2 data
>  
> x<- dtemp$xd
> y<- dtemp$z[ dtemp$ind]
> weights<- dtemp$weights[ dtemp$ind]
> 
> Krig( x, y, Covariance="Matern", 
+    aRange=1.0, smoothness=1.0, weights=weights) -> out
> 
> 
> 
>   set.seed(234)
>   ind0<- cbind( sample( 1:20, 5), sample( 1:24, 5))
> 
>   x0<- cbind( dtemp$x[ind0[,1]], dtemp$y[ind0[,2]]) 
> 
> # an  inline check plot(out$x, cex=2); points( x0, col="red", pch="+",cex=2)
> 
> # direct calculation as backup ( also checks weighted case)
> 
> Krig.Amatrix( out, x=x0)-> A
> test.for.zero( A%*%out$yM, predict( out, x0),tag="Amatrix vs. predict")
Testing:  Amatrix vs. predict
PASSED test at tolerance  1e-08
> 
> Sigma<- out$sigmahat*stationary.cov( 
+ out$xM, out$xM, aRange=1.0,smoothness=1.0, Covariance="Matern")
> 
> S0<- out$sigmahat*stationary.cov( 
+ x0, x0, aRange=1.0,smoothness=1.0, Covariance="Matern")
> 
> S1<- out$sigmahat*stationary.cov(
+ out$xM, x0, aRange=1.0,smoothness=1.0, Covariance="Matern")
> 
> 
> 
> #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)
> 
> test<- predictSE( out, x0, cov=TRUE)
> 
> test.for.zero( c( look), c( test), tag="Weighted case and exact for ozone2 full 
+ cov", tol=1e-8)
Testing:  Weighted case and exact for ozone2 full 
cov
PASSED test at tolerance  1e-08
> 
> 
> cat("all done testing predictSE.Krig ", fill=TRUE)
all done testing predictSE.Krig 
> options( echo=TRUE)
> 
> proc.time()
   user  system elapsed 
  2.991   0.107   3.124