R Under development (unstable) (2024-09-15 r87152 ucrt) -- "Unsuffered Consequences"
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> library(testthat)
>  Sys.setenv('OMP_THREAD_LIMIT'=2)
>  library(rlibkriging)

Attaching package: 'rlibkriging'

The following objects are masked from 'package:base':

    load, save

> 
> library(RobustGaSP)
#########
##
## Robust Gaussian Stochastic Process, RobustGaSP Package
## Copyright (C) 2016-2024 Mengyang Gu, Jesus Palomo and James O. Berger
#########

Attaching package: 'RobustGaSP'

The following object is masked from 'package:rlibkriging':

    simulate

The following object is masked from 'package:stats':

    simulate

> 
> kernel_type = function(kernel) {
+   if (kernel=="matern3_2") return("matern_3_2")
+   if (kernel=="matern5_2") return("matern_5_2")
+   stop(paste0("Cannot use ",kernel))
+ }
> kernel_type_num = function(kernel) {
+   if (kernel=="matern3_2") return(2)
+   if (kernel=="matern5_2") return(3)
+   stop(paste0("Cannot use ",kernel))
+ }
> 
> for (kernel in c("matern5_2","matern3_2")) {
+   context(paste0("Check Marginal Posterior for kernel ",kernel))
+   
+   f = function(x) 1-1/2*(sin(12*x)/(1+x)+2*cos(7*x)*x^5+0.7)
+   plot(f)
+   n <- 15
+   set.seed(123)
+   X <- as.matrix(runif(n))
+   y = f(X) + rnorm(n,0,0.1)
+   points(X,y)
+ 
+   k = RobustGaSP::rgasp(design=X,response=y,kernel_type=kernel_type(kernel), nugget.est=TRUE)
+ 
+   lmp = function(theta,nugget_est=FALSE) {
+     #cat("theta: ",theta,"\n")
+     param = c(log(1/theta),k@nugget)
+     if (!nugget_est) param = param[-length(param)]
+     #cat("log_marginal_lik\n")
+     lml = RobustGaSP::log_marginal_lik(param=param,nugget=k@nugget,nugget_est=nugget_est,
+       R0=k@R0,X=k@X,zero_mean=k@zero_mean,output=k@output,kernel_type=kernel_type_num(kernel),alpha=k@alpha)
+     #cat("  lml: ",lml,"\n")
+     #cat("log_approx_ref_prior\n")
+     larp = RobustGaSP::log_approx_ref_prior(param=param,nugget=k@nugget,nugget_est=nugget_est,
+       CL=k@CL,a=0.2,b=1/(length(y))^{1/dim(as.matrix(X))[2]}*(0.2+dim(as.matrix(X))[2]))
+     #cat("  larp: ",larp,"\n")
+     return(lml+larp)
+   }
+ 
+   plot(Vectorize(lmp),ylab="LMP",xlab="theta",xlim=c(0.01,2),ylim=c(-5,5))
+   abline(v=1/k@beta_hat)
+ 
+   lmp_deriv = function(theta, nugget_est=FALSE) {
+     #cat("theta: ",theta,"\n")
+     param = c(log(1/theta),k@nugget)
+     if (!nugget_est) param = param[-length(param)]
+     #cat("log_marginal_lik_deriv\n")
+     lml_d = RobustGaSP::log_marginal_lik_deriv(param=param,nugget=k@nugget,nugget_est=nugget_est,
+       R0=k@R0,X=k@X,zero_mean=k@zero_mean,output=k@output,kernel_type=kernel_type_num(kernel),alpha=k@alpha)
+     #cat("  lml_d: ",lml_d,"\n")
+     #cat("log_approx_ref_prior_deriv\n")
+     larp_d = RobustGaSP::log_approx_ref_prior_deriv(param=param,nugget=k@nugget,nugget_est=nugget_est,
+       CL=k@CL,a=0.2,b=1/(length(y))^{1/dim(as.matrix(X))[2]}*(0.2+dim(as.matrix(X))[2]))
+     #cat("  larp_d: ",larp_d,"\n")
+     return((lml_d + larp_d)* 1/theta * (-1/theta))
+   }
+ 
+   for (x in seq(0.01,2,,11)){
+     arrows(x,lmp(x),x+.1,lmp(x)+.1*lmp_deriv(x))
+   }
+ 
+   #library(rlibkriging)
+   r <- NuggetKriging(y, X, kernel, objective="LMP")#, 
+                      #optim="none", parameters=list(theta = matrix(1/k@beta_hat), nugget=k@nugget*k@sigma2_hat,sigma2=k@sigma2_hat))
+   ## Should be equal:
+   #lmp(1.0); lmp_deriv(1.0);
+   #logMargPostFun(r,1.0,return_grad = T)
+   #lmp(0.1); lmp_deriv(0.1);
+   #logMargPostFun(r,0.1,return_grad = T)
+   #ll2 = function(theta) logMargPostFun(r,theta)$logMargPost
+   # plot(Vectorize(ll2),col='red',add=T,xlim=c(0.01,2)) # FIXME fails with "error: chol(): decomposition failed"
+   alpha = r$sigma2()/(r$sigma2()+r$nugget()) #1/(1+k@nugget) #r$sigma2()/(r$nugget()+r$sigma2())
+   for (x in seq(0.01,2,,11)){
+     ll2x = logMargPostFun(r,c(x,alpha))$logMargPost
+     gll2x = logMargPostFun(r,c(x,alpha),return_grad = T)$logMargPostGrad[1]
+     arrows(x,ll2x,x+.1,ll2x+.1*gll2x,col='red')
+   }
+   
+ #lmp_deriv(c(k@beta_hat,k@nugget), TRUE)
+ #logMargPostFun(r,c(1/k@beta_hat,1/(1+k@nugget)),return_grad = T)
+ #logMargPostFun(r,c(r$theta(),r$sigma2()/(r$sigma2()+r$nugget())),return_grad = T)
+ 
+   precision <- 1e-4  # the following tests should work with it, since the computations are analytical
+   x=.5
+   test_that(desc="logMargPost is the same that RobustGaSP one", 
+             expect_equal(logMargPostFun(r,c(x,1/(1+k@nugget)))$logMargPost[1],lmp(x),tolerance = precision))
+   
+   test_that(desc="logMargPost Grad is the same that RobustGaSP one", 
+             expect_equal(logMargPostFun(r,c(x,1/(1+k@nugget)),return_grad = T)$logMargPostGrad[1],lmp_deriv(x),tolerance= precision))
+ }
The upper bounds of the range parameters are 22.0294 Inf 
The initial values of range parameters are 0.4405879 
Start of the optimization  1  : 
The number of iterations is  33 
 The value of the  marginal posterior  function is  -1.41711 
 Optimized range parameters are 0.04819661 
 Optimized nugget parameter is 1.035459 
 Convergence:  TRUE 
The initial values of range parameters are 0.008100239 
Start of the optimization  2  : 
The number of iterations is  30 
 The value of the  marginal posterior  function is  2.551403 
 Optimized range parameters are 0.1927243 
 Optimized nugget parameter is 0.1710318 
 Convergence:  TRUE 
Test passed 😀
Test passed 😀
The upper bounds of the range parameters are 1491.084 Inf 
The initial values of range parameters are 29.82168 
Start of the optimization  1  : 
The number of iterations is  18 
 The value of the  marginal posterior  function is  2.292713 
 Optimized range parameters are 0.2199567 
 Optimized nugget parameter is 0.1364529 
 Convergence:  TRUE 
The initial values of range parameters are 0.008100239 
Start of the optimization  2  : 
The number of iterations is  24 
 The value of the  marginal posterior  function is  2.292713 
 Optimized range parameters are 0.2199567 
 Optimized nugget parameter is 0.1364529 
 Convergence:  TRUE 
Test passed 😀
Test passed 😀
> 
> proc.time()
   user  system elapsed 
   1.21    0.18    1.39