R Under development (unstable) (2024-08-21 r87038 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(rlibkriging, lib.loc="bindings/R/Rlibs")
> ##library(testthat)
> 
> context("Fit: 1D")
> 
> f = function(x) 1-1/2*(sin(12*x)/(1+x)+2*cos(7*x)*x^5+0.7)
> n <- 5
> set.seed(123)
> X <- as.matrix(runif(n))
> y = f(X)
> k = NULL
> r = NULL
> k = DiceKriging::km(design=X,response=y,covtype = "gauss",control = list(trace=F),nugget.estim=T,optim.method='BFGS',multistart = 20)
Warning message:
executing %dopar% sequentially: no parallel backend registered 
> r <- NuggetKriging(y, X, "gauss", optim = "BFGS20")
> l = as.list(r)
> 
> # save(list=ls(),file="fit-nugget-1d.Rdata")
> 
> 
> alpha_k = k@covariance@sd2/(k@covariance@sd2+k@covariance@nugget)
> alpha_r = as.list(r)$sigma2/(as.list(r)$sigma2+as.list(r)$nugget)
> test_that(desc="Nugget / Fit: 1D / fit of alpha by DiceKriging is same that libKriging",
+           expect_equal(alpha_k,alpha_r, tol= 1e-4))
Test passed 🥳
> 
> ll_a = Vectorize(function(a) logLikelihoodFun(r,c(k@covariance@range.val,a))$logLikelihood)
> plot(ll_a,xlim=c(0.001,1),lwd=3)
> llk_a = Vectorize(function(a) DiceKriging::logLikFun(model=k,c(k@covariance@range.val,a)))
> curve(llk_a, add=TRUE, col='blue')
> for (a in seq(0.01,0.99,,21)){
+   envx = new.env()
+   ll2x = logLikelihoodFun(r,c(k@covariance@range.val,a))$logLikelihood
+   gll2x = logLikelihoodFun(r,c(k@covariance@range.val,a),return_grad = T)$logLikelihoodGrad[,2]
+   arrows(a,ll2x,a+.1,ll2x+.1*gll2x,col='red')
+ }
> abline(v=alpha_k,col='blue')
> abline(v=alpha_r,col='red')
> 
> ll_t = Vectorize(function(x) logLikelihoodFun(r,c(x,alpha_k))$logLikelihood)
> plot(ll_t,xlim=c(0.001,1))
> #ll = Vectorize(function(x) logLikelihoodFun(r,c(x,alpha_r))$logLikelihood)
> #plot(ll_,xlim=c(0.001,1))
> 
> theta_ref = optimize(ll_t,interval=c(0.001,1),maximum=T)$maximum
> abline(v=theta_ref,col='black')
> abline(v=as.list(r)$theta,col='red')
> abline(v=k@covariance@range.val,col='blue')
> 
> test_that(desc="Nugget / Fit: 1D / fit of theta by DiceKriging is right",
+           expect_equal(theta_ref, k@covariance@range.val, tol= 1e-3))
Test passed 😀
> 
> test_that(desc="Nugget / Fit: 1D / fit of theta by libKriging is right",
+           expect_equal(array(theta_ref), array(as.list(r)$theta), tol= 0.01))
Test passed 😀
> 
> # see joint ll over theta & alpha
> # ll = function(X) {if (!is.matrix(X)) X = matrix(X,ncol=2);
> # apply(X,1,
> #      function(x) {
> #        y=-logLikelihoodFun(r,c(unlist(x)))$logLikelihood
> #        #print(y);
> #        y})}
> # x=seq(0.01,0.99,,51)
> # without reparam: 
> # contour(x,x,matrix(ll(as.matrix(expand.grid(x,x))),nrow=length(x)),nlevels = 50)
> # abline(v=(theta_ref),col='black')
> # abline(v=(as.list(r)$theta),col='red')
> # abline(v=(k@covariance@range.val),col='blue')
> # abline(h=(alpha_k),col='blue')
> # abline(h=(alpha_r),col='red')
> # with reparam:
> # contour(log(x),-log(1-x),matrix(ll(as.matrix(expand.grid(x,x))),nrow=length(x)),nlevels = 50)
> # abline(v=log(theta_ref),col='black')
> # abline(v=log(as.list(r)$theta),col='red')
> # abline(v=log(k@covariance@range.val),col='blue')
> # abline(h=-log(1-alpha_k),col='blue')
> # abline(h=-log(1-alpha_r),col='red')
> 
> #############################################################
> 
> context("Fit: 1D, nugget preset")
> 
> f = function(x) 1-1/2*(sin(12*x)/(1+x)+2*cos(7*x)*x^5+0.7)
> n <- 5
> set.seed(123)
> X <- as.matrix(runif(n))
> y = f(X)
> nu=0.1
> k = NULL
> r = NULL
> k = DiceKriging::km(design=X,response=y,covtype = "gauss",control = list(trace=F),nugget.estim=FALSE, nugget = nu,optim.method='BFGS',multistart = 20)
> #equivalent to NoiseKriging, not NuggetKriging: 
> rr <- NoiseKriging(y, rep(0.1,nrow(y)), X, "gauss", optim = "BFGS20")
> r <- NuggetKriging(y, X, "gauss", optim = "BFGS20", parameters=list(nugget=nu, is_nugget_estim=FALSE ))
> l = as.list(r)
> 
> # save(list=ls(),file="fit-nuggetpreset-1d.Rdata")
> 
> alpha_k = k@covariance@sd2/(k@covariance@sd2+k@covariance@nugget)
> alpha_r = as.list(r)$sigma2/(as.list(r)$sigma2+as.list(r)$nugget)
> test_that(desc="Nugget / Fit: 1D / fit of alpha by DiceKriging is same that libKriging",
+           expect_equal(alpha_k,alpha_r, tol= 1e-4))
Test passed 😀
> 
> theta=k@covariance@range.val #r$theta()
> ll_a = Vectorize(function(a) r$logLikelihoodFun(c(theta,a))$logLikelihood)
> plot(ll_a,xlim=c(0.1,1),lwd=3)
> llk_a = Vectorize(function(a) {s2 = nu*a/(1-a); DiceKriging::logLikFun(model=k,c(theta,s2))})
> curve(llk_a, add=TRUE, col='blue',xlim=c(0.1,0.999))
> for (a in seq(0.01,0.99,,21)){
+   ll2x = r$logLikelihoodFun(c(theta,a))$logLikelihood
+   gll2x = r$logLikelihoodFun(c(theta,a),return_grad = T)$logLikelihoodGrad[,2]  
+   arrows(a,ll2x,a+.1,ll2x+.1*gll2x,col='red', lwd=5)
+ 
+   envx = new.env()
+   
+   s2 = nu*a/(1-a)
+   ll2x_k = DiceKriging::logLikFun(c(theta,s2),k, envir=envx)
+   gll2x_k = DiceKriging::logLikGrad(c(theta,s2),k, envir=envx)[2] * nu/(1-a)^2 # chain rule
+   arrows(a,ll2x_k,a+.1,ll2x_k+.1*gll2x_k,col='blue',lwd=3)
+ 
+   ll2x = rr$logLikelihoodFun(c(theta,s2))$logLikelihood
+   gll2x = rr$logLikelihoodFun(c(theta,s2),return_grad = T)$logLikelihoodGrad[,2]* nu/(1-a)^2
+   arrows(a,ll2x,a+.1,ll2x+.1*gll2x,col='green')
+ }
> abline(v=alpha_k,col='blue')
> abline(v=alpha_r,col='red')
> 
> ll_t = Vectorize(function(x) r$logLikelihoodFun(c(x,alpha_k))$logLikelihood)
> plot(ll_t,xlim=c(0.001,1))
> llk_t = Vectorize(function(x) DiceKriging::logLikFun(model=k,c(x,alpha_k)))
> curve(llk_t, add=TRUE, col='blue')
> #ll = Vectorize(function(x) logLikelihoodFun(r,c(x,alpha_r))$logLikelihood)
> #plot(ll_,xlim=c(0.001,1))
> 
> theta_ref = optimize(ll_t,interval=c(0.001,1),maximum=T)$maximum
> abline(v=theta_ref,col='black')
> abline(v=as.list(r)$theta,col='red')
> abline(v=k@covariance@range.val,col='blue')
> 
> test_that(desc="Nugget / Fit: 1D / fit of theta by DiceKriging is right",
+           expect_equal(theta_ref, k@covariance@range.val, tol= 1e-3))
Test passed 😀
> 
> test_that(desc="Nugget / Fit: 1D / fit of theta by libKriging is right",
+           expect_equal(array(theta_ref), array(as.list(r)$theta), tol= 0.01))
Test passed 🥳
> 
> # see joint ll over theta & alpha
> # ll = function(X) {if (!is.matrix(X)) X = matrix(X,ncol=2);
> # apply(X,1,
> #      function(x) {
> #        y=-logLikelihoodFun(r,c(unlist(x)))$logLikelihood
> #        #print(y);
> #        y})}
> # x=seq(0.01,0.99,,51)
> # without reparam: 
> # contour(x,x,matrix(ll(as.matrix(expand.grid(x,x))),nrow=length(x)),nlevels = 50)
> # abline(v=(theta_ref),col='black')
> # abline(v=(as.list(r)$theta),col='red')
> # abline(v=(k@covariance@range.val),col='blue')
> # abline(h=(alpha_k),col='blue')
> # abline(h=(alpha_r),col='red')
> # with reparam:
> # contour(log(x),-log(1-x),matrix(ll(as.matrix(expand.grid(x,x))),nrow=length(x)),nlevels = 50)
> # abline(v=log(theta_ref),col='black')
> # abline(v=log(as.list(r)$theta),col='red')
> # abline(v=log(k@covariance@range.val),col='blue')
> # abline(h=-log(1-alpha_k),col='blue')
> # abline(h=-log(1-alpha_r),col='red')
> 
> #############################################################
> 
> context("Fit: 2D (Branin)")
> 
> f = function(X) apply(X,1,DiceKriging::branin)
> n <- 15
> set.seed(1234)
> X <- cbind(runif(n),runif(n))
> y = f(X)
> k = NULL
> r = NULL
> k = DiceKriging::km(design=X,response=y,covtype = "gauss",control = list(trace=F),nugget.estim=T,optim.method='BFGS',multistart = 1)
> #rlibkriging:::optim_log(4)
> #rlibkriging:::optim_use_variogram_bounds_heuristic(T)
> #rlibkriging:::optim_set_max_iteration(100)
> r <- NuggetKriging(y, X, "gauss", optim = "BFGS")
> #plot(Vectorize(function(a) r$logLikelihoodFun(c(r$theta(),a))$logLikelihood))
> #sectionview(function(ta)r$logLikelihoodFun(ta)$logLikelihood,center=c(r$theta(),r$sigma2()/(r$sigma2()+r$nugget())))
> l = as.list(r)
> 
> # save(list=ls(),file="fit-nugget-2d.Rdata")
> 
> alpha_k = k@covariance@sd2/(k@covariance@sd2+k@covariance@nugget)
> alpha_r = as.list(r)$sigma2/(as.list(r)$sigma2+as.list(r)$nugget)
> test_that(desc="Nugget / Fit: 2D (Branin) / fit of alpha by DiceKriging is same that libKriging",
+           expect_equal(alpha_k,alpha_r, tol= 1e-3))
Test passed 😸
> 
> ll = function(X) {if (!is.matrix(X)) X = matrix(X,ncol=2);
+                   # print(dim(X));
+                   apply(X,1,
+                     function(x) {
+                       y=-logLikelihoodFun(r,c(unlist(x),alpha_k))$logLikelihood
+                       #print(y);
+                       y})}
> #DiceView::contourview(ll,dim=2,Xlim=c(0.01,2))
> x=seq(0.01,2,,51)
> contour(x,x,matrix(ll(as.matrix(expand.grid(x,x))),nrow=length(x)),nlevels = 30)
> 
> theta_ref = optim(par=matrix(c(.2,.5),ncol=2),ll,lower=c(0.01,0.01),upper=c(2,2),method="L-BFGS-B")$par
> points(theta_ref,col='black')
> points(as.list(r)$theta[1],as.list(r)$theta[2],col='red')
> points(k@covariance@range.val[1],k@covariance@range.val[2],col='blue')
> 
> test_that(desc="Nugget / Fit: 2D (Branin) / fit of theta 2D is _quite_ the same that DiceKriging one",
+           expect_equal(ll(array(as.list(r)$theta)), ll(k@covariance@range.val), tol=1e-1))
Test passed 🌈
> 
> #lll = function(ta) r$logLikelihoodFun(ta)$logLikelihood
> #DiceView::sectionview(lll,vectorized=T,center=c(r$theta(),r$sigma2()/(r$sigma2()+r$nugget())))
> 
> #############################################################
> 
> context("Fit: 2D (Branin) multistart")
> 
> f = function(X) apply(X,1,DiceKriging::branin)
> n <- 15
> set.seed(1234)
> X <- cbind(runif(n),runif(n))
> y = f(X)
> k = NULL
> r = NULL
> 
> parinit = matrix(runif(10*ncol(X)),ncol=ncol(X))
> k <- tryCatch( # needed to catch warning due to %dopar% usage when using multistart
+     withCallingHandlers(
+       {
+         error_text <- "No error."
+         DiceKriging::km(design=X,response=y,covtype = "gauss", parinit=parinit,control = list(trace=F),nugget.estim=T,optim.method='BFGS',multistart = 20)
+       },
+       warning = function(e) {
+         error_text <<- trimws(paste0("WARNING: ", e))
+         invokeRestart("muffleWarning")
+       }
+     ),
+     error = function(e) {
+       return(list(value = NA, error_text = trimws(paste0("ERROR: ", e))))
+     },
+     finally = {
+     }
+   )
> r <- NuggetKriging(y, X, "gauss", optim = "BFGS20", parameters=list(theta=parinit))
> l = as.list(r)
> 
> # save(list=ls(),file="fit-nugget-multistart.Rdata")
> 
> alpha_k = k@covariance@sd2/(k@covariance@sd2+k@covariance@nugget)
> alpha_r = as.list(r)$sigma2/(as.list(r)$sigma2+as.list(r)$nugget)
> test_that(desc="Nugget / Fit: 2D (Branin) multistart / fit of alpha by DiceKriging is same that libKriging",
+           expect_equal(alpha_k,alpha_r, tol= 1e-4))
Test passed 😀
> 
> ll = function(X) {if (!is.matrix(X)) X = matrix(X,ncol=2);
+ # print(dim(X));
+ apply(X,1,
+       function(x) {
+         # print(dim(x))
+         #print(matrix(unlist(x),ncol=2));
+         y=-logLikelihoodFun(r,c(unlist(x),alpha_k))$logLikelihood
+         #print(y);
+         y})}
> #DiceView::contourview(ll,xlim=c(0.01,2),ylim=c(0.01,2))
> x=seq(0.01,2,,51)
> contour(x,x,matrix(ll(as.matrix(expand.grid(x,x))),nrow=length(x)),nlevels = 30)
> 
> theta_ref = optim(par=matrix(c(.2,.5),ncol=2),ll,lower=c(0.01,0.01),upper=c(2,2),method="L-BFGS-B")$par
> points(theta_ref,col='black')
> points(as.list(r)$theta[1],as.list(r)$theta[2],col='red')
> points(k@covariance@range.val[1],k@covariance@range.val[2],col='blue')
> 
> test_that(desc="Nugget / Fit: 2D (Branin) multistart / fit of theta 2D is _quite_ the same that DiceKriging one",
+           expect_equal(ll(array(as.list(r)$theta)), ll(k@covariance@range.val), tol= 1e-1))
Test passed 😸
> 
> 
> ################################################################################
> 
> context("Fit: 2D _not_ in [0,1]^2")
> 
> # "unnormed" version of Branin: [0,1]x[0,15] -> ...
> branin_15 <- function (x) {
+   x1 <- x[1] * 15 - 5
+   x2 <- x[2] #* 15
+   (x2 - 5/(4 * pi^2) * (x1^2) + 5/pi * x1 - 6)^2 + 10 * (1 - 1/(8 * pi)) * cos(x1) + 10
+ }
> 
> f = function(X) apply(X,1,branin_15)
> n <- 15
> set.seed(1234)
> X <- cbind(runif(n,0,1),runif(n,0,15))
> y = f(X)
> k = NULL
> r = NULL
> k = DiceKriging::km(design=X,response=y,covtype = "gauss",control = list(trace=F),nugget.estim=TRUE,optim="BFGS",multistart=20)#,parinit = c(0.5,5))
> r <- NuggetKriging(y, X, "gauss",, optim = "BFGS")#, parameters=list(theta=matrix(c(0.5,5),ncol=2)))
> l = as.list(r)
> 
> # save(list=ls(),file="fit-nugget-2d-not01.Rdata")
> 
> alpha_k = k@covariance@sd2/(k@covariance@sd2+k@covariance@nugget)
> alpha_r = as.list(r)$sigma2/(as.list(r)$sigma2+as.list(r)$nugget)
> test_that(desc="Nugget / Fit: 2D _not_ in [0,1]^2 / fit of alpha by DiceKriging is same that libKriging",
+           expect_equal(alpha_k,alpha_r, tol= 1e-4))
Test passed 😸
> 
> ll_r = function(X) {if (!is.matrix(X)) X = matrix(X,ncol=2);
+ # print(dim(X));
+ apply(X,1,
+       function(x) {
+         # print(dim(x))
+         #print(matrix(unlist(x),ncol=2));
+         -logLikelihoodFun(r,c(unlist(x),alpha_k))$logLikelihood
+         #print(y);
+         })}
> #DiceView::contourview(ll,xlim=c(0.01,2),ylim=c(0.01,2))
> x1=seq(0.001,2,,51)
> x2=seq(0.001,30,,51)
> contour(x1,x2,matrix(ll_r(as.matrix(expand.grid(x1,x2))),nrow=length(x1)),nlevels = 30,col='red')
> points(as.list(r)$theta[1],as.list(r)$theta[2],col='red')
> ll_r(t(as.list(r)$theta))
[1] 66.31798
> 
> ll_k = function(X) {if (!is.matrix(X)) X = matrix(X,ncol=2);
+ apply(X,1,function(x) {-DiceKriging::logLikFun(c(x,alpha_k),k)})}
> contour(x1,x2,matrix(ll_k(as.matrix(expand.grid(x1,x2))),nrow=length(x1)),nlevels = 30,add=T)
> points(k@covariance@range.val[1],k@covariance@range.val[2])
> ll_k(k@covariance@range.val)
[1] 66.42473
> 
> theta_ref = optim(par=matrix(c(.2,10),ncol=2),ll_r,lower=c(0.001,0.001),upper=c(2,30),method="L-BFGS-B")$par
> points(theta_ref,col='black')
> 
> test_that(desc="Nugget / Fit: 2D _not_ in [0,1]^2 / fit of theta 2D is _quite_ the same that DiceKriging one",
+           expect_equal(ll_r(array(as.list(r)$theta)), ll_k(k@covariance@range.val), tol=1e-1))
Test passed 🌈
> 
> proc.time()
   user  system elapsed 
   6.45    0.42    6.84