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)
> 
> f <- function(x) {
+     1 - 1 / 2 * (sin(12 * x) / (1 + x) + 2 * cos(7 * x) * x^5 + 0.7)
+ }
> plot(f, xlim = c(-1, 2), ylim = c(0, 1))
> n <- 5
> X_o <- seq(from = 0, to = 1, length.out = n)
> nugget = 0.01
> set.seed(1234)
> y_o <- f(X_o) #+ rnorm(n, sd = sqrt(nugget))
> points(X_o, y_o)
> 
> lk <- NuggetKriging(y = matrix(y_o, ncol = 1),
+               X = matrix(X_o, ncol = 1),
+               kernel = "gauss",
+               regmodel = "constant",
+               optim = "none",
+               #normalize = TRUE,
+               parameters = list(theta = matrix(0.1), nugget=nugget, sigma2=0.09))
> 
> library(DiceKriging)

Attaching package: 'DiceKriging'

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

    leaveOneOutFun

> dk <- km(response = matrix(y_o, ncol = 1),
+               design = matrix(X_o, ncol = 1),
+               covtype = "gauss",
+               formula = ~1,
+               nugget = nugget,
+               nugget.estim=FALSE,
+               #optim = "none",
+               #normalize = TRUE,
+               coef.cov = lk$theta()[1,1],
+               coef.trend = lk$beta(),
+               coef.var = lk$sigma2())
> 
> test_that("DiceKriging/libKriging T matrix is the same", {
+     expect_equal(t(dk@T) , lk$T()*sqrt(lk$sigma2()+lk$nugget()))
+ })
Test passed 🌈
> 
> test_that("DiceKriging/libKriging covariance matrix is the same", {
+     expect_equal((lk$covMat(matrix(X_o,ncol=1),matrix(X_o,ncol=1)) + diag(nugget,n)), covMatrix(dk@covariance,dk@X)$C)
+ })
Test passed 🥳
> 
> ## Predict & simulate
> X_n = unique(sort(c(X_o,seq(-1,2,,51))))
> 
> ## ## Check that DiceKriging and libKriging matches (at factor alpha)
> ## 
> ## # DiceKriging / kmStruct.R / simulate.km :
> ## object = dk
> ## newdata = matrix(X_n, ncol = 1)
> ## Sigma21 <- covMat1Mat2(object@covariance, X1 = object@X, X2 = newdata, nugget.flag = FALSE)          ## size n x m
> ## Tinv.Sigma21 <- backsolve(t(object@T), Sigma21, upper.tri = FALSE)
> ## 
> ## # libKriging / NuggetKriging.cpp / simulate(...,with_nugget=TRUE) :
> ## alpha = lk$sigma2()/(lk$sigma2()+lk$nugget())
> ## R_on = lk$covMat(object@X, newdata) / (lk$sigma2()+lk$nugget())
> ## 
> ## test_that("DiceKriging/libKriging R_on matrix is the same", {
> ##     expect_equal(Sigma21, R_on * (lk$sigma2()+lk$nugget()))
> ## })
> ## 
> ## Rstar_on = backsolve(lk$T(), R_on, upper.tri = FALSE)
> ## 
> ## test_that("DiceKriging/libKriging Rstar_on matrix is the same", {
> ##     expect_equal(Rstar_on * sqrt(lk$sigma2()+lk$nugget()), Tinv.Sigma21)
> ## })
> ## 
> ## R_nn = lk$covMat(newdata, newdata) / (lk$sigma2()+lk$nugget())
> ## diag(R_nn) = 1
> ## 
> ## 
> ## # libK
> ## Sigma_nKo = R_nn - crossprod(Rstar_on, Rstar_on)
> ## chol(Sigma_nKo) # -> OK
> ## # DiceKriging
> ## Sigma_cond = covMatrix(object@covariance, newdata)[[1]] - t(Tinv.Sigma21) %*% Tinv.Sigma21
> ## chol(Sigma_cond) # -> OK
> ## 
> ## test_that("DiceKriging/libKriging Sigma_cond matrix is the same", {
> ##     expect_equal(Sigma_nKo *(lk$sigma2()+lk$nugget()), Sigma_cond)
> ## })
> ## 
> ## 
> ## # libKriging / NuggetKriging.cpp / simulate(...,with_nugget=FALSE) :
> ## R_on = lk$covMat(object@X, newdata) / (lk$sigma2()+lk$nugget())
> ## Rstar_on = backsolve(lk$T(), R_on, upper.tri = FALSE)
> ## R_nn = lk$covMat(newdata, newdata) / lk$sigma2()
> ## diag(R_nn) = 1
> ## Sigma_nKo = R_nn - crossprod(Rstar_on, Rstar_on)
> ## chol(Sigma_nKo) # -> ERROR
> 
> dp = predict(dk, newdata = data.frame(X = X_n), type="UK", checkNames=FALSE)
> lines(X_n,dp$mean,col='blue')
> polygon(c(X_n,rev(X_n)),c(dp$mean+2*dp$sd,rev(dp$mean-2*dp$sd)),col=rgb(0,0,1,0.2),border=NA)
> 
> lp = lk$predict(X_n) # libK predict
> lines(X_n,lp$mean,col='red')
> polygon(c(X_n,rev(X_n)),c(lp$mean+2*lp$stdev,rev(lp$mean-2*lp$stdev)),col=rgb(1,0,0,0.2),border=NA)
> 
> ls = lk$simulate(1000, 123, X_n, with_nugget=TRUE) # libK simulate
> for (i in 1:min(100,ncol(ls))) {
+     lines(X_n,ls[,i],col=rgb(1,0,0,.1),lwd=4)
+ }
> 
> ds = simulate(dk, nsim = ncol(ls), newdata = data.frame(X = X_n), type="UK", checkNames=FALSE, 
+ cond=TRUE, nugget.sim = 1e-10)
> for (i in 1:min(100,nrow(ds))) {
+     lines(X_n,ds[i,],col=rgb(0,0,1,.1),lwd=4)
+ }
> 
> # DiceKriging is not working for far X_n / X_o
> for (i in which(X_n >= 0 & X_n <= 1)) {
+     if (dp$sd[i] > 1e-3) # otherwise means that density is ~ dirac, so don't test
+     test_that(desc=paste0("DiceKriging simulate sample ( ~N(",mean(ds[,i]),",",sd(ds[,i]),") ) follows predictive distribution ( =N(",dp$mean[i],",",dp$sd[i],") ) at ",X_n[i]),
+         expect_true(ks.test(ds[,i], "pnorm", mean = dp$mean[i],sd = dp$sd[i])$p.value > 0.01))
+ }
Test passed 🥳
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> 
> for (i in 1:length(X_n)) {
+     if (lp$stdev[i,] > 1e-3) # otherwise means that density is ~ dirac, so don't test
+     test_that(desc=paste0("libKriging simulate sample ( ~N(",mean(ls[i,]),",",sd(ls[i,]),") ) follows predictive distribution ( =N(",lp$mean[i,],",",lp$stdev[i,],") ) at ",X_n[i]),
+         expect_true(ks.test(ls[i,], "pnorm", mean = lp$mean[i,],sd = lp$stdev[i,])$p.value > 0.01))
+ }
Test passed 🌈
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> 
> for (i in 1:length(X_n)) {
+     if (dp$sd[i] > 1e-3) # otherwise means that density is ~ dirac, so don't test
+     test_that(desc=paste0("DiceKriging/libKriging simulate samples ( ~N(",mean(ds[,i]),",",sd(ds[,i]),") / ~N(",mean(ls[i,]),",",sd(ls[i,]),") ) matching at ",X_n[i]),
+         expect_true(ks.test(ds[,i], ls[i,])$p.value > 0.01))
+ }
Test passed 😸
Test passed 🎉
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Test passed 🌈
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> 
> proc.time()
   user  system elapsed 
  12.34    1.71   14.18