tests/test-KrigingNuggetSimulate.R

In rlibkriging: Kriging Models using the 'libKriging' Library

if(requireNamespace('DiceKriging', quietly = TRUE)) { 
library(testthat)
 Sys.setenv('OMP_THREAD_LIMIT'=2)

library(rlibkriging)

##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 <- Kriging(y = matrix(y_o, ncol = 1),
              X = matrix(X_o, ncol = 1),
              kernel = "gauss",
              noise = "nugget",
              regmodel = "constant",
              optim = "none",
              #normalize = TRUE,
              parameters = list(theta = matrix(0.1), nugget=nugget, sigma2=0.09))

library(DiceKriging)
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_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)
})

## Predict & simulate
X_n = unique(sort(c(X_o,seq(-1,2,,5))))

## ## 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_noise=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_noise=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(100, 123, X_n, with_noise=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 > 0.001))
}

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 > 0.001))
}

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 > 0.001))
}
}