obliqueProfiles {profExtrema}

Oblique coordinate profiles starting from a kriging model

Description

The function obliqueProfiles computes the (oblique) profile extrema functions for the posterior mean of a Gaussian process and its confidence bounds

Usage

obliqueProfiles(object, allPsi, threshold, options_full = NULL,
  options_approx = NULL, uq_computations = FALSE, plot_level = 0,
  plot_options = NULL, CI_const = NULL, return_level = 1, ...)

Arguments

object

either a km model or a list containing partial results. If object is a km model then all computations are carried out. If object is a list, then the function carries out all computations to complete the list results.

allPsi

a list containing the matrices Psi (dim pxd) for which to compute the profile extrema

threshold

the threshold of interest

options_full

an optional list of options for getProfileExtrema, see getProfileExtrema for details.

options_approx

an optional list of options for approxProfileExtrema, see approxProfileExtrema for details.

uq_computations

boolean, if TRUE the uq computations for the profile mean are computed.

plot_level

an integer to select the plots to return (0=no plots, 1=basic plots, 2= all plots)

plot_options

an optional list of parameters for plots. See setPlotOptions for currently available options.

CI_const

an optional vector containing the constants for the CI. If not NULL, then profiles extrema for m_n(x) \pm CI_const[i]*s_n(x,x) are computed.

return_level

an integer to select the amount of details returned

...

additional parameters to be passed to obliqueProf_UQ.

Value

If return_level=1 a list containing

• profMean_full:the results of getProfileExtrema for the posterior mean

• profMean_approx:the results of approxProfileExtrema for the posterior mean

• res_UQ:the results of obliqueProf_UQ for the posterior mean

if return_level=2 the same list as above but also including

• abs_err:the vector of maximum absolute approximation errors for the profile inf /sup on posterior mean for the chosen approximation

• times: a list containing

  • full:computational time for the full computation of profile extrema

  • approx:computational time for the approximate computation of profile extrema

Author(s)

Dario Azzimonti

Examples

if (!requireNamespace("DiceKriging", quietly = TRUE)) {
stop("DiceKriging needed for this example to work. Please install it.",
     call. = FALSE)
}
# Compute a kriging model from 50 evaluations of the Branin function
# Define the function
g=function(x){
  return(-branin(x))
}
gp_des<-lhs::maximinLHS(20,2)
reals<-apply(gp_des,1,g)
kmModel<-km(design = gp_des,response = reals,covtype = "matern3_2")

threshold=-10

# Compute oblique profiles on the posterior mean
# (for theta=0 it is equal to coordinateProfiles)
options_full<-list(multistart=4,heavyReturn=TRUE,discretization=100)
options_approx<- list(multistart=4,heavyReturn=TRUE,initDesign=NULL,fullDesignSize=100)
theta=pi/4
allPsi = list(Psi1=matrix(c(cos(theta),sin(theta)),ncol=2),
Psi2=matrix(c(cos(theta+pi/2),sin(theta+pi/2)),ncol=2))

## Not run: 
profMeans<-obliqueProfiles(object = kmModel,allPsi = allPsi,threshold = threshold,
                           options_full = options_full,options_approx = options_approx,
                           uq_computations = FALSE,plot_level = 3,plot_options = NULL,
                           CI_const = NULL,return_level = 2)


# Approximate oblique profiles with UQ
plot_options<-list(save=FALSE, titleProf = "Coordinate profiles",
                   title2d = "Posterior mean",qq_fill=TRUE)
options_sims<-list(nsim=150)
obProfUQ<-obliqueProfiles(object=profMeans,threshold=threshold,allPsi = allPsi,
                           options_full=options_full, options_approx=options_approx,
                           uq_computations=TRUE, plot_level=3,plot_options=NULL,
                           CI_const=NULL,return_level=2,options_sims=options_sims)

## End(Not run)