print_robinv_uncertainty_2d: Excursion probability and maximum kriging mean plot in 2d

In IRSN/RobustInv: "Robust inversion of expensive black-box functions"

Description

Computes and can show two plots for functions with two controlled parameters and one or several nuisance parameters. One plot is the maximum of the kriging mean (taken w.r.t. the nuisance parameters) computed on a grid of controlled parameter values. The second plot is the excursion probability, pn, which is computed using conditional simulations.

Usage

print_robinv_uncertainty_2d(model, T, lower, upper, opt.index, inv.index,
  control = NULL, onlycompute = FALSE, cex.contourlab = 0.6,
  cex.main = 1, cex.axis = 1, cex.lab = 1, cex.points = 1,
  pch.points = 17, color.up = "red", color.down = "blue",
  maxmkplot = TRUE, xlab1 = NULL, ylab1 = NULL, main1 = NULL,
  pnplot = TRUE, xlab2 = NULL, ylab2 = NULL, main2 = NULL,
  newpar = TRUE)

Arguments

model	The current kriging model. km object.
T	Target threshold.
lower	Array of size d. Lower bound of the input domain.
upper	Array of size d. Upper bound of the input domain.
opt.index	Array with integers corresponding to the indices of the nuisance parameters.
inv.index	Array with integers corresponding to the indices of the controlled parameters.
control	A list with fields that will control how the different quantities involved are computed. control$resolution1 and control$resolution2 are the image resolution of the maximum kriging mean and excursion probability plots. The fields n.optpoints1 (resp. n.optpoints2) control the number of points (in the space of the nuisance parameters) taken to compute the maximum of the kriging mean (resp. to do conditional simulations). For the computation of the excursion probability, the fields n.optpoints2.candidates, choose_optpoints, nsimu are used in a similar way than in the integration_design_robinv function. See help on the integcontrol argument in that function.
onlycompute	Boolean. When FALSE, no plot is performed, but the maximum of the kriging mean (resp. the excursion probability pn) is still computed if maxmkplot=TRUE (resp. pnplot = TRUE).
cex.contourlab	Size of the contour labels for the different plots involved in this function.
cex.main	Title size for the different plots involved in this function.
cex.axis	Axis label size for the different plots involved in this function.
cex.lab	Label size for the different plots involved in this function.
cex.points	Point size for the maximum kriging mean plot. Useless if maxmkplot=FALSE.
pch.points	Point pch for the maximum kriging mean plot. Useless if maxmkplot=FALSE.
color.up	Color of the points where there is threshold exceedance. Useless if maxmkplot=FALSE.
color.down	Color of the points where there is no threshold exceedance. Useless if maxmkplot=FALSE.
maxmkplot	Boolean. When TRUE, the maximum of the kriging mean (taken w.r.t. the nuisance parameters) is computed. It is also ploted if onlycompute=FALSE.
xlab1	x axis label for the maximum of the kriging mean plot.
ylab1	y axis label for the maximum of the kriging mean plot.
main1	Title of the maximum of the kriging mean plot.
pnplot	Boolean. When TRUE, the excursion probability function, pn, is computed. It is also ploted if onlycompute=FALSE.
xlab2	x axis label for the excursion probability plot.
ylab2	y axis label for the excursion probability plot.
main2	Title of the excursion probability plot.
newpar	Boolean. When TRUE, the par() function is called. Usefull only if the two plots available in this function are both performed.

Value

A list containing the important computed quantities: (i) all.points1: the coordinates of the points (in the space of the controlled parameters) used for the maximum kriging mean plot, (ii) maxmk: Square matrix of size control$resolution1 containing the maximum of the kriging mean taken w.r.t. the nuisance parameters, (iii) all.points2 : the coordinates of the points (in the space of the controlled parameters) used for the excursion probability plot, (iv) pn: Square matrix of size control$resolution2 containing the excursion probability of the considered points (all.points), (v) uncertainty: scalar equal to mean(pn*(1-pn)) giving a measure of the current global uncertainty on the excursion set, (vi) colors.transluded: the colors used to plot the points on the maximum of kriging mean plot.

Author(s)

Clement Chevalier [e-mail]

Examples

library(KrigInv)
myfun <- function(x) return(-1 * branin_robinv(x))
d <- 3

set.seed(8)

n0 <- 30
T <- -10
opt.index <- c(3)
inv.index <- c(1,2)
lower <- rep(0,times=d)
upper <- rep(1,times=d)

design <- matrix(runif(d*n0),nrow=n0)
response <- myfun(design)
model <- km(formula = ~1,design = design,response = response,covtype = "matern3_2")

control <- list(resolution1 = 40, resolution2 = 20)
## Not run: 
print_robinv_uncertainty_2d(model=model,T=T,lower=lower,upper=upper,
                            opt.index = opt.index,inv.index = inv.index,
                            control = control)

## End(Not run)
######################################
# More complicated example with scaling
library(KrigInv)
myfun <- function(x){ return(-1*branin_robinv(x) - 50*sin(min(100,1/x[3]))  ) }
d <- 3

set.seed(8)

n0 <- 100
T <- 40
opt.index <- c(3)
inv.index <- c(1,2)
lower <- rep(0,times=d)
upper <- rep(1,times=d)

design <- matrix(runif(d*n0),nrow=n0)
response <- apply(X = design,FUN = myfun,MARGIN = 1) 
knots.number <- c(0,0,3)
knots <- generate_knots(knots.number = knots.number , d = d)

model <- km(formula = ~1,design = design,response = response,covtype = "matern3_2",scaling = TRUE,knots=knots)

control <- list(resolution1 = 40, resolution2 = 20 , unscale.opt.simulation.points = TRUE)
## Not run: 
print_robinv_uncertainty_2d(model=model,T=T,lower=lower,upper=upper,
                            opt.index = opt.index,inv.index = inv.index,
                            control = control)

## End(Not run)

IRSN/RobustInv documentation built on Nov. 20, 2019, 10:46 p.m.