precomputeUpdateData {KrigInv}

Useful precomputations to quickly update kriging mean and variance

Description

This function is used in combination with computeQuickKrigcov and computes an output list that serves as input in that function.

Usage

precomputeUpdateData(model, integration.points)

Arguments

model

A Kriging model of km class.

integration.points

p*d matrix of points for numerical integration in the X space.

Value

A list with components:

Kinv.c.olddata

Matrix equal to K^(-1)*c where K is the non conditional covariance matrix at the design points and c is the non conditional covariances between the design points and the integration points.

Kinv.F

Matrix equal to K^(-1)*F where F is a matrix with the values of the trend functions at the design points.

first.member

Matrix with a complicated expression.

Author(s)

Clement Chevalier (University of Neuchatel, Switzerland)

References

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2014), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set, Technometrics, vol. 56(4), pp 455-465

Chevalier C., Ginsbourger D. (2014), Corrected Kriging update formulae for batch-sequential data assimilation, in Pardo-Iguzquiza, E., et al. (Eds.) Mathematics of Planet Earth, pp 119-122

See Also

computeQuickKrigcov

Examples

#precomputeUpdateData

set.seed(9)
N <- 20 #number of observations
testfun <- branin

#a 20 points initial design
design <- data.frame( matrix(runif(2*N),ncol=2) )
response <- testfun(design)

#km object with matern3_2 covariance
#params estimated by ML from the observations
model <- km(formula=~., design = design, 
	response = response,covtype="matern3_2")

#the points where we want to compute prediction (if a point new.x is added to the doe)
n.grid <- 20 #you can run it with 100
x.grid <- y.grid <- seq(0,1,length=n.grid)
integration.points <- expand.grid(x.grid,y.grid)
integration.points <- as.matrix(integration.points)
precalc.data <- precomputeUpdateData(model=model,integration.points=integration.points)

#now we can compute quickly kriging covariances 
#between the integration.points and any other points
newdata <- matrix(c(0.6,0.6),ncol=2)
pred <- predict_nobias_km(object=model,newdata=newdata,type="UK",se.compute=TRUE)

kn <- computeQuickKrigcov(model=model,integration.points=integration.points,X.new=newdata,
                    precalc.data=precalc.data,F.newdata=pred$F.newdata,
                    c.newdata=pred$c)

z.grid <- matrix(kn, n.grid, n.grid)

#plots: contour of the covariances, DOE points and new point
#these covariances have been computed quickly with computeQuickKrigcov
image(x=x.grid,y=y.grid,z=z.grid,col=grey.colors(10))
contour(x=x.grid,y=y.grid,z=z.grid,15,add=TRUE)
points(design, col="black", pch=17, lwd=4,cex=2)
points(newdata, col="red", pch=17, lwd=4,cex=3)
title("Kriging covariances with the point (0.6,0.6), in red")