KrigInv (version 1.3.1)

precomputeUpdateData: Useful data 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.

References

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2011), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set ,http://hal.archives-ouvertes.fr/hal-00641108/

Chevalier C., Ginsbourger D. (2012), Corrected Kriging update formulae for batch-sequential data assimilation ,http://arxiv.org/pdf/1203.6452.pdf

See Also

computeQuickKrigcov, predict_nobias_km, predict_update_km

Examples

# NOT RUN {
#precomputeUpdateData

set.seed(8)
N <- 9 #number of observations
testfun <- branin

#a 9 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)
newdata <- expand.grid(x.grid,y.grid)
precalc.data <- precomputeUpdateData(model=model,integration.points=newdata)

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

kn <- computeQuickKrigcov(model=model,integration.points=newdata,X.new=other.x,
                    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 criterion, doe points and new point
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)
contour(x=x.grid,y=y.grid,z=z.grid,levels=0,add=TRUE,col="blue",lwd=5)
points(design, col="black", pch=17, lwd=4,cex=2)
points(other.x, col="red", pch=17, lwd=4,cex=3)
title("Kriging covariances with the point (0.6,0.6), in red")
# }