KrigInv (version 1.3.1)

computeQuickKrigcov: Quick computation of kriging covariances

Description

Computes kriging covariances between one new point and many integration points, using precomputed data.

Usage

computeQuickKrigcov(model,integration.points,X.new,
precalc.data, F.newdata , c.newdata)

Arguments

model

A Kriging model of km class.

integration.points

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

X.new

The new point where we calculate kriging covariances. The calculated covariances are the covariances between this new point and all the integration points.

precalc.data

List containing precalculated data. This list is generated using the function precomputeUpdateData

F.newdata

The value of the kriging trend basis function at point X.new

c.newdata

The (unconditional) covariance between X.new and the design points

Value

A vector containing kriging covariances

Details

This function requires to use another function in order to generate the proper arguments. The argument precalc.data can be generated using precomputeUpdateData. The arguments F.newdata and c.newdata can be obtained using predict_nobias_km, which returns a field F.newdata and a field c.

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

precomputeUpdateData, predict_nobias_km, predict_update_km

Examples

# NOT RUN {
#computeQuickKrigcov

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)

#precalculation
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")
# }