trend.deltax: Trend derivatives

In DiceKriging: Kriging Methods for Computer Experiments

Description

Computes the gradient of the vector of trend basis functions f(x)=(f1(x);...;fp(x))

Usage

trend.deltax(x, model, h = sqrt(.Machine$double.eps))

Arguments

x	a vector representing the specific location.
model	an object of class km.
h	the precision for numerical derivatives.

Value

A pxd matrix where the p rows contain the gradient of the trend basis functions.

Note

The gradient is computed analytically in 4 common practical situations: formula=~1 (constant trend), formula=~. (first-order polynomial), formula=~.^2 (first-order polynomial + second-order interactions), first-order polynomial + (pure) quadratic terms. In the other cases, the gradient is approximated by a finite difference of the form (g(x+h)-g(x-h))/2h, where h is tunable.

Author(s)

O. Roustant, Ecole des Mines de St-Etienne.

See Also

covVector.dx

Examples

X <- expand.grid(x1=seq(0,1,length=4), x2=seq(0,1,length=4), x3=seq(0,1,length=4))
fun <- function(x){
  (x[1]+2*x[2]+3*x[3])^2
}
y <- apply(X, 1, fun) 

x <- c(0.2, 0.4, 0.6)
coef.cov=c(0.5, 0.9, 1.3); coef.var=3

m <- km(~.^2, design=X, response=y, coef.cov=coef.cov, coef.var=coef.var)
grad.trend <- trend.deltax(x, m)
print(grad.trend)

m <- km(~. + I(x1^2) + I(x2^2) + I(x3^2), 
        design=X, response=y, coef.cov=coef.cov, coef.var=coef.var)
grad.trend <- trend.deltax(x, m)
print(grad.trend)

DiceKriging documentation built on Feb. 24, 2021, 1:07 a.m.