trend.deltax {DiceKriging} | R Documentation |
Computes the gradient of the vector of trend basis functions f(x)=(f1(x);...;fp(x))
trend.deltax(x, model, h = sqrt(.Machine$double.eps))
x |
a vector representing the specific location. |
model |
an object of class km. |
h |
the precision for numerical derivatives. |
A pxd
matrix where the p
rows contain the gradient of the trend basis functions.
The gradient is computed analytically in 3 common practical situations: formula=~1
(constant trend), formula=~.
(first order polynomial), formula=~.^2
(1st order polynomial + interactions). 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.
O. Roustant, Ecole des Mines de St-Etienne.
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)