# trend.deltax

0th

Percentile

##### Trend derivatives

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

Keywords
models, internal, optimize
##### 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 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.

##### See Also

covVector.dx

• trend.deltax
##### Examples
# NOT RUN {
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)
# }

Documentation reproduced from package DiceKriging, version 1.5.6, License: GPL-2 | GPL-3

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