R: Trend derivatives

trend.deltax {DiceKriging} | R Documentation

## Trend derivatives

### 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)

[Package DiceKriging version 1.6.0 Index]