R: Class "covScaling"

covScaling-class {DiceKriging} | R Documentation

## Class "covScaling"

### Description

Composition of isotropic kernels with coordinatewise non-linear scaling obtained by integrating piecewise affine functions

### Objects from the Class

In 1-dimension, the covariance kernels are parameterized as in (Rasmussen, Williams, 2006). Denote by `theta` the range parameter, `p` the exponent parameter (for power-exponential covariance), `s` the standard deviation, and `h=|x-y|`. Then we have `C(x,y) = s^2 * k(x,y)`, with:

Gauss | `k(x,y) = exp(-1/2*(h/theta)^2)`
Exponential | `k(x,y) = exp(-h/theta)`
Matern(3/2) | `k(x,y) = (1+sqrt(3)*h/theta)*exp(-sqrt(3)*h/theta)`
Matern(5/2) | `k(x,y) = (1+sqrt(5)*h/theta+(1/3)*5*(h/theta)^2)`
| `*exp(-sqrt(5)*h/theta)`
Power-exponential | `k(x,y) = exp(-(h/theta)^p)`

Here, in every dimension, the corresponding one-dimensional stationary kernel `k(x,y)` is replaced by `k(f(x),f(y))`, where `f` is a continuous monotonic function indexed by a finite number of parameters (see the references for more detail).

### Slots

`d`:

  Object of class `"integer"`. The spatial dimension.

`knots`:

  Object of class `"list"`. The j-th element is a vector containing the knots for dimension j.

`eta`:

  Object of class `"list"`. In correspondance with knots, the j-th element is a vector containing the scaling coefficients (i.e. the derivatives of the scaling function at the knots) for dimension j.

`name`:

  Object of class `"character"`. The covariance function name. To be chosen between `"gauss", "matern5_2", "matern3_2", "exp"`, and `"powexp"`

`paramset.n`:

  Object of class `"integer"`. 1 for covariance depending only on the ranges parameters, 2 for "powexp" which also depends on exponent parameters.

`var.names`:

  Object of class `"character"`. The variable names.

`sd2`:

  Object of class `"numeric"`. The variance of the stationary part of the process.

`known.covparam`:

  Object of class `"character"`. Internal use. One of: "None", "All".

`nugget.flag`:

  Object of class `"logical"`. Is there a nugget effect?

`nugget.estim`:

  Object of class `"logical"`. Is the nugget effect estimated or known?

`nugget`:

  Object of class `"numeric"`. If there is a nugget effect, its value (homogeneous to a variance).

`param.n`:

  Object of class `"integer"`. The total number of parameters.

### Extends

Class `"covKernel"`, directly.

### Methods

coef

  `signature(object = "covScaling")`: ...

covMat1Mat2

  `signature(object = "covScaling")`: ...

covMatrix

  `signature(object = "covScaling")`: ...

covMatrixDerivative

  `signature(object = "covScaling")`: ...

covParametersBounds

  `signature(object = "covScaling")`: ...

covparam2vect

  `signature(object = "covScaling")`: ...

vect2covparam

  `signature(object = "covScaling")`: ...

show

  `signature(object = "covScaling")`: ...

### Author(s)

Olivier Roustant, David Ginsbourger, Yves Deville

### References

Y. Xiong, W. Chen, D. Apley, and X. Ding (2007), Int. J. Numer. Meth. Engng, A non-stationary covariance-based Kriging method for metamodelling in engineering design.

### See Also

`km` `covTensorProduct` `covIso` `covKernel`

### Examples

    showClass("covScaling")

[Package DiceKriging version 1.5.8 Index]