covScaling-class {DiceKriging}

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")