# covScaling-class

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##### Class "covScaling"

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

Keywords
classes
##### 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"): ...

##### 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.

'>km '>covTensorProduct '>covIso '>covKernel

##### Aliases
• covScaling-class
• coef,covScaling-method
• covMat1Mat2,covScaling-method
• covMatrix,covScaling-method
• covMatrixDerivative,covScaling-method
• covParametersBounds,covScaling-method
• covparam2vect,covScaling-method
• vect2covparam,covScaling-method
• covVector.dx,covScaling-method
• show,covScaling-method
• inputnames,covScaling-method
• kernelname,covScaling-method
• ninput,covScaling-method
• nuggetflag,covScaling-method
• nuggetvalue,covScaling-method
• nuggetvalue<-,covScaling,numeric-method
• summary,covScaling-method
##### Examples
# NOT RUN {
showClass("covScaling")
# }

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

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