DiceKriging (version 1.6.0)

# covIso-class: Class of tensor-product spatial covariances with isotropic range

## Description

S4 class of isotropic spatial covariance kerlnes based upon the covTensorProduct class

## 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)

## Slots

d:

Object of class "integer". The spatial dimension.

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.

% \item{\code{range.n}:}{Object of class \code{"integer"}. The number of range parameters. }
range.names:

Object of class "character". Names of range parameters, for printing purpose. Default is "theta".

range.val:

Object of class "numeric". Values of range parameters.

% \item{\code{shape.n}:}{Object of class \code{"integer"}. The number of shape parameters (exponent parameters in "powexp"). } % \item{\code{shape.names}:}{Object of class \code{"character"}. Names of shape parameters, for printing purpose. Default is "p". } % \item{\code{shape.val}:}{Object of class \code{"numeric"}. Values of shape parameters. }

## Extends

Class "'>covKernel", directly.

## Methods

coef

signature(object = "covIso"): ...

covMat1Mat2

signature(object = "covIso"): ...

covMatrix

signature(object = "covIso"): ...

covMatrixDerivative

signature(object = "covIso"): ...

covParametersBounds

signature(object = "covIso"): ...

covparam2vect

signature(object = "covIso"): ...

vect2covparam

signature(object = "covIso"): ...

covVector.dx

signature(object = "covIso"): ...

inputnames

signature(x = "covIso"): ...

kernelname

signature(x = "covIso"): ...

ninput

signature(x = "covIso"): ...

nuggetflag

signature(x = "covIso"): ...

nuggetvalue

signature(x = "covIso"): ...

show

signature(object = "covIso"): ...

summary

signature(object = "covIso"): ...

## References

N.A.C. Cressie (1993), Statistics for spatial data, Wiley series in probability and mathematical statistics.

C.E. Rasmussen and C.K.I. Williams (2006), Gaussian Processes for Machine Learning, the MIT Press, http://www.gaussianprocess.org/gpml/

M.L. Stein (1999), Interpolation of spatial data, some theory for kriging, Springer.

## See Also

km '>covTensorProduct

## Examples

# NOT RUN {
showClass("covIso")
# }