# covTensorProduct-class

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##### Class of tensor-product spatial covariances

S4 class of tensor-product (or separable) covariances.

Keywords
models
##### Value

covTensorProduct

separable covariances depending on 1 set of parameters, such as Gaussian, exponential, Matern with fixed nu... or on 2 sets of parameters, such as power-exponential.

##### Objects from the Class

A d-dimensional tensor product (or separable) covariance kernel C(x,y) is the tensor product of 1-dimensional covariance kernels : C(x,y) = C(x1,y1)C(x2,y2)...C(xd,yd).

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.

range.n:

Object of class "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.

shape.n:

Object of class "integer". The number of shape parameters (exponent parameters in "powexp").

shape.names:

Object of class "character". Names of shape parameters, for printing purpose. Default is "p".

shape.val:

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

##### Methods

show

signature(x = "covTensorProduct") Print covariance function. See show,km-method.

coef

signature(x = "covTensorProduct") Get the coefficients of the covariance function.

% \item{coef<-}{\code{signature(x = "covTensorProduct")} Set the coefficients of the covariance function. }

##### 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.

covStruct.create to construct a covariance structure.

##### Aliases
• covTensorProduct-class
• show,covTensorProduct-method
• coef,covTensorProduct-method
• covMat1Mat2,covTensorProduct-method
• covMatrix,covTensorProduct-method
• covMatrixDerivative,covTensorProduct-method
• covParametersBounds,covTensorProduct-method
• covparam2vect,covTensorProduct-method
• vect2covparam,covTensorProduct-method
• covVector.dx,covTensorProduct-method
• inputnames,covTensorProduct-method
• kernelname,covTensorProduct-method
• ninput,covTensorProduct-method
• nuggetflag,covTensorProduct-method
• nuggetvalue,covTensorProduct-method
• nuggetvalue<-,covTensorProduct,numeric-method
• summary,covTensorProduct-method
Documentation reproduced from package DiceKriging, version 1.5.6, License: GPL-2 | GPL-3

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