DiceKriging (version 1.5.5)

covAffineScaling-class: Class "covAffineScaling"

Description

Composition of isotropic kernels with coordinatewise non-linear scaling obtained by integrating 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 2 parameters (see the references for more detail).

Slots

d:

Object of class "integer". The spatial dimension.

knots:

Object of class "numeric". A vector specifying the position of the two knots, common to all dimensions.

eta:

Object of class "matrix". A d*2 matrix of scaling coefficients, parametrizing the coordinatewise transformations in the d dimensions.

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 = "covAffineScaling"): ...

covMat1Mat2

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

covMatrix

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

covMatrixDerivative

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

covParametersBounds

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

covparam2vect

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

vect2covparam

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

inputnames

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

kernelname

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

ninput

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

nuggetflag

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

nuggetvalue

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

show

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

summary

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

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("covAffineScaling")
# }