Composition of isotropic kernels with coordinatewise nonlinear scaling obtained by integrating piecewise affine functions
In 1dimension, the covariance kernels are parameterized as in (Rasmussen, Williams, 2006). Denote by theta
the range parameter, p
the exponent parameter (for powerexponential covariance), s
the standard deviation, and h=xy
. 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) 

Powerexponential  k(x,y) = exp((h/theta)^p) 
Here, in every dimension, the corresponding onedimensional 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).
d
:Object of class "integer"
. The spatial dimension.
knots
:Object of class "list"
. The jth element is a vector containing the knots for dimension j.
eta
:Object of class "list"
. In correspondance with knots, the jth 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.
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
signature(object = "covScaling")
: ...
Y. Xiong, W. Chen, D. Apley, and X. Ding (2007), Int. J. Numer. Meth. Engng, A nonstationary covariancebased Kriging method for metamodelling in engineering design.
# NOT RUN { showClass("covScaling") # }