Composition of isotropic kernels with coordinatewise non-linear scaling obtained by integrating piecewise affine functions
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).
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.
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 non-stationary covariance-based Kriging method for metamodelling in engineering design.
# NOT RUN {
showClass("covScaling")
# }
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