S4 class of isotropic spatial covariance kerlnes based upon the covTensorProduct 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) |
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.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.
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
signature(x = "covIso")
: ...
signature(x = "covIso")
: ...
signature(x = "covIso")
: ...
signature(x = "covIso")
: ...
signature(x = "covIso")
: ...
signature(object = "covIso")
: ...
signature(object = "covIso")
: ...
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.
km
'>covTensorProduct
# NOT RUN {
showClass("covIso")
# }
Run the code above in your browser using DataLab