covTensorProduct-class {DiceKriging} | R Documentation |
S4 class of tensor product covariances.
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. |
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) |
d
:"integer"
. The spatial dimension. name
:"character"
. The covariance function name. To be chosen between "gauss", "matern5_2", "matern3_2", "exp"
, and "powexp"
paramset.n
:"integer"
. 1 for covariance depending only on the ranges parameters, 2 for "powexp" which also depends on exponent parameters. var.names
:"character"
. The variable names. sd2
:"numeric"
. The variance of the stationary part of the process. known.covparam
:"character"
. Internal use. One of: "None", "All". nugget.flag
:"logical"
. Is there a nugget effect? nugget.estim
:"logical"
. Is the nugget effect estimated or known? nugget
:"numeric"
. If there is a nugget effect, its value (homogeneous to a variance). param.n
:"integer"
. The total number of parameters. range.n
:"integer"
. The number of range parameters. range.names
:"character"
. Names of range parameters, for printing purpose. Default is "theta". range.val
:"numeric"
. Values of range parameters. shape.n
:"integer"
. The number of shape parameters (exponent parameters in "powexp"). shape.names
:"character"
. Names of shape parameters, for printing purpose. Default is "p". shape.val
:"numeric"
. Values of shape parameters.
signature(x = "covTensorProduct")
Print covariance function. See show.km
. signature(x = "covTensorProduct")
Get the coefficients of the covariance function. O. Roustant, D. Ginsbourger
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.