| matern35_scaledim {GpGp} | R Documentation |
Matern covariance function, smoothess = 3.5, different range parameter for each dimension
Description
From a matrix of locations and covariance parameters of the form (variance, range_1, ..., range_d, nugget), return the square matrix of all pairwise covariances.
Usage
matern35_scaledim(covparms, locs)
d_matern35_scaledim(covparms, locs)
d_matern45_scaledim(covparms, locs)
Arguments
covparms |
A vector with covariance parameters in the form (variance, range_1, ..., range_d, nugget) |
locs |
A matrix with |
Value
A matrix with n rows and n columns, with the i,j entry
containing the covariance between observations at locs[i,] and
locs[j,].
Functions
-
d_matern35_scaledim(): Derivatives with respect to parameters -
d_matern45_scaledim(): Derivatives with respect to parameters
Parameterization
The covariance parameter vector is (variance, range_1, ..., range_d, nugget). The covariance function is parameterized as
M(x,y) = \sigma^2 ( \sum_{j=0}^3 c_j || D^{-1}(x - y) ||^j ) exp( - || D^{-1}(x - y) || )
where c_0 = 1, c_1 = 1, c_2 = 2/5, c_3 = 1/15.
where D is a diagonal matrix with (range_1, ..., range_d) on the diagonals.
The nugget value \sigma^2 \tau^2 is added to the diagonal of the covariance matrix.
NOTE: the nugget is \sigma^2 \tau^2 , not \tau^2 .