exponential_anisotropic3D_alt {GpGp} | R Documentation |
Geometrically anisotropic exponential covariance function (three dimensions, alternate parameterization)
Description
From a matrix of locations and covariance parameters of the form (variance, B11, B12, B13, B22, B23, B33, smoothness, nugget), return the square matrix of all pairwise covariances.
Usage
exponential_anisotropic3D_alt(covparms, locs)
d_exponential_anisotropic3D_alt(covparms, locs)
Arguments
covparms |
A vector with covariance parameters in the form (variance, B11, B12, B13, B22, B23, B33, smoothness, 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_exponential_anisotropic3D_alt()
: Derivatives of anisotropic Matern covariance
Parameterization
The covariance parameter vector is (variance, B11, B12, B13, B22, B23, B33, smoothness, nugget) where B11, B12, B13, B22, B23, B33, transform the three coordinates as
u_1 = B11[ x_1 + B12 x_2 + (B13 + B12 B23) x_3]
u_2 = B22[ x_2 + B23 x_3]
u_3 = B33[ x_3 ]
(B13,B23) can be interpreted as a drift vector in space over time if first two dimensions are space and third is time. Assuming x is transformed to u and y transformed to v, the covariances are
M(x,y) = \sigma^2 exp( - || u - v || )
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
.