From a matrix of locations and covariance parameters of the form (variance, range_1, range_2, smoothness, nugget), return the square matrix of all pairwise covariances.
matern_spacetime(covparms, locs)d_matern_spacetime(covparms, locs)
A matrix with n rows and n columns, with the i,j entry
containing the covariance between observations at locs[i,] and
locs[j,].
A vector with covariance parameters in the form (variance, range_1, range_2, smoothness, nugget). range_1 is the spatial range, and range_2 is the temporal range.
A matrix with n rows and d+1 columns.
Each row of locs is a point in R^(d+1). The first d columns
should contain the spatial coordinates. The last column contains the times.
d_matern_spacetime(): Derivatives with respect to parameters
The covariance parameter vector is (variance, range_1, range_2, smoothness, nugget). The covariance function is parameterized as $$ M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| D^{-1}(x - y) || )^\nu K_\nu(|| D^{-1}(x - y) || ) $$ where D is a diagonal matrix with (range_1, ..., range_1, range_2) 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 \( \tau^2 \).