From a matrix of locations and covariance parameters of the form (variance, spatial range, temporal range, smoothness, category, nugget), return the square matrix of all pairwise covariances.
matern_spacetime_categorical(covparms, locs)d_matern_spacetime_categorical(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, spatial range, temporal range, smoothness, category, nugget)
A matrix with n rows and d columns.
Each row of locs gives a point in R^d.
d_matern_spacetime_categorical(): Derivatives of isotropic Matern covariance
The covariance parameter vector is (variance, range, smoothness, category, nugget) = \((\sigma^2,\alpha_1,\alpha_2,\nu,c^2,\tau^2)\), and the covariance function is parameterized as $$ d = ( || x - y ||^2/\alpha_1 + |s-t|^2/\alpha_2^2 )^{1/2} $$ $$ M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (d)^\nu K_\nu(d) $$ (x,s) and (y,t) are the space-time locations of a pair of observations. The nugget value \( \sigma^2 \tau^2 \) is added to the diagonal of the covariance matrix. The category variance \(c^2\) is added if two observation from same category NOTE: the nugget is \( \sigma^2 \tau^2 \), not \( \tau^2 \).