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.
matern_anisotropic3D_alt(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, B11, B12, B13, B22, B23, B33, smoothness, nugget)
A matrix with n rows and 3 columns.
Each row of locs is a point in R^3.
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 $$ u_1 = B11[ x_1 + B12 x_2 + (B13 + B12 B23) x_3] $$ $$ u_2 = B22[ x_2 + B23 x_3] $$ $$ u_3 = B33[ x_3 ] $$ NOTE: the u_1 transformation is different from previous versions of this function. NOTE: now (B13,B23) can be interpreted as a drift vector in space over time. Assuming x is transformed to u and y transformed to v, the covariances are $$ M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| u - v || )^\nu K_\nu(|| u - v ||) $$ 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 \( \tau^2 \).