From a matrix of locations and covariance parameters of the form (variance, L11, L21, L22, L31, L32, L33, smoothness, nugget), return the square matrix of all pairwise covariances.
matern_anisotropic3D(covparms, locs)d_matern_anisotropic3D(covparms, locs)
d_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, L11, L21, L22, L31, L32, L33, smoothness, nugget)
A matrix with n rows and 3 columns.
Each row of locs is a point in R^3.
d_matern_anisotropic3D(): Derivatives of anisotropic Matern covariance
d_matern_anisotropic3D_alt(): Derivatives of anisotropic Matern covariance
The covariance parameter vector is (variance, L11, L21, L22, L31, L32, L33, smoothness, nugget) where L11, L21, L22, L31, L32, L33 are the six non-zero entries of a lower-triangular matrix L. The covariances are $$ M(x,y) = \sigma^2 2^{1-\nu}/\Gamma(\nu) (|| L x - L y || )^\nu K_\nu(|| L x - L y ||) $$ This means that L11 is interpreted as an inverse range parameter in the first dimension. 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 \( \tau^2 \).