gdml_mat52_wrk#

mbgdml.analysis.models.gdml_mat52_wrk(r_desc, sig, n_perms, R_desc_perms)[source]#

Compute the Matérn 5/2 covariance function for a single structure with respect to a GDML train set.

Parameters:

  • r_desc (numpy.ndarray, ndim: 1) – GDML descriptor of a single structure with permutational symmetries specified by the model.

  • sig (float) – Trained kernel length scale.

  • n_perms (int) – Number of permutational symmetries.

  • R_desc_perms (numpy.ndarray, ndim: 2) – Training descriptors with permutational symmetries.

Returns:

(ndim: 1) Covariances between a single structure and the GDML training set.

Return type:

numpy.ndarray

Notes

The Matérn kernel when \(\nu = 5/2\) reduces to the following expression.

\[k_{5/2} (x_i, x_j) = \left( 1 + \frac{\sqrt{5}}{l} d(x_i, x_j) \ + \frac{5}{3l} d(x_i, x_j)^2 \right) \exp \left( - \frac{\sqrt{5}}{l} d (x_i, x_j) \right)\]

For GDML, sigma (sig) is the kernel length-scale parameter \(l\). \(d(x_i, x_j)\) is the Euclidean distance between \(x_i\) (r_desc) and \(x_j\) (a single training point in R_desc_perms).

Note

This can be a ray task if desired.