Set up the quasi-random Sobol' sequence points for numerical PCS integration.
max_num: The maximum number of integration points to use in the Sobol' sequence during optimisation. This can be considered as the number of molecular structures in an ensemble used form a uniform distribution of the dynamics.
oversample: The generation of the Sobol' sequence oversamples as N * Ov * 10**M, where N is the maximum number of points, Ov is the oversamling value, and M is the number of dimensions or torsion-tilt angles used in the system.
This allows the maximum number of integration points N used during the frame order target function optimisation to be specified. This is used in the quasi-random Sobol' sequence for the numerical integration of the PCS. The formula used to find the total number of Sobol' points is:
total_num = N * Ov * 10**M,
|N is the maximum number of Sobol' integration points,
|Ov is the oversampling factor.
|M is the number of dimensions or torsion-tilt angles used in the system.
The aim of the oversampling is to try to reach the maximum number of points. However if the system is not very dynamic, the maximum number of points may not be reached. In this case, simply increase the oversampling factor. The algorithm used for uniformly sampling the motional space is:
|Generate the Sobol' sequence for the total number of points.
|Convert all points to the torsion-tilt angle system.
|Skip all Sobol' points with angles greater than the current parameter values.
|Terminate the loop over the Sobol' points once the maximum number of points has been reached.