Implement inertial definition of filling factor

import math

import numpy as np

#import pdb

from sys import argv

## \brief Compute the particle's filling factor.

#

#  In this application the filling factor is defined as the ratio of the

#  volume of a homogeneous ellipsoid filled with as much mass as the particle

#  having the same principal moments of inertia of the particle and the sum

#  of the volumes of the spheres that compose the particle.

#  sum of the volumes of the spheres that compose the particle with respect

#  to the volume of a homogeneous ellipsoid that has the same rotational

#  properties as the particle.

#

#  \param stypes: `dict` Dictionary of sphere types.

#  \param i_tot_cm: `numpy.ndarray` Inertia tensor of the particle with respect

    eigenval, eigenvec = np.linalg.eigh(i_tot_cm)

    print("INFO: ellipsoid axes:", eigenval)

    print("INFO: ellipsoid directions:", eigenvec)

    eigenval /= mtot

    gf = 5.0 / (2.0 * mtot)

    I1, I2, I3 = eigenval

    a = np.sqrt(max(0.0, gf * (I2 + I3 - I1)))

    b = np.sqrt(max(0.0, gf * (I1 + I3 - I2)))

    c = np.sqrt(max(0.0, gf * (I1 + I2 - I3)))

    # Volume of the ellipsoid that has the same moments of inertia as the particle

    vell = 4.0 * math.pi * math.sqrt(eigenval[0] * eigenval[1] * eigenval[2]) / 3.0

    ff = vell / vtot

    vell = 4.0 * math.pi * a * b * c / 3.0

    ff = vtot / vell

    return ff

## \brief Create a dictionary of sphere types.

            cur_type = int(split_line[ti])

            if (cur_type > read_spheres + ti):

                type_id += 1

            if (len(stypes['vec_types']) < config['nsph']):

                stypes['vec_types'].append(type_id)

        read_spheres += len(split_line)

    stypes['num_types'] = type_id