Understanding results

PackLab keeps physical inputs, generated configurations, and derived correlations separate. This page maps the result objects returned by each public workflow.

RSA and Metropolis results

RSASimulator.run() and MetropolisSimulator.run() return a PackingResult representing one explicit sphere configuration:

result = monte_carlo.RSASimulator(domain, sampler, options).run()
positions = result.positions       # shape: (number_of_spheres, 3)
radii = result.radii               # shape: (number_of_spheres,)
statistics = result.statistics
centers, g_ij = result.compute_partial_pair_correlation_function(n_bins=80)

positions and radii identify the actual packing. statistics contains summary quantities such as sphere count and geometric packing fraction. centers carries length units and g_ij has shape (number_of_classes, number_of_classes, number_of_bins).

The plotting helpers return Matplotlib figures, so they can be labelled, saved, or embedded in a larger figure:

figure = result.plot_slice_2d(show=False)
figure.savefig("packing-slice.png", dpi=200)

Percus–Yevick results

PercusYevickSolver.compute(...) returns the analytical result evaluated on the requested distance and wavenumber grids:

py_result = solver.compute(distances)
distances = py_result.distances
wavenumber = py_result.wavenumber
partial_g = py_result.g
total_correlation = py_result.H

For a mixture with \(K\) size classes, g is indexed as g[i, j, distance_index] and H as H[i, j, wavenumber_index]. Match the class ordering to the radii and number fractions supplied to the domain. The result is an analytical equilibrium reference, not a generated sphere configuration.

Scattering results

compute_scattering_amplitudes returns a ScatteringDataset containing one item per requested diameter. Call process() before using mixture-level arrays:

dataset = scattering.compute_scattering_amplitudes(...)
dataset.process()
cross_sections = dataset.Csca
phi, theta, phase_function = dataset.get_phase_function(
    densities=py_result.densities,
    H=py_result.H,
    wavenumber=py_result.wavenumber,
)

The phase function combines optical amplitudes with the supplied analytical correlation tensor. It therefore inherits the assumptions of both the optical model and the chosen hard-sphere structure model.