.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/monte_carlo/04_metropolis_equilibration.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_monte_carlo_04_metropolis_equilibration.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_monte_carlo_04_metropolis_equilibration.py:


Equilibrating an RSA configuration with Metropolis moves
=========================================================

Random sequential addition (RSA) creates a valid hard-sphere packing, but it
is irreversible and does not sample the equilibrium hard-sphere ensemble.
This example uses that RSA configuration only as an initial state for
single-particle Metropolis moves. The Metropolis sampler keeps every radius,
class label, and the particle count fixed; it only changes sphere centres.

For a production equilibrium calculation, check that observables have reached
stationarity and estimate their uncertainty from independent samples. The
acceptance rate printed below helps tune the proposal displacement.

.. GENERATED FROM PYTHON SOURCE LINES 15-20

.. code-block:: Python


    from PackLab import monte_carlo, samplers
    from PackLab.units import ureg
    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 21-23

Create a convenient non-overlapping initial state with RSA
-----------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 23-39

.. code-block:: Python


    domain = monte_carlo.PackingDomain(
        5 * ureg.micrometer,
        5 * ureg.micrometer,
        5 * ureg.micrometer,
        use_periodic_boundaries=True,
    )
    radius_sampler = samplers.ConstantRadiusSampler(150 * ureg.nanometer, bins=1)

    rsa_options = monte_carlo.RSAOptions()
    rsa_options.random_seed = 12
    rsa_options.maximum_attempts = 50_000
    rsa_options.target_packing_fraction = 0.08
    initial_result = monte_carlo.RSASimulator(domain, radius_sampler, rsa_options).run()









.. GENERATED FROM PYTHON SOURCE LINES 40-42

Equilibrate with fixed-volume Metropolis sampling
-------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 42-63

.. code-block:: Python


    metropolis_options = monte_carlo.MetropolisOptions()
    metropolis_options.random_seed = 34
    metropolis_options.number_of_sweeps = 500
    metropolis_options.maximum_displacement = 50 * ureg.nanometer

    simulator = monte_carlo.MetropolisSimulator(
        domain,
        initial_result.sphere_configuration,
        metropolis_options,
    )
    equilibrated_result = simulator.run()

    statistics = simulator.statistics
    print(f"Metropolis acceptance rate: {statistics.acceptance_rate:.3f}")
    print(f"Completed sweeps: {statistics.completed_sweeps}")
    print(f"Packing fraction: {equilibrated_result.statistics.packing_fraction_geometry:.3f}")

    figure = equilibrated_result.plot_slice_2d(show=False)
    _ = figure.suptitle("Hard-sphere configuration after Metropolis equilibration")
    plt.show()



.. image-sg:: /gallery/monte_carlo/images/sphx_glr_04_metropolis_equilibration_001.png
   :alt: Hard-sphere configuration after Metropolis equilibration, 2D slice at z≈0.00 meter, thickness 0.00 meter | showing 61 spheres
   :srcset: /gallery/monte_carlo/images/sphx_glr_04_metropolis_equilibration_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Metropolis acceptance rate: 0.910
    Completed sweeps: 500
    Packing fraction: 0.080





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 4.542 seconds)


.. _sphx_glr_download_gallery_monte_carlo_04_metropolis_equilibration.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 04_metropolis_equilibration.ipynb <04_metropolis_equilibration.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 04_metropolis_equilibration.py <04_metropolis_equilibration.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 04_metropolis_equilibration.zip <04_metropolis_equilibration.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_