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

.. only:: html

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

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

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

.. _sphx_glr_gallery_validation_percus_yevick_grid_convergence.py:


Convergence of the Percus--Yevick reference
===========================================

Before comparing an RSA estimate to an analytical reference, verify that the
numerical inverse transform used by the Percus--Yevick calculation is resolved.
This example compares the beginner-friendly ``wavenumber="auto"`` grid with a
twice-refined grid on the same hard-sphere mixture.

This is a *numerical* convergence check for Percus--Yevick, not a claim that
RSA converges to Percus--Yevick. RSA and Percus--Yevick remain distinct models.

.. GENERATED FROM PYTHON SOURCE LINES 13-20

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from PackLab import analytical, ureg









.. GENERATED FROM PYTHON SOURCE LINES 21-23

Define one mixture and a real-space support
--------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 23-56

.. code-block:: Python


    radii = np.array([0.75, 1.5]) * ureg.micrometer
    number_fractions = np.array([0.5, 0.5])
    volume_fraction = 0.15
    domain = analytical.PercusYevickDomain(
        size=100_000 * ureg.micrometer,
        radii=radii,
        volume_fraction=volume_fraction,
        number_fractions=number_fractions,
    )
    distances = np.linspace(0.0, 12.0, 240) * ureg.micrometer

    automatic = analytical.PercusYevickSolver(
        densities=domain.particle_densities_per_radius,
        radii=domain.radii,
        wavenumber="auto",
    ).compute(distances)

    refined_grid = analytical.make_wavenumber_grid(
        radial_resolution=domain.radii.min() / 20,
        maximum_distance=distances.max(),
        samples_per_oscillation=24,
    )
    refined = analytical.PercusYevickSolver(
        densities=domain.particle_densities_per_radius,
        radii=domain.radii,
        wavenumber=refined_grid,
    ).compute(distances)

    print(f"Automatic grid: {len(automatic.wavenumber)} wavenumber points")
    print(f"Refined grid:   {len(refined.wavenumber)} wavenumber points")






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

 .. code-block:: none

    Automatic grid: 1922 wavenumber points
    Refined grid:   3842 wavenumber points




.. GENERATED FROM PYTHON SOURCE LINES 57-62

Plot the reference and its refinement error
-------------------------------------------
Agreement away from hard-core discontinuities indicates that the default grid
is sufficiently resolved for this radial range. If it is not, decrease
``radial_resolution`` or increase ``samples_per_oscillation``.

.. GENERATED FROM PYTHON SOURCE LINES 62-87

.. code-block:: Python


    figure, (curves_axis, error_axis) = plt.subplots(1, 2, figsize=(11, 4))

    for i, j in ((0, 0), (0, 1), (1, 1)):
        label = rf"$g_{{{i}{j}}}$"
        _ = curves_axis.plot(distances, automatic.g[i, j], label=f"auto {label}")
        _ = curves_axis.plot(distances, refined.g[i, j], "--", color="black", alpha=0.65)
        _ = error_axis.semilogy(
            distances,
            np.maximum(np.abs(automatic.g[i, j] - refined.g[i, j]), 1e-12),
            label=label,
        )

    curves_axis.set_title("Automatic grid (colour) and refined grid (dashed)")
    curves_axis.set_xlabel("separation $r$ [$\\mu$m]")
    curves_axis.set_ylabel(r"$g_{ij}(r)$")
    _ = curves_axis.legend()
    curves_axis.grid(alpha=0.2)

    error_axis.set_title("Absolute change after grid refinement")
    error_axis.set_xlabel("separation $r$ [$\\mu$m]")
    error_axis.set_ylabel(r"$|g_{ij}^{auto} - g_{ij}^{refined}|$")
    _ = error_axis.legend()
    error_axis.grid(alpha=0.2)
    figure.tight_layout()



.. image-sg:: /gallery/validation/images/sphx_glr_percus_yevick_grid_convergence_001.png
   :alt: Automatic grid (colour) and refined grid (dashed), Absolute change after grid refinement
   :srcset: /gallery/validation/images/sphx_glr_percus_yevick_grid_convergence_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.602 seconds)


.. _sphx_glr_download_gallery_validation_percus_yevick_grid_convergence.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: percus_yevick_grid_convergence.ipynb <percus_yevick_grid_convergence.ipynb>`

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

      :download:`Download Python source code: percus_yevick_grid_convergence.py <percus_yevick_grid_convergence.py>`

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

      :download:`Download zipped: percus_yevick_grid_convergence.zip <percus_yevick_grid_convergence.zip>`


.. only:: html

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

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