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

.. only:: html

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

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

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

.. _sphx_glr_gen_examples_utils_plot_fermi_integral_inversion.py:


Showcase the inversion of Fermi-Dirac-Ingerals
==============================================

The following code displays the quality of the inversion of the Fermi-Dirac
integral for the Functions presented in :cite:`Antia.1993` and the improments
published in :cite:`Fukushima.2015`.

.. GENERATED FROM PYTHON SOURCE LINES 9-36



.. image-sg:: /gen_examples/utils/images/sphx_glr_plot_fermi_integral_inversion_001.svg
   :alt: plot fermi integral inversion
   :srcset: /gen_examples/utils/images/sphx_glr_plot_fermi_integral_inversion_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as onp

    import jaxrts

    plt.style.use("science")

    xmin, xmax = 0, 200
    x = onp.linspace(xmin, xmax, 400)
    y = jaxrts.math.fermi_integral(x, 0.5)[:, 0]
    plt.plot(
        x[10:],
        (jaxrts.math.inverse_fermi_12_rational_approximation_antia(y) - x)[10:],
        label="Antia 1993",
    )
    plt.plot(
        x,
        jaxrts.math.inverse_fermi_12_fukushima_single_prec(y) - x,
        label="Fukushima 2015",
    )
    plt.plot(x, onp.zeros_like(x), color="black", linestyle="dashed")
    plt.xlabel(r"$x$")
    plt.ylabel(r"$\mathcal{F}^{-1}(\mathcal{F}_{real}(x))-x$")
    plt.legend()
    plt.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 3.677 seconds)


.. _sphx_glr_download_gen_examples_utils_plot_fermi_integral_inversion.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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