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

.. only:: html

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

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

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

.. _sphx_glr_auto_gallery_nonlinear_plot_nonlinear_accuracy.py:


Third-order uncertainty: statistical and working estimates
==========================================================

.. _third-order-accuracy-the-fits-against-solprop-s-frozen-coefficients:

The shaded band is the fitted Kerr gamma's propagated statistical one-sigma
uncertainty, scaled by the reduced chi-squared where it exceeds one. Bars at 400,
800 and 1800 nm are the working estimates in :doc:`/nonlinear_accuracy`, which
include leave-one-out sensitivity and each gas's systematic floor. They can be much
larger than the covariance alone suggests. These are relative uncertainties of the
electronic response, not the total nonlinear response or an error bar on
extrapolation. Ozone's model starts at 700 nm.

.. GENERATED FROM PYTHON SOURCE LINES 21-87



.. image-sg:: /auto_gallery/nonlinear/images/sphx_glr_plot_nonlinear_accuracy_001.svg
   :alt: He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO2, CH4, SF6, CO, N2O, O3
   :srcset: /auto_gallery/nonlinear/images/sphx_glr_plot_nonlinear_accuracy_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import warnings

    import matplotlib.pyplot as plt
    import numpy as np
    from _helpers import LINE_COLOURS

    from optmat.exceptions import ModelRangeWarning
    from optmat.gas.nonlinear import hyperpolarizability_models

    # The working estimates of docs/nonlinear_accuracy.md (Kerr at 400, 800 and 1800 nm, %),
    # checked against that page by tests/test_nonlinear_accuracy_page.py.
    ESTIMATES = {
        "He": (0.2, 0.1, 0.1),
        "Ne": (1, 1, 1),
        "Ar": (1, 1, 1),
        "Kr": (4, 4, 7),
        "Xe": (7, 1.5, 3),
        "H2": (1, 1, 1),
        "D2": (1, 1, 1),
        "N2": (1, 1, 1),
        "O2": (1.5, 2, 4),
        "CO2": (10, 3, 7),
        "CH4": (2, 2, 2),
        "SF6": (2, 4, 7),
        "CO": (10, 10, 10),
        "N2O": (20, 15, 15),
        "O3": (np.nan, 15, 15),
    }
    models = {gas.value: model for gas, model in hyperpolarizability_models().items()}

    fig, axes = plt.subplots(3, 5, figsize=(14, 8), layout="constrained", sharex=True)
    for axis, (name, estimates) in zip(axes.flat, ESTIMATES.items(), strict=True):
        model = models[name]
        low = max(400e-9, model.wavelength_range[0])
        wavelength = np.geomspace(low, 2000e-9, 200)
        with warnings.catch_warnings():
            warnings.simplefilter("ignore", ModelRangeWarning)
            kerr = model.gamma_au("kerr", wavelength)
            sigma = model.gamma_sigma_au("kerr", wavelength) / kerr * 100
        nm = wavelength * 1e9
        axis.fill_between(nm, -sigma, sigma, color=LINE_COLOURS[4], alpha=0.6, linewidth=0)
        axis.axhline(0.0, color=LINE_COLOURS[1], linewidth=0.6)
        probe = np.array([400.0, 800.0, 1800.0])
        axis.errorbar(
            probe,
            np.zeros(3),
            yerr=np.array(estimates),
            fmt="none",
            ecolor=LINE_COLOURS[0],
            elinewidth=1.4,
            capsize=3,
        )
        axis.set_title(name)
        axis.set_xscale("log")
        axis.set_xlim(370, 2100)
        axis.set_xticks([400, 600, 800, 1200, 1800], ["400", "600", "800", "1200", "1800"])
        axis.minorticks_off()
        axis.grid(alpha=0.25)
    for axis in axes[-1]:
        axis.set_xlabel("fundamental wavelength (nm)")
    for axis in axes[:, 0]:
        axis.set_ylabel("relative uncertainty (%)")
    axes[0, 0].plot([], [], color=LINE_COLOURS[4], lw=6, label="statistical 1 sigma")
    axes[0, 0].plot([], [], color=LINE_COLOURS[0], marker="|", ls="none", label="working")
    axes[0, 0].legend(fontsize=8, loc="lower right")
    plt.show()


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

   **Total running time of the script:** (0 minutes 1.759 seconds)


.. _sphx_glr_download_auto_gallery_nonlinear_plot_nonlinear_accuracy.py:

.. only:: html

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

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

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

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

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

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

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