.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gen_examples/analysis/plot_ITCFT.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_analysis_plot_ITCFT.py>`
        to download the full example code

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

.. _sphx_glr_gen_examples_analysis_plot_ITCFT.py:


Imaginary time correlation function thermometry
===============================================

This example showcases how apply the analysis functions to get temperatures
from the Laplace transform of the structure, as proposed by
:cite:`Dornheim.2022`.

.. GENERATED FROM PYTHON SOURCE LINES 9-147



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /gen_examples/analysis/images/sphx_glr_plot_ITCFT_001.svg
         :alt: plot ITCFT
         :srcset: /gen_examples/analysis/images/sphx_glr_plot_ITCFT_001.svg
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /gen_examples/analysis/images/sphx_glr_plot_ITCFT_002.svg
         :alt: plot ITCFT
         :srcset: /gen_examples/analysis/images/sphx_glr_plot_ITCFT_002.svg
         :class: sphx-glr-multi-img





.. code-block:: Python


    from functools import partial

    import jax
    import matplotlib.pyplot as plt
    from jax import numpy as jnp
    from jpu import numpy as jnpu

    import jaxrts

    ureg = jaxrts.ureg

    plt.style.use("science")

    state = jaxrts.PlasmaState(
        ions=[jaxrts.Element("C")],
        Z_free=jnp.array([3]),
        mass_density=jnp.array([1]) * ureg.gram / ureg.centimeter**3,
        T_e=40 * ureg.electron_volt / ureg.k_B,
    )
    setup = jaxrts.Setup(
        scattering_angle=ureg("30°"),
        energy=ureg("9000 eV"),
        measured_energy=ureg("9000 eV")
        + jnp.linspace(-200, 200, 500) * ureg.electron_volt,
        instrument=partial(
            jaxrts.instrument_function.instrument_gaussian,
            sigma=ureg("3eV") / ureg.hbar / (2 * jnp.sqrt(2 * jnp.log(2))),
        ),
    )

    # Turn off the dispersion correction
    setup.correct_k_dispersion = False

    state["screening length"] = jaxrts.models.ArbitraryDegeneracyScreeningLength()
    state["screening"] = jaxrts.models.LinearResponseScreening()
    state["ionic scattering"] = jaxrts.models.OnePotentialHNCIonFeat()
    state["free-free scattering"] = jaxrts.models.RPA_DandreaFit()
    state["bound-free scattering"] = jaxrts.models.SchumacherImpulse()
    state["free-bound scattering"] = jaxrts.models.DetailedBalance()


    S_ee = state.probe(setup)

    # We compare two approaches, the default minimization finding with the more
    # forward grid finding
    tau = jnp.linspace(1, 60, 500) / (1 * ureg.kiloelectron_volt)

    # x is the cut-off Energy
    x = jnp.linspace(1, 180) * ureg.electron_volt

    T_grid, L_grid = jax.vmap(
        jaxrts.analysis.ITCFT_grid, in_axes=(None, None, None, 0), out_axes=(0, 1)
    )(S_ee, tau, setup, x)

    T_auto = jax.vmap(
        jaxrts.analysis.ITCFT,
        in_axes=(None, None, None, 0),
        out_axes=(0),
    )(S_ee, jnpu.max(tau), setup, x)

    fig, ax = plt.subplots()
    ax.plot(
        x.m_as(ureg.electron_volt),
        (T_grid * ureg.k_B).m_as(ureg.electron_volt),
        label="grid",
    )
    ax.plot(
        x.m_as(ureg.electron_volt),
        (T_auto * ureg.k_B).m_as(ureg.electron_volt),
        label="auto",
    )
    ax.set_ylim(
        jnp.array([-4, 1]) + (state.T_e * ureg.k_B).m_as(ureg.electron_volt)
    )
    ax.hlines(
        [(state.T_e * ureg.k_B).m_as(ureg.electron_volt)],
        *ax.get_xlim(),
        color="gray",
        ls="dashed",
    )

    ax.set_ylabel("$k_B T$ [eV]")
    ax.set_xlabel("$x$ [eV]")
    ax.legend()
    fig.tight_layout()

    # Plot different Laplace-Transforms for both methods.
    fig, ax = plt.subplots()

    E_shift = -(setup.measured_energy - setup.energy)
    instrument = setup.instrument(E_shift / (1 * ureg.hbar))
    for i, x in enumerate([20, 40, 80, 120]):
        minimizer = jaxrts.analysis.ITCF(
            S_ee, E_shift, instrument, E_shift, ureg(f"{x}eV"), raw=False
        )

        T_auto = minimizer.get_T(60 / (1 * ureg.kiloelectron_volt))
        tau = jnp.linspace(1e-8, 60)
        L_auto = [minimizer(t * (1 / ureg.kiloelectron_volt)) for t in tau]
        T_grid, L_grid = jaxrts.analysis.ITCFT_grid(
            S_ee, tau / (1 * ureg.kiloelectron_volt), setup, ureg(f"{x}eV")
        )
        ax.plot(
            tau,
            L_auto,
            ls="dashed",
            color=f"C{i}",
            label="grid" if i == 0 else None,
        )
        ax.plot(
            tau,
            L_grid.m_as(ureg.dimensionless),
            ls="solid",
            color=f"C{i}",
            alpha=0.5,
            label="auto" if i == 0 else None,
        )
        ax.scatter(
            [0.5 / (T_grid * ureg.k_B).m_as(ureg.kiloelectron_volt)],
            [jnpu.min(L_grid).m_as(ureg.dimensionless)],
            color="black",
            label="minimum grid" if i == 0 else None,
        )
        ax.scatter(
            [0.5 / (T_auto * ureg.k_B).m_as(ureg.kiloelectron_volt)],
            [jnpu.min(L_grid).m_as(ureg.dimensionless)],
            color="black",
            marker="x",
            label="minumum auto" if i == 0 else None,
        )

    ax.set_xlabel("$\\tau$ [1/keV]")
    ax.set_ylabel("$\\mathcal{L}$")
    ax.legend()

    fig.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 15.365 seconds)


.. _sphx_glr_download_gen_examples_analysis_plot_ITCFT.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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