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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_user-guide_model-gallery_temporal_plot_generalized_gaussian_temporal.py>`
        to download the full example code. or to run this example in your browser via Binder

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

.. _sphx_glr_user-guide_model-gallery_temporal_plot_generalized_gaussian_temporal.py:


.. _generalized-gaussian-temporal-model:

Generalized Gaussian temporal model
===================================

This model parametrises a generalized Gaussian time model.

.. math::
        F(t) = \exp \left( - 0.5 \cdot \left( \frac{|t - t_{\rm{ref}}|}{t_{\rm{rise}}} \right) ^ {1 / \eta} \right) \text{ for } t < t_{\rm{ref}}

        F(t) = \exp \left( - 0.5 \cdot \left( \frac{|t - t_{\rm{ref}}|}{t_{\rm{decay}}} \right) ^ {1 / \eta} \right) \text{ for } t > t_{\rm{ref}}

.. GENERATED FROM PYTHON SOURCE LINES 17-20

Example plot
------------
Here is an example plot of the model:

.. GENERATED FROM PYTHON SOURCE LINES 20-43

.. code-block:: Python


    from astropy import units as u
    from astropy.time import Time
    from astropy.units import Quantity
    import matplotlib.pyplot as plt
    from gammapy.modeling.models import (
        GeneralizedGaussianTemporalModel,
        Models,
        PowerLawSpectralModel,
        SkyModel,
    )

    t_rise = Quantity(0.1, "d")
    t_decay = Quantity(1, "d")
    eta = Quantity(2 / 3, "")
    t_ref = Time("2020-10-01")
    time_range = [t_ref - 1 * u.d, t_ref + 1 * u.d]
    gen_gaussian_model = GeneralizedGaussianTemporalModel(
        t_ref=t_ref.mjd * u.d, t_rise=t_rise, t_decay=t_decay, eta=eta
    )
    gen_gaussian_model.plot(time_range)
    plt.grid(which="both")




.. image-sg:: /user-guide/model-gallery/temporal/images/sphx_glr_plot_generalized_gaussian_temporal_001.png
   :alt: plot generalized gaussian temporal
   :srcset: /user-guide/model-gallery/temporal/images/sphx_glr_plot_generalized_gaussian_temporal_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 44-47

YAML representation
-------------------
Here is an example YAML file using the model:

.. GENERATED FROM PYTHON SOURCE LINES 47-56

.. code-block:: Python


    model = SkyModel(
        spectral_model=PowerLawSpectralModel(),
        temporal_model=gen_gaussian_model,
        name="generalized_gaussian_model",
    )
    models = Models([model])

    print(models.to_yaml())




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

 .. code-block:: none

    components:
    -   name: generalized_gaussian_model
        type: SkyModel
        spectral:
            type: PowerLawSpectralModel
            parameters:
            -   name: index
                value: 2.0
            -   name: amplitude
                value: 1.0e-12
                unit: cm-2 s-1 TeV-1
            -   name: reference
                value: 1.0
                unit: TeV
        temporal:
            type: GeneralizedGaussianTemporalModel
            parameters:
            -   name: t_ref
                value: 59123.0
                unit: d
            -   name: t_rise
                value: 0.1
                unit: d
            -   name: t_decay
                value: 1.0
                unit: d
            -   name: eta
                value: 0.6666666666666666
            scale: utc
    metadata:
        creator: Gammapy 1.3.dev224+g5774c346f
        date: '2024-05-02T16:14:46.922429'
        origin: null






.. _sphx_glr_download_user-guide_model-gallery_temporal_plot_generalized_gaussian_temporal.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/gammapy/gammapy-webpage/main?urlpath=lab/tree/notebooks/dev/user-guide/model-gallery/temporal/plot_generalized_gaussian_temporal.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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


.. only:: html

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

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