.. 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_linear_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_linear_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_linear_temporal.py:


.. _linear-temporal-model:

Linear temporal model
=======================

This model parametrises a linear time model.

.. math:: F(t) = \alpha + \beta \cdot (t - t_{\rm{ref}})

.. GENERATED FROM PYTHON SOURCE LINES 14-17

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

.. GENERATED FROM PYTHON SOURCE LINES 17-35

.. code-block:: Python


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

    time_range = [Time.now(), Time.now() + 2 * u.d]
    linear_model = LinearTemporalModel(
        alpha=1, beta=0.5 / u.d, t_ref=(time_range[0].mjd - 0.1) * u.d
    )
    linear_model.plot(time_range)
    plt.grid(which="both")




.. image-sg:: /user-guide/model-gallery/temporal/images/sphx_glr_plot_linear_temporal_001.png
   :alt: plot linear temporal
   :srcset: /user-guide/model-gallery/temporal/images/sphx_glr_plot_linear_temporal_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 36-39

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

.. GENERATED FROM PYTHON SOURCE LINES 39-48

.. code-block:: Python


    model = SkyModel(
        spectral_model=PowerLawSpectralModel(),
        temporal_model=linear_model,
        name="linear-model",
    )
    models = Models([model])

    print(models.to_yaml())




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

 .. code-block:: none

    components:
    -   name: linear-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: LinearTemporalModel
            parameters:
            -   name: alpha
                value: 1.0
            -   name: beta
                value: 0.5
                unit: d-1
            -   name: t_ref
                value: 60436.45079852542
                unit: d
            scale: utc
    metadata:
        creator: Gammapy 1.3.dev250+gf001e71f2
        date: '2024-05-06T13:13:09.096614'
        origin: null






.. _sphx_glr_download_user-guide_model-gallery_temporal_plot_linear_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_linear_temporal.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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


.. only:: html

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

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