.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "modeling/gallery/spectral/plot_logparabola.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_modeling_gallery_spectral_plot_logparabola.py: .. _logparabola-spectral-model: Log parabola spectral model =========================== This model parametrises a log parabola spectrum. It is defined by the following equation: .. math:: \phi(E) = \phi_0 \left( \frac{E}{E_0} \right) ^ { - \alpha - \beta \log{ \left( \frac{E}{E_0} \right) } } Note that :math:`log` refers to the natural logarithm. This is consistent with the `Fermi Science Tools `_ and `ctools `_. The `Sherpa `_ package, however, uses :math:`log_{10}`. If you have parametrization based on :math:`log_{10}` you can use the :func:`~gammapy.modeling.models.LogParabolaSpectralModel.from_log10` method. .. GENERATED FROM PYTHON SOURCE LINES 28-31 Example plot ------------ Here is an example plot of the model: .. GENERATED FROM PYTHON SOURCE LINES 31-46 .. code-block:: default from astropy import units as u import matplotlib.pyplot as plt from gammapy.modeling.models import LogParabolaSpectralModel, Models, SkyModel energy_bounds = [0.1, 100] * u.TeV model = LogParabolaSpectralModel( alpha=2.3, amplitude="1e-12 cm-2 s-1 TeV-1", reference=1 * u.TeV, beta=0.5, ) model.plot(energy_bounds) plt.grid(which="both") .. image-sg:: /modeling/gallery/spectral/images/sphx_glr_plot_logparabola_001.png :alt: plot logparabola :srcset: /modeling/gallery/spectral/images/sphx_glr_plot_logparabola_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 47-50 YAML representation ------------------- Here is an example YAML file using the model: .. GENERATED FROM PYTHON SOURCE LINES 50-55 .. code-block:: default model = SkyModel(spectral_model=model, name="log-parabola-model") models = Models([model]) print(models.to_yaml()) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none components: - name: log-parabola-model type: SkyModel spectral: type: LogParabolaSpectralModel parameters: - name: amplitude value: 1.0e-12 unit: cm-2 s-1 TeV-1 - name: reference value: 1.0 unit: TeV frozen: true - name: alpha value: 2.3 - name: beta value: 0.5 .. _sphx_glr_download_modeling_gallery_spectral_plot_logparabola.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_logparabola.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_logparabola.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_