.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_cov_model/05_additional_para.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_02_cov_model_05_additional_para.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02_cov_model_05_additional_para.py:


Additional Parameters
=====================

Let's pimp our self-defined model ``Gau`` from the introductory example
by setting the exponent as an additional parameter:

.. math::
   \rho(r) := \exp\left(-\left(\frac{r}{\ell}\right)^{\alpha}\right)

This leads to the so called **stable** covariance model and we can define it by

.. GENERATED FROM PYTHON SOURCE LINES 13-27

.. code-block:: Python


    import numpy as np

    import gstools as gs


    class Stab(gs.CovModel):
        def default_opt_arg(self):
            return {"alpha": 1.5}

        def cor(self, h):
            return np.exp(-(h**self.alpha))









.. GENERATED FROM PYTHON SOURCE LINES 28-34

As you can see, we override the method :any:`CovModel.default_opt_arg`
to provide a standard value for the optional argument ``alpha``.
We can access it in the correlation function by ``self.alpha``

Now we can instantiate this model by either setting alpha implicitly with
the default value or explicitly:

.. GENERATED FROM PYTHON SOURCE LINES 34-40

.. code-block:: Python


    model1 = Stab(dim=2, var=2.0, len_scale=10)
    model2 = Stab(dim=2, var=2.0, len_scale=10, alpha=0.5)
    ax = model1.plot()
    model2.plot(ax=ax)




.. image-sg:: /examples/02_cov_model/images/sphx_glr_05_additional_para_001.png
   :alt: 05 additional para
   :srcset: /examples/02_cov_model/images/sphx_glr_05_additional_para_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-48

Apparently, the parameter alpha controls the slope of the variogram
and consequently the roughness of a generated random field.

.. note::

   You don't have to override the :any:`CovModel.default_opt_arg`,
   but you will get a ValueError if you don't set it on creation.


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

   **Total running time of the script:** (0 minutes 0.066 seconds)


.. _sphx_glr_download_examples_02_cov_model_05_additional_para.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 05_additional_para.ipynb <05_additional_para.ipynb>`

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      :download:`Download Python source code: 05_additional_para.py <05_additional_para.py>`

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      :download:`Download zipped: 05_additional_para.zip <05_additional_para.zip>`


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