.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_cov_model/00_intro.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_00_intro.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02_cov_model_00_intro.py:


Introductory example
====================

Let us start with a short example of a self defined model (Of course, we
provide a lot of predefined models [See: :any:`gstools.covmodel`],
but they all work the same way).
Therefore we reimplement the Gaussian covariance model
by defining just the "normalized"
`correlation <https://en.wikipedia.org/wiki/Autocovariance#Normalization>`_
function:

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.. code-block:: Python


    import numpy as np

    import gstools as gs


    # use CovModel as the base-class
    class Gau(gs.CovModel):
        def cor(self, h):
            return np.exp(-(h**2))









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Here the parameter ``h`` stands for the normalized range ``r / len_scale``.
Now we can instantiate this model:

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.. code-block:: Python


    model = Gau(dim=2, var=2.0, len_scale=10)








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To have a look at the variogram, let's plot it:

.. GENERATED FROM PYTHON SOURCE LINES 33-36

.. code-block:: Python


    model.plot()




.. image-sg:: /examples/02_cov_model/images/sphx_glr_00_intro_001.png
   :alt: 00 intro
   :srcset: /examples/02_cov_model/images/sphx_glr_00_intro_001.png
   :class: sphx-glr-single-img





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This is almost identical to the already provided :any:`Gaussian` model.
There, a scaling factor is implemented so the len_scale coincides with the
integral scale:

.. GENERATED FROM PYTHON SOURCE LINES 40-45

.. code-block:: Python


    gau_model = gs.Gaussian(dim=2, var=2.0, len_scale=10)
    gau_model.plot()





.. image-sg:: /examples/02_cov_model/images/sphx_glr_00_intro_002.png
   :alt: 00 intro
   :srcset: /examples/02_cov_model/images/sphx_glr_00_intro_002.png
   :class: sphx-glr-single-img





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Parameters
----------

We already used some parameters, which every covariance models has.
The basic ones are:

    - **dim** : dimension of the model
    - **var** : variance of the model (on top of the subscale variance)
    - **len_scale** : length scale of the model
    - **nugget** : nugget (subscale variance) of the model

These are the common parameters used to characterize
a covariance model and are therefore used by every model in GSTools.
You can also access and reset them:

.. GENERATED FROM PYTHON SOURCE LINES 60-69

.. code-block:: Python


    print("old model:", model)
    model.dim = 3
    model.var = 1
    model.len_scale = 15
    model.nugget = 0.1
    print("new model:", model)






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

 .. code-block:: none

    old model: Gau(dim=2, var=2.0, len_scale=10.0)
    new model: Gau(dim=3, var=1.0, len_scale=15.0, nugget=0.1)




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.. note::

   - The sill of the variogram is calculated by ``sill = variance + nugget``
     So we treat the variance as everything **above** the nugget,
     which is sometimes called **partial sill**.
   - A covariance model can also have additional parameters.


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

   **Total running time of the script:** (0 minutes 0.086 seconds)


.. _sphx_glr_download_examples_02_cov_model_00_intro.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 00_intro.ipynb <00_intro.ipynb>`

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

      :download:`Download Python source code: 00_intro.py <00_intro.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 00_intro.zip <00_intro.zip>`


.. only:: html

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

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