.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/02_cov_model/04_different_scales.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_04_different_scales.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02_cov_model_04_different_scales.py:


Different scales
================

Besides the length-scale, there are many other ways of characterizing a certain
scale of a covariance model. We provide two common scales with the covariance
model.

Integral scale
--------------

The `integral scale <https://en.wikipedia.org/wiki/Integral_length_scale>`_
of a covariance model is calculated by:

.. math:: I = \int_0^\infty \rho(r) dr

You can access it by:

.. GENERATED FROM PYTHON SOURCE LINES 19-27

.. code-block:: Python


    import gstools as gs

    model = gs.Stable(dim=3, var=2.0, len_scale=10)
    print("Main integral scale:", model.integral_scale)
    print("All integral scales:", model.integral_scale_vec)






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

 .. code-block:: none

    Main integral scale: 9.027452929509336
    All integral scales: [9.02745293 9.02745293 9.02745293]




.. GENERATED FROM PYTHON SOURCE LINES 28-30

You can also specify integral length scales like the ordinary length scale,
and len_scale/anis will be recalculated:

.. GENERATED FROM PYTHON SOURCE LINES 30-39

.. code-block:: Python


    model = gs.Stable(dim=3, var=2.0, integral_scale=[10, 4, 2])
    print("Anisotropy ratios:", model.anis)
    print("Main length scale:", model.len_scale)
    print("All length scales:", model.len_scale_vec)
    print("Main integral scale:", model.integral_scale)
    print("All integral scales:", model.integral_scale_vec)






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

 .. code-block:: none

    Anisotropy ratios: [0.4 0.2]
    Main length scale: 11.077321674324725
    All length scales: [11.07732167  4.43092867  2.21546433]
    Main integral scale: 10.0
    All integral scales: [10.  4.  2.]




.. GENERATED FROM PYTHON SOURCE LINES 40-46

Percentile scale
----------------

Another scale characterizing the covariance model, is the percentile scale.
It is the distance, where the normalized
variogram reaches a certain percentage of its sill.

.. GENERATED FROM PYTHON SOURCE LINES 46-55

.. code-block:: Python


    model = gs.Stable(dim=3, var=2.0, len_scale=10)
    per_scale = model.percentile_scale(0.9)
    int_scale = model.integral_scale
    len_scale = model.len_scale
    print("90% Percentile scale:", per_scale)
    print("Integral scale:", int_scale)
    print("Length scale:", len_scale)





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

 .. code-block:: none

    90% Percentile scale: 17.437215135964117
    Integral scale: 9.027452929509336
    Length scale: 10.0




.. GENERATED FROM PYTHON SOURCE LINES 56-63

.. note::

   The nugget is neglected by the percentile scale.


Comparison
----------

.. GENERATED FROM PYTHON SOURCE LINES 63-70

.. code-block:: Python


    ax = model.plot()
    ax.axhline(1.8, color="k", label=r"90% percentile")
    ax.axvline(per_scale, color="k", linestyle="--", label=r"90% percentile scale")
    ax.axvline(int_scale, color="k", linestyle="-.", label=r"integral scale")
    ax.axvline(len_scale, color="k", linestyle=":", label=r"length scale")
    ax.legend()



.. image-sg:: /examples/02_cov_model/images/sphx_glr_04_different_scales_001.png
   :alt: 04 different scales
   :srcset: /examples/02_cov_model/images/sphx_glr_04_different_scales_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.054 seconds)


.. _sphx_glr_download_examples_02_cov_model_04_different_scales.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 04_different_scales.ipynb <04_different_scales.ipynb>`

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

      :download:`Download Python source code: 04_different_scales.py <04_different_scales.py>`

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

      :download:`Download zipped: 04_different_scales.zip <04_different_scales.zip>`


.. only:: html

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

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