.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/03_variogram/01_find_best_model.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_03_variogram_01_find_best_model.py>`
        to download the full example code.

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

.. _sphx_glr_examples_03_variogram_01_find_best_model.py:


Finding the best fitting variogram model
----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 5-11

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    import gstools as gs








.. GENERATED FROM PYTHON SOURCE LINES 12-13

Generate a synthetic field with an exponential model.

.. GENERATED FROM PYTHON SOURCE LINES 13-20

.. code-block:: Python


    x = np.random.RandomState(19970221).rand(1000) * 100.0
    y = np.random.RandomState(20011012).rand(1000) * 100.0
    model = gs.Exponential(dim=2, var=2, len_scale=8)
    srf = gs.SRF(model, mean=0, seed=19970221)
    field = srf((x, y))








.. GENERATED FROM PYTHON SOURCE LINES 21-22

Estimate the variogram of the field with 40 bins and plot the result.

.. GENERATED FROM PYTHON SOURCE LINES 22-26

.. code-block:: Python


    bins = np.arange(40)
    bin_center, gamma = gs.vario_estimate((x, y), field, bins)








.. GENERATED FROM PYTHON SOURCE LINES 27-28

Define a set of models to test.

.. GENERATED FROM PYTHON SOURCE LINES 28-42

.. code-block:: Python


    models = {
        "Gaussian": gs.Gaussian,
        "Exponential": gs.Exponential,
        "Matern": gs.Matern,
        "Stable": gs.Stable,
        "Rational": gs.Rational,
        "Circular": gs.Circular,
        "Spherical": gs.Spherical,
        "SuperSpherical": gs.SuperSpherical,
        "JBessel": gs.JBessel,
    }
    scores = {}








.. GENERATED FROM PYTHON SOURCE LINES 43-44

Iterate over all models, fit their variogram and calculate the r2 score.

.. GENERATED FROM PYTHON SOURCE LINES 44-56

.. code-block:: Python


    # plot the estimated variogram
    plt.scatter(bin_center, gamma, color="k", label="data")
    ax = plt.gca()

    # fit all models to the estimated variogram
    for model in models:
        fit_model = models[model](dim=2)
        para, pcov, r2 = fit_model.fit_variogram(bin_center, gamma, return_r2=True)
        fit_model.plot(x_max=40, ax=ax)
        scores[model] = r2




.. image-sg:: /examples/03_variogram/images/sphx_glr_01_find_best_model_001.png
   :alt: 01 find best model
   :srcset: /examples/03_variogram/images/sphx_glr_01_find_best_model_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 57-58

Create a ranking based on the score and determine the best models

.. GENERATED FROM PYTHON SOURCE LINES 58-65

.. code-block:: Python


    ranking = sorted(scores.items(), key=lambda item: item[1], reverse=True)
    print("RANKING by Pseudo-r2 score")
    for i, (model, score) in enumerate(ranking, 1):
        print(f"{i:>6}. {model:>15}: {score:.5}")

    plt.show()




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

 .. code-block:: none

    RANKING by Pseudo-r2 score
         1.          Stable: 0.98218
         2.          Matern: 0.98176
         3.  SuperSpherical: 0.98141
         4.     Exponential: 0.98041
         5.        Rational: 0.97711
         6.       Spherical: 0.97334
         7.        Circular: 0.96725
         8.        Gaussian: 0.95928
         9.         JBessel: 0.95831





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

   **Total running time of the script:** (0 minutes 0.529 seconds)


.. _sphx_glr_download_examples_03_variogram_01_find_best_model.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 01_find_best_model.ipynb <01_find_best_model.ipynb>`

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

      :download:`Download Python source code: 01_find_best_model.py <01_find_best_model.py>`

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

      :download:`Download zipped: 01_find_best_model.zip <01_find_best_model.zip>`


.. only:: html

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

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