.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/03_variogram/03_directional_2d.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_03_directional_2d.py>`
        to download the full example code.

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

.. _sphx_glr_examples_03_variogram_03_directional_2d.py:


Directional variogram estimation and fitting in 2D
--------------------------------------------------

In this example, we demonstrate how to estimate a directional variogram by
setting the direction angles in 2D.

Afterwards we will fit a model to this estimated variogram and show the result.

.. GENERATED FROM PYTHON SOURCE LINES 10-16

.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    import gstools as gs








.. GENERATED FROM PYTHON SOURCE LINES 17-18

Generating synthetic field with anisotropy and a rotation of 22.5 degree.

.. GENERATED FROM PYTHON SOURCE LINES 18-25

.. code-block:: Python


    angle = np.pi / 8
    model = gs.Exponential(dim=2, len_scale=[10, 5], angles=angle)
    x = y = range(101)
    srf = gs.SRF(model, seed=123456)
    field = srf((x, y), mesh_type="structured")








.. GENERATED FROM PYTHON SOURCE LINES 26-28

Now we are going to estimate a directional variogram with an angular
tolerance of 11.25 degree and a bandwith of 8.

.. GENERATED FROM PYTHON SOURCE LINES 28-39

.. code-block:: Python


    bins = range(0, 40, 2)
    bin_center, dir_vario, counts = gs.vario_estimate(
        *((x, y), field, bins),
        direction=gs.rotated_main_axes(dim=2, angles=angle),
        angles_tol=np.pi / 16,
        bandwidth=8,
        mesh_type="structured",
        return_counts=True,
    )








.. GENERATED FROM PYTHON SOURCE LINES 40-41

Afterwards we can use the estimated variogram to fit a model to it:

.. GENERATED FROM PYTHON SOURCE LINES 41-48

.. code-block:: Python


    print("Original:")
    print(model)
    model.fit_variogram(bin_center, dir_vario)
    print("Fitted:")
    print(model)





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

 .. code-block:: none

    Original:
    Exponential(dim=2, var=1.0, len_scale=10.0, anis=[0.5], angles=[0.393])
    Fitted:
    Exponential(dim=2, var=0.942, len_scale=9.14, anis=[0.529], angles=[0.393])




.. GENERATED FROM PYTHON SOURCE LINES 49-50

Plotting.

.. GENERATED FROM PYTHON SOURCE LINES 50-64

.. code-block:: Python


    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=[10, 5])

    ax1.scatter(bin_center, dir_vario[0], label="emp. vario: pi/8")
    ax1.scatter(bin_center, dir_vario[1], label="emp. vario: pi*5/8")
    ax1.legend(loc="lower right")

    model.plot("vario_axis", axis=0, ax=ax1, x_max=40, label="fit on axis 0")
    model.plot("vario_axis", axis=1, ax=ax1, x_max=40, label="fit on axis 1")
    ax1.set_title("Fitting an anisotropic model")

    srf.plot(ax=ax2)
    plt.show()




.. image-sg:: /examples/03_variogram/images/sphx_glr_03_directional_2d_001.png
   :alt: Fitting an anisotropic model, Field 2D structured: (101, 101)
   :srcset: /examples/03_variogram/images/sphx_glr_03_directional_2d_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 65-67

Without fitting a model, we see that the correlation length in the main
direction is greater than the transversal one.


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

   **Total running time of the script:** (0 minutes 3.912 seconds)


.. _sphx_glr_download_examples_03_variogram_03_directional_2d.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 03_directional_2d.ipynb <03_directional_2d.ipynb>`

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

      :download:`Download Python source code: 03_directional_2d.py <03_directional_2d.py>`

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

      :download:`Download zipped: 03_directional_2d.zip <03_directional_2d.zip>`


.. only:: html

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

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