.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/11_plurigaussian/06_periodic.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_11_plurigaussian_06_periodic.py>`
        to download the full example code.

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

.. _sphx_glr_examples_11_plurigaussian_06_periodic.py:


Creating PGS with periodic boundaries
-------------------------------------

Plurigaussian fields with periodic boundaries (P-PGS) are used in various
applications, including the simulation of interactions between the landsurface
and the atmosphere, as well as the application of homogenisation theory to
porous media, e.g. `Ricketts 2024 <https://doi.org/10.1007/s11242-024-02074-z>`__.

In this example we will use GSTools's Fourier generator to create periodic
random fields, which can in turn be used to generate P-PGS.

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.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import gstools as gs

    dim = 2
    # define the spatial grid, see the periodic random field [examples](https://geostat-framework.readthedocs.io/projects/gstools/en/latest/examples/01_random_field/08_fourier.html)
    # for details.

    # domain size and periodicity
    lithotypes = 200
    # no. of cells in both dimensions
    N = [170, 153]

    x = np.linspace(0, lithotypes, N[0], endpoint=False)
    y = np.linspace(0, lithotypes, N[1], endpoint=False)








.. GENERATED FROM PYTHON SOURCE LINES 32-36

The parameters of the covariance model are very similar to previous examples.
The interesting part is the SRF class. We set the `generator` to `"Fourier"`,
which inherently generates periodic SRFs. The Fourier generator needs an
extra parameter `period` which defines the periodicity.

.. GENERATED FROM PYTHON SOURCE LINES 36-42

.. code-block:: Python


    model = gs.Gaussian(dim=dim, var=0.8, len_scale=40)
    srf = gs.SRF(model, generator="Fourier", period=lithotypes)
    field1 = srf.structured([x, y], seed=19770319)
    field2 = srf.structured([x, y], seed=19860912)








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Very similar to previous examples, we create a simple lithotypes field.

.. GENERATED FROM PYTHON SOURCE LINES 44-56

.. code-block:: Python


    M = [200, 160]

    # size of the rectangle
    rect = [40, 32]

    lithotypes = np.zeros(M)
    lithotypes[
        M[0] // 2 - rect[0] // 2 : M[0] // 2 + rect[0] // 2,
        M[1] // 2 - rect[1] // 2 : M[1] // 2 + rect[1] // 2,
    ] = 1








.. GENERATED FROM PYTHON SOURCE LINES 57-58

With the two SRFs and the lithotypes ready, we can create our first P-PGS.

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: Python


    pgs = gs.PGS(dim, [field1, field2])
    P = pgs(lithotypes)








.. GENERATED FROM PYTHON SOURCE LINES 63-68

Finally, we can plot the PGS, but we will also show the lithotypes and the
two original periodic Gaussian fields. Especially with `field1` you can
nicely see the periodic structures in the black structure in the upper right
corner. This transfers to the P-PGS, where you can see that the structures
seemlessly match the opposite boundaries.

.. GENERATED FROM PYTHON SOURCE LINES 68-77

.. code-block:: Python


    fig, axs = plt.subplots(2, 2)

    axs[0, 0].imshow(field1, cmap="copper", origin="lower")
    axs[0, 1].imshow(field2, cmap="copper", origin="lower")
    axs[1, 0].imshow(lithotypes, cmap="copper", origin="lower")
    axs[1, 1].imshow(P, cmap="copper", origin="lower")

    plt.show()



.. image-sg:: /examples/11_plurigaussian/images/sphx_glr_06_periodic_001.png
   :alt: 06 periodic
   :srcset: /examples/11_plurigaussian/images/sphx_glr_06_periodic_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.238 seconds)


.. _sphx_glr_download_examples_11_plurigaussian_06_periodic.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 06_periodic.ipynb <06_periodic.ipynb>`

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

      :download:`Download Python source code: 06_periodic.py <06_periodic.py>`

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

      :download:`Download zipped: 06_periodic.zip <06_periodic.zip>`


.. only:: html

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

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