.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/11_plurigaussian/00_simple.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_00_simple.py>`
        to download the full example code.

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

.. _sphx_glr_examples_11_plurigaussian_00_simple.py:


A First and Simple Example
--------------------------

As a first example, we will create a two dimensional plurigaussian field
(PGS). Thus, we need two spatial random fields(SRF) and on top of that, we
need a field describing the categorical data and its spatial relation.
We will start off by creating the two SRFs with a Gaussian variogram, which
makes the fields nice and smooth. But before that, we will import all
necessary libraries and define a few variables, like the number of grid
cells in each dimension.

.. GENERATED FROM PYTHON SOURCE LINES 13-26

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    import gstools as gs

    dim = 2
    # no. of cells in both dimensions
    N = [180, 140]

    x = np.arange(N[0])
    y = np.arange(N[1])








.. GENERATED FROM PYTHON SOURCE LINES 27-30

In this first example we will use the same geostatistical parameters for
both fields for simplicity. Thus, we can use the same SRF instance for the
two fields.

.. GENERATED FROM PYTHON SOURCE LINES 30-36

.. code-block:: Python


    model = gs.Gaussian(dim=dim, var=1, len_scale=10)
    srf = gs.SRF(model)
    field1 = srf.structured([x, y], seed=20170519)
    field2 = srf.structured([x, y], seed=19970221)








.. GENERATED FROM PYTHON SOURCE LINES 37-42

Now, we will create the lithotypes field describing the categorical data. For
now, we will only have two categories and we will address them by the
integers 0 and 1. We start off by creating a matrix of 0s from which we will
select a rectangle and fill that with 1s. This field does not have to match
the shape of the SRFs.

.. GENERATED FROM PYTHON SOURCE LINES 42-54

.. code-block:: Python


    centroid = [200, 160]

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

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








.. GENERATED FROM PYTHON SOURCE LINES 55-58

With the two SRFs and the L-field ready, we can create our first PGS. First, we
set up an instance of the PGS class and then we are ready to calculate the
field by calling the instance and handing over the L-field.

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 63-65

Finally, we can plot the PGS, but we will also show the L-field and the two
original Gaussian fields.

.. GENERATED FROM PYTHON SOURCE LINES 65-76

.. 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")

    # For more information on Plurigaussian fields and how they naturally extend
    # truncated Gaussian fields, we can recommend the book
    # [Plurigaussian Simulations in Geosciences](https://doi.org/10.1007/978-3-642-19607-2)



.. image-sg:: /examples/11_plurigaussian/images/sphx_glr_00_simple_001.png
   :alt: 00 simple
   :srcset: /examples/11_plurigaussian/images/sphx_glr_00_simple_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 1.550 seconds)


.. _sphx_glr_download_examples_11_plurigaussian_00_simple.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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