.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/11_plurigaussian/03_correlations.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_03_correlations.py>`
        to download the full example code.

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

.. _sphx_glr_examples_11_plurigaussian_03_correlations.py:


Understanding the Influence of Variograms
-----------------------------------------

Up until now, we have only used very smooth Gaussian variograms for the
underlying spatial random fields. Now, we will combine a smooth Gaussian
field with a much rougher exponential field. This example should feel
familiar, if you had a look at the previous examples.

.. GENERATED FROM PYTHON SOURCE LINES 10-23

.. 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 = [200, 200]

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








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Now, we generate fields with a Gaussian and an Exponential variogram.

.. GENERATED FROM PYTHON SOURCE LINES 25-33

.. code-block:: Python


    model1 = gs.Gaussian(dim=dim, var=1, len_scale=[50, 25])
    srf1 = gs.SRF(model1)
    field1 = srf1.structured([x, y], seed=20170519)
    model2 = gs.Exponential(dim=dim, var=1, len_scale=[40, 40])
    srf2 = gs.SRF(model2)
    field2 = srf2.structured([x, y], seed=19970221)








.. GENERATED FROM PYTHON SOURCE LINES 34-36

The lithotypes will consist of a circle which contains one category and the
surrounding is the second category.

.. GENERATED FROM PYTHON SOURCE LINES 36-51

.. code-block:: Python


    # no. of grid cells of the lithotypes
    M = [200, 200]

    # radius of circle
    radius = 25

    x_lith = np.arange(M[0])
    y_lith = np.arange(M[1])
    lithotypes = np.zeros(M)
    mask = (x_lith[:, np.newaxis] - M[0] // 2) ** 2 + (
        y_lith[np.newaxis, :] - M[1] // 2
    ) ** 2 < radius**2
    lithotypes[mask] = 1








.. GENERATED FROM PYTHON SOURCE LINES 52-53

With the two SRFs and the lithotypes ready, we can create the PGS.

.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 57-58

And now the plotting of the two Gaussian fields, the lithotypes, and the PGS.

.. GENERATED FROM PYTHON SOURCE LINES 58-66

.. 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")




.. image-sg:: /examples/11_plurigaussian/images/sphx_glr_03_correlations_001.png
   :alt: 03 correlations
   :srcset: /examples/11_plurigaussian/images/sphx_glr_03_correlations_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 67-70

In this PGS, we can see two different spatial structures combined. We see large
and rather smooth structures and shapes, which are surrounded by very rough and
unconnected patches.


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

   **Total running time of the script:** (0 minutes 2.116 seconds)


.. _sphx_glr_download_examples_11_plurigaussian_03_correlations.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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