.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/01_random_field/09_fourier_trans.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_01_random_field_09_fourier_trans.py>`
        to download the full example code.

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

.. _sphx_glr_examples_01_random_field_09_fourier_trans.py:


Generating a Transformed Periodic Random Field
----------------------------------------------

Building on the precious example, we are now going to generate periodic
spatial random fields with a transformation applied, resulting in a level set.

.. GENERATED FROM PYTHON SOURCE LINES 8-50



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/01_random_field/images/sphx_glr_09_fourier_trans_001.png
         :alt: Field 2D structured: (300, 200)
         :srcset: /examples/01_random_field/images/sphx_glr_09_fourier_trans_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/01_random_field/images/sphx_glr_09_fourier_trans_002.png
         :alt: Field 2D structured: (300, 200)
         :srcset: /examples/01_random_field/images/sphx_glr_09_fourier_trans_002.png
         :class: sphx-glr-multi-img





.. code-block:: Python


    import numpy as np

    import gstools as gs

    # We start off by defining the spatial grid. As in the previous example, we do
    # not want to include the endpoints.
    L = np.array((500, 400))
    x = np.linspace(0, L[0], 300, endpoint=False)
    y = np.linspace(0, L[1], 200, endpoint=False)

    # Instead of using a Gaussian covariance model, we will use the much rougher
    # exponential model and we will introduce an anisotropy by using two different
    # length scales in the x- and y-directions
    model = gs.Exponential(dim=2, var=2, len_scale=[80, 20])

    # Same as before, we set up the spatial random field. But this time, we will
    #  use a periodicity which is equal to the domain size in x-direction, but
    # half the domain size in y-direction. And we will use different `mode_no` for
    # the different dimensions.
    srf = gs.SRF(
        model,
        generator="Fourier",
        period=[L[0], L[1] / 2],
        mode_no=[30, 20],
        seed=1681903,
    )
    # and compute it on our spatial domain
    srf((x, y), mesh_type="structured")

    # With the field generated, we can now apply transformations starting with a
    # discretization of the field into 4 different values
    thresholds = np.linspace(np.min(srf.field), np.max(srf.field), 4)
    srf.transform("discrete", store="transform_discrete", values=thresholds)
    srf.plot("transform_discrete")

    # This is already a nice result, but we want to pronounce the peaks of the
    # field. We can do this by applying a log-normal transformation on top
    srf.transform(
        "lognormal", field="transform_discrete", store="transform_lognormal"
    )
    srf.plot("transform_lognormal")


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

   **Total running time of the script:** (0 minutes 1.187 seconds)


.. _sphx_glr_download_examples_01_random_field_09_fourier_trans.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 09_fourier_trans.ipynb <09_fourier_trans.ipynb>`

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

      :download:`Download Python source code: 09_fourier_trans.py <09_fourier_trans.py>`

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

      :download:`Download zipped: 09_fourier_trans.zip <09_fourier_trans.zip>`


.. only:: html

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

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