:orphan:

Random Field Generation
=======================

The main feature of GSTools is the spatial random field generator :any:`SRF`,
which can generate random fields following a given covariance model.
The generator provides a lot of nice features, which will be explained in
the following

GSTools generates spatial random fields with a given covariance model or
semi-variogram. This is done by using the so-called randomization method.
The spatial random field is represented by a stochastic Fourier integral
and its discretised modes are evaluated at random frequencies.

In case you want to generate spatial random fields with periodic boundaries,
you can use the so-called Fourier method. See the corresponding examples for
how to do that. The spatial random field is represented by a stochastic
Fourier integral and its discretised modes are evaluated at equidistant
frequencies.

GSTools supports arbitrary and non-isotropic covariance models.

Examples
--------


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    <div class="sphx-glr-thumbcontainer" tooltip="We are going to start with a very simple example of a spatial random field with an isotropic Gaussian covariance model and following parameters:">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_00_gaussian_thumb.png
    :alt:

  :doc:`/examples/01_random_field/00_gaussian`

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      <div class="sphx-glr-thumbnail-title">A Very Simple Example</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Creating an ensemble of random fields would also be a great idea. Let&#x27;s reuse most of the previous code.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_01_srf_ensemble_thumb.png
    :alt:

  :doc:`/examples/01_random_field/01_srf_ensemble`

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      <div class="sphx-glr-thumbnail-title">Creating an Ensemble of Fields</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Only using Gaussian covariance fields gets boring. Now we are going to create much rougher random fields by using an exponential covariance model and we are going to make them anisotropic.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_02_fancier_thumb.png
    :alt:

  :doc:`/examples/01_random_field/02_fancier`

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      <div class="sphx-glr-thumbnail-title">Creating Fancier Fields</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="For many applications, the random fields are needed on an unstructured grid. Normally, such a grid would be read in, but we can simply generate one and then create a random field at those coordinates.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_03_unstr_srf_export_thumb.png
    :alt:

  :doc:`/examples/01_random_field/03_unstr_srf_export`

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      <div class="sphx-glr-thumbnail-title">Using an Unstructured Grid</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We can even generate the same field realisation on different grids. Let&#x27;s try to merge two unstructured rectangular fields.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_04_srf_merge_thumb.png
    :alt:

  :doc:`/examples/01_random_field/04_srf_merge`

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      <div class="sphx-glr-thumbnail-title">Merging two Fields</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="GSTools provides an interface for meshes, to support meshio and ogs5py meshes.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_05_mesh_ensemble_thumb.png
    :alt:

  :doc:`/examples/01_random_field/05_mesh_ensemble`

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      <div class="sphx-glr-thumbnail-title">Generating Fields on Meshes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="PyVista is a helper module for the Visualization Toolkit (VTK) that takes a different approach on interfacing with VTK through NumPy and direct array access.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_06_pyvista_support_thumb.png
    :alt:

  :doc:`/examples/01_random_field/06_pyvista_support`

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      <div class="sphx-glr-thumbnail-title">Using PyVista meshes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="GSTools provides experimental support for higher dimensions.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_07_higher_dimensions_thumb.png
    :alt:

  :doc:`/examples/01_random_field/07_higher_dimensions`

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      <div class="sphx-glr-thumbnail-title">Higher Dimensions</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="In this simple example we are going to learn how to generate periodic spatial random fields. The Fourier method comes naturally with the property of periodicity, so we&#x27;ll use it to create the random field.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_08_fourier_thumb.png
    :alt:

  :doc:`/examples/01_random_field/08_fourier`

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      <div class="sphx-glr-thumbnail-title">Generating a Simple Periodic Random Field</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Building on the precious example, we are now going to generate periodic spatial random fields with a transformation applied, resulting in a level set.">

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  .. image:: /examples/01_random_field/images/thumb/sphx_glr_09_fourier_trans_thumb.png
    :alt:

  :doc:`/examples/01_random_field/09_fourier_trans`

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      <div class="sphx-glr-thumbnail-title">Generating a Transformed Periodic Random Field</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /examples/01_random_field/00_gaussian
   /examples/01_random_field/01_srf_ensemble
   /examples/01_random_field/02_fancier
   /examples/01_random_field/03_unstr_srf_export
   /examples/01_random_field/04_srf_merge
   /examples/01_random_field/05_mesh_ensemble
   /examples/01_random_field/06_pyvista_support
   /examples/01_random_field/07_higher_dimensions
   /examples/01_random_field/08_fourier
   /examples/01_random_field/09_fourier_trans



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