.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\ExtendedFields\plot_intrinsic.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_ExtendedFields_plot_intrinsic.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_ExtendedFields_plot_intrinsic.py:


================================
Textured images with large trend
================================

.. codeauthor:: Frédéric Richard <frederic.richard_at_univ-amu.fr>

In this example, we show how to simulate textured images with large trends.

Basic AFBF have :term:`stationary<stationarity>` :term:`increments`.
This is ensured by the fact that the Hurst function :math:`\beta`
ranges in the interval :math:`(0,1)`. However, the package PyAFBF
enables the simulation of more generic fields for which :math:`\beta`
have values above 1. Increments of order 0 of such fields might not be
stationary anymore. They are :term:`intrinsic` fields of an order k,
which depends on the maximal value of the Hurst function. Such fields
may show large polynomial trends, the degree of which corresponding
to the order k.

.. note::
    Even when extended to an intrinsic random field,
    the hurst function of an AFBF
    has a minimum :math:`H`` which remains in :math:`(0,1)`.

.. seealso::
    The definition and theory of intrinsic random fields are presented
    in :cite:p:`Chiles-2012`. These fields have been used for modeling
    in the framework of AFBF
    :cite:p:`Richard-2017,Richard-2016,Richard-2015b,Richard-2015,
    Richard-2010`.

.. GENERATED FROM PYTHON SOURCE LINES 70-89



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


    *

      .. image:: /auto_examples/ExtendedFields/images/sphx_glr_plot_intrinsic_001.png
          :alt: Intrinsic field.
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/ExtendedFields/images/sphx_glr_plot_intrinsic_002.png
          :alt: Hurst function
          :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    C:\Users\frede\Nextcloud\Synchro\Recherche\Deep-Texture\PyAFBF\afbf\Classes\SpatialData.py:318: MatplotlibDeprecationWarning: Adding an axes using the same arguments as a previous axes currently reuses the earlier instance.  In a future version, a new instance will always be created and returned.  Meanwhile, this warning can be suppressed, and the future behavior ensured, by passing a unique label to each axes instance.
      fig = plt.subplot()






|

.. code-block:: default

    import numpy as np
    from afbf import tbfield

    # Definition and simulation of an AFBF.
    Z = tbfield('afbf-smooth')

    Z.hurst.ChangeParameters(
        np.array([[1.3, 0.1]]),
        np.array([[-1.2, -1.1, 1.1,  1.2]])
        )
    Z.hurst.trans = 1
    Z.NormalizeModel()

    Z.FindOrder()
    Z.DisplayParameters()
    np.random.seed(1)
    z = Z.Simulate()
    z.name = 'Intrinsic field.'
    z.Display(1)


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

   **Total running time of the script:** ( 0 minutes  9.853 seconds)


.. _sphx_glr_download_auto_examples_ExtendedFields_plot_intrinsic.py:


.. only :: html

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



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

     :download:`Download Python source code: plot_intrinsic.py <plot_intrinsic.py>`



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

     :download:`Download Jupyter notebook: plot_intrinsic.ipynb <plot_intrinsic.ipynb>`


.. only:: html

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

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