.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\ExtendedFields\plot_extendedfield.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_extendedfield.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_ExtendedFields_plot_extendedfield.py:


========================================
Textured images with spectral variations
========================================

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

In this example, we show how to simulate a field having a topothesy whose
values may vary depending both on the direction and the amplitude.


.. note::
    The obtained simulation relates to a model with a semi-variogram
    of the form:

    .. math::
        v(x) = \int_{\mathbb{R}^2} \vert e^{i\langle x, w \rangle} - 1 \vert^2
        \tau(w) \vert w \vert^{2H-2} dw.

    where, contrarily to usual AFBF, the value :math:`\tau(w)` does not only
    depend on the direction :math:`\arg(w)` of :math:`w`,
    but also on its amplitude :math:`\vert w \vert`.

.. GENERATED FROM PYTHON SOURCE LINES 62-115



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


    *

      .. image:: /auto_examples/ExtendedFields/images/sphx_glr_plot_extendedfield_001.png
          :alt: Extended field.
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/ExtendedFields/images/sphx_glr_plot_extendedfield_002.png
          :alt: Generalized topothesy
          :class: sphx-glr-multi-img





.. code-block:: default

    import numpy as np
    from afbf import perfunction, tbfield
    from matplotlib import pyplot as plt

    nb_angle = 4  # Number of angle subdivisions.
    nb_spect = 3  # Number of spectrum subdivisions.

    # Definition of a fractional Brownian field.
    Z = tbfield('fbf')
    Z.hurst.ChangeParameters(
        np.array([0.1])
        )
    Z.NormalizeModel()


    Z.ExtendTopothesy(nb_spect, nb_angle)
    for j in range(nb_spect):
        # Set uniformly spaced interval for the step functions.
        Z.gtopo[j].SetUniformStepInterval()

    np.random.seed(1)
    z = Z.Simulate()
    z.name = 'Extended field.'
    z.Display(1)


    # Visualize the generalized topothesy.
    gtopo = perfunction('step-smooth', nb_spect)  # Topothesy at an angle.
    gtopo.SetUniformStepInterval()

    z = np.linspace(-np.pi / 2, np.pi / 2, 1000)
    im = np.zeros((z.size, z.size))
    for i in range(z.size):
        # Setting parameters of the topothesy at angle z[i]
        for j in range(nb_spect):
            Z.gtopo[j].Evaluate(np.array([z[i]]))
            # The value of Z.gtopo[j] at z[i] gives the values of the jth
            # parameter of the generalized topothesy at the ith angle.
            gtopo.fparam[0, j] = Z.gtopo[j].values[0, 0]

        # Evaluate the topothesy at angle z[i]
        gtopo.Evaluate(z)
        im[i, :] = gtopo.values.reshape((1, z.size))

    plt.figure(2)
    plt.imshow(im, cmap='gray')
    plt.title('Generalized topothesy')
    plt.xlabel(r'Amplitude $\rho$')
    plt.ylabel(r'Angle $\varphi$')
    loc, lab = plt.yticks(
        np.linspace(0, z.size, 5),
        [r'$-\pi/2$', r'$-\pi/4$', r'$0$', r'$\pi/4$', r'$\pi/2$']
        )


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

   **Total running time of the script:** ( 2 minutes  31.324 seconds)


.. _sphx_glr_download_auto_examples_ExtendedFields_plot_extendedfield.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_extendedfield.py <plot_extendedfield.py>`



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

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


.. only:: html

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

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