.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py:


Create a custom covariance model
================================

This example illustrates how the user can define his own covariance model.




.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import math as m
    ot.Log.Show(ot.Log.NONE)








Create the time grid


.. code-block:: default

    N = 32
    a = 4.0
    mesh = ot.IntervalMesher([N]).build(ot.Interval(-a, a))









Create the covariance function at (s,t)


.. code-block:: default

    def C(s, t):
        return m.exp( -4.0 * abs(s - t) / (1 + (s * s + t * t)))









Create the large covariance matrix


.. code-block:: default

    covariance = ot.CovarianceMatrix(mesh.getVerticesNumber())
    for k in range(mesh.getVerticesNumber()):
        t = mesh.getVertices()[k]
        for l in range(k + 1):
            s = mesh.getVertices()[l]
            covariance[k, l] = C(s[0], t[0])








Create the covariance model


.. code-block:: default

    covmodel = ot.UserDefinedCovarianceModel(mesh, covariance)









Draw the covariance model


.. code-block:: default

    def f(x):
        return [covmodel([x[0]], [x[1]])[0, 0]]

    func = ot.PythonFunction(2, 1, f)
    func.setDescription(['$s$', '$t$', '$cov$'])
    cov_graph = func.draw([-a] * 2, [a] * 2, [512] * 2)
    cov_graph.setLegendPosition('')
    view = viewer.View(cov_graph)
    plt.show()



.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_userdefined_covariance_model_001.png
    :alt: $cov$ as a function of ($s$,$t$)
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  1.617 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.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_userdefined_covariance_model.py <plot_userdefined_covariance_model.py>`



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

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


.. only:: html

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

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