.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_probabilistic_modeling/stochastic_processes/plot_userdefined_covariance_model.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <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
================================

.. GENERATED FROM PYTHON SOURCE LINES 6-9

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



.. GENERATED FROM PYTHON SOURCE LINES 11-18

.. code-block:: Python

    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)








.. GENERATED FROM PYTHON SOURCE LINES 19-20

Create the time grid

.. GENERATED FROM PYTHON SOURCE LINES 20-25

.. code-block:: Python

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









.. GENERATED FROM PYTHON SOURCE LINES 26-27

Create the covariance function at (s,t)

.. GENERATED FROM PYTHON SOURCE LINES 27-31

.. code-block:: Python

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









.. GENERATED FROM PYTHON SOURCE LINES 32-33

Create the large covariance matrix

.. GENERATED FROM PYTHON SOURCE LINES 33-40

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 41-42

Create the covariance model

.. GENERATED FROM PYTHON SOURCE LINES 42-45

.. code-block:: Python

    covmodel = ot.UserDefinedCovarianceModel(mesh, covariance)









.. GENERATED FROM PYTHON SOURCE LINES 46-47

Draw the covariance model

.. GENERATED FROM PYTHON SOURCE LINES 47-57

.. code-block:: Python

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






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

   **Total running time of the script:** (0 minutes 2.089 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_userdefined_covariance_model.py:

.. only:: html

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

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

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

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

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