.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.py:


Create a parametric spectral density function
=============================================

This example illustrates how the User can create a density spectral
function from parametric models.

The library implements the *Cauchy spectral model* as a parametric model for the spectral density function
:math:`S`.

The library defines this model thanks to the object *CauchyModel*.


.. code-block:: default

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








1. Define a spectral density function from correlation matrix


.. code-block:: default

    amplitude = [1.0, 2.0, 3.0]
    scale = [4.0, 5.0, 6.0]
    spatialCorrelation = ot.CorrelationMatrix(3)
    spatialCorrelation[0, 1] = 0.8
    spatialCorrelation[0, 2] = 0.6
    spatialCorrelation[1, 2] = 0.1
    spectralModel_Corr = ot.CauchyModel(amplitude, scale, spatialCorrelation)
    spectralModel_Corr






.. raw:: html

    <p>class=CauchyModel amplitude=[4,5,6] scale=[1,2,3] spatial correlation=<br>
    [[ 1   0.8 0.6 ]<br>
     [ 0.8 1   0.1 ]<br>
     [ 0.6 0.1 1   ]]</p>
    <br />
    <br />

2. Define a spectral density function from a covariance matrix


.. code-block:: default

    spatialCovariance = ot.CovarianceMatrix(3)
    spatialCovariance[0, 0] = 4.0
    spatialCovariance[1, 1] = 5.0
    spatialCovariance[2, 2] = 6.0
    spatialCovariance[0, 1] = 1.2
    spatialCovariance[0, 2] = 0.9
    spatialCovariance[1, 2] = -0.2
    spectralModel_Cov = ot.CauchyModel(scale, spatialCovariance)
    spectralModel_Cov





.. raw:: html

    <p>class=CauchyModel amplitude=[2,2.23607,2.44949] scale=[4,5,6] spatial correlation=<br>
    [[  1          0.268328   0.183712  ]<br>
     [  0.268328   1         -0.0365148 ]<br>
     [  0.183712  -0.0365148  1         ]]</p>
    <br />
    <br />


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

   **Total running time of the script:** ( 0 minutes  0.002 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.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_parametric_spectral_density.py <plot_parametric_spectral_density.py>`



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

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


.. only:: html

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

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