.. 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_parametric_spectral_density.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_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
=============================================

.. GENERATED FROM PYTHON SOURCE LINES 6-13

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*.

.. GENERATED FROM PYTHON SOURCE LINES 15-19

.. code-block:: Python

    import openturns as ot

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 20-21

1. Define a spectral density function from correlation matrix

.. GENERATED FROM PYTHON SOURCE LINES 21-30

.. code-block:: Python

    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

    <div class="output_subarea output_html rendered_html output_result">
    class=CauchyModel amplitude=class=Point name=Unnamed dimension=3 values=[4,5,6] scale=class=Point name=Unnamed dimension=3 values=[1,2,3] spatial correlation=class=CorrelationMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,0.8,0.6,0.8,1,0.1,0.6,0.1,1] isDiagonal=false
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 31-32

2. Define a spectral density function from a covariance matrix

.. GENERATED FROM PYTHON SOURCE LINES 32-41

.. code-block:: Python

    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

    <div class="output_subarea output_html rendered_html output_result">
    class=CauchyModel amplitude=class=Point name=Unnamed dimension=3 values=[2,2.23607,2.44949] scale=class=Point name=Unnamed dimension=3 values=[4,5,6] spatial correlation=class=CorrelationMatrix dimension=3 implementation=class=MatrixImplementation name=Unnamed rows=3 columns=3 values=[1,0.268328,0.183712,0.268328,1,-0.0365148,0.183712,-0.0365148,1] isDiagonal=false
    </div>
    <br />
    <br />


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_parametric_spectral_density.py:

.. only:: html

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

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

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

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

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