.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_spectral.py:


Create a gaussian process from spectral density
===============================================

In this example we are going to build a gaussian process from its spectral density.


.. 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)








define a spectral model


.. code-block:: default

    amplitude = [1.0, 2.0]
    scale = [4.0, 5.0]
    spatialCorrelation = ot.CorrelationMatrix(2)
    spatialCorrelation[0,1] = 0.8
    mySpectralModel = ot.CauchyModel(scale, amplitude, spatialCorrelation)








define a mesh


.. code-block:: default

    myTimeGrid =  ot.RegularGrid(0.0, 0.1, 20)








create the process


.. code-block:: default

    process = ot.SpectralGaussianProcess(mySpectralModel, myTimeGrid)
    print(process)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

     SpectralGaussianProcess=SpectralGaussianProcess dimension=2 spectralModel=class=CauchyModel amplitude=[1,2] scale=[4,5] spatial correlation=
    [[ 1   0.8 ]
     [ 0.8 1   ]] maximal frequency=5 n frequency=10




draw a sample


.. code-block:: default

    sample = process.getSample(6)
    graph = sample.drawMarginal(0)
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_gaussian_process_spectral_001.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.077 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_spectral.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_gaussian_process_spectral.py <plot_gaussian_process_spectral.py>`



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

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


.. only:: html

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

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