.. 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_gaussian_process_covariance_hmat.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_gaussian_process_covariance_hmat.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py:


Create a gaussian process from a cov. model using HMatrix
=========================================================

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In this basic example we build a gaussian process from its covariance model and use the `HMatrix` method as a sampling method.
Several methods and parameters are presented to set the HMatrix compression.
This is an advanced topic and we should highlight key ideas only in this example.

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.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt

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








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Definition of the covariance model
----------------------------------

We define our Gaussian process from its covariance model. We consider a Gaussian kernel with the following parameters.

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.. code-block:: Python

    dimension = 1
    amplitude = [1.0] * dimension
    scale = [1] * dimension
    covarianceModel = ot.GeneralizedExponential(scale, amplitude, 2)








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We define the time grid on which we want to sample the Gaussian process.

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.. code-block:: Python

    tmin = 0.0
    step = 0.01
    n = 10001
    timeGrid = ot.RegularGrid(tmin, step, n)








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Finally we define the Gaussian process.

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.. code-block:: Python

    process = ot.GaussianProcess(covarianceModel, timeGrid)
    print(process)





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

 .. code-block:: none

    GaussianProcess(trend=[x0]->[0.0], covariance=GeneralizedExponential(scale=[1], amplitude=[1], p=2))




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Basics on the HMatrix algebra
-----------------------------

The `HMatrix` framework uses efficient linear algebra techniques to speed-up the
(Cholesky) factorization of the covariance matrix.
This method can be tuned with several parameters. We should concentrate on the easiest ones.

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We set the sampling method to `HMAT` (default is the classical/dense case).

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.. code-block:: Python

    process.setSamplingMethod(ot.GaussianProcess.HMAT)









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The `HMatrix` framework uses an algebraic algorithm to compress sub-blocks of the matrix. Several algorithms are available and can be set from the ResourceMap key.

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.. code-block:: Python

    ot.ResourceMap.SetAsString("HMatrix-CompressionMethod", "AcaRandom")








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There are two threshold used in the HMatrix framework. The `AssemblyEpsilon` is the most important one.


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.. code-block:: Python

    ot.ResourceMap.SetAsScalar("HMatrix-AssemblyEpsilon", 1e-7)
    ot.ResourceMap.SetAsScalar("HMatrix-RecompressionEpsilon", 1e-7)









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Process sampling
----------------

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We eventually draw samples of this covariance model.

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.. code-block:: Python

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




.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_gaussian_process_covariance_hmat_001.png
   :alt: Unnamed - 0 marginal
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_gaussian_process_covariance_hmat_001.png
   :class: sphx-glr-single-img





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We notice here that we are able to sample the covariance model over a mesh of size `10000`, which is usually tricky on a laptop. This is mainly due to the compression.

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Reset default settings

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.. code-block:: Python

    ot.ResourceMap.Reload()








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

   **Total running time of the script:** (0 minutes 2.123 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_gaussian_process_covariance_hmat.py:

.. only:: html

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

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

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

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

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