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.. "auto_probabilistic_modeling/stochastic_processes/plot_gaussian_process_covariance_hmat.py"
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.. only:: html

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

        Click :ref:`here <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.

.. GENERATED FROM PYTHON SOURCE LINES 12-17

.. code-block:: default

    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:: default

    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:: default

    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:: default

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





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

 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:: default

    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:: default

    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:: default

    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:: default

    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.


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

   **Total running time of the script:** ( 0 minutes  2.310 seconds)


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 .. container:: sphx-glr-footer
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