.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_processsample_manipulation.py:


Process sample manipulation
===========================


.. code-block:: default

    # sphinx_gallery_thumbnail_number = 2








The objective here is to create and manipulate a process sample. A process sample is a collection of fields which share the same mesh :math:`\mathcal{M} \in \mathbb{R}^n`.

A process sample can be obtained as :math:`K` realizations of a multivariate stochastic process :math:`X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d` of dimension :math:`d` where :math:`\mathcal{D} \in \mathbb{R}^n`, when the realizations are discretized on the same mesh :math:`\mathcal{M}` of :math:`\mathcal{D}`. The  values :math:`(\underline{x}_0^k, \dots, \underline{x}_{N-1}^k)` of the field :math:`k` are defined by:

.. math:: 
    \forall i \in [0, N-1],\quad \underline{x}_i= X(\omega_k)(\underline{t}_i)



.. code-block:: default

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








First, define a regular 2-d mesh


.. code-block:: default

    discretization = [10, 5]
    mesher = ot.IntervalMesher(discretization)
    lowerBound = [0.0, 0.0]
    upperBound = [2.0, 1.0]
    interval = ot.Interval(lowerBound, upperBound)
    mesh = mesher.build(interval)
    mesh = ot.RegularGrid(0.0, 0.01, 100)
    graph = mesh.draw()
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_processsample_manipulation_001.png
    :alt: Mesh Unnamed
    :class: sphx-glr-single-img





Allocate a process sample from a field


.. code-block:: default

    field = ot.Field()
    sampleSize = 10
    processSample = ot.ProcessSample(sampleSize, field)
    #field.draw()








Create a process sample as realizations of a process


.. code-block:: default

    amplitude = [1.0]
    scale = [0.2]*1
    myCovModel = ot.ExponentialModel(scale, amplitude)
    myProcess = ot.GaussianProcess(myCovModel, mesh)
    processSample = myProcess.getSample(10)
    #processSample








draw the sample, without interpolation


.. code-block:: default

    graph = processSample.drawMarginal(0, False)
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_processsample_manipulation_002.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img





draw the sample, with interpolation


.. code-block:: default

    graph = processSample.drawMarginal(0)
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_processsample_manipulation_003.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img





Compute the  mean of the process sample
The result is a field


.. code-block:: default

    graph = processSample.computeMean().drawMarginal()
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_processsample_manipulation_004.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img





Draw the quantile field


.. code-block:: default

    graph = processSample.computeQuantilePerComponent(0.9).drawMarginal(0)
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_processsample_manipulation_005.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img





Draw the field with interpolation


.. code-block:: default

    graph = processSample.drawMarginal(0)
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_processsample_manipulation_006.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img





processSample


.. code-block:: default

    plt.show()








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

   **Total running time of the script:** ( 0 minutes  0.557 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_processsample_manipulation.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_processsample_manipulation.py <plot_processsample_manipulation.py>`



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

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


.. only:: html

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

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