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

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

.. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py:


Create a white noise process
============================

.. GENERATED FROM PYTHON SOURCE LINES 6-26

This example details how to create and manipulate a white noise.
A second order white noise
:math:`\varepsilon: \Omega \times \mathbb{D} \rightarrow \mathbb{R}^d` is a stochastic
process of dimension :math:`d` such that the covariance function
:math:`C(\underline{s},\underline{t})=\delta(\underline{t}-\underline{s})C(\underline{s},\underline{s})`
where :math:`C(\underline{s},\underline{s})` is the covariance matrix of the process at
vertex :math:`\underline{s}` and :math:`\delta` the Kroenecker function.

A process :math:`\varepsilon` is a white noise if all finite family of
locations :math:`(\underline{t}_i)_{i=1, \dots, n} \in \mathbb{D}`,
:math:`(\varepsilon_{\underline{t}_i})_{i=1, \dots, n}` is independent and
identically distributed.

The library proposes to model it through the object *WhiteNoise* defined
on a mesh and a distribution with zero mean and finite standard
deviation.

If the distribution has a mean different from zero, The library writes
message to prevent the User and does not allow the creation of such a
white noise.

.. GENERATED FROM PYTHON SOURCE LINES 28-34

.. code-block:: Python

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

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








.. GENERATED FROM PYTHON SOURCE LINES 35-36

Define the distribution

.. GENERATED FROM PYTHON SOURCE LINES 36-39

.. code-block:: Python

    sigma = 1.0
    dist = ot.Normal(0.0, sigma)








.. GENERATED FROM PYTHON SOURCE LINES 40-41

Define the mesh

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    tgrid = ot.RegularGrid(0.0, 1.0, 100)








.. GENERATED FROM PYTHON SOURCE LINES 44-45

Create the process

.. GENERATED FROM PYTHON SOURCE LINES 45-48

.. code-block:: Python

    process = ot.WhiteNoise(dist, tgrid)
    process






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=WhiteNoise distribution=class=Normal name=Normal dimension=1 mean=class=Point name=Unnamed dimension=1 values=[0] sigma=class=Point name=Unnamed dimension=1 values=[1] correlationMatrix=class=CorrelationMatrix dimension=1 implementation=class=MatrixImplementation name=Unnamed rows=1 columns=1 values=[1]
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 49-50

Draw a realization

.. GENERATED FROM PYTHON SOURCE LINES 50-55

.. code-block:: Python

    realization = process.getRealization()
    graph = realization.drawMarginal(0)
    graph.setTitle("Realization of a white noise with distribution N(0,1)")
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_white_noise_process_001.png
   :alt: Realization of a white noise with distribution N(0,1)
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_white_noise_process_001.png
   :class: sphx-glr-single-img





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Draw a sample

.. GENERATED FROM PYTHON SOURCE LINES 57-68

.. code-block:: Python

    sample = process.getSample(5)
    graph = sample.drawMarginal(0)
    graph.setTitle(
        str(sample.getSize()) + " realizations of a white noise with distribution N(0,1)"
    )
    for k in range(sample.getSize()):
        drawable = graph.getDrawable(k)
        drawable.setLegend("realization " + str(k + 1))
        graph.setDrawable(drawable, k)
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_white_noise_process_002.png
   :alt: 5 realizations of a white noise with distribution N(0,1)
   :srcset: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_white_noise_process_002.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.py:

.. only:: html

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

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

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

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

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