` 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
============================
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.
.. 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)
Define the distribution
.. code-block:: default
sigma = 1.0
dist = ot.Normal(0.0, sigma)
Define the mesh
.. code-block:: default
tgrid = ot.RegularGrid(0.0, 1.0, 100)
Create the process
.. code-block:: default
process = ot.WhiteNoise(dist, tgrid)
process
.. raw:: html
WhiteNoise(Normal(mu = 0, sigma = 1))
Draw a realization
.. code-block:: default
realization = process.getRealization()
graph = realization.drawMarginal(0)
graph.setTitle('Realization of a white noise with distribution N(0,1)')
view = viewer.View(graph)
.. image:: /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)
:class: sphx-glr-single-img
Draw a sample
.. code-block:: default
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:: /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)
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.178 seconds)
.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_white_noise_process.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_white_noise_process.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_white_noise_process.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_