.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.py:


Add a trend to a process
========================

In this example we are going to add a trend to a process.

The TrendTransform class enables to create a new process Y from a process X (no hypothesis on X needed):

.. math::
   Y(\omega, t) = X(\omega, t) + f(t)



.. 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)








Create a process


.. code-block:: default

    grid = ot.RegularGrid(0.0, 0.1, 10)
    amplitude=[5.0]
    scale=[0.2]
    covModel = ot.ExponentialModel(scale, amplitude)
    X = ot.GaussianProcess(covModel, grid)








Draw a sample


.. code-block:: default

    sample = X.getSample(6)
    sample.setName('X')
    graph = sample.drawMarginal(0)
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_add_trend_001.png
    :alt: X - 0 marginal
    :class: sphx-glr-single-img





Define a trend function


.. code-block:: default

    f = ot.SymbolicFunction(['t'], ['30*t'])
    fTrend = ot.TrendTransform(f, grid)








Add it to the process


.. code-block:: default

    Y = ot.CompositeProcess(fTrend, X)
    Y.setName('Y')








Draw a sample


.. code-block:: default

    sample = Y.getSample(6)
    sample.setName('Y')
    graph = sample.drawMarginal(0)
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_add_trend_002.png
    :alt: Y - 0 marginal
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.145 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_add_trend.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_add_trend.py <plot_add_trend.py>`



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

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


.. only:: html

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

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