.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py:


Apply a Box-Cox transformation to a Field
=========================================

The objective of this Use Case is to estimate a Box Cox transformation
from a field which all values are positive (eventually after a shift
to satisfy the positiveness) and to apply it on the field.
The object *BoxCoxFactory* enables to create a factory of
Box Cox transformation.
Then, we estimate the Box Cox transformation
:math:`h_{\underline{\lambda}}` from the initial field values
:math:`(\underline{x}_0, \dots, \underline{x}_{N-1})` thanks to the method
*build* of the object *BoxCoxFactory*, which produces an object of
type *BoxCoxTransform*.
If the field values :math:`(\underline{x}_0, \dots, \underline{x}_{N-1})` have
some negative values, it is possible to translate the values with
respect a given shift :math:`\underline{\alpha}` which has to be mentioned
either at the creation of the object *BoxCoxFactory* or when using the
method *build*.
Then the Box Cox transformation is the composition of
:math:`h_{\underline{\lambda}}` and this translation.

The object *BoxCoxTransform* enables to:

-  transform the field values
   :math:`(\underline{x}_{0}, \dots,\underline{x}_{N-1})` of dimension :math:`d`
   into the values :math:`(\underline{y}_{0}, \dots, \underline{y}_{N-1})` with
   stabilized variance, such that for each vertex :math:`\underline{t}_i` we
   have:

   :math:`\underline{y}_{i} = h_{\underline{\lambda}}(\underline{x}_{i})`

    or

   :math:`\underline{y}_{i} = h_{\underline{\lambda}}(\underline{x}_{i} + \underline{\alpha})`

   thanks to the operand *()*. The field based on the values
   :math:`\underline{y}_{i}` shares the same mesh than the initial field.

-  create the inverse Box Cox transformation such that :

   :math:`\underline{x}_{i}= h^{-1}_{\underline{\lambda}}(\underline{y}_{i})`

    or

   :math:`\underline{x}_{i} = h^{-1}_{\underline{\lambda}}(\underline{y}_{i}) - \underline{\alpha}`

   thanks to the method *getInverse()* which produces an object of type
   *InverseBoxCoxTransform* that can be evaluated on a field.
   The new field based shares the same mesh than the initial field.



.. code-block:: default

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








Define a process


.. code-block:: default

    myIndices= ot.Indices([10,5])
    myMesher =ot.IntervalMesher(myIndices)
    myInterval = ot.Interval([0.0, 0.0], [2.0, 1.0])
    myMesh = myMesher.build(myInterval)
    amplitude = [1.0]
    scale = [0.2, 0.2]
    myCovModel = ot.ExponentialModel(scale, amplitude)
    myXproc = ot.GaussianProcess(myCovModel, myMesh)
    g = ot.SymbolicFunction(['x1'],  ['exp(x1)'])
    myDynTransform = ot.ValueFunction(g, myMesh)
    myXtProcess = ot.CompositeProcess(myDynTransform, myXproc)








Draw a field


.. code-block:: default

    field = myXtProcess.getRealization()
    graph = field.drawMarginal(0)
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_box_cox_transform_001.png
    :alt: Unnamed - 0 marginal
    :class: sphx-glr-single-img





Draw values


.. code-block:: default

    marginal = ot.HistogramFactory().build(field.getValues())
    graph = marginal.drawPDF()
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_box_cox_transform_002.png
    :alt: y0 PDF
    :class: sphx-glr-single-img





Build the transformed field through Box-Cox


.. code-block:: default

    myModelTransform = ot.BoxCoxFactory().build(field)
    myStabilizedField = myModelTransform(field)








Draw values


.. code-block:: default

    marginal = ot.HistogramFactory().build(myStabilizedField.getValues())
    graph = marginal.drawPDF()
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_probabilistic_modeling/stochastic_processes/images/sphx_glr_plot_box_cox_transform_003.png
    :alt: y0 PDF
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  1.174 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.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_box_cox_transform.py <plot_box_cox_transform.py>`



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

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


.. only:: html

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

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