.. 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_box_cox_transform.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_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:


Use the Box-Cox transformation
==============================

.. GENERATED FROM PYTHON SOURCE LINES 6-53

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.


.. GENERATED FROM PYTHON SOURCE LINES 56-62

.. 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 63-64

Define a process

.. GENERATED FROM PYTHON SOURCE LINES 64-76

.. code-block:: Python

    myIndices = [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)








.. GENERATED FROM PYTHON SOURCE LINES 77-78

Draw a field

.. GENERATED FROM PYTHON SOURCE LINES 78-82

.. code-block:: Python

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




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





.. GENERATED FROM PYTHON SOURCE LINES 83-84

Draw values

.. GENERATED FROM PYTHON SOURCE LINES 84-88

.. code-block:: Python

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




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





.. GENERATED FROM PYTHON SOURCE LINES 89-90

Build the transformed field through Box-Cox

.. GENERATED FROM PYTHON SOURCE LINES 90-93

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 94-95

Draw values

.. GENERATED FROM PYTHON SOURCE LINES 95-99

.. code-block:: Python

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



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






.. _sphx_glr_download_auto_probabilistic_modeling_stochastic_processes_plot_box_cox_transform.py:

.. only:: html

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

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

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

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

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