.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_probabilistic_modeling/random_vectors/plot_composite_random_vector.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_probabilistic_modeling_random_vectors_plot_composite_random_vector.py>`
        to download the full example code

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

.. _sphx_glr_auto_probabilistic_modeling_random_vectors_plot_composite_random_vector.py:


Composite random vector
=======================

.. GENERATED FROM PYTHON SOURCE LINES 6-11

In this example we are going to create a random variable :math:`\underline{Y}` which realizations are the images of the realizations of another random vector :math:`\underline{X}` by a function.

.. math::
    \underline{Y} = f(\underline{X})


.. GENERATED FROM PYTHON SOURCE LINES 13-19

.. code-block:: default

    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)








.. GENERATED FROM PYTHON SOURCE LINES 20-21

Create a random vector based on a distribution

.. GENERATED FROM PYTHON SOURCE LINES 21-24

.. code-block:: default

    dist2d = ot.Normal(2)
    X = ot.RandomVector(dist2d)








.. GENERATED FROM PYTHON SOURCE LINES 25-26

Create the function

.. GENERATED FROM PYTHON SOURCE LINES 26-29

.. code-block:: default

    f = ot.SymbolicFunction(['x1', 'x2'], ['x1 + x2', 'x1*x2'])
    f






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>[x1,x2]->[x1 + x2,x1*x2]</p>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 30-31

Create the composite random vector

.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: default

    Y = ot.CompositeRandomVector(f, X)








.. GENERATED FROM PYTHON SOURCE LINES 34-35

.. code-block:: default

    Y.getSample(5)





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <TABLE><TR><TD></TD><TH>y0</TH><TH>y1</TH></TR>
    <TR><TH>0</TH><TD>2.581711</TD><TD>1.467319</TD></TR>
    <TR><TH>1</TH><TD>0.662747</TD><TD>0.09873994</TD></TR>
    <TR><TH>2</TH><TD>1.662492</TD><TD>-0.1625065</TD></TR>
    <TR><TH>3</TH><TD>2.275467</TD><TD>-0.07481222</TD></TR>
    <TR><TH>4</TH><TD>-1.518201</TD><TD>0.5676912</TD></TR>
    </TABLE>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** ( 0 minutes  0.002 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_random_vectors_plot_composite_random_vector.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_composite_random_vector.py <plot_composite_random_vector.py>`



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

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


.. only:: html

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

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