.. 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

        :ref:`Go to the end <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 7-13

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

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


.. GENERATED FROM PYTHON SOURCE LINES 15-18

.. code-block:: Python

    import openturns as ot









.. GENERATED FROM PYTHON SOURCE LINES 19-20

Create a random vector based on a distribution

.. GENERATED FROM PYTHON SOURCE LINES 20-23

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Create the function

.. GENERATED FROM PYTHON SOURCE LINES 25-28

.. code-block:: Python

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






.. raw:: html

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

.. GENERATED FROM PYTHON SOURCE LINES 29-30

Create the composite random vector

.. GENERATED FROM PYTHON SOURCE LINES 30-32

.. code-block:: Python

    Y = ot.CompositeRandomVector(f, X)








.. GENERATED FROM PYTHON SOURCE LINES 33-34

.. code-block:: Python

    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>-0.6579715</td><td>-0.7700886</td></tr>
      <tr><th>1</th><td>0.7672126</td><td>-0.5283197</td></tr>
      <tr><th>2</th><td>-1.831343</td><td>-0.7635766</td></tr>
      <tr><th>3</th><td>1.082242</td><td>-0.5102336</td></tr>
      <tr><th>4</th><td>1.603824</td><td>0.6429862</td></tr>
    </table>
    </div>
    <br />
    <br />


.. _sphx_glr_download_auto_probabilistic_modeling_random_vectors_plot_composite_random_vector.py:

.. only:: html

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

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

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

    .. 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-zip

      :download:`Download zipped: plot_composite_random_vector.zip <plot_composite_random_vector.zip>`