.. only:: html

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

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

    .. _sphx_glr_auto_functional_modeling_vectorial_functions_plot_symbolic_function.py:


Create a symbolic function
==========================

In this example we are going to create a function from mathematical formulas:

.. math:: 
   f(x_1, x_2) = -(6 + x_0^2 - x_1)

Analytical expressions of the gradient and hessian are automatically computed except if the function is not differentiable everywhere. In that case a finite difference method is used.


.. 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 symbolic function


.. code-block:: default

    function = ot.SymbolicFunction(['x0', 'x1'],
                                   ['-(6 + x0^2 - x1)'])
    print(function)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [x0,x1]->[-(6 + x0^2 - x1)]




evaluate function


.. code-block:: default

    x = [2.0, 3.0]
    print('x=', x, 'f(x)=', function(x))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    x= [2.0, 3.0] f(x)= [-7]




show gradient


.. code-block:: default

    print(function.getGradient())





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    | d(y0) / d(x0) = -2*x0
    | d(y0) / d(x1) = 1





use gradient


.. code-block:: default

    print('x=', x, 'df(x)=', function.gradient(x))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    x= [2.0, 3.0] df(x)= [[ -4 ]
     [  1 ]]




draw isocontours of f around [2,3]


.. code-block:: default

    graph = function.draw(0, 1, 0, [2.0, 3.0], [1.5, 2.5], [2.5, 3.5])
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_functional_modeling/vectorial_functions/images/sphx_glr_plot_symbolic_function_001.png
    :alt: y0 as a function of (x0,x1)
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.115 seconds)


.. _sphx_glr_download_auto_functional_modeling_vectorial_functions_plot_symbolic_function.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_symbolic_function.py <plot_symbolic_function.py>`



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

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


.. only:: html

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

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