.. only:: html

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

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

    .. _sphx_glr_auto_functional_modeling_vectorial_functions_plot_quadratic_function.py:


Create a quadratic function
===========================

In this example we are going to create a quadratic function of the form

.. math::
   f : \underline{X} \mapsto \underline{\underline{A}} ( \underline{X} - \underline{b} ) + \underline{c} + \frac{1}{2} \underline{X}^T \times \underline{\underline{\underline{M}}} \times \underline{X}



.. 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 quadratic function


.. code-block:: default

    inputDimension = 3
    outputDimension = 2
    center = [1.0] * inputDimension
    constant = [-1.0, 2.0] # c
    linear = ot.Matrix(inputDimension, outputDimension) # A
    quadratic = ot.SymmetricTensor(inputDimension, outputDimension) # M
    quadratic[0,0,1] = 3.0
    function = ot.QuadraticFunction(center, constant, linear, quadratic)
    x = [7.0, 8.0, 9.0]
    print(function(x))





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

 Out:

 .. code-block:: none

    [-1,56]




draw y1 with x1=2.0, x2=1.0, x0 in [0, 2]


.. code-block:: default

    graph = ot.ParametricFunction(function, [1, 2], [2.0, 1.0]).getMarginal(1).draw(0.0, 2.0)
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_functional_modeling/vectorial_functions/images/sphx_glr_plot_quadratic_function_001.png
    :alt: y1 as a function of x0
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.077 seconds)


.. _sphx_glr_download_auto_functional_modeling_vectorial_functions_plot_quadratic_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_quadratic_function.py <plot_quadratic_function.py>`



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

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


.. only:: html

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

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