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

.. only:: html

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

        :ref:`Go to the end <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
===========================

.. GENERATED FROM PYTHON SOURCE LINES 6-12

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}


.. GENERATED FROM PYTHON SOURCE LINES 14-20

.. 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 21-22

create a quadratic function

.. GENERATED FROM PYTHON SOURCE LINES 22-33

.. code-block:: Python

    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

 .. code-block:: none

    [-1,56]




.. GENERATED FROM PYTHON SOURCE LINES 34-35

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

.. GENERATED FROM PYTHON SOURCE LINES 35-40

.. code-block:: Python

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



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






.. _sphx_glr_download_auto_functional_modeling_vectorial_functions_plot_quadratic_function.py:

.. only:: html

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

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

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

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

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