.. only:: html

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

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

    .. _sphx_glr_auto_functional_modeling_vectorial_functions_plot_linear_combination_function.py:


Create a linear combination of functions
========================================

In this example we are going to build a linear combination of several functions.

.. math::
   f = \sum \alpha_i f_i

Here

.. math::
   f_1(x) = [x_1^2+x_2,x_1+x_2+x_3]
   f_2(x) = [x_1 + 2 * x_2 + x_3,x_1+x_2+x_3]

with coefficients

.. math::
   a_1 = 2, a_2 = 4



.. 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)








assume a list of functions to combine


.. code-block:: default

    functions = list()
    functions.append(ot.SymbolicFunction(['x1', 'x2', 'x3'],
                                         ['x1^2 + x2', 'x1 + x2 + x3']))
    functions.append(ot.SymbolicFunction(['x1', 'x2', 'x3'],
                                         ['x1 + 2 * x2 + x3', 'x1 + x2 - x3']))








create the combination function


.. code-block:: default

    coefficients = [2.0, 4.0]
    function = ot.LinearCombinationFunction(functions, coefficients)








evaluate the function


.. code-block:: default

    x = [1.0, 2.0, 3.0]
    y = function(x)
    print('x=', x, 'y=', y)




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

 Out:

 .. code-block:: none

    x= [1.0, 2.0, 3.0] y= [38,12]





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

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


.. _sphx_glr_download_auto_functional_modeling_vectorial_functions_plot_linear_combination_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_linear_combination_function.py <plot_linear_combination_function.py>`



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

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


.. only:: html

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

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