.. 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_linear_combination_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_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
========================================

.. GENERATED FROM PYTHON SOURCE LINES 6-22

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


.. GENERATED FROM PYTHON SOURCE LINES 24-28

.. code-block:: Python

    import openturns as ot

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 29-30

assume a list of functions to combine

.. GENERATED FROM PYTHON SOURCE LINES 30-36

.. code-block:: Python

    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"])
    )








.. GENERATED FROM PYTHON SOURCE LINES 37-38

create the combination function

.. GENERATED FROM PYTHON SOURCE LINES 38-41

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 42-43

evaluate the function

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: Python

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




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

 .. code-block:: none

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





.. _sphx_glr_download_auto_functional_modeling_vectorial_functions_plot_linear_combination_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_linear_combination_function.ipynb <plot_linear_combination_function.ipynb>`

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

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