.. 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_python_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_python_function.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_functional_modeling_vectorial_functions_plot_python_function.py:


Create a Python function
========================

.. GENERATED FROM PYTHON SOURCE LINES 6-13

In this example we are going to create a Function object (ie usable in the OpenTURNS context) from a pure Python function.

The pure Python function to wrap must accept a sequence of floats and return a sequence of float.

.. math::
   f(x) = [x_0+x_1+x_2, (x_1-1)*e^{x_0} * x_2]


.. GENERATED FROM PYTHON SOURCE LINES 15-22

.. code-block:: Python

    import numpy as np
    import openturns as ot
    import math as m

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









.. GENERATED FROM PYTHON SOURCE LINES 23-24

define a pure Python function from R^3 to R^2

.. GENERATED FROM PYTHON SOURCE LINES 24-31

.. code-block:: Python

    def regularFunc(X):
        x0, x1, x2 = X
        y0 = x0 + x1 + x2
        y1 = (x1 - 1.0) * m.exp(x0) * x2
        return [y0, y1]









.. GENERATED FROM PYTHON SOURCE LINES 32-33

create a Function object from a regular Python function

.. GENERATED FROM PYTHON SOURCE LINES 33-35

.. code-block:: Python

    function = ot.PythonFunction(3, 2, regularFunc)








.. GENERATED FROM PYTHON SOURCE LINES 36-37

evaluate the function on a Point

.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: Python

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





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

 .. code-block:: none

    x= [1.0, 2.0, 3.0] f(x)= [6,8.15485]




.. GENERATED FROM PYTHON SOURCE LINES 41-42

evaluate the function on a Sample

.. GENERATED FROM PYTHON SOURCE LINES 42-45

.. code-block:: Python

    xs = [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]]
    print("xs=", xs, "\nf(xs)=", function(xs))





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

 .. code-block:: none

    xs= [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]] 
    f(xs)=     [ y0         y1         ]
    0 : [    6          8.15485 ]
    1 : [   15       1310.36    ]




.. GENERATED FROM PYTHON SOURCE LINES 46-47

now we can use the Function object services such as the gradient

.. GENERATED FROM PYTHON SOURCE LINES 47-49

.. code-block:: Python

    function.gradient(x)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>[[ 1       8.15485 ]<br>
     [ 1       8.15485 ]<br>
     [ 1       2.71828 ]]</p>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 50-61

Performance issues
------------------

When this function is used internally to evaluate a Sample, it loops over its points.
This requires many memory allocations; moreover this loop is done in Python, it may thus be slow if Sample is large.
We can define a function to operate on a Sample, and return a Sample.

For maximum performance, argument is in fact not a Sample, but a wrapper
object which contains a pointer to data.  When using Numpy arrays without
copies and loops, performance is similar to C code, but Python definition
is somewhat convoluted; please refer to Numpy documentation to learn how to efficiently define such functions.

.. GENERATED FROM PYTHON SOURCE LINES 63-64

define the same function on a Sample

.. GENERATED FROM PYTHON SOURCE LINES 64-78

.. code-block:: Python



    def regularFuncSample(X):
        # Create a numpy array with the contents of X without copy
        xarray = np.array(X, copy=False)
        # Get columns as vectors, there is also no copy
        x0, x1, x2 = xarray.T
        # Allocate a numpy array to store result
        y = np.zeros((len(X), 2))
        y[:, 0] = x0 + x1 + x2
        y[:, 1] = (x1 - 1.0) * np.exp(x0) * x2
        return y









.. GENERATED FROM PYTHON SOURCE LINES 79-80

create a Function object from a regular Python function

.. GENERATED FROM PYTHON SOURCE LINES 80-82

.. code-block:: Python

    functionSample = ot.PythonFunction(3, 2, func_sample=regularFuncSample)








.. GENERATED FROM PYTHON SOURCE LINES 83-84

evaluate the function on a Sample

.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: Python

    print("xs=", xs, "\nf(xs)=", functionSample(xs))





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

 .. code-block:: none

    xs= [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]] 
    f(xs)=     [ y0         y1         ]
    0 : [    6          8.15485 ]
    1 : [   15       1310.36    ]




.. GENERATED FROM PYTHON SOURCE LINES 87-88

evaluate the function on a Point

.. GENERATED FROM PYTHON SOURCE LINES 88-90

.. code-block:: Python

    print("x=", x, "f(x)=", functionSample(x))





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

 .. code-block:: none

    x= [1.0, 2.0, 3.0] f(x)= [6,8.15485]




.. GENERATED FROM PYTHON SOURCE LINES 91-93

The most efficient solution is to provide evaluations both on Point and Sample.
This requires two Python function definitions, but if your code takes a lot of time, you should consider this option.

.. GENERATED FROM PYTHON SOURCE LINES 95-96

.. code-block:: Python

    functionFast = ot.PythonFunction(3, 2, func=regularFunc, func_sample=regularFuncSample)








.. _sphx_glr_download_auto_functional_modeling_vectorial_functions_plot_python_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_python_function.ipynb <plot_python_function.ipynb>`

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

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