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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_functional_modeling_field_functions_plot_viscous_fall_field_function_connection.py>`
        to download the full example code

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

.. _sphx_glr_auto_functional_modeling_field_functions_plot_viscous_fall_field_function_connection.py:


Define a connection function with a field output
================================================

.. GENERATED FROM PYTHON SOURCE LINES 6-8

In this example, we define a function which has a vector input and a field output. The goal of this example is to show how to use the `PointToFieldConnection` to combine two functions.
A detailed explanation of the model is presented :ref:`here <use-case-viscous-fall>`.

.. GENERATED FROM PYTHON SOURCE LINES 10-12

Define the model
----------------

.. GENERATED FROM PYTHON SOURCE LINES 14-21

.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    import numpy as np
    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 22-23

We first define the time grid associated with the model.

.. GENERATED FROM PYTHON SOURCE LINES 25-30

.. code-block:: default

    tmin = 0.0  # Minimum time
    tmax = 12.  # Maximum time
    gridsize = 100  # Number of time steps
    mesh = ot.IntervalMesher([gridsize-1]).build(ot.Interval(tmin, tmax))








.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: default

    vertices = mesh.getVertices()








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Creation of the input distribution.

.. GENERATED FROM PYTHON SOURCE LINES 37-43

.. code-block:: default

    distZ0 = ot.Uniform(100.0, 150.0)
    distV0 = ot.Normal(55.0, 10.0)
    distM = ot.Normal(80.0, 8.0)
    distC = ot.Uniform(0.0, 30.0)
    distribution = ot.ComposedDistribution([distZ0, distV0, distM, distC])








.. GENERATED FROM PYTHON SOURCE LINES 44-48

.. code-block:: default

    dimension = distribution.getDimension()
    dimension






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

 Out:

 .. code-block:: none


    4



.. GENERATED FROM PYTHON SOURCE LINES 49-50

Then we define the Python function which computes the altitude at each time value. This function has 5 inputs: `z0`, `v0`, `m`, `c` and `zmin`.

.. GENERATED FROM PYTHON SOURCE LINES 52-67

.. code-block:: default

    def AltiFunc(X):
        g = 9.81
        z0 = X[0]
        v0 = X[1]
        m = X[2]
        c = X[3]
        zmin = X[4]
        tau = m / c
        vinf = - m * g / c
        t = np.array(vertices)
        z = z0 + vinf * t + tau * (v0 - vinf) * (1 - np.exp(- t / tau))
        z = np.maximum(z, zmin)
        return [[zeta[0]] for zeta in z]









.. GENERATED FROM PYTHON SOURCE LINES 68-72

.. code-block:: default

    outputDimension = 1
    altitudeWithFiveInputs = ot.PythonPointToFieldFunction(
        5, mesh, outputDimension, AltiFunc)








.. GENERATED FROM PYTHON SOURCE LINES 73-75

Restrict the number of inputs
-----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 77-78

We define a function which has 4 inputs and 5 outputs: the 5th ouput `zmin` is set to zero.

.. GENERATED FROM PYTHON SOURCE LINES 80-83

.. code-block:: default

    projectionFunction = ot.SymbolicFunction(
        ["z0", "v0", "m", "c"], ["z0", "v0", "m", "c", "0.0"])








.. GENERATED FROM PYTHON SOURCE LINES 84-85

Then we use the `PointToFieldConnection` to create a function which has 4 inputs and returns the output field.

.. GENERATED FROM PYTHON SOURCE LINES 87-90

.. code-block:: default

    altitudeWithFourInputs = ot.PointToFieldConnection(
        altitudeWithFiveInputs, projectionFunction)








.. GENERATED FROM PYTHON SOURCE LINES 91-93

Sample trajectories
--------------------

.. GENERATED FROM PYTHON SOURCE LINES 95-96

In order to sample trajectories, we use the `getSample` method of the input distribution and apply the field function.

.. GENERATED FROM PYTHON SOURCE LINES 98-102

.. code-block:: default

    size = 10
    inputSample = distribution.getSample(size)
    outputSample = altitudeWithFourInputs(inputSample)








.. GENERATED FROM PYTHON SOURCE LINES 103-104

Draw some curves.

.. GENERATED FROM PYTHON SOURCE LINES 106-112

.. code-block:: default

    graph = outputSample.drawMarginal(0)
    graph.setTitle('Viscous free fall: %d trajectories' % (size))
    graph.setXTitle(r'$t$')
    graph.setYTitle(r'$z$')
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_functional_modeling/field_functions/images/sphx_glr_plot_viscous_fall_field_function_connection_001.png
   :alt: Viscous free fall: 10 trajectories
   :srcset: /auto_functional_modeling/field_functions/images/sphx_glr_plot_viscous_fall_field_function_connection_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.129 seconds)


.. _sphx_glr_download_auto_functional_modeling_field_functions_plot_viscous_fall_field_function_connection.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_viscous_fall_field_function_connection.py <plot_viscous_fall_field_function_connection.py>`



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

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


.. only:: html

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

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