.. 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
================================================

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>`.

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


.. 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)








We first define the time grid associated with the model. 


.. 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))









.. code-block:: default

    vertices = mesh.getVertices()








Creation of the input distribution.


.. 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])









.. code-block:: default

    dimension = distribution.getDimension()
    dimension






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

 Out:

 .. code-block:: none


    4



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`. 


.. 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]










.. code-block:: default

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








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

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


.. code-block:: default

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








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


.. code-block:: default

    altitudeWithFourInputs = ot.PointToFieldConnection(altitudeWithFiveInputs, projectionFunction)








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

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


.. code-block:: default

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








Draw some curves.


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






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

   **Total running time of the script:** ( 0 minutes  0.093 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

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