.. 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.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_field_functions_plot_viscous_fall_field_function.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.py:


Define a function with a field output: the viscous free fall example
====================================================================

.. GENERATED FROM PYTHON SOURCE LINES 6-10

In this example, we define a function which has a vector input and a field output.
This is why we use the `PythonPointToFieldFunction` class to create the associated function and propagate the uncertainties through it.

We consider a viscous free fall as explained :ref:`here <use-case-viscous-fall>`.

.. GENERATED FROM PYTHON SOURCE LINES 12-14

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

.. GENERATED FROM PYTHON SOURCE LINES 16-23

.. code-block:: Python

    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 24-25

We first define the time grid associated with the model.

.. GENERATED FROM PYTHON SOURCE LINES 27-32

.. code-block:: Python

    tmin = 0.0  # Minimum time
    tmax = 12.0  # Maximum time
    gridsize = 100  # Number of time steps
    mesh = ot.IntervalMesher([gridsize - 1]).build(ot.Interval(tmin, tmax))








.. GENERATED FROM PYTHON SOURCE LINES 33-34

The `getVertices` method returns the time values in this mesh.

.. GENERATED FROM PYTHON SOURCE LINES 36-39

.. code-block:: Python

    vertices = mesh.getVertices()
    vertices[0:5]






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>v0</th></tr>
      <tr><th>0</th><td>0</td></tr>
      <tr><th>1</th><td>0.1212121</td></tr>
      <tr><th>2</th><td>0.2424242</td></tr>
      <tr><th>3</th><td>0.3636364</td></tr>
      <tr><th>4</th><td>0.4848485</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 40-41

Creation of the input distribution.

.. GENERATED FROM PYTHON SOURCE LINES 43-49

.. code-block:: Python

    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 50-54

.. code-block:: Python

    dimension = distribution.getDimension()
    dimension






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

 .. code-block:: none


    4



.. GENERATED FROM PYTHON SOURCE LINES 55-59

Then we define the Python function which computes the altitude at each time value.
In order to compute all altitudes with a vectorized evaluation, we first
convert the vertices into a `numpy` `array` and use the `numpy` function
`exp` and `maximum`: this increases the evaluation performance of the script.

.. GENERATED FROM PYTHON SOURCE LINES 62-76

.. code-block:: Python

    def AltiFunc(X):
        g = 9.81
        z0 = X[0]
        v0 = X[1]
        m = X[2]
        c = X[3]
        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, 0.0)
        return [[zeta[0]] for zeta in z]









.. GENERATED FROM PYTHON SOURCE LINES 77-80

In order to create a `Function` from this Python function, we use the `PythonPointToFieldFunction` class.
Since the altitude is the only output field, the third argument `outputDimension` is equal to `1`.
If we had computed the speed as an extra output field, we would have set `2` instead.

.. GENERATED FROM PYTHON SOURCE LINES 82-85

.. code-block:: Python

    outputDimension = 1
    alti = ot.PythonPointToFieldFunction(dimension, mesh, outputDimension, AltiFunc)








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

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

.. GENERATED FROM PYTHON SOURCE LINES 93-97

.. code-block:: Python

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








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.. code-block:: Python

    ot.ResourceMap.SetAsUnsignedInteger("Drawable-DefaultPalettePhase", size)








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Draw some curves.

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.. code-block:: Python

    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_001.png
   :alt: Viscous free fall: 10 trajectories
   :srcset: /auto_functional_modeling/field_functions/images/sphx_glr_plot_viscous_fall_field_function_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 112-116

We see that the object first moves up and then falls down.
Not all objects, however, achieve the same maximum altitude.
We see that some trajectories reach a higher maximum altitude than others.
Moreover, at the final time :math:`t_{max}`, one trajectory hits the ground: :math:`z(t_{max})=0` for this trajectory.

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Reset default settings

.. GENERATED FROM PYTHON SOURCE LINES 119-120

.. code-block:: Python

    ot.ResourceMap.Reload()








.. _sphx_glr_download_auto_functional_modeling_field_functions_plot_viscous_fall_field_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_viscous_fall_field_function.ipynb <plot_viscous_fall_field_function.ipynb>`

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

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