.. 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_logistic_growth_model.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_logistic_growth_model.py>`
        to download the full example code

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

.. _sphx_glr_auto_functional_modeling_field_functions_plot_logistic_growth_model.py:


Logistic growth model
=====================

.. GENERATED FROM PYTHON SOURCE LINES 6-7

In this example, we use the :ref:`logistic growth model <use-case-logistic>` in order to show how to define a function which has a vector input and a field output. We use the `OpenTURNSPythonPointToFieldFunction` class to define the derived class and its methods.

.. GENERATED FROM PYTHON SOURCE LINES 11-13

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

.. GENERATED FROM PYTHON SOURCE LINES 15-23

.. code-block:: default

    from __future__ import print_function
    from openturns.usecases import logistic_model as logistic_model
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    from numpy import linspace, exp, maximum
    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 24-25

We load the logistic model from the usecases module :

.. GENERATED FROM PYTHON SOURCE LINES 25-28

.. code-block:: default

    lm = logistic_model.LogisticModel()









.. GENERATED FROM PYTHON SOURCE LINES 29-30

We get the data from the LogisticModel data class (22 dates with population) :

.. GENERATED FROM PYTHON SOURCE LINES 30-34

.. code-block:: default

    ustime = lm.data.getMarginal(0)
    uspop = lm.data.getMarginal(1)









.. GENERATED FROM PYTHON SOURCE LINES 35-36

We get the input parameters distribution distX :

.. GENERATED FROM PYTHON SOURCE LINES 36-39

.. code-block:: default

    distX = lm.distX









.. GENERATED FROM PYTHON SOURCE LINES 40-41

We define the model :

.. GENERATED FROM PYTHON SOURCE LINES 43-68

.. code-block:: default

    class Popu(ot.OpenTURNSPythonPointToFieldFunction):

        def __init__(self, t0=1790.0, tfinal=2000.0, nt=1000):
            grid = ot.RegularGrid(t0, (tfinal - t0) / (nt - 1), nt)
            super(Popu, self).__init__(3, grid, 1)
            self.setInputDescription(['y0', 'a', 'b'])
            self.setOutputDescription(['N'])
            self.ticks_ = [t[0] for t in grid.getVertices()]
            self.phi_ = ot.SymbolicFunction(['t', 'y', 'a', 'b'], ['a*y - b*y^2'])

        def _exec(self, X):
            y0 = X[0]
            a = X[1]
            b = X[2]
            phi_ab = ot.ParametricFunction(self.phi_, [2, 3], [a, b])
            phi_t = ot.ParametricFunction(phi_ab, [0], [0.0])
            solver = ot.RungeKutta(phi_t)
            initialState = [y0]
            values = solver.solve(initialState, self.ticks_)
            return values * [1.0e-6]


    F = Popu(1790.0, 2000.0, 1000)
    popu = ot.PointToFieldFunction(F)








.. GENERATED FROM PYTHON SOURCE LINES 69-71

Generate a sample from the model
--------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 73-74

Sample from the model

.. GENERATED FROM PYTHON SOURCE LINES 76-80

.. code-block:: default

    size = 10
    inputSample = distX.getSample(size)
    outputSample = popu(inputSample)








.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 84-85

Draw some curves

.. GENERATED FROM PYTHON SOURCE LINES 87-98

.. code-block:: default

    graph = outputSample.drawMarginal(0)
    graph.setTitle('US population')
    graph.setXTitle(r'$t$ (years)')
    graph.setYTitle(r'$N$ (millions)')
    cloud = ot.Cloud(ustime, uspop)
    cloud.setPointStyle('circle')
    cloud.setLegend('Data')
    graph.add(cloud)
    graph.setLegendPosition('topleft')
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_functional_modeling/field_functions/images/sphx_glr_plot_logistic_growth_model_001.png
   :alt: US population
   :srcset: /auto_functional_modeling/field_functions/images/sphx_glr_plot_logistic_growth_model_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.260 seconds)


.. _sphx_glr_download_auto_functional_modeling_field_functions_plot_logistic_growth_model.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_logistic_growth_model.py <plot_logistic_growth_model.py>`



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

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


.. only:: html

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

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