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

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. 

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
    from numpy import linspace, exp, maximum
    ot.Log.Show(ot.Log.NONE)








We load the logistic model from the usecases module :


.. code-block:: default

    from openturns.usecases import logistic_model as logistic_model
    lm = logistic_model.LogisticModel()









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


.. code-block:: default

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










We get the input parameters distribution distX :


.. code-block:: default

    distX = lm.distX










We define the model :


.. 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)








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

Sample from the model


.. code-block:: default

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









.. code-block:: default

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








Draw some curves


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






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

   **Total running time of the script:** ( 0 minutes  0.178 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

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