.. 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

        :ref:`Go to the end <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 6-9

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 13-15

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

.. GENERATED FROM PYTHON SOURCE LINES 17-24

.. code-block:: Python

    from openturns.usecases import logistic_model
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 25-26

We load the logistic model from the usecases module :

.. GENERATED FROM PYTHON SOURCE LINES 26-29

.. code-block:: Python

    lm = logistic_model.LogisticModel()









.. GENERATED FROM PYTHON SOURCE LINES 30-31

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

.. GENERATED FROM PYTHON SOURCE LINES 31-35

.. code-block:: Python

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









.. GENERATED FROM PYTHON SOURCE LINES 36-37

We get the input parameters distribution distX :

.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: Python

    distX = lm.distX









.. GENERATED FROM PYTHON SOURCE LINES 41-42

We define the model :

.. GENERATED FROM PYTHON SOURCE LINES 45-69

.. code-block:: Python

    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 70-72

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

.. GENERATED FROM PYTHON SOURCE LINES 74-75

Sample from the model

.. GENERATED FROM PYTHON SOURCE LINES 77-81

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 82-84

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 85-86

Draw some curves

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.. code-block:: Python

    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("upper left")
    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





.. GENERATED FROM PYTHON SOURCE LINES 101-102

Reset default settings

.. GENERATED FROM PYTHON SOURCE LINES 102-103

.. code-block:: Python

    ot.ResourceMap.Reload()








.. _sphx_glr_download_auto_functional_modeling_field_functions_plot_logistic_growth_model.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

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

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