.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_numerical_methods/iterative_statistics/plot_iterative_extrema.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py>`
        to download the full example code

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

.. _sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py:


Estimate extrema iteratively
============================

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In this example, we compute extrema iteratively.

.. GENERATED FROM PYTHON SOURCE LINES 10-13

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv








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We first create a one-dimensional Uniform random variable to generate data.

.. GENERATED FROM PYTHON SOURCE LINES 15-18

.. code-block:: Python

    dim = 1
    distNormal = ot.Uniform()








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The :class:`~openturns.IterativeExtrema` class needs the dimension of the sample
(here 1):

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.. code-block:: Python

    iterExtrema = ot.IterativeExtrema(dim)








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We can now perform the simulations.
In our case most of the data should be in the [-3,3] interval.
Consequently with few samples the expected minimum should be around -3
and the expected maximum should be around 3.
We first increment the object with one :class:`~openturns.Point` at a time.
At any given step the current minimum is obtained thanks to
the :meth:`~openturns.IterativeExtrema.getMin` method, the current maximum
with the :meth:`~openturns.IterativeExtrema.getMax` method and the
current number of iterations is given by the
:meth:`~openturns.IterativeMoments.getIterationNumber` method.

.. GENERATED FROM PYTHON SOURCE LINES 38-47

.. code-block:: Python

    size = 2000
    minEvolution = ot.Sample()
    maxEvolution = ot.Sample()
    for i in range(size):
        point = distNormal.getRealization()
        iterExtrema.increment(point)
        minEvolution.add(iterExtrema.getMin())
        maxEvolution.add(iterExtrema.getMax())








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We display the evolution of the minimum (in blue) and the maximum (orange).

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.. code-block:: Python

    iterationSample = ot.Sample.BuildFromPoint(range(1, size + 1))
    #
    curveMin = ot.Curve(iterationSample, minEvolution)
    curveMin.setLegend("min.")
    #
    curveMax = ot.Curve(iterationSample, maxEvolution)
    curveMax.setLegend("max.")
    #
    graph = ot.Graph("Evolution of the min/max", "iteration nb", "min/max", True)
    graph.add(curveMin)
    graph.add(curveMax)
    graph.setLegendPosition("upper left")
    graph.setLogScale(ot.GraphImplementation.LOGX)
    view = otv.View(graph)




.. image-sg:: /auto_numerical_methods/iterative_statistics/images/sphx_glr_plot_iterative_extrema_001.png
   :alt: Evolution of the min/max
   :srcset: /auto_numerical_methods/iterative_statistics/images/sphx_glr_plot_iterative_extrema_001.png
   :class: sphx-glr-single-img





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We can also increment with a :class:`~openturns.Sample`.

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.. code-block:: Python

    sample = distNormal.getSample(size)
    iterExtrema.increment(sample)








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We print the total number of iterations and the extrema.

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.. code-block:: Python

    print("Total number of iterations: " + str(iterExtrema.getIterationNumber()))
    print("Minimum: ", iterExtrema.getMin())
    print("Maximum: ", iterExtrema.getMax())

    otv.View.ShowAll()




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

 .. code-block:: none

    Total number of iterations: 4000
    Minimum:  [-0.999998]
    Maximum:  [0.999377]





.. _sphx_glr_download_auto_numerical_methods_iterative_statistics_plot_iterative_extrema.py:

.. only:: html

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

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

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

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

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