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

.. only:: html

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

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

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

.. _sphx_glr_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py:


Create a threshold event
========================

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Abstract
--------

We present in this example the creation and the use of a :class:`~openturns.ThresholdEvent` to estimate a simple integral.


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.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv
    from matplotlib import pylab as plt









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We consider a standard Gaussian random vector :math:`X` and build a random vector from this distribution.

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.. code-block:: Python

    distX = ot.Normal()
    vecX = ot.RandomVector(distX)








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We consider the simple model :math:`f:x \mapsto |x|` and consider the output random variable :math:`Y = f(X)`.

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.. code-block:: Python

    f = ot.SymbolicFunction(["x1"], ["abs(x1)"])
    vecY = ot.CompositeRandomVector(f, vecX)








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We define a very simple :class:`~openturns.ThresholdEvent` which happpens whenever :math:`|X| < 1.0` :

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.. code-block:: Python

    thresholdEvent = ot.ThresholdEvent(vecY, ot.Less(), 1.0)








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For the normal distribution, it is a well-known fact that the values lower than one standard deviation (here exactly 1)
away from the mean (here 0) account roughly for 68.27% of the set.
So the probability of the event is:


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.. code-block:: Python

    print("Probability of the event : %.4f" % 0.6827)





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

 .. code-block:: none

    Probability of the event : 0.6827




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We can also use a basic estimator to get the probability of the event by drawing samples from the initial distribution `distX` and counting those which realize the event:

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.. code-block:: Python

    print(
        "Probability of the event (event sampling) : %.4f"
        % thresholdEvent.getSample(1000).computeMean()[0]
    )






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

 .. code-block:: none

    Probability of the event (event sampling) : 0.6830




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The geometric interpretation is simply the area under the PDF of the standard normal distribution for :math:`x \in [-1,1]` which we draw thereafter.

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.. code-block:: Python

    def linearSample(xmin, xmax, npoints):
        """
        Returns a sample created from a regular grid
        from xmin to xmax with npoints points.
        """
        step = (xmax - xmin) / (npoints - 1)
        rg = ot.RegularGrid(xmin, step, npoints)
        vertices = rg.getVertices()
        return vertices









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The boundary of the event are the lines :math:`x = -1.0` and :math:`x = 1.0`

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.. code-block:: Python

    a, b = -1, 1








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.. code-block:: Python

    nplot = 100  # Number of points in the plot
    x = linearSample(a, b, nplot)
    y = distX.computePDF(x)


    def drawInTheBounds(vLow, vUp, n_test):
        """
        Draw the area within the bounds.
        """
        palette = ot.Drawable.BuildDefaultPalette(2)
        myPaletteColor = palette[0]
        polyData = [[vLow[i], vLow[i + 1], vUp[i + 1], vUp[i]] for i in range(n_test - 1)]
        polygonList = [
            ot.Polygon(polyData[i], myPaletteColor, myPaletteColor)
            for i in range(n_test - 1)
        ]
        boundsPoly = ot.PolygonArray(polygonList)
        return boundsPoly


    vLow = [[x[i, 0], 0.0] for i in range(nplot)]
    vUp = [[x[i, 0], y[i, 0]] for i in range(nplot)]
    area = distX.computeCDF(b) - distX.computeCDF(a)
    boundsPoly = drawInTheBounds(vLow, vUp, nplot)








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We add the colored area to the PDF graph.

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.. code-block:: Python

    graph = distX.drawPDF()
    graph.add(boundsPoly)
    graph.setTitle("Probability of the event E = %.4f" % (area))
    graph.setLegends([""])
    view = otv.View(graph)




.. image-sg:: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_create_threshold_event_001.png
   :alt: Probability of the event E = 0.6827
   :srcset: /auto_reliability_sensitivity/reliability/images/sphx_glr_plot_create_threshold_event_001.png
   :class: sphx-glr-single-img





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Display all figures

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.. code-block:: Python

    plt.show()








.. _sphx_glr_download_auto_reliability_sensitivity_reliability_plot_create_threshold_event.py:

.. only:: html

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

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

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

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

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