.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_reliability_sensitivity_reliability_processes_plot_event_process.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_reliability_sensitivity_reliability_processes_plot_event_process.py:


Create an event based on a process
==================================

This example gives elements to create an event based on a multivariate stochastic process.
Let :math:`X: \Omega \times \mathcal{D} \rightarrow \mathbb{R}^d` be a stochastic process
of dimension :math:`d`, where :math:`\mathcal{D} \in \mathbb{R}^n` is discretized on the mesh
:math:`\mathcal{M}`. We suppose that :math:`\mathcal{M}` contains :math:`N` vertices.

We define the event :math:`\mathcal{E}` as:

.. math::
   \begin{aligned} 
     \displaystyle \mathcal{E}(X) = \bigcup_{\underline{t}\in \mathcal{M}}\left\{X_{\underline{t}} \in \mathcal{A} \right\} 
   \end{aligned}

where :math:`\mathcal{A}` is a domain of :math:`\mathbb{R}^d`.

A particular domain :math:`\mathcal{A}` is the cartesian product of type:

.. math::
   \begin{aligned} 
     \mathcal{A} = \prod_{i=1}^d [a_i,b_i]
   \end{aligned}

In that case, the library defines :math:`\mathcal{A}` by its both extreme points : :math:`\underline{a}` and :math:`\underline{b}`.

In the general case, :math:`\mathcal{A}` is a *Domain* object that is able to
check if it contains a given point in :math:`\mathbb{R}^d`.

The library creates an *Event* object from the process :math:`X` and the
domain :math:`\mathcal{A}`. Then, it is possible to get a realization of the event
:math:`\mathcal{E}`, which is scalar :math:`1_{\mathcal{E}(X)}(\underline{x}_0, \dots, \underline{x}_{N-1})`
if :math:`(\underline{x}_0, \dots,\underline{x}_{N-1})` is a realization of :math:`X` on
:math:`\mathcal{M}`.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








Define a 2-d mesh


.. code-block:: default

    indices = ot.Indices([40, 20])
    mesher = ot.IntervalMesher(indices)
    lowerBound = [0., 0.]
    upperBound = [2., 1.]
    interval = ot.Interval(lowerBound, upperBound)
    mesh = mesher.build(interval)








Create the covariance model


.. code-block:: default

    amplitude = [1.0, 2.0, 3.0]
    scale = [4.0, 5.0]
    spatialCorrelation = ot.CorrelationMatrix(3)
    spatialCorrelation[0, 1] = 0.8
    spatialCorrelation[0, 2] = 0.6
    spatialCorrelation[1, 2] = 0.1
    covmodel = ot.ExponentialModel(scale, amplitude, spatialCorrelation)

    # Create a normal process
    process = ot.GaussianProcess(covmodel, mesh)








Create a domain A in R^3: [0.8; 1.2]*[1.5; 1.6]*[0.5; 0.7]


.. code-block:: default

    lowerBound = [0.8, 1.5, 0.5]
    upperBound = [1.2, 1.6, 0.7]
    domain = ot.Interval(lowerBound, upperBound)

    # Create the event
    event = ot.ProcessEvent(process, domain)








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

   **Total running time of the script:** ( 0 minutes  0.002 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_reliability_processes_plot_event_process.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_event_process.py <plot_event_process.py>`



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

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


.. only:: html

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

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