.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_example/plot_example1.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_example_plot_example1.py>`
        to download the full example code

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

.. _sphx_glr_auto_example_plot_example1.py:


Example 1: Use of AK- MCS on Four Branch function
-------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 7-16

.. code-block:: default


    import openturns as ot
    from openturns.viewer import View
    import numpy as np
    import otak

    ot.RandomGenerator.SetSeed(1)









.. GENERATED FROM PYTHON SOURCE LINES 17-18

| Definition of Input distribution

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: default


    dim_inputs = 2
    dist_x = ot.Normal([0.0, 0.0], [1., 1.], ot.CorrelationMatrix(dim_inputs))
    inputVector = ot.RandomVector(dist_x)








.. GENERATED FROM PYTHON SOURCE LINES 24-25

| Definition of limit state function

.. GENERATED FROM PYTHON SOURCE LINES 25-41

.. code-block:: default


    def four_branch(x):
        x1 = x[0]
        x2  = x[1]
        k = x[2]
        g1 = 3+0.1*(x1-x2)**2-(x1+x2)/np.sqrt(2)
        g2 = 3+0.1*(x1-x2)**2+(x1+x2)/np.sqrt(2)
        g3 = (x1-x2)+k/np.sqrt(2)
        g4 =(x2-x1)+k/np.sqrt(2)
        return [min((g1,g2,g3,g4))]

    my_four_branch = ot.PythonFunction(3, 1, four_branch)

    index_frozen = [2]
    my_four_branch_6 = ot.ParametricFunction(my_four_branch, index_frozen, [6])








.. GENERATED FROM PYTHON SOURCE LINES 42-43

| Definition of event

.. GENERATED FROM PYTHON SOURCE LINES 43-47

.. code-block:: default

    Y = ot.CompositeRandomVector(my_four_branch_6, inputVector)
    my_event4b = ot.ThresholdEvent(Y,ot.Less(),0.0)









.. GENERATED FROM PYTHON SOURCE LINES 48-49

| Run of AK MCS

.. GENERATED FROM PYTHON SOURCE LINES 49-73

.. code-block:: default


    dim_4b = 2
    basis = ot.ConstantBasisFactory(dim_4b).build()
    covarianceModel = ot.MaternModel(dim_4b)
    n_MC_4b = 10000
    n_DoE_4b = 20
    sim_budget_4b = 200
    verbose = False
    criterion = 2

    my_AK_four_branch = otak.AK_MCSAlgorithm(my_event4b,
                                        n_MC_4b,
                                        n_DoE_4b,
                                        sim_budget_4b,
                                        basis,
                                        covarianceModel,
                                        criterion,
                                        verbose)

    my_AK_four_branch.compute_proba()

    print('Probability of failure',my_AK_four_branch.getFailureProbability())
    print('Simulation budget',my_AK_four_branch.getSimBudget())
    print('Coefficient of variation',my_AK_four_branch.getCoefficientOfVariation())




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

 Out:

 .. code-block:: none

    Probability of failure 0.0044
    Simulation budget 61
    Coefficient of variation 0.1504236441762821





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

   **Total running time of the script:** ( 0 minutes  7.062 seconds)


.. _sphx_glr_download_auto_example_plot_example1.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_example1.py <plot_example1.py>`



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

     :download:`Download Jupyter notebook: plot_example1.ipynb <plot_example1.ipynb>`


.. only:: html

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

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