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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_plot_subset_inverse_sampling_R_S.py:


Subset inverse sampling on an R-S model
=======================================

.. GENERATED FROM PYTHON SOURCE LINES 7-30

This example demonstrates :class:`~otrobopt.SubsetInverseSampling` on a
simple Resistance-Stress (R-S) model.

The limit state function is:

.. math::

    G(\mathbf{U}) = U_1 - U_2

where :math:`U_1 \sim \mathcal{N}(7, 1)` represents the resistance and
:math:`U_2 \sim \mathcal{N}(2, 1)` represents the stress. Failure occurs
when :math:`G < 0`.

The subset inverse simulation algorithm estimates the threshold value
:math:`q` such that:

.. math::

    \mathbb{P}(G(\mathbf{U}) \leq q) = p_t

where :math:`p_t` is a target probability. This is the inverse problem:
instead of computing the probability for a given threshold, we find the
threshold for a given probability.

.. GENERATED FROM PYTHON SOURCE LINES 32-37

.. code-block:: Python

    import openturns as ot
    import otrobopt

    ot.RandomGenerator.SetSeed(0)








.. GENERATED FROM PYTHON SOURCE LINES 38-39

Define the limit state function and the probabilistic model.

.. GENERATED FROM PYTHON SOURCE LINES 39-52

.. code-block:: Python

    limitState = ot.SymbolicFunction(['u1', 'u2'], ['u1 - u2'])
    dim = limitState.getInputDimension()

    mean = [7.0, 2.0]
    sigma = [1.0, 1.0]
    R = ot.IdentityMatrix(dim)
    distribution = ot.Normal(mean, sigma, R)

    # Build the event
    vect = ot.RandomVector(distribution)
    output = ot.CompositeRandomVector(limitState, vect)
    event = ot.ThresholdEvent(output, ot.Less(), 0.0)








.. GENERATED FROM PYTHON SOURCE LINES 53-55

Run the subset inverse sampling algorithm for a target probability
:math:`p_t = 2 \times 10^{-4}`.

.. GENERATED FROM PYTHON SOURCE LINES 55-61

.. code-block:: Python

    targetProbability = 0.0002

    algo = otrobopt.SubsetInverseSampling(event, targetProbability)
    algo.setMaximumOuterSampling(10000)
    algo.run()








.. GENERATED FROM PYTHON SOURCE LINES 62-63

Retrieve and display the results.

.. GENERATED FROM PYTHON SOURCE LINES 63-74

.. code-block:: Python

    result = algo.getResult()
    pf = result.getProbabilityEstimate()
    threshold = algo.getThresholdPerStep()[-1]
    threshold_cl = algo.getThresholdConfidenceLength(0.90)

    print('Target probability =', targetProbability)
    print('Estimated probability =', pf)
    print('Threshold at target =', threshold)
    print('Threshold confidence length (90%) =', threshold_cl)
    print('Number of steps =', algo.getNumberOfSteps())
    print('Coefficient of variation =', result.getCoefficientOfVariation())




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

 .. code-block:: none

    Target probability = 0.0002
    Estimated probability = 0.00020000000000000025
    Threshold at target = 0.020271550198725088
    Threshold confidence length (90%) = 0.02133651921248595
    Number of steps = 4
    Coefficient of variation = 0.08323641030222287





.. _sphx_glr_download_auto_examples_plot_subset_inverse_sampling_R_S.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_subset_inverse_sampling_R_S.zip <plot_subset_inverse_sampling_R_S.zip>`