.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/reliability/form/FORM_linear_function_3d.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_reliability_form_FORM_linear_function_3d.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_reliability_form_FORM_linear_function_3d.py:


2. FORM - Linear function - Three Random variables
====================================================

.. GENERATED FROM PYTHON SOURCE LINES 8-18

In the third example we have the limit state to be a linear function of three (:math:`d=3`) independent Gaussian
random variables

.. math:: g(X_1, X_2, X_3) = 6.2X_1 -X_2X_3^2

.. math:: \mu_{X_1}=20, \mu_{X_2}=5, \mu_{X_3}=4

.. math:: \sigma_{X_1}=3.5, \sigma_{X_2}=0.8, \sigma_{X_3}=0.4

The probability of failure in this case is :math:`P_f ≈ 0.079` for :math:`\beta = 1.413`

.. GENERATED FROM PYTHON SOURCE LINES 23-24

Initially we have to import the necessary modules.

.. GENERATED FROM PYTHON SOURCE LINES 27-48

.. code-block:: default


    from UQpy.run_model.RunModel import RunModel
    from UQpy.run_model.model_execution.PythonModel import PythonModel
    from UQpy.distributions import Normal
    from UQpy.reliability import FORM

    dist1 = Normal(loc=20., scale=3.5)
    dist2 = Normal(loc=5., scale=0.8)
    dist3 = Normal(loc=4., scale=0.4)

    model = PythonModel(model_script='local_pfn.py', model_object_name="example3",)
    run_model = RunModel(model=model)

    form = FORM(distributions=[dist1, dist2, dist3], runmodel_object=run_model)
    form.run()

    print('Design point in standard normal space: %s' % form.design_point_u)
    print('Design point in original space: %s' % form.design_point_x)
    print('Hasofer-Lind reliability index: %s' % form.beta)
    print('FORM probability of failure: %s' % form.failure_probability)



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

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_reliability_form_FORM_linear_function_3d.py:

.. only:: html

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


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/reliability/form/FORM_linear_function_3d.ipynb
        :alt: Launch binder
        :width: 150 px



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

      :download:`Download Python source code: FORM_linear_function_3d.py <FORM_linear_function_3d.py>`

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

      :download:`Download Jupyter notebook: FORM_linear_function_3d.ipynb <FORM_linear_function_3d.ipynb>`


.. only:: html

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

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