.. 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_2d.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_2d.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_2d.py:


1. FORM - Linear function - Two Random variables
===================================================

In the second example we have the limit state to be a linear function of two (:math:`d=2`) independent Gaussian random
variables

.. GENERATED FROM PYTHON SOURCE LINES 12-17

:math:`g(U) = -\frac{1}{\sqrt{d}}\sum_{i=1}^{d} u_i + \beta`

The probability of failure in this case is :math:`P(F) ≈ 10^{−3}` for :math:`β = 3.0902`

Initially we have to import the necessary modules.

.. GENERATED FROM PYTHON SOURCE LINES 20-42

.. code-block:: default


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


    dist1 = Normal(loc=0., scale=1.)
    dist2 = Normal(loc=0., scale=1.)

    model = PythonModel(model_script='local_pfn.py', model_object_name="example2")
    RunModelObject2 = RunModel(model=model)

    Z = FORM(distributions=[dist1, dist2], runmodel_object=RunModelObject2)
    Z.run()

    # print results
    print('Design point in standard normal space: %s' % Z.design_point_u)
    print('Design point in original space: %s' % Z.design_point_x)
    print('Hasofer-Lind reliability index: %s' % Z.beta)
    print('FORM probability of failure: %s' % Z.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_2d.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_2d.ipynb
        :alt: Launch binder
        :width: 150 px



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

      :download:`Download Python source code: FORM_linear_function_2d.py <FORM_linear_function_2d.py>`

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

      :download:`Download Jupyter notebook: FORM_linear_function_2d.ipynb <FORM_linear_function_2d.ipynb>`


.. only:: html

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

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