:orphan:

#################
Software Tutorial
#################

Below is a gallery of examples showing how to use different methods in PyApprox with the least amount of code.

These examples provide less mathematical background than the set of tutorials found here.



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    <div class="sphx-glr-thumbnails">


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    <div class="sphx-glr-thumbcontainer" tooltip="PyApprox supports multivariate random variables comprised of independent univariate variables. ...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_variables_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_variables.py`

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      <div class="sphx-glr-thumbnail-title">Random Variables</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We start by defining a function of two random variables. We will use the Rosenbrock benchmark. ...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_setup_model_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_setup_model.py`

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      <div class="sphx-glr-thumbnail-title">Model Definition</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Model interfacing">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_interface_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_interface.py`

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      <div class="sphx-glr-thumbnail-title">Model interfacing</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Lets first generate parameter sweeps for the oakley benchmark. Each sweep will  be a random dir...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_parameter_sweeps_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_parameter_sweeps.py`

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      <div class="sphx-glr-thumbnail-title">Parameter Sweeps</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Low-discrepancy quadrature">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_low_discrepancy_quadrature_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_low_discrepancy_quadrature.py`

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      <div class="sphx-glr-thumbnail-title">Low-discrepancy quadrature</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="To generate a univariate quadrature rule for uniform random variables">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_gaussian_quadrature_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_gaussian_quadrature.py`

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      <div class="sphx-glr-thumbnail-title">Univariate Gaussian Quadrature</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We must define the univariate grids that we will use to construct the tensor product grid. Whil...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_barycentric_interpolation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_barycentric_interpolation.py`

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      <div class="sphx-glr-thumbnail-title">Multivariate Lagrange Interpolation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Multivariate Piecewise Polynomial Interpolation">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_multivariate_piecewise_polynomial_interpolation_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_multivariate_piecewise_polynomial_interpolation.py`

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      <div class="sphx-glr-thumbnail-title">Multivariate Piecewise Polynomial Interpolation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="First lets define a Integrator class which can be used to integrate multivariate functions with...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_pde_convergence_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_pde_convergence.py`

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      <div class="sphx-glr-thumbnail-title">Convergence studies</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="We will use the Genz benchmark to illustrate how to use a sparse grid as a surrogate for uncert...">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_sparse_grid_uq_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_sparse_grid_uq.py`

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      <div class="sphx-glr-thumbnail-title">Sparse Grid Interpolation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="First lets load all the necessary modules and set the random seeds for reproducibility.">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_paper_demo_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_paper_demo.py`

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      <div class="sphx-glr-thumbnail-title">End-to-End Model Analysis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Multi-fidelity Quadrature">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_multifidelity_quadrature_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_multifidelity_quadrature.py`

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      <div class="sphx-glr-thumbnail-title">Multi-fidelity Quadrature</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Multi-index Collocation">

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  .. image:: /auto_examples/images/thumb/sphx_glr_plot_multiindex_collocation_ex_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_plot_multiindex_collocation_ex.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Multi-index Collocation</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /auto_examples/plot_variables
   /auto_examples/plot_setup_model
   /auto_examples/plot_interface
   /auto_examples/plot_parameter_sweeps
   /auto_examples/plot_low_discrepancy_quadrature
   /auto_examples/plot_gaussian_quadrature
   /auto_examples/plot_barycentric_interpolation
   /auto_examples/plot_multivariate_piecewise_polynomial_interpolation
   /auto_examples/plot_pde_convergence
   /auto_examples/plot_sparse_grid_uq
   /auto_examples/plot_paper_demo
   /auto_examples/plot_multifidelity_quadrature
   /auto_examples/plot_multiindex_collocation_ex


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


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

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