.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_parameter_sweeps.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_parameter_sweeps.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_plot_parameter_sweeps.py:


Parameter Sweeps
----------------
When analyzing complex models or functions it is often useful to gain insight
into its smoothness and non-linearity before undertaking more computationally
intensive analysis such as uncertainty quantification or sensitivity analysis.
Knowledge about smoothness and non-linearity can be used to inform what
algorithms are used for these later tasks.

Lets first generate parameter sweeps for the oakley benchmark. Each sweep will 
be a random direction through the parameter domain. The domain is assumed to 
be the cartesian product of the centered truncated intervals of each
1D variable marginal. For unbounded variables each interval captures 99% of the
PDF. For bounded variables the true bounds are used (i.e. are not truncated)

.. GENERATED FROM PYTHON SOURCE LINES 16-28

.. code-block:: default

    from pyapprox import analysis
    from pyapprox.util.visualization import plt, mathrm_label
    from pyapprox.benchmarks import setup_benchmark
    import numpy as np
    np.random.seed(1)

    benchmark = setup_benchmark("oakley")
    axs = analysis.generate_parameter_sweeps_and_plot_from_variable(
        benchmark.fun, benchmark.variable, num_samples_per_sweep=20, num_sweeps=3)
    plt.gcf().suptitle(mathrm_label("Oakely model parameter sweeps"))
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_parameter_sweeps_001.png
   :alt: $\mathrm{Oakely\;model\;parameter\;sweeps}$, $\mathrm{QoI\;0}$
   :srcset: /auto_examples/images/sphx_glr_plot_parameter_sweeps_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 29-30

Now lets plot parameter sweeps for the Sobol G function

.. GENERATED FROM PYTHON SOURCE LINES 30-36

.. code-block:: default

    benchmark = setup_benchmark("sobol_g", nvars=4)
    axs = analysis.generate_parameter_sweeps_and_plot_from_variable(
        benchmark.fun, benchmark.variable, num_samples_per_sweep=50, num_sweeps=3)
    plt.gcf().suptitle(mathrm_label("Sobol G model parameter sweeps"))
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_parameter_sweeps_002.png
   :alt: $\mathrm{Sobol\;G\;model\;parameter\;sweeps}$, $\mathrm{QoI\;0}$
   :srcset: /auto_examples/images/sphx_glr_plot_parameter_sweeps_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    [2.10729798e-04 2.16355425e-01 4.96284418e-04 4.46077822e-05] [0.99978927 0.78364457 0.99950372 0.99995539]




.. GENERATED FROM PYTHON SOURCE LINES 37-40

The Sobol G function is not as smooth as the Oakely function. The former
has discontinuous first derivatives which can be seen by inspecting their
aprameter sweeps


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

   **Total running time of the script:** ( 0 minutes  0.125 seconds)


.. _sphx_glr_download_auto_examples_plot_parameter_sweeps.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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