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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_sampler_plot_saltelli.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_sampler_plot_saltelli.py:


Saltelli sampling
=================

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This example shows how to draw samples using Saltelli sampling. 
Assume that there is a three-dimensional problem where X, Y, and Z are the
three random variables.

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.. code-block:: default


    import numpy as np

    ndim = 3
    # range of X is 10 to 20, range of Y is 100 to 200, range of Z is 1000 to 2000
    bounds = np.array([[10,20], [100,200], [1000,2000]])








.. GENERATED FROM PYTHON SOURCE LINES 20-22

Given this setting, we can import :class:`.Saltelli`, create an instance, and
call the :py:meth:`.Saltelli.sample` method to draw required number of samples.

.. GENERATED FROM PYTHON SOURCE LINES 23-29

.. code-block:: default


    from psimpy.sampler import Saltelli

    saltelli_sampler = Saltelli(ndim, bounds, calc_second_order=False)
    saltelli_samples = saltelli_sampler.sample(nbase=128)








.. GENERATED FROM PYTHON SOURCE LINES 30-34

In above codes, we set ``calc_second_order`` to `False`. It means that picked
samples can be used in following Sobol' analysis to compute first-order and
total-effect Sobol' indices but not second-order Sobol' indices. It leads to 
:math:`nbase*(ndim+2)` samples as shown below

.. GENERATED FROM PYTHON SOURCE LINES 35-51

.. code-block:: default


    import matplotlib.pyplot as plt

    fig = plt.figure()
    ax = fig.add_subplot(projection='3d')

    ax.scatter(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:,2], marker='o')
    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')

    plt.tight_layout()

    print('Number of samples: ', f'{len(saltelli_samples)}')





.. image-sg:: /auto_examples/sampler/images/sphx_glr_plot_saltelli_001.png
   :alt: plot saltelli
   :srcset: /auto_examples/sampler/images/sphx_glr_plot_saltelli_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Number of samples:  640




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If we want to draw samples which can also be used to compute second-order
Sobol' indices, we need to set ``calc_second_order`` to `True`.
It leads to :math:`nbase*(2*ndim+2)` samples.

.. GENERATED FROM PYTHON SOURCE LINES 56-73

.. code-block:: default


    saltelli_sampler = Saltelli(ndim, bounds, calc_second_order=True)
    saltelli_samples = saltelli_sampler.sample(nbase=128)

    fig = plt.figure()
    ax = fig.add_subplot(projection='3d')

    ax.scatter(saltelli_samples[:,0], saltelli_samples[:,1], saltelli_samples[:,2], marker='o')
    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')

    plt.tight_layout()

    print('Number of samples: ', f'{len(saltelli_samples)}')





.. image-sg:: /auto_examples/sampler/images/sphx_glr_plot_saltelli_002.png
   :alt: plot saltelli
   :srcset: /auto_examples/sampler/images/sphx_glr_plot_saltelli_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Number of samples:  1024




.. GENERATED FROM PYTHON SOURCE LINES 74-78

.. note:: If one has a two-dimensional problem, there is no need to set
    ``calc_second_order`` to `True`. The reason is that the second-order Sobol'
    index can be directly computed based on the first-order and total-effect
    Sobol' index in that case.


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

   **Total running time of the script:** ( 0 minutes  0.355 seconds)


.. _sphx_glr_download_auto_examples_sampler_plot_saltelli.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_saltelli.py <plot_saltelli.py>`

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

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


.. only:: html

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

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