.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/dimension_reduction/pod/pod_1.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_dimension_reduction_pod_pod_1.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_dimension_reduction_pod_pod_1.py:


POD on data
=====================

In this example, the Direct Proper Orthogonal Decomposition (POD) method is used to decompose a set of data and extract
basis functions which can be used for the reconstruction of the solution.

.. GENERATED FROM PYTHON SOURCE LINES 11-13

Import the necessary libraries. Here we import standard libraries such as numpy, matplotlib, and we also import the
POD class from UQpy.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: default


    from UQpy.dimension_reduction import DirectPOD
    import time
    import numpy as np


.. GENERATED FROM PYTHON SOURCE LINES 22-24

Input dataset in the form of a second order tensor consists of three snapshot solutions. Using the POD method we
reconstruct the input dataset by keeping a predefined number of modes.

.. GENERATED FROM PYTHON SOURCE LINES 27-45

.. code-block:: default


    Data = np.zeros((3, 5, 3))

    Data[:, :, 0] = [
        [0.9073, 1.7842, 2.1236, 1.1323, 1.6545],
        [0.8924, 1.7753, -0.6631, 0.5654, 2.1235],
        [2.1488, 4.2495, 1.8260, 0.3423, 4.9801]]

    Data[:, :, 1] = [
        [0.7158, 1.6970, -0.0740, 5.478, 1.0987],
        [-0.4898, -1.5077, 1.9103, 6.7121, 0.5334],
        [0.3054, 0.3207, 2.1335, 1.1082, 5.5435]]

    Data[:, :, 2] = [
        [-0.3698, 0.0151, 1.4429, 2.5463, 6.9871],
        [2.4288, 4.0337, -1.7495, -0.5012, 1.7654],
        [2.3753, 4.7146, -0.2716, 1.6543, 0.9121]]


.. GENERATED FROM PYTHON SOURCE LINES 46-49

The Direct POD method is used to compute the reconstructed solutions and reduced-order solutions in the spatial
dimension of the data. Full reconstruction is achieved when the number of modes chosen, equals the number of
dimensions.

.. GENERATED FROM PYTHON SOURCE LINES 52-58

.. code-block:: default


    start_time = time.time()

    pod = DirectPOD(solution_snapshots=Data, n_modes=1)
    Data_reconstr = pod.reconstructed_solution


.. GENERATED FROM PYTHON SOURCE LINES 59-60

Print the reconstructed dataset.

.. GENERATED FROM PYTHON SOURCE LINES 63-73

.. code-block:: default


    print('Reconstructed snapshot no.1:')
    print(Data_reconstr[:, :, 0])

    if np.allclose(Data, Data_reconstr[0]) == True:
        print('Input data and reconstructed data are identical.')

    elapsed_time = time.time() - start_time
    time.strftime("%H:%M:%S", time.gmtime(elapsed_time))
    print('Elapsed time: ', round(elapsed_time, 8))


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

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


.. _sphx_glr_download_auto_examples_dimension_reduction_pod_pod_1.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/dimension_reduction/pod/pod_1.ipynb
        :alt: Launch binder
        :width: 150 px



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

      :download:`Download Python source code: pod_1.py <pod_1.py>`

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

      :download:`Download Jupyter notebook: pod_1.ipynb <pod_1.ipynb>`


.. only:: html

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

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