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

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

.. _sphx_glr_auto_examples_plot_boosting_density_representation.py:


Boosting density representation
===============================

Describes how speed up histogram representation of ensemble spectral density.

.. GENERATED FROM PYTHON SOURCE LINES 7-15

.. code-block:: Python


    # Author: Alejandro Santorum Varela
    # License: BSD 3-Clause

    import time

    from skrmt.ensemble import GaussianEnsemble, WishartEnsemble








.. GENERATED FROM PYTHON SOURCE LINES 16-18

We can sample a random matrix of the Gaussian Ensemble with a relatively
large size and plot its spectral density.

.. GENERATED FROM PYTHON SOURCE LINES 18-25

.. code-block:: Python


    goe = GaussianEnsemble(beta=1, n=5000)

    t1 = time.time()
    goe.plot_eigval_hist(bins=60, density=False, normalize=False)
    t2 = time.time()




.. image-sg:: /auto_examples/images/sphx_glr_plot_boosting_density_representation_001.png
   :alt: Eigenvalue histogram
   :srcset: /auto_examples/images/sphx_glr_plot_boosting_density_representation_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 26-27

The time needed to compute the previous histogram is:

.. GENERATED FROM PYTHON SOURCE LINES 27-29

.. code-block:: Python

    print(t2-t1, 'seconds')





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

 .. code-block:: none

    5.188860654830933 seconds




.. GENERATED FROM PYTHON SOURCE LINES 30-32

We can speed up this procedure using the tridiagonal form of Gaussian
Ensemble random matrices: ``tridiagonal_form=True``.

.. GENERATED FROM PYTHON SOURCE LINES 32-39

.. code-block:: Python


    goe_tridiag = GaussianEnsemble(beta=1, n=5000, tridiagonal_form=True)

    t1 = time.time()
    goe_tridiag.plot_eigval_hist(bins=60, density=False, normalize=False)
    t2 = time.time()




.. image-sg:: /auto_examples/images/sphx_glr_plot_boosting_density_representation_002.png
   :alt: Eigenvalue histogram
   :srcset: /auto_examples/images/sphx_glr_plot_boosting_density_representation_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 40-41

The time needed to compute the previous histogram is:

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    print(t2-t1, 'seconds')





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

 .. code-block:: none

    0.2870519161224365 seconds




.. GENERATED FROM PYTHON SOURCE LINES 44-45

This boosting trick can be used with Wishart Ensemble too

.. GENERATED FROM PYTHON SOURCE LINES 45-52

.. code-block:: Python


    wre = WishartEnsemble(beta=1, p=5000, n=10000)

    t1 = time.time()
    wre.plot_eigval_hist(bins=60, density=False, normalize=False)
    t2 = time.time()




.. image-sg:: /auto_examples/images/sphx_glr_plot_boosting_density_representation_003.png
   :alt: Eigenvalue histogram
   :srcset: /auto_examples/images/sphx_glr_plot_boosting_density_representation_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 53-54

The time needed to compute the previous histogram is:

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

    print(t2-t1, 'seconds')





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

 .. code-block:: none

    5.173484563827515 seconds




.. GENERATED FROM PYTHON SOURCE LINES 57-58

Using tridiagonal form of the Wishart Ensemble by setting ``tridiagonal_form=True``.

.. GENERATED FROM PYTHON SOURCE LINES 58-65

.. code-block:: Python


    wre_tridiag = WishartEnsemble(beta=1, p=5000, n=10000, tridiagonal_form=True)

    t1 = time.time()
    wre_tridiag.plot_eigval_hist(bins=60, density=False, normalize=False)
    t2 = time.time()




.. image-sg:: /auto_examples/images/sphx_glr_plot_boosting_density_representation_004.png
   :alt: Eigenvalue histogram
   :srcset: /auto_examples/images/sphx_glr_plot_boosting_density_representation_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 66-67

The time needed to compute the previous histogram is:

.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: Python

    print(t2-t1, 'seconds')





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

 .. code-block:: none

    0.2900412082672119 seconds





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

   **Total running time of the script:** (0 minutes 14.780 seconds)


.. _sphx_glr_download_auto_examples_plot_boosting_density_representation.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_boosting_density_representation.zip <plot_boosting_density_representation.zip>`


.. only:: html

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

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