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

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

.. _sphx_glr_auto_examples_plot_wishart_ensemble.py:


Wishart Ensemble
=================

Defines Wishart Ensemble random matrices

.. GENERATED FROM PYTHON SOURCE LINES 7-13

.. code-block:: Python


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

    from skrmt.ensemble import WishartEnsemble








.. GENERATED FROM PYTHON SOURCE LINES 14-16

Wishart Ensemble contains random matrices formed by the multiplication
of two random matrices whose entries are gaussian distributed.

.. GENERATED FROM PYTHON SOURCE LINES 18-25

Wishart Real Ensemble (WRE)
---------------------------

Random matrices of WRE are formed by multiplying a random real standard
gaussian matrix of size :math:`p \times n` by its transpose.

They are also known as 1-Laguerre random matrices (beta = 1).

.. GENERATED FROM PYTHON SOURCE LINES 27-29

A random matrix of Wishart Real Ensemble can be sampled using
scikit-rmt with the following code.

.. GENERATED FROM PYTHON SOURCE LINES 29-33

.. code-block:: Python


    wre = WishartEnsemble(beta=1, p=3, n=5)
    print(wre.matrix)





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

 .. code-block:: none

    [[ 2.52187748  0.90213238  0.9233787 ]
     [ 0.90213238  2.68877397 -0.34174262]
     [ 0.9233787  -0.34174262  0.81725582]]




.. GENERATED FROM PYTHON SOURCE LINES 34-41

Wishart Complex Ensemble (WCE)
------------------------------

Random matrices of WCE are formed by multiplying a random complex
standard gaussian matrix of size :math:`p \times n` by its transpose.

They are also known as 2-Laguerre random matrices (beta = 2).

.. GENERATED FROM PYTHON SOURCE LINES 43-45

A random matrix of Wishart Complex Ensemble can be sampled using
scikit-rmt with the following code.

.. GENERATED FROM PYTHON SOURCE LINES 45-49

.. code-block:: Python


    wce = WishartEnsemble(beta=2, p=3, n=5)
    print(wce.matrix)





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

 .. code-block:: none

    [[14.06746504+1.18556151e-16j  0.8944584 -2.38001326e-01j
      -0.83235695-5.19899908e+00j]
     [ 0.8944584 +2.38001326e-01j 10.75632892-1.21034686e-16j
      -0.19185687+1.03864421e-01j]
     [-0.83235695+5.19899908e+00j -0.19185687-1.03864421e-01j
       4.73265095+1.69405758e-18j]]




.. GENERATED FROM PYTHON SOURCE LINES 50-60

Wishart Quaternion Ensemble (WQE)
---------------------------------

Random matrices of WQE are formed by sampling two random complex standard
guassian matrices (:math:`\mathbf{X}` and :math:`\mathbf{Y}`), stacking
them to create matrix :math:`\mathbf{A} = (\mathbf{X}\ \mathbf{Y}; -\mathbf{Y}^*\ \mathbf{X}^*)`.
Finally matrix :math:`\mathbf{A}` is multiplied by its transpose to generate
a matrix WQE randon matrix.

They are also known as 4-Laguerre random matrices (beta = 4).

.. GENERATED FROM PYTHON SOURCE LINES 62-64

A random matrix of Wishart Quaternion Ensemble can be sampled using
scikit-rmt with the following code.

.. GENERATED FROM PYTHON SOURCE LINES 64-66

.. code-block:: Python


    wqe = WishartEnsemble(beta=4, p=2, n=5)
    print(wqe.matrix)



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

 .. code-block:: none

    [[ 1.59520988e+01+0.00000000e+00j  5.32889278e+00+5.03594358e+00j
       2.50068009e-16+0.00000000e+00j -1.36971229e+00-7.23141196e+00j]
     [ 5.32889278e+00-5.03594358e+00j  2.02861721e+01+0.00000000e+00j
       1.36971229e+00+7.23141196e+00j  1.79871143e-16-4.44089210e-16j]
     [ 2.50068009e-16+0.00000000e+00j  1.36971229e+00-7.23141196e+00j
       1.59520988e+01+0.00000000e+00j  5.32889278e+00-5.03594358e+00j]
     [-1.36971229e+00+7.23141196e+00j  1.79871143e-16+4.44089210e-16j
       5.32889278e+00+5.03594358e+00j  2.02861721e+01+0.00000000e+00j]]





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

   **Total running time of the script:** (0 minutes 0.004 seconds)


.. _sphx_glr_download_auto_examples_plot_wishart_ensemble.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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