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

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

.. _sphx_glr_auto_examples_plot_gaussian_ensemble.py:


Gaussian Ensemble
=================

Defines Gaussian 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 GaussianEnsemble








.. GENERATED FROM PYTHON SOURCE LINES 14-16

Gaussian Ensemble contains random matrices whose inputs are gaussian
distributed.

.. GENERATED FROM PYTHON SOURCE LINES 18-28

Gaussian Orthogonal Ensemble (GOE)
----------------------------------

Random matrices of GOE have real entries gaussian distributed. These
matrices are invariant under orthogonal conjugation, i.e., if
:math:`\mathbf{X} \in \text{GOE}` and :math:`\mathbf{O}` is an orthogonal
matrix, then :math:`\mathbf{O} \mathbf{X} \mathbf{O}^T` is equally
distributed as :math:`\mathbf{X}`.

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

.. GENERATED FROM PYTHON SOURCE LINES 30-32

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

.. GENERATED FROM PYTHON SOURCE LINES 32-36

.. code-block:: Python


    goe = GaussianEnsemble(beta=1, n=4)
    print(goe.matrix)





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

 .. code-block:: none

    [[-1.12173516 -1.88154934  0.99084342 -0.36152007]
     [-1.88154934  0.4066097  -0.62418723  0.73193813]
     [ 0.99084342 -0.62418723 -1.65812296  1.7959167 ]
     [-0.36152007  0.73193813  1.7959167  -0.157581  ]]




.. GENERATED FROM PYTHON SOURCE LINES 37-48

Gaussian Unitary Ensemble (GUE)
-------------------------------

Random matrices of GUE have complex entries gaussian distributed, i.e.,
their real part and their complex part are gaussian distributed. These
matrices are invariant under unitary conjugation, i.e., if
:math:`\mathbf{X} \in \text{GUE}` and :math:`\mathbf{O}` is an unitary
matrix, then :math:`\mathbf{O} \mathbf{X} \mathbf{O}^T` is equally
distributed as :math:`\mathbf{X}`.

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

.. GENERATED FROM PYTHON SOURCE LINES 50-52

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

.. GENERATED FROM PYTHON SOURCE LINES 52-56

.. code-block:: Python


    gue = GaussianEnsemble(beta=2, n=4)
    print(gue.matrix)





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

 .. code-block:: none

    [[-1.39147258+0.j          0.10204265+0.15235105j  0.64083085+0.02625899j
      -0.26261269-0.81049254j]
     [ 0.10204265-0.15235105j -1.63595668+0.j         -1.53717783+1.53735075j
      -1.75492192+0.01811866j]
     [ 0.64083085-0.02625899j -1.53717783-1.53735075j  2.28373677+0.j
       0.80168935-0.78350495j]
     [-0.26261269+0.81049254j -1.75492192-0.01811866j  0.80168935+0.78350495j
      -2.31203799+0.j        ]]




.. GENERATED FROM PYTHON SOURCE LINES 57-65

Gaussian Symplectic Ensemble (GSE)
----------------------------------

Random matrices of GSE have quaternionic entries gaussian distributed, i.e.,
their four dimensions are gaussian distributed. These matrices are invariant
under conjugation by the symplectic group.

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

.. GENERATED FROM PYTHON SOURCE LINES 67-69

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

.. GENERATED FROM PYTHON SOURCE LINES 69-71

.. code-block:: Python


    gse = GaussianEnsemble(beta=4, n=2)
    print(gse.matrix)



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

 .. code-block:: none

    [[-2.48945835+0.j         -4.10973093+2.71227021j  0.        +0.j
       0.99992279+0.80557055j]
     [-4.10973093-2.71227021j -0.26802827+0.j         -0.99992279-0.80557055j
       0.        +0.j        ]
     [ 0.        +0.j         -0.99992279+0.80557055j -2.48945835+0.j
      -4.10973093-2.71227021j]
     [ 0.99992279-0.80557055j  0.        +0.j         -4.10973093+2.71227021j
      -0.26802827+0.j        ]]





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

   **Total running time of the script:** (0 minutes 0.002 seconds)


.. _sphx_glr_download_auto_examples_plot_gaussian_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_gaussian_ensemble.ipynb <plot_gaussian_ensemble.ipynb>`

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

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

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

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


.. only:: html

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

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