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

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

.. _sphx_glr_auto_examples_plot_manova_ensemble.py:


Manova Ensemble
=================

Defines Manova 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 ManovaEnsemble








.. GENERATED FROM PYTHON SOURCE LINES 14-16

Manova Ensemble random matrices are considered to be double Wishart random
matrices.

.. GENERATED FROM PYTHON SOURCE LINES 18-28

Manova Real Ensemble (MRE)
---------------------------

Random matrices of MRE are formed by sampling two random real standard
guassian matrices (:math:`\mathbf{X}` and :math:`\mathbf{Y}`) of size
:math:`m \times n_1` and :math:`m \times n_2` respectively. Then, matrix
:math:`\mathbf{A} = \dfrac{\mathbf{X}\mathbf{X}^T}{\mathbf{X}\mathbf{X}^T  + \mathbf{Y}\mathbf{Y}^T}`
generates a matrix of the MRE.

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

.. GENERATED FROM PYTHON SOURCE LINES 30-32

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

.. GENERATED FROM PYTHON SOURCE LINES 32-36

.. code-block:: Python


    mre = ManovaEnsemble(beta=1, m=3, n1=5, n2=5)
    print(mre.matrix)





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

 .. code-block:: none

    [[ 0.37357168 -0.0229562  -0.12886666]
     [ 0.10982747  0.65232374  0.22545803]
     [ 0.10811206  0.11454821  0.78460693]]




.. GENERATED FROM PYTHON SOURCE LINES 37-47

Manova Complex Ensemble (MCE)
------------------------------

Random matrices of MCE are formed by sampling two random complex standard
guassian matrices (:math:`\mathbf{X}` and :math:`\mathbf{Y}`) of size
:math:`m \times n_1` and :math:`m \times n_2` respectively. Then, matrix
:math:`\mathbf{A} = \dfrac{\mathbf{X}\mathbf{X}^T}{\mathbf{X}\mathbf{X}^T  + \mathbf{Y}\mathbf{Y}^T}`
generates a matrix of the MCE.

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

.. GENERATED FROM PYTHON SOURCE LINES 49-51

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

.. GENERATED FROM PYTHON SOURCE LINES 51-55

.. code-block:: Python


    mce = ManovaEnsemble(beta=2, m=3, n1=5, n2=5)
    print(mce.matrix)





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

 .. code-block:: none

    [[ 0.42539464+0.1414285j   0.14444995-0.05260573j -0.26449982+0.3652106j ]
     [ 0.0397875 +0.22067762j  0.39708865-0.10969292j -0.19966326+0.60321587j]
     [ 0.04435281-0.0831098j  -0.14731224-0.13789568j  0.73233881-0.03173559j]]




.. GENERATED FROM PYTHON SOURCE LINES 56-74

Manova Quaternion Ensemble (MQE)
---------------------------------

Random matrices of MQE are formed by sampling two random complex standard 
guassian matrices (:math:`\mathbf{X_1}` and :math:`\mathbf{X_2}`), both of
size :math:`m \times n_1`. Another two random complex standard guassian matrices
(:math:`\mathbf{Y_1}` and :math:`\mathbf{Y_2}`), both of size :math:`m \times n_2`,
are sampled. They are stacked forming matrices :math:`\mathbf{X}` and
:math:`\mathbf{Y}`:

:math:`\mathbf{X} = (\mathbf{X_1}\ \mathbf{X_2}; -\mathbf{X_2}^*\ \mathbf{X_1}^*)`

:math:`\mathbf{Y} = (\mathbf{Y_1}\ \mathbf{Y_2}; -\mathbf{Y_2}^*\ \mathbf{Y_1}^*)`

Finally, matrix :math:`\mathbf{A} = \dfrac{\mathbf{X}\mathbf{X}^T}{\mathbf{X}\mathbf{X}^T  + \mathbf{Y}\mathbf{Y}^T}`
generates a matrix of the MQE.

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

.. GENERATED FROM PYTHON SOURCE LINES 76-78

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

.. GENERATED FROM PYTHON SOURCE LINES 78-80

.. code-block:: Python


    mqe = ManovaEnsemble(beta=4, m=2, n1=5, n2=5)
    print(mqe.matrix)



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

 .. code-block:: none

    [[ 0.51844198+0.01160693j -0.01631465+0.00406845j -0.00299089-0.00824204j
       0.05202532+0.05268844j]
     [-0.02577827-0.00708927j  0.50089801+0.01283598j -0.08565466-0.09086775j
       0.00342764+0.00592337j]
     [ 0.00299089-0.00824204j -0.05202532+0.05268844j  0.51844198-0.01160693j
      -0.01631465-0.00406845j]
     [ 0.08565466-0.09086775j -0.00342764+0.00592337j -0.02577827+0.00708927j
       0.50089801-0.01283598j]]





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

   **Total running time of the script:** (0 minutes 0.009 seconds)


.. _sphx_glr_download_auto_examples_plot_manova_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_manova_ensemble.ipynb <plot_manova_ensemble.ipynb>`

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

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

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

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


.. only:: html

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

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