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

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

.. _sphx_glr_auto_examples_plot_complex_histograms.py:


Complex histograms
==================

Shows how spectrum of random matrices with complex eigenvalues is plotted.

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.. code-block:: Python


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

    from skrmt.ensemble import CircularEnsemble








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Several ensembles have symmetric or hermitian matrices, so their eigenvalues
are real. However, there are some cases where random matrices are not
symmetric either hermitian. Therefore, their eigenvalues can be complex.

This is the case of Circular Unitary Ensemble (CUE) and Circular Symplectic
Ensemble (CSE).

scikit-rmt takes into account this possibility and uses histograms in 2D in
order to represent spectrum distribution of given ensembles.

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In this example, eigenvalue spectrum of CUE random matrix is shown.

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.. code-block:: Python


    cue = CircularEnsemble(beta=2, n=1000)
    cue.plot_eigval_hist(bins=80)




.. image-sg:: /auto_examples/images/sphx_glr_plot_complex_histograms_001.png
   :alt: Complex eigenvalues histogram, Complex plane, Eigenvalue heatmap
   :srcset: /auto_examples/images/sphx_glr_plot_complex_histograms_001.png
   :class: sphx-glr-single-img





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And the eigenvalue spectrum of CSE.

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.. code-block:: Python


    cse = CircularEnsemble(beta=4, n=1000)
    cse.plot_eigval_hist(bins=80)




.. image-sg:: /auto_examples/images/sphx_glr_plot_complex_histograms_002.png
   :alt: Complex eigenvalues histogram, Complex plane, Eigenvalue heatmap
   :srcset: /auto_examples/images/sphx_glr_plot_complex_histograms_002.png
   :class: sphx-glr-single-img





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The provided heatmap gives an illustration of the eigenvalue accumulation.


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

   **Total running time of the script:** (0 minutes 9.131 seconds)


.. _sphx_glr_download_auto_examples_plot_complex_histograms.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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