.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "intro/scipy/auto_examples/solutions/plot_periodicity_finder.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_intro_scipy_auto_examples_solutions_plot_periodicity_finder.py>`
        to download the full example code

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

.. _sphx_glr_intro_scipy_auto_examples_solutions_plot_periodicity_finder.py:


==========================
Crude periodicity finding
==========================

Discover the periods in evolution of animal populations
(:download:`../../../../data/populations.txt`)

.. GENERATED FROM PYTHON SOURCE LINES 11-13

Load the data
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 13-19

.. code-block:: default


    import numpy as np
    data = np.loadtxt('../../../../data/populations.txt')
    years = data[:, 0]
    populations = data[:, 1:]








.. GENERATED FROM PYTHON SOURCE LINES 20-22

Plot the data
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 22-30

.. code-block:: default


    import matplotlib.pyplot as plt
    plt.figure()
    plt.plot(years, populations * 1e-3)
    plt.xlabel('Year')
    plt.ylabel(r'Population number ($\cdot10^3$)')
    plt.legend(['hare', 'lynx', 'carrot'], loc=1)




.. image-sg:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_periodicity_finder_001.png
   :alt: plot periodicity finder
   :srcset: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_periodicity_finder_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7fe7b09f2af0>



.. GENERATED FROM PYTHON SOURCE LINES 31-33

Plot its periods
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 33-47

.. code-block:: default

    import scipy as sp

    ft_populations = sp.fftpack.fft(populations, axis=0)
    frequencies = sp.fftpack.fftfreq(populations.shape[0], years[1] - years[0])
    periods = 1 / frequencies

    plt.figure()
    plt.plot(periods, abs(ft_populations) * 1e-3, 'o')
    plt.xlim(0, 22)
    plt.xlabel('Period')
    plt.ylabel(r'Power ($\cdot10^3$)')

    plt.show()




.. image-sg:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_periodicity_finder_002.png
   :alt: plot periodicity finder
   :srcset: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_periodicity_finder_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /opt/build/repo/intro/scipy/examples/solutions/plot_periodicity_finder.py:37: RuntimeWarning: divide by zero encountered in divide
      periods = 1 / frequencies




.. GENERATED FROM PYTHON SOURCE LINES 48-51

There's probably a period of around 10 years (obvious from the
plot), but for this crude a method, there's not enough data to say
much more.


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

   **Total running time of the script:** ( 0 minutes  0.118 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_solutions_plot_periodicity_finder.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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