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

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

.. _sphx_glr_auto_examples_plot_nlogn_scaling.py:


=================
Scaling behaviour
=================

Compute the autocorrelation for varying time series lengths.

The figure displays the timing and a :math:`N log N` scaling law, demonstrating
the claimed complexity.

.. GENERATED FROM PYTHON SOURCE LINES 11-72



.. image-sg:: /auto_examples/images/sphx_glr_plot_nlogn_scaling_001.png
   :alt: plot nlogn scaling
   :srcset: /auto_examples/images/sphx_glr_plot_nlogn_scaling_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    import numpy as np
    import tidynamics
    import matplotlib.pyplot as plt
    import time

    plt.rcParams['figure.figsize'] = 5.12, 3.84
    plt.rcParams['figure.subplot.bottom'] = 0.18
    plt.rcParams['figure.subplot.left'] = 0.16


    all_N = []
    N = 64
    for i in range(14):
        all_N.append(N + int(N/3))
        all_N.append(N + int(N/2))
        all_N.append(N + int(2*N/3))
        N = 2*N
    all_N = np.array(all_N)

    max_direct_N = 32768
    all_time = []
    direct_time = []
    n_runs = 5

    for N in all_N:
        t = 0
        direct_t = 0
        for i in range(n_runs):
            data = np.random.random(size=N)
            t0 = time.time()
            acf = tidynamics.acf(data)
            t += time.time() - t0
            if N <= max_direct_N:
                t0 = time.time()
                acf = np.correlate(data, data, mode='full')
                direct_t += time.time() - t0

        all_time.append(t/n_runs)
        if N <= max_direct_N:
            direct_time.append(direct_t/n_runs)

    plt.plot(all_N, all_time, label='actual compute time')
    plt.plot(all_N,
             all_time[-1] * all_N*np.log(all_N) / (all_N[-1]*np.log(all_N[-1])),
             label=r'$N\log N$ scaling')
    plt.plot(all_N[:len(direct_time)], direct_time,
             label='np.correlate compute time', ls='--')

    data_len = len(direct_time)
    plt.plot(all_N[:data_len],
             all_N[:data_len]**2 * direct_time[data_len-1] / all_N[data_len-1]**2,
             label=r'$N^2$ scaling', ls=':')

    plt.xlabel(r'$N$')
    plt.ylabel('time')

    plt.loglog()
    plt.legend()

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  13.530 seconds)


.. _sphx_glr_download_auto_examples_plot_nlogn_scaling.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_nlogn_scaling.py <plot_nlogn_scaling.py>`

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

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


.. only:: html

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

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