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

    Click :ref:`here <sphx_glr_download_auto_examples_hammersleypoints_plot_hammersley_points.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_hammersleypoints_plot_hammersley_points.py:


###################
Hammersley 2D-plane
###################

Hammersley points are a series of pseudo random points with a low discrepancy that are suitable for use in solid state NMR simulations where powder averaging is performed.

References
==========

- Hammersley, J. M.; Handscomb, D. C. (1964). Monte Carlo Methods. doi:10.1007/978-94-009-5819-7
- Tien-Tsin Wong, Wai-Shing Luk & Pheng-Ann Heng (1997) Sampling with Hammersley and Halton Points, Journal of Graphics Tools, 2:2, 9-24, doi: 10.1080/10867651.1997.10487471

Examples of Hammersley points for tiling a 2-D plane
====================================================



.. image:: /auto_examples/hammersleypoints/images/sphx_glr_plot_hammersley_points_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    C:\Users\ERIC\Documents\pygamma_gallery\docsource\sphinx\examples\hammersleypoints\plot_hammersley_points.py:82: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      plt.show()






|


.. code-block:: default


    import numpy as np
    from matplotlib import pyplot as plt



    def return_point(m, n, p):
        """
        m is the index number of the Hammersley point to calculate
        n is the maximun number of points
        p is the order of the Hammersley point, 1,2,3,4,... etc
        l is the power of x to go out to and is hard coded to 10 in this example
        :return type double
        """

        if p == 1:
            return m / n

        v = 0.0

        for j in range(10, -1, -1):
            num = m // p ** j

            if num > 0:
                m -= num * p ** j
                v += num / (p ** (j + 1))

        return (v)

    if __name__ == "__main__":

        npts = 500
        h_1 = np.zeros(npts)
        h_2 = np.zeros(npts)
        h_3 = np.zeros(npts)
        h_4 = np.zeros(npts)
        h_5 = np.zeros(npts)
        h_7 = np.zeros(npts)

        for m in range(npts):
            h_1[m] = return_point(m, npts, 1)
            h_2[m] = return_point(m, npts, 2)
            h_3[m] = return_point(m, npts, 3)
            h_4[m] = return_point(m, npts, 4)
            h_5[m] = return_point(m, npts, 5)
            h_7[m] = return_point(m, npts, 7)

        fig, axs = plt.subplots(2, 2, figsize=(10, 10), sharey=True)

        ax =axs.flatten()

        ax[0].plot(h_1, h_2, '.')
        ax[1].plot(h_1, h_2, '.')
        ax[2].plot(h_1, h_4, '.')
        ax[3].plot(h_1, h_5, '.')
        ax[0].set_xlabel("p=1", fontsize=14)
        ax[0].set_ylabel("p=2", fontsize=14)
        ax[1].set_xlabel("p=1", fontsize=14)
        ax[1].set_ylabel("p=3", fontsize=14)
        ax[2].set_xlabel("p=1", fontsize=14)
        ax[2].set_ylabel("p=4", fontsize=14);
        ax[3].set_xlabel("p=1", fontsize=14)
        ax[3].set_ylabel("p=5", fontsize=14);


        plt.show()

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

   **Total running time of the script:** ( 0 minutes  0.174 seconds)


.. _sphx_glr_download_auto_examples_hammersleypoints_plot_hammersley_points.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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