.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/topology/data/plot_05_mapper.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_topology_data_plot_05_mapper.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

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

.. _sphx_glr_api_gallery_topology_data_plot_05_mapper.py:


Mapper (Singh, Mémoli and Carlsson 2007)
========================================

Mapper summarizes a data set as a graph. Slice the data by a lens
function, cluster each slice, and join clusters that share points. It
is a discrete Reeb graph. Here 3-dimensional data sampled near a
circle with a dangling branch are seen through their height. Mapper
recovers one loop and one flare, and the graph's Betti numbers
:math:`(1, 1)` match the loop.

.. GENERATED FROM PYTHON SOURCE LINES 14-37



.. image-sg:: /api/gallery/topology/data/images/sphx_glr_plot_05_mapper_001.png
   :alt: Mapper: a loop with a branch, data (first two of three coordinates), coloured by the lens y, Mapper graph, 6 intervals: β = (1, 1), Mapper graph, 12 intervals: β = (1, 1)
   :srcset: /api/gallery/topology/data/images/sphx_glr_plot_05_mapper_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    6 intervals: 11 nodes, 11 edges, Betti numbers (1, 1)
    12 intervals: 25 nodes, 25 edges, Betti numbers (1, 1)

    Text(0.5, 0.98, 'Mapper: a loop with a branch')





|

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from mathematicskit.topology import betti_numbers, mapper_graph
    from mathematicskit.topology.visualizers import plot_mapper_graph

    rng = np.random.default_rng(5)
    t = rng.uniform(0, 2 * np.pi, 500)
    loop = np.column_stack([np.cos(t), 1.5 * np.sin(t), 0.3 * np.sin(2 * t)])
    s = rng.uniform(0, 1, 150)
    branch = np.column_stack([1 + 1.5 * s, 0.4 * s**2, 0 * s])
    points = np.vstack([loop, branch]) + rng.normal(0, 0.05, (650, 3))

    fig, axes = plt.subplots(1, 3, figsize=(15, 4.6))
    axes[0].scatter(points[:, 0], points[:, 1], c=points[:, 1], s=6, cmap="viridis")
    axes[0].set_aspect("equal")
    axes[0].set_title("data (first two of three coordinates), coloured by the lens y")
    for ax, n in zip(axes[1:], (6, 12), strict=True):
        result = mapper_graph(points, points[:, 1], eps=0.3, n_intervals=n, overlap=0.35)
        print(f"{n} intervals: {len(result.nodes)} nodes, {len(result.edges)} edges, Betti numbers {betti_numbers(result.graph)}")
        plot_mapper_graph(result, points, ax=ax)
        ax.set_title(f"Mapper graph, {n} intervals: β = {betti_numbers(result.graph)}")
    fig.suptitle("Mapper: a loop with a branch")


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

   **Total running time of the script:** (0 minutes 0.080 seconds)


.. _sphx_glr_download_api_gallery_topology_data_plot_05_mapper.py:

.. only:: html

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/topology/data/plot_05_mapper.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_05_mapper.ipynb <plot_05_mapper.ipynb>`

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

      :download:`Download Python source code: plot_05_mapper.py <plot_05_mapper.py>`

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

      :download:`Download zipped: plot_05_mapper.zip <plot_05_mapper.zip>`


.. only:: html

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

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