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

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

.. _sphx_glr_auto_examples_vietoris_rips_plot_submatrix_index_tool.py:


.. _vietoris_submatrix_index_tool:

Submatrix Index Tool
========================================

A common pain point in computational homological algebra is passing between matrix and integer indices
for boundary and other matrices. OAT offers a :class:`oat_python.core.vietoris_rips.SubmatrixIndexTool`
to help wth this.

.. GENERATED FROM PYTHON SOURCE LINES 13-21

See also
-------------------------------

See the :ref:`vietoris_rips_matrices` gallery for more examples!


Setup
-------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-33

.. code-block:: Python

    import oat_python as oat

    from fractions import Fraction
    import matplotlib.pyplot as plt
    import numpy as np
    import pandas as pd
    import plotly.graph_objects as go
    from scipy.sparse import csr_matrix








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Generate a point cloud

.. GENERATED FROM PYTHON SOURCE LINES 35-38

.. code-block:: Python


    points               =   oat.point_cloud.sphere_or_slice(n_points=100)








.. GENERATED FROM PYTHON SOURCE LINES 39-40

Plot the point cloud

.. GENERATED FROM PYTHON SOURCE LINES 40-45

.. code-block:: Python

    trace               =   go.Scatter3d(x=points[:,0],y=points[:,1],z=points[:,2], mode="markers", marker=dict(opacity=1, size=4, color=points[:,2], colorscale="Aggrnyl"))
    fig                 =   go.Figure(data=trace)
    fig.update_layout(title=dict(text="Point cloud"), height=800,width=850) 
    fig






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.. GENERATED FROM PYTHON SOURCE LINES 46-48

Compute persistent homology
-------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 50-51

We compute persistent homology by factoring the boundary matrix.  The following cell generates a sparse distance matrix and feeds it to the persistent homology solver.  The result is a decomposition boundary matrix.  We will extract information from this matrix in the following cells.

.. GENERATED FROM PYTHON SOURCE LINES 53-54

Prepare a dissimilarity matrix

.. GENERATED FROM PYTHON SOURCE LINES 54-60

.. code-block:: Python


    dissimilarity_matrix    =   oat.dissimilarity.sparse_matrix_for_points(            
                                    points                   =   points,
                                    max_dissimilarity        =   0.5,
                                )








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Create and decompose the boundary matrix

.. GENERATED FROM PYTHON SOURCE LINES 62-68

.. code-block:: Python


    decomposition           =   oat.core.vietoris_rips.BoundaryMatrixDecomposition(
                                    dissimilarity_matrix    =   dissimilarity_matrix,
                                    max_homology_dimension  =   1,
                                )








.. GENERATED FROM PYTHON SOURCE LINES 69-73

Access indices
------------------------------------



.. GENERATED FROM PYTHON SOURCE LINES 75-76

Create a `oat_python.core.vietoris_rips.SubmatrixIndexTool` whose rows and columns are the vertices and edges of the Vietoris-Rips complex, respectively.

.. GENERATED FROM PYTHON SOURCE LINES 78-84

.. code-block:: Python

    submatrix_index_tool    =   decomposition.submatrix_index_tool(
                                    row_dimensions      =   [0,],
                                    column_dimensions   =   [1,]
                                )
    submatrix_index_tool





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

 .. code-block:: none


    <SubmatrixIndexTool: 100 row indices, 292 column indices>



.. GENERATED FROM PYTHON SOURCE LINES 85-86

The number of row and column indices can be accessed via lookup functions:

.. GENERATED FROM PYTHON SOURCE LINES 88-90

.. code-block:: Python

    submatrix_index_tool.number_of_rows()





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

 .. code-block:: none


    100



.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. code-block:: Python

    submatrix_index_tool.number_of_columns()





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

 .. code-block:: none


    292



.. GENERATED FROM PYTHON SOURCE LINES 94-95

The (ordered) lists of row and column indices can also be exported to dataframe format, for inspection:

.. GENERATED FROM PYTHON SOURCE LINES 97-103

.. code-block:: Python

    oat.plot.display_dataframes_side_by_side(
        submatrix_index_tool.row_indices()[:5],
        submatrix_index_tool.column_indices()[:5],
        titles=["Row indices (vertices)","Column indices (edges)"]
    )






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div style="display:inline-block; vertical-align:top; margin-right:20px;"><h4>Row indices (vertices)</h4><table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>simplex</th>
          <th>filtration</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>(0,)</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1,)</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(2,)</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>3</th>
          <td>(3,)</td>
          <td>0.0</td>
        </tr>
        <tr>
          <th>4</th>
          <td>(4,)</td>
          <td>0.0</td>
        </tr>
      </tbody>
    </table></div><div style="display:inline-block; vertical-align:top; margin-right:20px;"><h4>Column indices (edges)</h4><table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>simplex</th>
          <th>filtration</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>(0, 1)</td>
          <td>0.200000</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(96, 99)</td>
          <td>0.220606</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(98, 99)</td>
          <td>0.272721</td>
        </tr>
        <tr>
          <th>3</th>
          <td>(0, 2)</td>
          <td>0.282843</td>
        </tr>
        <tr>
          <th>4</th>
          <td>(1, 4)</td>
          <td>0.319210</td>
        </tr>
      </tbody>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 104-108

Write a submatrix to CSR
----------------------------------

A common task in data analysis is to export a submatrix of the boundary matrix into standard Python sparse matrix format, such as SciPy's CSR. In order to do this, you have to specify which rows and columns you want, and in what order. The :class:`oat_python.core.vietoris_rips.SubmatrixIndexTool` lets you specify these criteria exactly.

.. GENERATED FROM PYTHON SOURCE LINES 110-116

.. code-block:: Python

    boundary_matrix         =   decomposition.boundary_matrix_oracle()
    boundary_submatrix      =   boundary_matrix.write_submatrix_to_csr(
                                    submatrix_index_tool
                                )
    boundary_submatrix





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

 .. code-block:: none


    <100x292 sparse matrix of type '<class 'numpy.float64'>'
    	with 584 stored elements in Compressed Sparse Row format>



.. GENERATED FROM PYTHON SOURCE LINES 117-122

.. code-block:: Python

    plt.figure(figsize=(6, 6))
    plt.spy(boundary_submatrix, markersize=2, color="orange")
    plt.title(r'Boundary Matrix ($\partial_1$)', y=-0.18)  # Move title to the bottom
    plt.tight_layout()




.. image-sg:: /auto_examples/vietoris_rips/images/sphx_glr_plot_submatrix_index_tool_001.png
   :alt: Boundary Matrix ($\partial_1$)
   :srcset: /auto_examples/vietoris_rips/images/sphx_glr_plot_submatrix_index_tool_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_fontconfig_pattern.py:85: PyparsingDeprecationWarning: 'parseString' deprecated - use 'parse_string'
      parse = parser.parseString(pattern)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_fontconfig_pattern.py:89: PyparsingDeprecationWarning: 'resetCache' deprecated - use 'reset_cache'
      parser.resetCache()
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2010: PyparsingDeprecationWarning: 'oneOf' deprecated - use 'one_of'
      p.space          = oneOf(self._space_widths)("space")
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2012: PyparsingDeprecationWarning: 'oneOf' deprecated - use 'one_of'
      p.style_literal  = oneOf(
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2015: PyparsingDeprecationWarning: 'leaveWhitespace' deprecated - use 'leave_whitespace'
      p.symbol         = Regex(
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2024: PyparsingDeprecationWarning: 'oneOf' deprecated - use 'one_of'
      p.start_group    = Optional(r"\math" + oneOf(self._fontnames)("font")) + "{"
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2027: PyparsingDeprecationWarning: 'oneOf' deprecated - use 'one_of'
      p.delim          = oneOf(self._delims)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:1984: PyparsingDeprecationWarning: 'setName' deprecated - use 'set_name'
      val.setName(key)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:1987: PyparsingDeprecationWarning: 'setParseAction' deprecated - use 'set_parse_action'
      val.setParseAction(getattr(self, key))
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:1748: PyparsingDeprecationWarning: 'setParseAction' deprecated - use 'set_parse_action'
      return Empty().setParseAction(raise_error)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2088: PyparsingDeprecationWarning: 'endQuoteChar' argument is deprecated, use 'end_quote_char'
      p.text = cmd(r"\text", QuotedString('{', '\\', endQuoteChar="}"))
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2097: PyparsingDeprecationWarning: 'oneOf' deprecated - use 'one_of'
      + OneOrMore(oneOf(["_", "^"]) - p.placeable)("subsuper")
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2146: PyparsingDeprecationWarning: 'unquoteResults' argument is deprecated, use 'unquote_results'
      p.math_string   = QuotedString('$', '\\', unquoteResults=False)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2147: PyparsingDeprecationWarning: 'leaveWhitespace' deprecated - use 'leave_whitespace'
      p.non_math      = Regex(r"(?:(?:\\[$])|[^$])*").leaveWhitespace()
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2170: PyparsingDeprecationWarning: 'parseString' deprecated - use 'parse_string'
      result = self._expression.parseString(s)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2197: PyparsingDeprecationWarning: 'parseString' deprecated - use 'parse_string'
      return self._math_expression.parseString(toks[0][1:-1], parseAll=True)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/pyparsing/util.py:466: PyparsingDeprecationWarning: 'parseAll' argument is deprecated, use 'parse_all'
      return fn(self, *args, **kwargs)
    /home/docs/checkouts/readthedocs.org/user_builds/oat-python/envs/latest/lib/python3.9/site-packages/matplotlib/_mathtext.py:2178: PyparsingDeprecationWarning: 'resetCache' deprecated - use 'reset_cache'
      ParserElement.resetCache()




.. GENERATED FROM PYTHON SOURCE LINES 123-125

Change index types
----------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 127-128

Get a row vector from the CSR matrix

.. GENERATED FROM PYTHON SOURCE LINES 128-134

.. code-block:: Python


    # Right now we have to convert row coefficients to fractions, but in the future this will be taken care of automatically
    row_vector             =   boundary_submatrix[0].toarray().flatten()
    row_vector             =   np.vectorize(Fraction.from_float)(row_vector) 
    row_vector[:10]





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

 .. code-block:: none


    array([Fraction(-1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(-1, 1),
           Fraction(0, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1),
           Fraction(0, 1), Fraction(0, 1)], dtype=object)



.. GENERATED FROM PYTHON SOURCE LINES 135-136

Convert integer indices to simplex indices:

.. GENERATED FROM PYTHON SOURCE LINES 138-144

.. code-block:: Python

    chain                   =   submatrix_index_tool.row_vector_dataframe_for_dense_array(
                                    row_vector
                                )
    chain







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>simplex</th>
          <th>filtration</th>
          <th>coefficient</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>(0, 1)</td>
          <td>0.200000</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(0, 2)</td>
          <td>0.282843</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(0, 3)</td>
          <td>0.346410</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>3</th>
          <td>(0, 4)</td>
          <td>0.400000</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>4</th>
          <td>(0, 5)</td>
          <td>0.447214</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>5</th>
          <td>(0, 6)</td>
          <td>0.489898</td>
          <td>-1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.228 seconds)


.. _sphx_glr_download_auto_examples_vietoris_rips_plot_submatrix_index_tool.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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