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

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

.. _sphx_glr_auto_examples_vietoris_rips_plot_matrices.py:


.. _vietoris_rips_matrices:

Sparse Matrices
========================================

Sparse matrices in applied topology present several challenges.

- They are often large, consuming huge amounts of memory.
- They are indexed by simplices, cubes, of other objects, rather than integers
- They have a variety of different coefficient rings

This tutorial introduces some highly effective OAT tools to meet these challenges. We will focus on the boundary matrix of a Vietoris-Rips complex for illustration, but many of the methods carry over to different types of sparse matrix offered by OAT.

.. GENERATED FROM PYTHON SOURCE LINES 17-25

.. code-block:: Python

    import oat_python as oat

    from fractions import Fraction
    import numpy as np
    import pandas as pd
    import plotly.graph_objects as go









.. GENERATED FROM PYTHON SOURCE LINES 26-28

Vietoris Rips Complex
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 30-31

Create a Vietoris-Rips complex from a points of points

.. GENERATED FROM PYTHON SOURCE LINES 31-35

.. code-block:: Python

    points                      =   np.random.rand(5, 3)
    dissimilarity_matrix        =   oat.dissimilarity.sparse_matrix_for_points(points, max_dissimilarity=np.inf)
    vietoris_rips               =   oat.core.vietoris_rips.VietorisRipsComplex(dissimilarity_matrix)








.. GENERATED FROM PYTHON SOURCE LINES 36-38

Simplices
----------------

.. GENERATED FROM PYTHON SOURCE LINES 40-41

List all simplices in a given dimension(s)

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    vietoris_rips.simplices_for_dimensions(dimensions=[0,1])






.. 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>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>(0,)</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1,)</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(2,)</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>3</th>
          <td>(3,)</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>4</th>
          <td>(4,)</td>
          <td>0.000000</td>
        </tr>
        <tr>
          <th>5</th>
          <td>(0, 2)</td>
          <td>0.370513</td>
        </tr>
        <tr>
          <th>6</th>
          <td>(2, 4)</td>
          <td>0.619095</td>
        </tr>
        <tr>
          <th>7</th>
          <td>(1, 4)</td>
          <td>0.632122</td>
        </tr>
        <tr>
          <th>8</th>
          <td>(1, 3)</td>
          <td>0.660166</td>
        </tr>
        <tr>
          <th>9</th>
          <td>(3, 4)</td>
          <td>0.682666</td>
        </tr>
        <tr>
          <th>10</th>
          <td>(1, 2)</td>
          <td>0.726618</td>
        </tr>
        <tr>
          <th>11</th>
          <td>(2, 3)</td>
          <td>0.830129</td>
        </tr>
        <tr>
          <th>12</th>
          <td>(0, 1)</td>
          <td>0.877768</td>
        </tr>
        <tr>
          <th>13</th>
          <td>(0, 3)</td>
          <td>0.901882</td>
        </tr>
        <tr>
          <th>14</th>
          <td>(0, 4)</td>
          <td>0.940755</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 44-45

Look up a simplex's filtration value

.. GENERATED FROM PYTHON SOURCE LINES 45-47

.. code-block:: Python

    vietoris_rips.filtration_value(simplex=[0, 1, 2])





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

 .. code-block:: none


    0.8777684218544266



.. GENERATED FROM PYTHON SOURCE LINES 48-49

An error is returned if the simplex is not in the complex, or if it is not formatted as a strictly ascending sequence of nonnegative integers

.. GENERATED FROM PYTHON SOURCE LINES 49-70

.. code-block:: Python


    try:
        vietoris_rips.filtration_value(simplex=(0, 0,))
    except Exception as e:
        print(f"Error: {e}")    

    try:
        vietoris_rips.filtration_value(simplex=(1, 0))
    except Exception as e:
        print(f"Error: {e}")        

    try:
        vietoris_rips.filtration_value(simplex=(0,100))
    except Exception as e:
        print(f"Error: {e}")    

    try:
        vietoris_rips.filtration_value(simplex=(-1,))
    except Exception as e:
        print(f"Error: {e}")        





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

 .. code-block:: none

    Error: Simplex [0, 0] is not strictly sorted.
    Error: Simplex [1, 0] is not strictly sorted.
    Error: The input [0, 100] is not a valid simplex in this Vietoris-Rips complex.
    Error: out of range integral type conversion attempted




.. GENERATED FROM PYTHON SOURCE LINES 71-73

Boundary matrix oracle (memory light)
---------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 75-79

We begin by creating a *boundary matrix oracle*. 

To conserve memory, this object stores only a copy of the dissimilarity matrix in memory, and computes computes
rows, columns, and entries of the boundary matrix on demand.

.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: Python

    boundary_matrix_oracle          =   vietoris_rips.boundary_matrix_oracle()








.. GENERATED FROM PYTHON SOURCE LINES 84-86

Rows and columns
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 88-90

.. code-block:: Python

    boundary_matrix_oracle.row_for_simplex([0,1])






.. 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, 2)</td>
          <td>0.877768</td>
          <td>1</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(0, 1, 3)</td>
          <td>0.901882</td>
          <td>1</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(0, 1, 4)</td>
          <td>0.940755</td>
          <td>1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. code-block:: Python

    boundary_matrix_oracle.column_for_simplex([0,1])






.. 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,)</td>
          <td>0.0</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1,)</td>
          <td>0.0</td>
          <td>1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 94-96

Entries
------------------

.. GENERATED FROM PYTHON SOURCE LINES 98-99

Look up an entry

.. GENERATED FROM PYTHON SOURCE LINES 99-104

.. code-block:: Python

    boundary_matrix_oracle.entry_for_row_and_column(
        row_simplex=(0,1),
        column_simplex=(0,1,2)
    )





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

 .. code-block:: none


    Fraction(1, 1)



.. GENERATED FROM PYTHON SOURCE LINES 105-106

Keywords don't have to be explicit

.. GENERATED FROM PYTHON SOURCE LINES 106-111

.. code-block:: Python

    boundary_matrix_oracle.entry_for_row_and_column(
        [0,1],
        [0,1,2]
    )





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

 .. code-block:: none


    Fraction(1, 1)



.. GENERATED FROM PYTHON SOURCE LINES 112-114

Boundaries and coboundaries
-----------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 116-117

Define a vector as a linear combination of simplices

.. GENERATED FROM PYTHON SOURCE LINES 117-125

.. code-block:: Python

    vector = {
        "simplex": [(0,), (1,), (0, 1), (1, 2)],
        "coefficient": [Fraction(1, 2), Fraction(-3, 4), Fraction(2, 3), Fraction(5, 6)]
    }

    vector = pd.DataFrame(vector)
    vector






.. 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>coefficient</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>(0,)</td>
          <td>1/2</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1,)</td>
          <td>-3/4</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(0, 1)</td>
          <td>2/3</td>
        </tr>
        <tr>
          <th>3</th>
          <td>(1, 2)</td>
          <td>5/6</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 126-127

Multiply the vector with the boundary matrix as a column vector (i.e. compute the boundary)

.. GENERATED FROM PYTHON SOURCE LINES 127-129

.. code-block:: Python

    boundary_matrix_oracle.boundary_for_chain(vector)






.. 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,)</td>
          <td>0.0</td>
          <td>-2/3</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1,)</td>
          <td>0.0</td>
          <td>-1/6</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(2,)</td>
          <td>0.0</td>
          <td>5/6</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 130-131

Multiply the vector with the boundary matrix as a row vector (i.e. compute the coboundary)

.. GENERATED FROM PYTHON SOURCE LINES 131-133

.. code-block:: Python

    boundary_matrix_oracle.coboundary_for_cochain(vector)






.. 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, 2)</td>
          <td>0.370513</td>
          <td>-1/2</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1, 4)</td>
          <td>0.632122</td>
          <td>3/4</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(1, 3)</td>
          <td>0.660166</td>
          <td>3/4</td>
        </tr>
        <tr>
          <th>3</th>
          <td>(1, 2)</td>
          <td>0.726618</td>
          <td>3/4</td>
        </tr>
        <tr>
          <th>4</th>
          <td>(1, 2, 4)</td>
          <td>0.726618</td>
          <td>5/6</td>
        </tr>
        <tr>
          <th>5</th>
          <td>(1, 2, 3)</td>
          <td>0.830129</td>
          <td>5/6</td>
        </tr>
        <tr>
          <th>6</th>
          <td>(0, 1)</td>
          <td>0.877768</td>
          <td>-5/4</td>
        </tr>
        <tr>
          <th>7</th>
          <td>(0, 1, 2)</td>
          <td>0.877768</td>
          <td>3/2</td>
        </tr>
        <tr>
          <th>8</th>
          <td>(0, 1, 3)</td>
          <td>0.901882</td>
          <td>2/3</td>
        </tr>
        <tr>
          <th>9</th>
          <td>(0, 3)</td>
          <td>0.901882</td>
          <td>-1/2</td>
        </tr>
        <tr>
          <th>10</th>
          <td>(0, 1, 4)</td>
          <td>0.940755</td>
          <td>2/3</td>
        </tr>
        <tr>
          <th>11</th>
          <td>(0, 4)</td>
          <td>0.940755</td>
          <td>-1/2</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 134-138

Row and column numbers
-------------------------------

Boundary matrices are naturally indexed by simplices, not but row/column numbers. However, it's common to represent submatrices of the boundary matrix with numbered rows and columns. OAT offers a tool to help translate between simplices and numbers.

.. GENERATED FROM PYTHON SOURCE LINES 140-142

Assign submatrix row and column numbers
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 144-145

Initialize the index tool with no row or column indices

.. GENERATED FROM PYTHON SOURCE LINES 145-154

.. code-block:: Python

    submatrix_index_tool        =   vietoris_rips.submatrix_index_tool()

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







.. 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</h4><table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>simplex</th>
          <th>filtration</th>
        </tr>
      </thead>
      <tbody>
      </tbody>
    </table></div><div style="display:inline-block; vertical-align:top; margin-right:20px;"><h4>Column indices</h4><table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>simplex</th>
          <th>filtration</th>
        </tr>
      </thead>
      <tbody>
      </tbody>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 155-156

Provide custom lists of row and column indices

.. GENERATED FROM PYTHON SOURCE LINES 156-165

.. code-block:: Python

    submatrix_index_tool.set_row_indices([(0,1), (1,2),])
    submatrix_index_tool.set_column_indices([(0,1,2), (0,1,3)])

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






.. 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</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>0.877768</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1, 2)</td>
          <td>0.726618</td>
        </tr>
      </tbody>
    </table></div><div style="display:inline-block; vertical-align:top; margin-right:20px;"><h4>Column indices</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, 2)</td>
          <td>0.877768</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(0, 1, 3)</td>
          <td>0.901882</td>
        </tr>
      </tbody>
    </table></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 166-167

An error will be returned if the list of row (respectively) column indices contains duplicate entries.

.. GENERATED FROM PYTHON SOURCE LINES 167-172

.. code-block:: Python

    try:
        submatrix_index_tool.set_row_indices([(0,1), (0,1)])
    except Exception as e:
        print(f"Error: {e}")





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

 .. code-block:: none

    Error: User-provided indices include one or more duplicates, including WeightedSimplex { weight: OrderedFloat(0.8777684218544266), vertices: [0, 1] }.




.. GENERATED FROM PYTHON SOURCE LINES 173-175

Select indices by simplex dimension
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 177-178

Indexing is managed by this `submatrix_index_tool`

.. GENERATED FROM PYTHON SOURCE LINES 178-186

.. code-block:: Python

    submatrix_index_tool        =   vietoris_rips.submatrix_index_tool(
                                        row_dimensions=[0, 1],
                                        column_dimensions=[1,2],  
                                    )

    print("\nThe first few row indices:")
    submatrix_index_tool.row_indices().head()





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

 .. code-block:: none


    The first few row indices:


.. 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>
        </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>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 187-189

Translate simplices and row/column numbers
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 191-192

Look up the column number for a simplex

.. GENERATED FROM PYTHON SOURCE LINES 192-195

.. code-block:: Python

    column_number   =   submatrix_index_tool.submatrix_column_number_for_simplex([1,2,3])
    column_number





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

 .. code-block:: none


    12



.. GENERATED FROM PYTHON SOURCE LINES 196-197

Look up the simplex for a column number

.. GENERATED FROM PYTHON SOURCE LINES 197-200

.. code-block:: Python

    weighted_simplex = submatrix_index_tool.weighted_simplex_for_submatrix_column_number( column_number )
    weighted_simplex





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

 .. code-block:: none


    <WeightedSimplex simplex=[1, 2, 3] | weight=0.830129>



.. GENERATED FROM PYTHON SOURCE LINES 201-202

The WeightedSimplex object is just a wrapper around the simplex and the weight

.. GENERATED FROM PYTHON SOURCE LINES 202-206

.. code-block:: Python

    print(weighted_simplex)
    print(weighted_simplex.simplex())
    print(weighted_simplex.weight())





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

 .. code-block:: none

    Simplex: (1, 2, 3)   Weight: 0.830129
    (1, 2, 3)
    0.830129490771365




.. GENERATED FROM PYTHON SOURCE LINES 207-209

Convert column vector types
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 211-214

.. code-block:: Python

    column_vector      =    boundary_matrix_oracle.column_for_simplex([0,1,2])
    dense_array        =    submatrix_index_tool.dense_array_for_column_vector_dataframe(column_vector)








.. GENERATED FROM PYTHON SOURCE LINES 215-217

.. code-block:: Python

    column_vector






.. 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, 2)</td>
          <td>0.370513</td>
          <td>-1</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(1, 2)</td>
          <td>0.726618</td>
          <td>1</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(0, 1)</td>
          <td>0.877768</td>
          <td>1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 218-220

.. code-block:: Python

    dense_array





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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 221-222

Reconstruct the original column vector

.. GENERATED FROM PYTHON SOURCE LINES 222-225

.. code-block:: Python

    reconstructed_column_vector = submatrix_index_tool.column_vector_dataframe_for_dense_array(dense_array)
    column_vector.equals(reconstructed_column_vector)





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

 .. code-block:: none


    True



.. GENERATED FROM PYTHON SOURCE LINES 226-228

Convert row vector types
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 230-232

.. code-block:: Python

    row_vector         =    boundary_matrix_oracle.row_for_simplex([0,1])
    dense_array        =    submatrix_index_tool.dense_array_for_row_vector_dataframe(row_vector)







.. GENERATED FROM PYTHON SOURCE LINES 233-235

.. code-block:: Python

    row_vector






.. 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, 2)</td>
          <td>0.877768</td>
          <td>1</td>
        </tr>
        <tr>
          <th>1</th>
          <td>(0, 1, 3)</td>
          <td>0.901882</td>
          <td>1</td>
        </tr>
        <tr>
          <th>2</th>
          <td>(0, 1, 4)</td>
          <td>0.940755</td>
          <td>1</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 236-238

.. code-block:: Python

    dense_array





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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 239-240

Reconstruct the original column vector

.. GENERATED FROM PYTHON SOURCE LINES 240-243

.. code-block:: Python

    reconstructed_row_vector = submatrix_index_tool.row_vector_dataframe_for_dense_array(dense_array)
    row_vector.equals(reconstructed_row_vector)





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

 .. code-block:: none


    True



.. GENERATED FROM PYTHON SOURCE LINES 244-248

Common Python (sparse) matrix formats
-------------------------------------------

OAT offers convenient tools to export submatrices to common formats. The first step is specifying which rows and columns you want to export to this format. We do this with a `SubmatrixIndexTool`, which also provides a number of convenient methods for mapping between simplices and row/column numbers. See the tutorial on Vietoris Rips boundary matrices for more details.

.. GENERATED FROM PYTHON SOURCE LINES 250-252

SciPy sparse matrix: CSR format
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 254-256

.. code-block:: Python

    submatrix               =   boundary_matrix_oracle.write_submatrix_to_csr( submatrix_index_tool )








.. GENERATED FROM PYTHON SOURCE LINES 257-259

.. code-block:: Python

    submatrix





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

 .. code-block:: none


    <15x20 sparse matrix of type '<class 'numpy.float64'>'
    	with 50 stored elements in Compressed Sparse Row format>



.. GENERATED FROM PYTHON SOURCE LINES 260-262

SciPy sparse matrix: (row,column,coefficient) triplet format
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 264-265

get a list of the nonzero triplets

.. GENERATED FROM PYTHON SOURCE LINES 265-268

.. code-block:: Python

    sparse_coo              =   submatrix.tocoo() # convert to COOrdinate format
    list(zip(sparse_coo.row, sparse_coo.col, sparse_coo.data)) # zip the row, column, and data arrays together to get a list of (row, column, value) triplets





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

 .. code-block:: none


    [(0, 0, -1.0), (0, 7, -1.0), (0, 8, -1.0), (0, 9, -1.0), (1, 2, -1.0), (1, 3, -1.0), (1, 5, -1.0), (1, 7, 1.0), (2, 0, 1.0), (2, 1, -1.0), (2, 5, 1.0), (2, 6, -1.0), (3, 3, 1.0), (3, 4, -1.0), (3, 6, 1.0), (3, 8, 1.0), (4, 1, 1.0), (4, 2, 1.0), (4, 4, 1.0), (4, 9, 1.0), (5, 14, -1.0), (5, 16, 1.0), (5, 18, 1.0), (6, 11, 1.0), (6, 13, -1.0), (6, 18, 1.0), (7, 10, -1.0), (7, 11, -1.0), (7, 17, 1.0), (8, 10, 1.0), (8, 12, -1.0), (8, 15, 1.0), (9, 10, 1.0), (9, 13, 1.0), (9, 19, 1.0), (10, 11, 1.0), (10, 12, 1.0), (10, 14, 1.0), (11, 12, 1.0), (11, 13, 1.0), (11, 16, 1.0), (12, 14, 1.0), (12, 15, 1.0), (12, 17, 1.0), (13, 15, -1.0), (13, 16, -1.0), (13, 19, 1.0), (14, 17, -1.0), (14, 18, -1.0), (14, 19, -1.0)]



.. GENERATED FROM PYTHON SOURCE LINES 269-271

Dense numpy array
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 273-274

print a dense version of the matrix

.. GENERATED FROM PYTHON SOURCE LINES 274-276

.. code-block:: Python

    submatrix.todense()





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

 .. code-block:: none


    matrix([[-1.,  0.,  0.,  0.,  0.,  0.,  0., -1., -1., -1.,  0.,  0.,  0.,
              0.,  0.,  0.,  0.,  0.,  0.,  0.],
            [ 0.,  0., -1., -1.,  0., -1.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,
              0.,  0.,  0.,  0.,  0.,  0.,  0.],
            [ 1., -1.,  0.,  0.,  0.,  1., -1.,  0.,  0.,  0.,  0.,  0.,  0.,
              0.,  0.,  0.,  0.,  0.,  0.,  0.],
            [ 0.,  0.,  0.,  1., -1.,  0.,  1.,  0.,  1.,  0.,  0.,  0.,  0.,
              0.,  0.,  0.,  0.,  0.,  0.,  0.],
            [ 0.,  1.,  1.,  0.,  1.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,
              0.,  0.,  0.,  0.,  0.,  0.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
              0., -1.,  0.,  1.,  0.,  1.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,
             -1.,  0.,  0.,  0.,  0.,  1.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., -1., -1.,  0.,
              0.,  0.,  0.,  0.,  1.,  0.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0., -1.,
              0.,  0.,  1.,  0.,  0.,  0.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,
              1.,  0.,  0.,  0.,  0.,  0.,  1.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  1.,
              0.,  1.,  0.,  0.,  0.,  0.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,
              1.,  0.,  0.,  1.,  0.,  0.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
              0.,  1.,  1.,  0.,  1.,  0.,  0.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
              0.,  0., -1., -1.,  0.,  0.,  1.],
            [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
              0.,  0.,  0.,  0., -1., -1., -1.]])



.. GENERATED FROM PYTHON SOURCE LINES 277-279

Sparse dataframe
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 281-282

you can use the the submatrix_index_tool to export a CSR matrix to a sparse pandas DataFrame with labeled rows and column

.. GENERATED FROM PYTHON SOURCE LINES 282-284

.. code-block:: Python

    submatrix_index_tool.sparse_dataframe_for_csr_matrix(submatrix)






.. 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>simplex</th>
          <th>(0, 2)</th>
          <th>(2, 4)</th>
          <th>(1, 4)</th>
          <th>(1, 3)</th>
          <th>(3, 4)</th>
          <th>(1, 2)</th>
          <th>(2, 3)</th>
          <th>(0, 1)</th>
          <th>(0, 3)</th>
          <th>(0, 4)</th>
          <th>(1, 3, 4)</th>
          <th>(1, 2, 4)</th>
          <th>(1, 2, 3)</th>
          <th>(2, 3, 4)</th>
          <th>(0, 1, 2)</th>
          <th>(0, 1, 3)</th>
          <th>(0, 2, 3)</th>
          <th>(0, 1, 4)</th>
          <th>(0, 2, 4)</th>
          <th>(0, 3, 4)</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>(0,)</th>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(1,)</th>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(2,)</th>
          <td>1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(3,)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(4,)</th>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(0, 2)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(2, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(1, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(1, 3)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(3, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
        </tr>
        <tr>
          <th>(1, 2)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(2, 3)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(0, 1)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(0, 3)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
        </tr>
        <tr>
          <th>(0, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>-1.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 285-286

this method is identical to calling the following:

.. GENERATED FROM PYTHON SOURCE LINES 286-293

.. code-block:: Python

    df              =   pd.DataFrame.sparse.from_spmatrix(
                            submatrix, 
                            index=submatrix_index_tool.row_indices().simplex.tolist(), 
                            columns=submatrix_index_tool.column_indices().simplex,
                        )  
    df






.. 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>simplex</th>
          <th>(0, 2)</th>
          <th>(2, 4)</th>
          <th>(1, 4)</th>
          <th>(1, 3)</th>
          <th>(3, 4)</th>
          <th>(1, 2)</th>
          <th>(2, 3)</th>
          <th>(0, 1)</th>
          <th>(0, 3)</th>
          <th>(0, 4)</th>
          <th>(1, 3, 4)</th>
          <th>(1, 2, 4)</th>
          <th>(1, 2, 3)</th>
          <th>(2, 3, 4)</th>
          <th>(0, 1, 2)</th>
          <th>(0, 1, 3)</th>
          <th>(0, 2, 3)</th>
          <th>(0, 1, 4)</th>
          <th>(0, 2, 4)</th>
          <th>(0, 3, 4)</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>(0,)</th>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(1,)</th>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(2,)</th>
          <td>1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(3,)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(4,)</th>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(0, 2)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(2, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(1, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(1, 3)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(3, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
        </tr>
        <tr>
          <th>(1, 2)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(2, 3)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(0, 1)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
          <td>1.0</td>
          <td>0</td>
          <td>1.0</td>
          <td>0</td>
          <td>0</td>
        </tr>
        <tr>
          <th>(0, 3)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>0</td>
          <td>0</td>
          <td>1.0</td>
        </tr>
        <tr>
          <th>(0, 4)</th>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>0</td>
          <td>-1.0</td>
          <td>-1.0</td>
          <td>-1.0</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 294-296

Matplotlib scatter
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 298-308

.. code-block:: Python

    import matplotlib.pyplot as plt

    # Suppose `csr` is your scipy.sparse.csr_matrix
    plt.figure(figsize=(6, 6))
    plt.spy(submatrix, markersize=5)
    plt.title("Sparsity Pattern (matplotlib)")
    plt.xlabel("Columns")
    plt.ylabel("Rows")
    plt.show()




.. image-sg:: /auto_examples/vietoris_rips/images/sphx_glr_plot_matrices_001.png
   :alt: Sparsity Pattern (matplotlib)
   :srcset: /auto_examples/vietoris_rips/images/sphx_glr_plot_matrices_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 309-311

Plotly
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 313-359

.. code-block:: Python



    # points: your scipy.sparse.coo_matrix
    # row_labels: list of row labels (length = points.shape[0])
    # col_labels: list of column labels (length = points.shape[1])

    points = submatrix.tocoo()

    row_labels = submatrix_index_tool.row_indices().simplex.tolist()
    col_labels = submatrix_index_tool.column_indices().simplex.tolist()
    hover_text = [
        f"row: {row_labels[r]}<br>column: {col_labels[c]}<br>coefficient: {v}"
        for r, c, v in zip(points.row, points.col, points.data)
    ]

    fig = go.Figure(go.Scattergl(
        x=points.col,
        y=points.row,
        mode='markers',
        marker=dict(size=4),
        text=hover_text,
        hoverinfo="text"
    ))

    fig.update_layout(
        title="Hover over points to see row/column/coefficient!",
        xaxis_title="Columns",
        yaxis_title="Rows",
        xaxis=dict(
            tickmode='array',
            tickvals=list(range(len(col_labels))),
            ticktext=[str(label) for label in col_labels]
        ),
        yaxis=dict(
            tickmode='array',
            tickvals=list(range(len(row_labels))),
            ticktext=[str(label) for label in row_labels],
            autorange='reversed'
        ),
        width=1200,
        height=800
    )

    fig







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

   **Total running time of the script:** (0 minutes 0.108 seconds)


.. _sphx_glr_download_auto_examples_vietoris_rips_plot_matrices.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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