summaryrefslogtreecommitdiff
path: root/cython/doc/rips_complex_user.rst
diff options
context:
space:
mode:
Diffstat (limited to 'cython/doc/rips_complex_user.rst')
-rw-r--r--cython/doc/rips_complex_user.rst240
1 files changed, 240 insertions, 0 deletions
diff --git a/cython/doc/rips_complex_user.rst b/cython/doc/rips_complex_user.rst
new file mode 100644
index 00000000..f9760976
--- /dev/null
+++ b/cython/doc/rips_complex_user.rst
@@ -0,0 +1,240 @@
+Rips complex user manual
+=========================
+Definition
+----------
+
+======================================================= ===================================== =====================================
+:Authors: Clément Maria, Pawel Dlotko, Vincent Rouvreau :Introduced in: GUDHI 2.0.0 :Copyright: GPL v3
+======================================================= ===================================== =====================================
+
++-------------------------------------------+----------------------------------------------------------------------+
+| :doc:`rips_complex_user` | :doc:`rips_complex_ref` |
++-------------------------------------------+----------------------------------------------------------------------+
+
+`Rips complex <https://en.wikipedia.org/wiki/Vietoris%E2%80%93Rips_complex>`_ is a one skeleton graph that allows to
+construct a simplicial complex from it. The input can be a point cloud with a given distance function, or a distance
+matrix.
+
+The filtration value of each edge is computed from a user-given distance function, or directly from the distance
+matrix.
+
+All edges that have a filtration value strictly greater than a given threshold value are not inserted into the complex.
+
+When creating a simplicial complex from this one skeleton graph, Rips inserts the one skeleton graph into the data
+structure, and then expands the simplicial complex when required.
+
+Vertex name correspond to the index of the point in the given range (aka. the point cloud).
+
+.. figure::
+ img/rips_complex_representation.png
+ :align: center
+
+ Rips-complex one skeleton graph representation
+
+On this example, as edges (4,5), (4,6) and (5,6) are in the complex, simplex (4,5,6) is added with the filtration value
+set with :math:`max(filtration(4,5), filtration(4,6), filtration(5,6))`. And so on for simplex (0,1,2,3).
+
+If the Rips_complex interfaces are not detailed enough for your need, please refer to rips_persistence_step_by_step.cpp
+example, where the graph construction over the Simplex_tree is more detailed.
+
+Point cloud
+-----------
+
+Example from a point cloud
+^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This example builds the one skeleton graph from the given points, and max_edge_length value.
+Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it.
+
+Finally, it is asked to display information about the simplicial complex.
+
+.. testcode::
+
+ import gudhi
+ rips_complex = gudhi.RipsComplex(points=[[1, 1], [7, 0], [4, 6], [9, 6], [0, 14], [2, 19], [9, 17]],
+ max_edge_length=12.0)
+
+ simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+ result_str = 'Rips complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
+ repr(simplex_tree.num_simplices()) + ' simplices - ' + \
+ repr(simplex_tree.num_vertices()) + ' vertices.'
+ print(result_str)
+ fmt = '%s -> %.2f'
+ for filtered_value in simplex_tree.get_filtration():
+ print(fmt % tuple(filtered_value))
+
+When launching (Rips maximal distance between 2 points is 12.0, is expanded
+until dimension 1 - one skeleton graph in other words), the output is:
+
+.. testoutput::
+
+ Rips complex is of dimension 1 - 18 simplices - 7 vertices.
+ [0] -> 0.00
+ [1] -> 0.00
+ [2] -> 0.00
+ [3] -> 0.00
+ [4] -> 0.00
+ [5] -> 0.00
+ [6] -> 0.00
+ [2, 3] -> 5.00
+ [4, 5] -> 5.39
+ [0, 2] -> 5.83
+ [0, 1] -> 6.08
+ [1, 3] -> 6.32
+ [1, 2] -> 6.71
+ [5, 6] -> 7.28
+ [2, 4] -> 8.94
+ [0, 3] -> 9.43
+ [4, 6] -> 9.49
+ [3, 6] -> 11.00
+
+Example from OFF file
+^^^^^^^^^^^^^^^^^^^^^
+
+This example builds the :doc:`Rips_complex <rips_complex_ref>` from the given
+points in an OFF file, and max_edge_length value.
+Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it.
+
+Finally, it is asked to display information about the Rips complex.
+
+
+.. testcode::
+
+ import gudhi
+ rips_complex = gudhi.RipsComplex(off_file='alphacomplexdoc.off', max_edge_length=12.0)
+ simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+ result_str = 'Rips complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
+ repr(simplex_tree.num_simplices()) + ' simplices - ' + \
+ repr(simplex_tree.num_vertices()) + ' vertices.'
+ print(result_str)
+ fmt = '%s -> %.2f'
+ for filtered_value in simplex_tree.get_filtration():
+ print(fmt % tuple(filtered_value))
+
+the program output is:
+
+.. testoutput::
+
+ Rips complex is of dimension 1 - 18 simplices - 7 vertices.
+ [0] -> 0.00
+ [1] -> 0.00
+ [2] -> 0.00
+ [3] -> 0.00
+ [4] -> 0.00
+ [5] -> 0.00
+ [6] -> 0.00
+ [2, 3] -> 5.00
+ [4, 5] -> 5.39
+ [0, 2] -> 5.83
+ [0, 1] -> 6.08
+ [1, 3] -> 6.32
+ [1, 2] -> 6.71
+ [5, 6] -> 7.28
+ [2, 4] -> 8.94
+ [0, 3] -> 9.43
+ [4, 6] -> 9.49
+ [3, 6] -> 11.00
+
+Distance matrix
+---------------
+
+Example from a distance matrix
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+This example builds the one skeleton graph from the given distance matrix, and max_edge_length value.
+Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it.
+
+Finally, it is asked to display information about the simplicial complex.
+
+.. testcode::
+
+ import gudhi
+ rips_complex = gudhi.RipsComplex(distance_matrix=[[],
+ [6.0827625303],
+ [5.8309518948, 6.7082039325],
+ [9.4339811321, 6.3245553203, 5],
+ [13.0384048104, 15.6524758425, 8.94427191, 12.0415945788],
+ [18.0277563773, 19.6468827044, 13.152946438, 14.7648230602, 5.3851648071],
+ [17.88854382, 17.1172427686, 12.0830459736, 11, 9.4868329805, 7.2801098893]],
+ max_edge_length=12.0)
+
+ simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+ result_str = 'Rips complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
+ repr(simplex_tree.num_simplices()) + ' simplices - ' + \
+ repr(simplex_tree.num_vertices()) + ' vertices.'
+ print(result_str)
+ fmt = '%s -> %.2f'
+ for filtered_value in simplex_tree.get_filtration():
+ print(fmt % tuple(filtered_value))
+
+When launching (Rips maximal distance between 2 points is 12.0, is expanded
+until dimension 1 - one skeleton graph in other words), the output is:
+
+.. testoutput::
+
+ Rips complex is of dimension 1 - 18 simplices - 7 vertices.
+ [0] -> 0.00
+ [1] -> 0.00
+ [2] -> 0.00
+ [3] -> 0.00
+ [4] -> 0.00
+ [5] -> 0.00
+ [6] -> 0.00
+ [2, 3] -> 5.00
+ [4, 5] -> 5.39
+ [0, 2] -> 5.83
+ [0, 1] -> 6.08
+ [1, 3] -> 6.32
+ [1, 2] -> 6.71
+ [5, 6] -> 7.28
+ [2, 4] -> 8.94
+ [0, 3] -> 9.43
+ [4, 6] -> 9.49
+ [3, 6] -> 11.00
+
+Example from csv file
+^^^^^^^^^^^^^^^^^^^^^
+
+This example builds the :doc:`Rips_complex <rips_complex_ref>` from the given
+points in an OFF file, and max_edge_length value.
+Then it creates a :doc:`Simplex_tree <simplex_tree_ref>` with it.
+
+Finally, it is asked to display information about the Rips complex.
+
+
+.. testcode::
+
+ import gudhi
+ rips_complex = gudhi.RipsComplex(csv_file='full_square_distance_matrix.csv', max_edge_length=12.0)
+ simplex_tree = rips_complex.create_simplex_tree(max_dimension=1)
+ result_str = 'Rips complex is of dimension ' + repr(simplex_tree.dimension()) + ' - ' + \
+ repr(simplex_tree.num_simplices()) + ' simplices - ' + \
+ repr(simplex_tree.num_vertices()) + ' vertices.'
+ print(result_str)
+ fmt = '%s -> %.2f'
+ for filtered_value in simplex_tree.get_filtration():
+ print(fmt % tuple(filtered_value))
+
+the program output is:
+
+.. testoutput::
+
+ Rips complex is of dimension 1 - 18 simplices - 7 vertices.
+ [0] -> 0.00
+ [1] -> 0.00
+ [2] -> 0.00
+ [3] -> 0.00
+ [4] -> 0.00
+ [5] -> 0.00
+ [6] -> 0.00
+ [2, 3] -> 5.00
+ [4, 5] -> 5.39
+ [0, 2] -> 5.83
+ [0, 1] -> 6.08
+ [1, 3] -> 6.32
+ [1, 2] -> 6.71
+ [5, 6] -> 7.28
+ [2, 4] -> 8.94
+ [0, 3] -> 9.43
+ [4, 6] -> 9.49
+ [3, 6] -> 11.00
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-01 22:20:49 +0000