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Diffstat (limited to 'cython/doc/rips_complex_user.rst')
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1 files changed, 79 insertions, 5 deletions
diff --git a/cython/doc/rips_complex_user.rst b/cython/doc/rips_complex_user.rst index 96ba9944..a8c06cf9 100644 --- a/cython/doc/rips_complex_user.rst +++ b/cython/doc/rips_complex_user.rst @@ -1,3 +1,7 @@ +:orphan: + +.. To get rid of WARNING: document isn't included in any toctree + Rips complex user manual ========================= Definition @@ -101,8 +105,8 @@ Finally, it is asked to display information about the Rips complex. .. testcode:: import gudhi - rips_complex = gudhi.RipsComplex(off_file=gudhi.__root_source_dir__ + \ - '/data/points/alphacomplexdoc.off', max_edge_length=12.0) + point_cloud = gudhi.read_off(off_file=gudhi.__root_source_dir__ + '/data/points/alphacomplexdoc.off') + rips_complex = gudhi.RipsComplex(points=point_cloud, 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 - ' + \ @@ -197,7 +201,7 @@ 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. +distance matrix in a csv 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. @@ -206,8 +210,9 @@ Finally, it is asked to display information about the Rips complex. .. testcode:: import gudhi - rips_complex = gudhi.RipsComplex(csv_file=gudhi.__root_source_dir__ + \ - '/data/distance_matrix/full_square_distance_matrix.csv', max_edge_length=12.0) + distance_matrix = gudhi.read_lower_triangular_matrix_from_csv_file(csv_file=gudhi.__root_source_dir__ + \ + '/data/distance_matrix/full_square_distance_matrix.csv') + rips_complex = gudhi.RipsComplex(distance_matrix=distance_matrix, 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 - ' + \ @@ -240,3 +245,72 @@ the program output is: [0, 3] -> 9.43 [4, 6] -> 9.49 [3, 6] -> 11.00 + +Correlation matrix +------------------ + +Example from a correlation matrix +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Analogously to the case of distance matrix, Rips complexes can be also constructed based on correlation matrix. +Given a correlation matrix M, comportment-wise 1-M is a distance matrix. +This example builds the one skeleton graph from the given corelation matrix and threshold 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 + import numpy as np + + # User defined correlation matrix is: + # |1 0.06 0.23 0.01 0.89| + # |0.06 1 0.74 0.01 0.61| + # |0.23 0.74 1 0.72 0.03| + # |0.01 0.01 0.72 1 0.7 | + # |0.89 0.61 0.03 0.7 1 | + correlation_matrix=np.array([[1., 0.06, 0.23, 0.01, 0.89], + [0.06, 1., 0.74, 0.01, 0.61], + [0.23, 0.74, 1., 0.72, 0.03], + [0.01, 0.01, 0.72, 1., 0.7], + [0.89, 0.61, 0.03, 0.7, 1.]], float) + + distance_matrix = np.ones((correlation_matrix.shape),float) - correlation_matrix + rips_complex = gudhi.RipsComplex(distance_matrix=distance_matrix, max_edge_length=1.0) + + 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 - 15 simplices - 5 vertices. + [0] -> 0.00 + [1] -> 0.00 + [2] -> 0.00 + [3] -> 0.00 + [4] -> 0.00 + [0, 4] -> 0.11 + [1, 2] -> 0.26 + [2, 3] -> 0.28 + [3, 4] -> 0.30 + [1, 4] -> 0.39 + [0, 2] -> 0.77 + [0, 1] -> 0.94 + [2, 4] -> 0.97 + [0, 3] -> 0.99 + [1, 3] -> 0.99 + +.. note:: + As persistence diagrams points will be under the diagonal, + bottleneck distance and persistence graphical tool will not work properly, + this is a known issue. |