diff options
Diffstat (limited to 'src/python/gudhi/cubical_complex.pyx')
| -rw-r--r-- | src/python/gudhi/cubical_complex.pyx | 34 |
1 files changed, 17 insertions, 17 deletions
diff --git a/src/python/gudhi/cubical_complex.pyx b/src/python/gudhi/cubical_complex.pyx index 9ebd0b30..ca979eda 100644 --- a/src/python/gudhi/cubical_complex.pyx +++ b/src/python/gudhi/cubical_complex.pyx @@ -172,31 +172,31 @@ cdef class CubicalComplex: return self.pcohptr.get_persistence() def cofaces_of_persistence_pairs(self): - """A persistence interval is described by a pair of cells, one that creates the - feature and one that kills it. The filtration values of those 2 cells give coordinates - for a point in a persistence diagram, or a bar in a barcode. Structurally, in the - cubical complexes provided here, the filtration value of any cell is the minimum of the - filtration values of the maximal cells that contain it. Connecting persistence diagram - coordinates to the corresponding value in the input (i.e. the filtration values of + """A persistence interval is described by a pair of cells, one that creates the + feature and one that kills it. The filtration values of those 2 cells give coordinates + for a point in a persistence diagram, or a bar in a barcode. Structurally, in the + cubical complexes provided here, the filtration value of any cell is the minimum of the + filtration values of the maximal cells that contain it. Connecting persistence diagram + coordinates to the corresponding value in the input (i.e. the filtration values of the top-dimensional cells) is useful for differentiation purposes. - This function returns a list of pairs of top-dimensional cells corresponding to - the persistence birth and death cells of the filtration. The cells are represented by - their indices in the input list of top-dimensional cells (and not their indices in the - internal datastructure that includes non-maximal cells). Note that when two adjacent + This function returns a list of pairs of top-dimensional cells corresponding to + the persistence birth and death cells of the filtration. The cells are represented by + their indices in the input list of top-dimensional cells (and not their indices in the + internal datastructure that includes non-maximal cells). Note that when two adjacent top-dimensional cells have the same filtration value, we arbitrarily return one of the two when calling the function on one of their common faces. - :returns: The top-dimensional cells/cofaces of the positive and negative cells, + :returns: The top-dimensional cells/cofaces of the positive and negative cells, together with the corresponding homological dimension, in two lists of numpy arrays of integers. - The first list contains the regular persistence pairs, grouped by dimension. + The first list contains the regular persistence pairs, grouped by dimension. It contains numpy arrays of shape [number_of_persistence_points, 2]. - The indices of the arrays in the list correspond to the homological dimensions, and the - integers of each row in each array correspond to: (index of positive top-dimensional cell, - index of negative top-dimensional cell). - The second list contains the essential features, grouped by dimension. + The indices of the arrays in the list correspond to the homological dimensions, and the + integers of each row in each array correspond to: (index of positive top-dimensional cell, + index of negative top-dimensional cell). + The second list contains the essential features, grouped by dimension. It contains numpy arrays of shape [number_of_persistence_points, 1]. - The indices of the arrays in the list correspond to the homological dimensions, and the + The indices of the arrays in the list correspond to the homological dimensions, and the integers of each row in each array correspond to: (index of positive top-dimensional cell). """ |