homology.dim0.unionfind

homology.dim0.unionfind()

Apply the UnionFind algorithm to compute zero-dimensional persistence diagram. Connected components are born at the height of a vertex. Connected components merge/die at the height of the joining edge.

Parameters:

myobject : multidim.SimplicialComplex, multidim.PointCloud,

or timeseries.Signal The algorithm requires heights on the vertices and heights on the edges.

cutoff : numpy.float64

Stop computing persistence at height cutoff.

Returns:

birth_index : numpy.ndarray

death_index : numpy.ndarray

birth_height : numpy.ndarray

death_height : numpy.ndarray

mergetree : stdtypes.dict

The mergetree is a dictionary keyed by the index of vertices where a merge occurred. The values of the dictionary are the previous representatives that were merged.

Notes

If the input object has \(n\) edges, then this functiomn calls homology.dim0.merge() a total of \(n\) times, and it calls persistence.fast_algorithms.root() a total of \(2n\) times.

References

[1]	H. Edelsbrunner and J. Harer, Computational Topology: An Introduction. American Mathematical Soc., 2010.