Persistence and filtration optimization

[senchromatic]

Done:

• Created a sparse, column-oriented matrix to represent the matrix of all simplices added during filtration; perform column reduction to extract pivots, which are birth-death times
• Fixed a major bottleneck, wherein edges from subcomplexes were being re-added to the filtration for higher diameters (improve efficiency from quadratic to linear time with respect to number of simplices)
• Add a maximum diameter parameter to exclude diameters close to 1.0 (non-meaningful boundary maps)
• get_low cache optimization (from M^4 to M^3 time complexity) and return value re-use in column reduction

Todo:

• Benchmark new runtime after optimization
• Plot persistence diagram

[aepereira]

Nice!