Module zigzag 

Zigzag persistence for sequences of simplicial complexes.

Zigzag persistence generalises ordinary persistence to handle sequences where simplices can be both added and removed. The “zigzag” refers to the sequence of maps alternating between forward (inclusion) and backward (deletion) directions:

K_0 → K_1 ← K_2 → K_3 ← K_4 → …

This implementation uses a vineyard-inspired approach:

1. Maintain a totally ordered filtration of currently-active simplices.
2. On addition: append the simplex and reduce.
3. On removal: locate the simplex, perform transpositions to move it to the end, then delete it and close any open intervals.

References

• Carlsson & de Silva (2010). Zigzag Persistence. FoCM.
• Cohen-Steiner, Edelsbrunner & Morozov (2006). Vines and Vineyards.

Structs

ZigzagPersistence

Incremental zigzag persistence computation.

ZigzagStep

A single step in a zigzag filtration sequence.

Enums

ZigzagDirection

Direction of a zigzag step.

Functions

compute_zigzag

Compute zigzag persistence for a sequence of steps.