Computing Persistence Diagram Bundles

10/12/2022

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by   Abigail Hickok, et al.

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Persistence diagram (PD) bundles, a generalization of vineyards, were recently introduced as a way of studying the persistent homology of a set of filtrations parameterized by a topological space 𝒯. In this paper, I present an algorithm for computing piecewise-linear PD bundles, a wide class that includes many of the PD bundles that one may encounter in practice. I give full implementation details for the case in which (𝒯) ≤ 2, and I outline the generalization to higher dimensions.