Dowker persistence

This repository contains code for computing the Dowker persistence diagrams of two point clouds in dimensions 0 or 1. Please note that we use the term "Dowker" and "Witness" interchangeably.

Install

Download Julia. You may run into dependency issues for more recent versions of Julia. I recommend using Julia version 1.7.2.

Quick start

import Pkg
Pkg.activate(".")
Pkg.instantiate()
include("dowker_persistence.jl")
include("Eirene_var.jl)
using .Dowker
using .Eirene_var
using DelimitedFiles

# load points
P1 = readdlm("toy_example/R1_coordinates.csv", ',', Float64)
P2 = readdlm("toy_example/R2_coordinates.csv", ',', Float64)

# compute cross-system distance
D1, D2, D_P1_P2, D_P2_P1 = compute_distance(P1, P2)

# compute Dowker persistence
W_P1_P2 = compute_Witness_persistence(D_P1_P2, maxdim = 1)
W_barcode = Eirene_var.barcode(W_P1_P2["eirene_output"], dim = 1)

# plot Dowker persistence diagram
plot_PD(W_barcode, title = "Dowker persistence diagram")

Examples

• See 1_compute_dowker_persistence.ipynb for example computation of Dowker persistence diagram, cycle representatives, and persistence images.
• See 2_more_examples.ipynb for Dowker persistence diagrams on a few toy examples.