pkg> add https://github.com/wildart/SmithNormalForm.jl.git#0.2.1
pkg> add https://github.com/wildart/ComputationalHomology.jl.git#master
pkg> add https://github.com/wildart/TDA.jl.git#master

using TDA, ComputationalHomology, Plots
# crate some intervals of various dimensions
ints = Dict(0=>diagram(2.0=>6.0, 5.0=>10.0, 1.0=>Inf), 1=>diagram(9.0=>12.0))

# plot persistance diagram
plot(ints)
# plot barcode
plot(ints, seriestype=:barcode)

using TDA, ComputationalHomology, Plots
# generate simplicial complex
cplx = ComputationalHomology.sphere(2)
# generate some points on circle
D = mapslices(p->p./sqrt(sum(p.^2)), randn(30,2), dims=2)
# plot points
plot(D[:,1], D[:,2], seriestype = :scatter, markersize = 2)
# plot nerve
plot!(cplx, D, linewidth = 2) # or plot(cplx)

using TDA, Plots

# generate and plot some dataset
X = hcat(TDA.circlepoints(500, 0.5, noise=0.05)...)'
plot(X[1,:], X[2,:], seriestype=:scatter)

# define Mapper filter function for dataset: f(x) = ||x.x - p.x||
fltfn = (data)->vec(mapslices(p->p[1]-minimum(data[1,:]), data, dims=1))
# plot data colored by filter function values
plot(X[1,:], X[2,:], label="", zcolor=fltfn(X), seriestype=:scatter, ms=2)

# call Mapper algorithm with the particular filter function.
mpr = TDA.mapper(X, filter=fltfn, seed=0, intervals=5, overlap=0.2)

# plot topological layout - mapper graph (by default circular layout is used)
plot(mpr, c=:viridis)
# use `constant_layout` for positioning Mapper graph vertices
# at centers of cover patches
plot(mpr, c=:viridis, complex_layout=TDA.constant_layout)