Skip to content

Examples

Flood PH of noisy torus points

In the following example, we sample n_pts=1000000 points from a noisy torus in 3D, then construct the Flood complex on top of n_lms=1000 landmarks (see Illustration ) and compute persistent homology (up to dimension 3) using gudhi based on the constructed filtered Flood simplicial complex.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
from flooder import (
    generate_noisy_torus_points_3d, 
    flood_complex, 
    generate_landmarks)

DEVICE = "cuda"
n_pts = 1_000_000  # Number of points to sample from torus
n_lms = 1_000      # Number of landmarks for Flood complex

pts = generate_noisy_torus_points_3d(n_pts).to(DEVICE)
lms = generate_landmarks(pts, n_lms)

stree = flood_complex(pts, lms, return_simplex_tree=True)
stree.compute_persistence()
ph_diags = [stree.persistence_intervals_in_dimension(i) for i in range(3)]

Importantly, one can either call flood_complex with the already pre-selected (here via FPS) landmarks, or one can just specify the number of desired landmarks, e.g., via

1
stree = flood_complex(pts, n_lms, return_simplex_tree=True)

in which case FPS is called internally.