Drawing Unravelled Persistence Diagrams

First we create and plot a point cloud of a sphere and of a torus.

from tadasets import sphere, torus, plot3d

my_sphere = sphere( r = 2, n = 100 )
my_torus  = torus( c = 2, a = 1, n = 100 )

plot3d( my_sphere );
plot3d( my_torus  );

Then we compute persistence intervals for each point cloud.

import numpy as np
import torch
import gudhi

simplex_trees = [
    gudhi.AlphaComplex( points = point_cloud ).create_simplex_tree() for
    point_cloud in ( my_sphere, my_torus )
]

[ simplex_tree.compute_persistence() for simplex_tree in simplex_trees ];

persistence_intervals = [
    [ torch.from_numpy( 
        np.float32( simplex_tree.persistence_intervals_in_dimension(dim) )
    ) for dim in range(3) ] for
    simplex_tree in simplex_trees
]

Then we complement the notebook to allow us to draw several unravelled persistence diagrams without rendering the HTML document invalid and we instantiate the class Draw with its default parameters.

from functools import partial
from persunraveltorch.draw import Draw

Draw.complement_notebook()

draw = Draw()

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Then we draw unravelled persistence diagrams corresponding to the previously created point clouds using the arctan function to map all intervals into the range between 0 and π/2. (You can choose different bounds when instantiating Draw using the range_intervals keyword argument.)

draw( list(
    map( partial(map, torch.atan), persistence_intervals )
) )

Then we draw the same diagrams again except that we scale all persistence intervals with a factor of 1.7 before applying arctan.

draw( list(
    map(
        partial(map, lambda intervals_d: torch.atan(1.7 * intervals_d)),
        persistence_intervals
    )
) )

Finally, we save the first version as a standalone SVG file.

with open('unravelled-diagrams.svg', 'w') as svg_file:
    svg_file.write(
        draw(
            standalone = True,
            intervals = list(
                map( partial(map, torch.atan), persistence_intervals )
            )
        )
    )