Docs: filtrations module¶
Contents:
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euchar.filtrations.Delaunay_ed_tri_2D(points)¶ Delaunay triangulation simplices of two dimensional points.
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euchar.filtrations.Delaunay_ed_tri_tetra_3D(points)¶ Delauanay triangulation simplices of three dimensional points.
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euchar.filtrations.alpha_filtration_2D(points)¶ Simplices and corresponding parametrization of 2D point cloud.
- points
np.ndarray of shape (N, 3)
- simplices
array of integers of shape (N,3) using -1 as placeholder Ex. [1,-1,-1] is vertex 1 and [3,5,-1] is edge (3,5).
- parametrization
array of floats corresponding to the Alpha filtration parameter of each simplex.
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euchar.filtrations.alpha_filtration_3D(points)¶ Simplices and corresponding parametrization of 3D point cloud.
- points
np.ndarray of shape (N, 3)
- simplices
array of integers of shape (N, 4) using -1 as placeholder Ex. [1,-1,-1,-1] is vertex 1 and [3,5,-1,-1] is edge (3,5).
- parametrization
array of floats corresponding to the Alpha filtration parameter of each simplex.
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euchar.filtrations.inverse_density_filtration(points, simplices, n_neighbors)¶ Parametrization of simplices based on inverse of local density at vertices. The inverse of the density at each p in points is estimated as the root mean square of the distances from p to its n nearest neighbors.
- points
np.ndarray of shape (N, d)
- simplices
np.ndarray of shape (M, d+1)
- n_neighbors
int, number of nearest neighbors of a point p in points used to estimate the local density around p.
- density_parametrization
1-D np.ndarray, parametrization of simplices. The value of a simplex is the maximum of any of its vertices.
