# An example torus built using gudhi's Simplex Tree
from gudhi import SimplexTree
import numpy as np
[docs]
class LowerStarSC(SimplexTree):
"""
Class to create a simplicial compex that has a lower star filtration, based on Gudhi's SimplexTree.
Inherits from:
SimplexTree: A simplex tree structure from the Gudhi library.
Methods:
__init__(): Initializes the simplex tree.
"""
[docs]
def __init__(self):
"""Initialize class. Due to SimplexTree C++ weirdness, this does nothing but initialize the instance.
"""
super().__init__()
[docs]
def assign_filtration(self, vertex, value):
"""Sets the filtration value for a given vertex. Vertex can be provided either as an integer, or as a single integer in a list representing the integer label of the vertex.
Args:
vertex (Union[int, tuple]): Name of the vertex (an integer or a single-element list).
value (float): Filtration value to set.
"""
if isinstance(vertex, int):
vertex = [vertex]
elif len(vertex) != 1:
raise ValueError("vertex must be an integer, or a single-element list.")
super().assign_filtration(vertex, value)
# Set all adjacent simplices to have at least this filtration value
for simplex, filt in self.get_star(vertex):
simplex_val = max([self.filtration([v]) for v in simplex])
super().assign_filtration(simplex, simplex_val)
[docs]
def max_filtration(self):
"""Returns the maximum filtration value among all simplices in the torus.
Returns:
float: Maximum filtration value.
"""
max_filt = max(f for _, f in self.get_filtration())
return max_filt
[docs]
def min_filtration(self):
"""Returns the minimum filtration value among all simplices in the torus.
Returns:
float: Minimum filtration value.
"""
min_filt = min(f for _, f in self.get_filtration())
return min_filt
[docs]
def assign_random_values(self, min, max, seed=None):
"""Assign uniform random filtrations sampled in (min, max) for all vertices.
Args:
min (float): Minimum value for random function values
max (float): Maximum value for random function value
seed (int, optional): Random seed for reproducibility. Default is None.
"""
if seed is not None:
rng = np.random.default_rng(seed)
filtvals = rng.uniform(min, max, self.num_vertices())
else:
filtvals = np.random.uniform(min, max, self.num_vertices())
for v, val in zip(range(self.num_vertices()), filtvals):
self.assign_filtration(v, val)
[docs]
def num_vertices(self):
"""Return the number of vertices (0-simplices) in the simplex tree."""
return sum(1 for simplex in self.get_simplices() if len(simplex[0]) == 1)
[docs]
def iter_vertices(self):
"""Yield the names (tuples) of all vertices (0-simplices) in the simplex tree."""
for simplex in self.get_simplices():
if len(simplex[0]) == 1:
yield simplex[0][0]
if __name__ == "__main__":
LS = LowerStarSC()
LS.insert([0, 1, 2])
LS.insert([1, 3])
LS.insert([2,3])
LS.assign_random_values(0.0, 1.0)
for simplex, filt in LS.get_filtration():
print(f"Simplex: {simplex}, Filtration: {filt}")