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PersistentHomology

oxiphysics_geometry::topology_geometry

Struct PersistentHomology 

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pub struct PersistentHomology {
    pub pairs: Vec<BirthDeathPair>,
}
Expand description

Persistent homology computation for filtrations.

Computes birth-death pairs (persistence diagram) for 0-dim and 1-dim topological features (connected components and loops).

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§pairs: Vec<BirthDeathPair>

Computed birth-death pairs

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impl PersistentHomology

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pub fn new() -> Self

Creates an empty persistent homology.

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pub fn compute_0d(points: &[[f64; 3]]) -> Self

Computes 0-dimensional persistent homology from a point cloud.

Uses union-find (single-linkage clustering) to track connected components. Each merge event creates a birth-death pair.

§Arguments
  • points - Point cloud as [x,y,z] array
  • filtration_values - Per-edge filtration values (distances)
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pub fn diagram(&self) -> &[BirthDeathPair]

Returns all pairs in the persistence diagram.

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pub fn significant_features(&self, threshold: f64) -> usize

Returns the number of features with persistence > threshold.

§Arguments
  • threshold - Minimum persistence to count as a feature
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pub fn bottleneck_distance(&self, other: &Self) -> f64

Computes the bottleneck distance between two persistence diagrams.

d_B = inf_γ sup_{x ∈ D1} ||x - γ(x)||_∞

Uses a greedy approximation.

§Arguments
  • other - Other persistence diagram

Trait Implementations§

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impl Clone for PersistentHomology

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fn clone(&self) -> PersistentHomology

Returns a duplicate of the value. Read more
1.0.0 (const: unstable) · Source§

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl Debug for PersistentHomology

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fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
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impl Default for PersistentHomology

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fn default() -> Self

Returns the “default value” for a type. Read more

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