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PersistentHomology

oxiphysics_core::topology

Struct PersistentHomology 

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pub struct PersistentHomology {
    pub filtration: Vec<(f64, Vec<usize>)>,
}
Expand description

Persistent homology computed from a filtered simplicial complex.

The filtration is a sequence of (threshold, simplex) pairs in increasing order of threshold, representing the birth time of each simplex.

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§filtration: Vec<(f64, Vec<usize>)>

Filtration: list of (birth_time, simplex) pairs.

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impl PersistentHomology

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pub fn new(filtration: Vec<(f64, Vec<usize>)>) -> Self

Create a new PersistentHomology from a filtration.

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pub fn compute_barcode(&self) -> Vec<(usize, f64, f64)>

Compute the persistence barcode.

Returns a list of (dimension, birth, death) tuples. Features that never die get death = f64::INFINITY.

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pub fn compute_diagram(&self) -> Vec<(usize, f64, f64)>

Compute the persistence diagram.

Returns (dimension, birth, death) triples using the standard boundary-matrix reduction algorithm (over ℤ/2ℤ).

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pub fn total_persistence(&self) -> f64

Total persistence: sum of lifetimes Σ |death - birth| (finite bars only).

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pub fn bottleneck_distance(&self, other: &Self) -> f64

Bottleneck distance between two persistence diagrams.

Uses the greedy matching approximation over finite bars.

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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<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

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fn clone_into(&self, target: &mut T)

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impl<T, U> TryFrom<U> for T
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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
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type Error = <U as TryFrom<T>>::Error

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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.