A computed weighted alpha complex.
Simplices are Simplex[Int] of site indices in increasing order. cells is in a valid filtration order: faces always precede cofaces.
Attributes
- Companion
- object
- Experimental
- true
- Graph
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- Supertypes
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class Objecttrait Matchableclass Any
Members list
Value members
Concrete methods
(simplex, filtration value) pairs in filtration order.
(simplex, filtration value) pairs in filtration order.
Attributes
The weight w(sigma) of Definition 10, i.e. the power at the witness. Unweighted: the squared circumradius.
The weight w(sigma) of Definition 10, i.e. the power at the witness. Unweighted: the squared circumradius.
Attributes
The alpha radius. Only equals the circumradius when p = 0.
The alpha radius. Only equals the circumradius when p = 0.
Attributes
Number of simplices in each dimension -- the (|X_k|) tuples quoted throughout "Examples and applications".
Number of simplices in each dimension -- the (|X_k|) tuples quoted throughout "Examples and applications".
Attributes
Returns a string representation of the object.
Returns a string representation of the object.
The default representation is platform dependent.
Attributes
- Returns
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a string representation of the object.
- Definition Classes
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Any
The witness map Phi of Definition 11: the unique minimiser of the power over the face V_sigma. Empty when the input carried no coordinates.
The witness map Phi of Definition 11: the unique minimiser of the power over the face V_sigma. Empty when the input carried no coordinates.
Attributes
Concrete fields
Filtration order: increasing weight, breaking ties by dimension so that faces precede cofaces, then by simplexOrdering[Int] (the same colex/lex vertex-set order every other Ripser-flavored tie-break in this codebase uses) for determinism -- not a string comparison on c.show, which sorted "10" before "9" and gave no guarantee of agreeing with any other ordering in the codebase.
Filtration order: increasing weight, breaking ties by dimension so that faces precede cofaces, then by simplexOrdering[Int] (the same colex/lex vertex-set order every other Ripser-flavored tie-break in this codebase uses) for determinism -- not a string comparison on c.show, which sorted "10" before "9" and gave no guarantee of agreeing with any other ordering in the codebase.