AlphaComplexDQP

org.appliedtopology.tda4j.alpha.AlphaComplexDQP
See theAlphaComplexDQP companion object
final class AlphaComplexDQP(val space: PowerDistance, val maxPower: Double, val maxDimension: Int, cellsByDim: IndexedSeq[IndexedBuffer[Simplex[Int]]], weights: HashMap[Simplex[Int], Double], witnesses: HashMap[Simplex[Int], Array[Double]])

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
Supertypes
class Object
trait Matchable
class Any

Members list

Value members

Concrete methods

def barcodeInput: IndexedSeq[(Simplex[Int], Double)]

(simplex, filtration value) pairs in filtration order.

(simplex, filtration value) pairs in filtration order.

Attributes

def cellsOfDimension(k: Int): IndexedSeq[Simplex[Int]]
def contains(cell: Simplex[Int]): Boolean
def dimension: Int
def filtrationValue(cell: Simplex[Int]): Double

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

def radiusOf(cell: Simplex[Int]): Double

The alpha radius. Only equals the circumradius when p = 0.

The alpha radius. Only equals the circumradius when p = 0.

Attributes

def size: Int
def sizeByDimension: IndexedSeq[Int]

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

override def toString: String

Returns a string representation of the object.

Returns a string representation of the object.

The default representation is platform dependent.

Attributes

Returns

a string representation of the object.

Definition Classes
Any
def witness(cell: Simplex[Int]): Option[Array[Double]]

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

lazy val cells: IndexedSeq[Simplex[Int]]

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.

Attributes

val maxDimension: Int
val maxPower: Double