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Swapped out to making
Simplex a type alias for SortedSet with top…
…ological methods added through self-type style type class implementations.
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Mikael Vejdemo-Johansson
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Oct 23, 2024
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,81 +1,44 @@ | ||
| package org.appliedtopology.tda4j | ||
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| import scala.collection.{SortedIterableFactory, SortedSetFactoryDefaults, StrictOptimizedSortedSetOps, mutable} | ||
| import scala.collection.immutable.{Set, SortedMap, SortedSet, SortedSetOps, TreeSet} | ||
| import scala.math.Ordering.IntOrdering | ||
| import scala.math.Ordering.Double.IeeeOrdering | ||
| import scala.collection.mutable | ||
| import scala.collection.immutable.SortedSet | ||
| import math.Ordering.Implicits.sortedSetOrdering | ||
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| /** Class representing an abstract simplex. Abstract simplices are given by sets (of totally ordered vertices) | ||
| * and inherit from `Cell` so that the class has a `boundary` and a `dim` method. | ||
| /** Simplices really are just sets, outright. We provide an implementation of the [OrderedCell] typeclass | ||
| * for simplicial complex structures, to enable their use. | ||
| * | ||
| * You should never have reason to use the constructor directly (...and if you do, you should make sure to give the | ||
| * internal `SortedSet` yourself) - instead use the factory method in the companion object. In code this means that | ||
| * instead of `new Simplex[Self](a,b,c)` you would write `Simplex[Self](a,b,c)`. | ||
| * | ||
| * @param vertices | ||
| * Vertices of the simplex | ||
| * @param ordering | ||
| * Ordering of the vertex type | ||
| * @tparam VertexT | ||
| * Vertex type | ||
| */ | ||
| case class Simplex[VertexT : Ordering] private[tda4j] (vertices : SortedSet[VertexT]) { | ||
| override def toString(): String = | ||
| vertices.mkString(s"∆(", ",", ")") | ||
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| def union(other: Simplex[VertexT]) = | ||
| new Simplex(vertices.union(other.vertices)) | ||
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| def incl(x : VertexT) = | ||
| new Simplex(vertices + x) | ||
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| def contains(x : VertexT) = vertices.contains(x) | ||
| } | ||
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| def simplexOrdering[VertexT : Ordering as vtxOrdering]: Ordering[Simplex[VertexT]] = | ||
| Ordering.by{(spx: Simplex[VertexT]) => spx.vertices}(sortedSetOrdering[SortedSet, VertexT](vtxOrdering)) | ||
| type Simplex[VertexT] = SortedSet[VertexT] | ||
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| given [VertexT : Ordering] => Ordering[Simplex[VertexT]] = simplexOrdering | ||
| extension [VertexT : Ordering](spx : Simplex[VertexT]) | ||
| def show : String = spx.mkString(s"∆(", ",", ")") | ||
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| // Ordering.by{(spx: Simplex[VertexT]) => spx.vertices}(sortedSetOrdering[SortedSet, VertexT](vtxOrdering)) | ||
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| /** Simplex companion object with factory methods | ||
| */ | ||
| object Simplex { | ||
| def apply[VertexT: Ordering](vertices: VertexT*) = | ||
| new Simplex[VertexT](SortedSet.from(vertices)) | ||
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| def empty[VertexT: Ordering]: Simplex[VertexT] = | ||
| new Simplex[VertexT](SortedSet.empty) | ||
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| def from[VertexT: Ordering](source: IterableOnce[VertexT]): Simplex[VertexT] = | ||
| new Simplex(SortedSet.from(source.iterator)) | ||
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| def simplexIsOrderedCell[VertexT](using vtxOrd : Ordering[VertexT])(using ord : Ordering[Simplex[VertexT]]) : Simplex[VertexT] is OrderedCell = | ||
| new (Simplex[VertexT] is OrderedCell): | ||
| override lazy val ordering = ord | ||
| extension (t: Simplex[VertexT]) { | ||
| def boundary[CoefficientT](using fr: (CoefficientT is Field)): Chain[Simplex[VertexT], CoefficientT] = | ||
| if (t.dim <= 0) Chain()(using ord) | ||
| else Chain.from( | ||
| t.vertices | ||
| .to(Seq) | ||
| .zipWithIndex | ||
| .map((vtx, i) => Simplex.from(t.vertices.toSeq.patch(i, Seq.empty, 1))) | ||
| .zip(Iterator.unfold(fr.one)(s => Some((s, fr.negate(s))))) | ||
| )(using ord) | ||
| def dim: Int = t.vertices.size - 1 | ||
| } | ||
| def compare(x: Simplex[VertexT], y: Simplex[VertexT]): Int = ord.compare(x, y) | ||
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| given [VertexT : Ordering as vtxOrdering] => (Simplex[VertexT] is OrderedCell) = | ||
| simplexIsOrderedCell(using vtxOrdering)(using simplexOrdering[VertexT](using vtxOrdering)) | ||
| } | ||
| object Simplex: | ||
| def from[VertexT : Ordering, T <: Seq[VertexT]](vertices : T) : Simplex[VertexT] = SortedSet.from(vertices) | ||
| def apply[VertexT : Ordering](vertices : VertexT*) : Simplex[VertexT] = SortedSet.from(vertices) | ||
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| /** Convenience method for defining simplices | ||
| * | ||
| * The character ∆ is typed as Alt+J on Mac GB layout, and has unicode code 0x0394. | ||
| */ | ||
| def ∆[T: Ordering](ts: T*): Simplex[T] = Simplex.from(ts) | ||
| * | ||
| * The character ∆ is typed as Alt+J on Mac GB layout, and has unicode code 0x0394. | ||
| */ | ||
| def ∆[VertexT : Ordering](vertices : VertexT*) : Simplex[VertexT] = SortedSet.from(vertices) | ||
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| def simplexOrdering[VertexT](using vtxOrd : Ordering[VertexT]) : Ordering[Simplex[VertexT]] = sortedSetOrdering(vtxOrd) | ||
| def SortedSet_is_OrderedCell[VertexT](using vtxOrd : Ordering[VertexT])(setOrdering : Ordering[SortedSet[VertexT]] = simplexOrdering(using vtxOrd)): (SortedSet[VertexT] is OrderedCell) = | ||
| new(SortedSet[VertexT] is OrderedCell) { | ||
| override lazy val ordering = setOrdering | ||
| extension (spx: SortedSet[VertexT]) { | ||
| override def dim = spx.size - 1 | ||
| override def boundary[CoefficientT: Field as fr] = | ||
| if (spx.dim <= 0) Chain() | ||
| else Chain.from( | ||
| spx.to(Seq) | ||
| .zipWithIndex | ||
| .map((vtx, i) => spx -- spx.slice(i, i + 1)) | ||
| .zip(Iterator.unfold(fr.one)(s => Some((s, fr.negate(s))))) | ||
| ) | ||
| } | ||
| } | ||
| given default_SortedSet_is_OrderedCell[VertexT : Ordering] : (SortedSet[VertexT] is OrderedCell) = | ||
| SortedSet_is_OrderedCell[VertexT]() |
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