Persistence.hs

module Moonlight.Homology.Persistence
  ( BiFilteredCell (..),
    BiPersistencePair (..),
    FiltrationValue (..),
    FilteredFiniteChainComplex,
    filteredBaseComplex,
    filteredCellBirths,
    filteredCriticalValues,
    mkFilteredFiniteChainComplex,
    mod2PersistentPairs,
    CriticalBettiTable,
    criticalBettiDegreeCount,
    criticalBettiRankCount,
    criticalBettiTableValues,
    criticalBettiVectors,
    mod2PersistentPairsWithCriticalBettiTable,
    persistentBettiAt,
    persistentBettiAtMany,
    persistentBettiAtCriticalValues,
    mod2PersistenceTopologyWitness,
    ChainMapEndpoint (..),
    ZigzagDirection (..),
    ZigzagFailure (..),
    FiniteChainMap,
    finiteChainMapSource,
    finiteChainMapTarget,
    finiteChainMapAt,
    mkFiniteChainMapChecked,
    ZigzagArrow (..),
    zigzagArrowDirection,
    FiniteChainZigzag,
    mkFiniteChainZigzag,
    finiteChainZigzagComplexes,
    finiteChainZigzagArrows,
    ZigzagInterval (..),
    rationalZigzagIntervals,
    zigzagBettiAt,
  )
where

import Data.Kind (Type)
import Moonlight.Homology.Pure.Chain (HomologicalDegree)
import Moonlight.Homology.Topology (BasisCellRef)
import Moonlight.Homology.Pure.Filtration (FiltrationValue (..))
import Moonlight.Homology.Pure.Topology.Core
  ( FilteredFiniteChainComplex,
    filteredBaseComplex,
    filteredCellBirths,
    filteredCriticalValues,
  )
import Moonlight.Homology.Pure.Topology.Persistence
  ( mkFilteredFiniteChainComplex,
    mod2PersistentPairs,
    CriticalBettiTable,
    criticalBettiDegreeCount,
    criticalBettiRankCount,
    criticalBettiTableValues,
    criticalBettiVectors,
    mod2PersistentPairsWithCriticalBettiTable,
    persistentBettiAt,
    persistentBettiAtMany,
    persistentBettiAtCriticalValues,
    mod2PersistenceTopologyWitness,
  )
import Moonlight.Homology.Pure.Topology.Zigzag
  ( ChainMapEndpoint (..),
    FiniteChainMap,
    FiniteChainZigzag,
    ZigzagArrow (..),
    ZigzagDirection (..),
    ZigzagFailure (..),
    ZigzagInterval (..),
    finiteChainMapAt,
    finiteChainMapSource,
    finiteChainMapTarget,
    finiteChainZigzagArrows,
    finiteChainZigzagComplexes,
    mkFiniteChainMapChecked,
    mkFiniteChainZigzag,
    rationalZigzagIntervals,
    zigzagArrowDirection,
    zigzagBettiAt,
  )

-- | A cell with two independent filtration parameters. Forward-looking
-- vocabulary for two-parameter persistence: no function in this package
-- produces or consumes these values yet — they fix the types downstream
-- multi-parameter code will speak.
type BiFilteredCell :: Type
data BiFilteredCell = BiFilteredCell
  { bfcCell :: BasisCellRef,
    bfcBirth1 :: FiltrationValue,
    bfcBirth2 :: FiltrationValue
  }
  deriving stock (Eq, Show)

-- | A two-parameter birth/death pair. Forward-looking vocabulary; see
-- 'BiFilteredCell'.
type BiPersistencePair :: Type
data BiPersistencePair = BiPersistencePair
  { bppDegree :: HomologicalDegree,
    bppBirth :: (FiltrationValue, FiltrationValue),
    bppDeath :: Maybe (FiltrationValue, FiltrationValue)
  }
  deriving stock (Eq, Show)