hgeometry-combinatorial 0.10.0.0 → 0.14
raw patch · 71 files changed
Files
- cbits/erf.c +97/−0
- changelog +55/−0
- changelog.org +55/−0
- docs/Data/PlanarGraph/planargraph-1711135548958680232.svg +199/−0
- docs/Data/PlanarGraph/planargraph-1902492848341357096.svg +166/−0
- docs/Data/PlanarGraph/planargraph-2506803680640023584.svg +135/−0
- docs/Data/PlanarGraph/planargraph-2635031442529484236.compact.svg +193/−0
- docs/Data/PlanarGraph/planargraph-2635031442529484236.svg +403/−0
- docs/Data/PlanarGraph/planargraph-2959979592048325618.svg +108/−0
- doctests.hs +10/−1
- hgeometry-combinatorial.cabal +76/−13
- src/Algorithms/BinarySearch.hs +149/−0
- src/Algorithms/DivideAndConquer.hs +31/−15
- src/Algorithms/FloydWarshall.hs +56/−0
- src/Algorithms/Graph/BFS.hs +66/−0
- src/Algorithms/Graph/DFS.hs +28/−4
- src/Algorithms/Graph/MST.hs +7/−0
- src/Algorithms/LogarithmicMethod.hs +151/−0
- src/Control/CanAquire.hs +87/−0
- src/Control/Monad/State/Persistent.hs +11/−1
- src/Data/BalBST.hs +0/−378
- src/Data/BinaryTree.hs +6/−39
- src/Data/BinaryTree/Zipper.hs +0/−64
- src/Data/CircularList/Util.hs +10/−3
- src/Data/CircularSeq.hs +47/−15
- src/Data/Double/Approximate.hs +83/−0
- src/Data/Double/Shaman.hs +295/−0
- src/Data/DynamicOrd.hs +19/−11
- src/Data/Ext.hs +16/−2
- src/Data/IndexedDoublyLinkedList.hs +216/−0
- src/Data/IndexedDoublyLinkedList/Bare.hs +197/−0
- src/Data/Intersection.hs +6/−3
- src/Data/LSeq.hs +119/−31
- src/Data/List/Alternating.hs +93/−0
- src/Data/List/Set.hs +70/−0
- src/Data/List/Util.hs +144/−0
- src/Data/List/Zipper.hs +79/−0
- src/Data/Measured.hs +11/−0
- src/Data/Measured/Class.hs +21/−0
- src/Data/Measured/Size.hs +48/−0
- src/Data/OrdSeq.hs +68/−37
- src/Data/PlanarGraph.hs +8/−6
- src/Data/PlanarGraph/AdjRep.hs +8/−7
- src/Data/PlanarGraph/Core.hs +172/−47
- src/Data/PlanarGraph/Dart.hs +10/−1
- src/Data/PlanarGraph/Dual.hs +84/−24
- src/Data/PlanarGraph/IO.hs +43/−17
- src/Data/PlanarGraph/Immutable.hs +1404/−0
- src/Data/PlanarGraph/Internal.hs +92/−0
- src/Data/PlanarGraph/Mutable.hs +692/−0
- src/Data/PlanarGraph/Persistent.hs +71/−0
- src/Data/Range.hs +97/−59
- src/Data/RealNumber/Rational.hs +101/−0
- src/Data/Sequence/Util.hs +10/−58
- src/Data/Set/Util.hs +65/−5
- src/Data/SlowSeq.hs +0/−205
- src/Data/Tree/Util.hs +68/−14
- src/Data/UnBounded.hs +103/−22
- src/Data/Util.hs +24/−23
- src/Data/Vector/Circular/Util.hs +74/−0
- src/Data/Yaml/Util.hs +1/−0
- test/Algorithms/DivideAndConquerSpec.hs +2/−1
- test/Algorithms/Graph/BFSSpec.hs +26/−0
- test/Algorithms/Graph/DFSSpec.hs +29/−0
- test/Algorithms/LogarithmicMethodSpec.hs +45/−0
- test/Data/CircularSeqSpec.hs +3/−0
- test/Data/EdgeOracleSpec.hs +1/−1
- test/Data/IndexedDoublyLinkedListSpec.hs +36/−0
- test/Data/PlanarGraphSpec.hs +2/−2
- test/Data/RangeSpec.hs +5/−0
- test/Data/RealNumber/RationalSpec.hs +25/−0
+ cbits/erf.c view
@@ -0,0 +1,97 @@+#include <math.h>++double erf_log(double number, double error, double result)+{+ long double precise = logl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_exp(double number, double error, double result)+{+ long double precise = expl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_pow(double n1, double e1, double n2, double e2, double result)+{+ long double precise = powl((long double)n1 + (long double)e1, (long double)n2 + (long double)e2);+ return (double) (precise - (long double)result);+}++double erf_sin(double number, double error, double result)+{+ long double precise = sinl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_cos(double number, double error, double result)+{+ long double precise = cosl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_tan(double number, double error, double result)+{+ long double precise = tanl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_asin(double number, double error, double result)+{+ long double precise = asinl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_acos(double number, double error, double result)+{+ long double precise = acosl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_atan(double number, double error, double result)+{+ long double precise = atanl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_sinh(double number, double error, double result)+{+ long double precise = sinhl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_cosh(double number, double error, double result)+{+ long double precise = coshl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_tanh(double number, double error, double result)+{+ long double precise = tanhl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_asinh(double number, double error, double result)+{+ long double precise = asinhl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_acosh(double number, double error, double result)+{+ long double precise = acoshl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_atanh(double number, double error, double result)+{+ long double precise = atanhl((long double)number + (long double)error);+ return (double) (precise - (long double)result);+}++double erf_atan2(double n1, double e1, double n2, double e2, double result)+{+ long double precise = atan2l((long double)n1 + (long double)e1, (long double)n2 + (long double)e2);+ return (double) (precise - (long double)result);+}
+ changelog view
@@ -0,0 +1,55 @@+#+STARTUP: showeverything++* Changelog++** 0.14++- Got rid of proxies to build planar graphs, use TypeApplication+ instead. Also slightly changed some of the types to better reflect+ what they need; in particular 'buildGraph' now takes only the+ adjacency lists (no face information). And 'fromAdjRep' which+ computes a PlanarGraph from its adjacencylists (including vertex and+ edge info.)+- Cleaning up the public API by hiding several internal modules.++** 0.13++- Moved 'intersects' from the HasIntersectionWith class into a new+ class IsIntersectableWith. This allows separate (weaker) constraints+ for checking *if* geometries intersect rather than computing exact+ intersections.+- Bug fixes in the orientations of boundaries in PlanarGraph.+- Implementation of Logaritmic Method, wich allows us to transform a+ static data structure into an insertion only data structure++** 0.12++- Add Data.Double.Approximate: Floating point numbers take take+ imprecision into account when ordering.+- Add Data.Double.Shaman: Floating point numbers that keep track of+ error bounds while not being more than an order of magnitude slower+ than native floating point numbers.+- Add Data.PlanarGraph.Immutable and Data.PlanarGraph.Mutable: New+ planargraph implementation that supports efficient updates and queries.++** 0.11++- Changed the implementation of Two and Three in Data.Util+ (hgeometry-combinatorial). Now they have proper Functor, Foldable,+ and Traversable instances.+- Added Data.RealNumber.Rational wrapping the Rational type giving+ some more readable show/read instances+- Added function to compute levels in a Rose-Tree+- Moved the binary searching functions from Data.Sequence.Util into+ Algorithms.BinarySearch, also added a version for fractional types+ that stops at a given threshold.+- Removed Data.BalBST and Data.SlowSeq+- Moved Measured from Data.BinaryTree into a separate module.++** 0.10++- More Instances++** 0.9++- First release in which hgeometry-combinatorial was split off from hgeometry.
changelog.org view
@@ -0,0 +1,55 @@+#+STARTUP: showeverything++* Changelog++** 0.14++- Got rid of proxies to build planar graphs, use TypeApplication+ instead. Also slightly changed some of the types to better reflect+ what they need; in particular 'buildGraph' now takes only the+ adjacency lists (no face information). And 'fromAdjRep' which+ computes a PlanarGraph from its adjacencylists (including vertex and+ edge info.)+- Cleaning up the public API by hiding several internal modules.++** 0.13++- Moved 'intersects' from the HasIntersectionWith class into a new+ class IsIntersectableWith. This allows separate (weaker) constraints+ for checking *if* geometries intersect rather than computing exact+ intersections.+- Bug fixes in the orientations of boundaries in PlanarGraph.+- Implementation of Logaritmic Method, wich allows us to transform a+ static data structure into an insertion only data structure++** 0.12++- Add Data.Double.Approximate: Floating point numbers take take+ imprecision into account when ordering.+- Add Data.Double.Shaman: Floating point numbers that keep track of+ error bounds while not being more than an order of magnitude slower+ than native floating point numbers.+- Add Data.PlanarGraph.Immutable and Data.PlanarGraph.Mutable: New+ planargraph implementation that supports efficient updates and queries.++** 0.11++- Changed the implementation of Two and Three in Data.Util+ (hgeometry-combinatorial). Now they have proper Functor, Foldable,+ and Traversable instances.+- Added Data.RealNumber.Rational wrapping the Rational type giving+ some more readable show/read instances+- Added function to compute levels in a Rose-Tree+- Moved the binary searching functions from Data.Sequence.Util into+ Algorithms.BinarySearch, also added a version for fractional types+ that stops at a given threshold.+- Removed Data.BalBST and Data.SlowSeq+- Moved Measured from Data.BinaryTree into a separate module.++** 0.10++- More Instances++** 0.9++- First release in which hgeometry-combinatorial was split off from hgeometry.
+ docs/Data/PlanarGraph/planargraph-1711135548958680232.svg view
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doctests.hs view
@@ -31,7 +31,6 @@ , "DeriveFunctor" , "DeriveFoldable" , "DeriveTraversable"- , "AutoDeriveTypeable" , "DeriveGeneric" , "FlexibleInstances" , "FlexibleContexts"@@ -55,12 +54,22 @@ modules = [ "Data.Range" , "Data.CircularList.Util"+ , "Data.Vector.Circular.Util" , "Data.Permutation" , "Data.CircularSeq" , "Data.LSeq" , "Data.PlanarGraph" , "Data.PlanarGraph.Dart" , "Data.PlanarGraph.Core"+ , "Data.PlanarGraph.Mutable"+ , "Data.PlanarGraph.Immutable" , "Data.Tree.Util" , "Data.Set.Util"++ , "Data.List.Util"+ , "Data.List.Alternating"+ , "Data.List.Zipper"++ , "Data.Double.Approximate"+ , "Data.Double.Shaman" ]
hgeometry-combinatorial.cabal view
@@ -2,7 +2,7 @@ -- documentation, see http://haskell.org/cabal/users-guide/ name: hgeometry-combinatorial-version: 0.10.0.0+version: 0.14 synopsis: Data structures, and Data types. description: The Non-geometric data types and algorithms used in HGeometry.@@ -13,7 +13,7 @@ maintainer: frank@fstaals.net -- copyright: -tested-with: GHC >= 8.4+tested-with: GHC >= 8.8 category: Geometry build-type: Simple@@ -24,10 +24,13 @@ -- examples/**/*.out extra-source-files: README.md+ changelog changelog.org Extra-doc-files: docs/Data/PlanarGraph/testG.png docs/Data/PlaneGraph/planegraph.png+ docs/Data/PlanarGraph/*.svg+ docs/Data/PlanarGraph/*.compact.svg -- docs/**/*.png cabal-version: 2.0@@ -42,60 +45,98 @@ exposed-modules: -- * Algorithmic Strategies Algorithms.DivideAndConquer+ Algorithms.BinarySearch+ Algorithms.LogarithmicMethod -- * Graph Algorithms Algorithms.Graph.DFS+ Algorithms.Graph.BFS Algorithms.Graph.MST+ Algorithms.FloydWarshall Algorithms.StringSearch.KMP ++++ -- * Numeric Data Types+ Data.RealNumber.Rational+ Data.Double.Approximate+ Data.Double.Shaman++ -- * Measurements+ Data.Measured+ Data.Measured.Class+ Data.Measured.Size+ -- * General Data Types Data.UnBounded Data.Intersection Data.Range+ Data.Ext+ -- Data.Ext.Multi+ Data.LSeq Data.CircularSeq Data.Sequence.Util Data.BinaryTree- Data.BinaryTree.Zipper Data.CircularList.Util- Data.BalBST+ Data.Vector.Circular.Util Data.OrdSeq- Data.SlowSeq Data.Tree.Util Data.Util + Data.IndexedDoublyLinkedList+ -- Data.IndexedDoublyLinkedList.Unboxed+ Data.IndexedDoublyLinkedList.Bare+ Data.DynamicOrd+ Data.Set.Util + Data.List.Set+ Data.List.Util+ Data.List.Zipper+ Data.List.Alternating+ -- * Planar Graphs Data.Permutation Data.PlanarGraph+ Data.PlanarGraph.Persistent+ Data.PlanarGraph.Mutable+ Data.PlanarGraph.Immutable Data.PlanarGraph.AdjRep Data.PlanarGraph.IO- Data.PlanarGraph.Dart- Data.PlanarGraph.Core- Data.PlanarGraph.Dual Data.PlanarGraph.EdgeOracle+ Data.PlanarGraph.Dart -- * Other System.Random.Shuffle+ Control.Monad.State.Persistent++ Control.CanAquire+ Data.Yaml.Util - other-modules:+ other-modules: Data.PlanarGraph.Internal+ Data.PlanarGraph.Core+ Data.PlanarGraph.Dual + -- other-extensions: build-depends: base >= 4.11 && < 5+ , array >= 0.4 , bifunctors >= 4.1 , bytestring >= 0.10 , containers >= 0.5.9+ -- , data-default , dlist >= 0.7- , lens >= 4.2+ , lens >= 4.18 , contravariant >= 1.5 , semigroupoids >= 5 , semigroups >= 0.18@@ -103,17 +144,26 @@ , deepseq >= 1.1 , fingertree >= 0.1 , MonadRandom >= 0.5+ , random >= 1.1 , QuickCheck >= 2.5 , quickcheck-instances >= 0.3 , reflection >= 2.1+ , primitive >= 0.6.3.0+ , linear >= 1.21+ , hashable >= 1.2+ , witherable >= 0.4 , vector >= 0.11 , data-clist >= 0.1.2.3+ , vector-circular >= 0.1.4+ , nonempty-vector >= 0.2.0.0 , vector-builder >= 0.3.7+ , unordered-containers , aeson >= 1.0 , yaml >= 0.8 , text >= 1.1.1.0+ , math-functions , mtl , template-haskell@@ -153,6 +203,9 @@ , FlexibleContexts , MultiParamTypeClasses + c-sources: cbits/erf.c+ extra-libraries: m+ test-suite doctests type: exitcode-stdio-1.0 ghc-options: -threaded@@ -176,11 +229,16 @@ other-modules: Algorithms.StringSearch.KMPSpec Algorithms.DivideAndConquerSpec+ Algorithms.LogarithmicMethodSpec+ Algorithms.Graph.DFSSpec+ Algorithms.Graph.BFSSpec Data.RangeSpec Data.EdgeOracleSpec Data.PlanarGraphSpec Data.OrdSeqSpec Data.CircularSeqSpec+ Data.IndexedDoublyLinkedListSpec+ Data.RealNumber.RationalSpec build-depends: base@@ -189,6 +247,7 @@ , quickcheck-instances >= 0.3 , approximate-equality >= 1.1.0.2 , hgeometry-combinatorial+ , deepseq , lens , data-clist , linear@@ -198,11 +257,17 @@ , vector , containers , random- , singletons , filepath , directory , yaml , MonadRandom+ , semigroupoids+ -- -- Such a mess:+ -- if impl(ghc == 9.*)+ -- build-depends: singletons == 3.*+ -- , singletons-th == 3.*+ -- else+ -- build-depends: singletons == 2.* default-extensions: TypeFamilies , GADTs@@ -227,8 +292,6 @@ , DeriveFunctor , DeriveFoldable , DeriveTraversable-- , AutoDeriveTypeable , FlexibleInstances , FlexibleContexts
+ src/Algorithms/BinarySearch.hs view
@@ -0,0 +1,149 @@+{-# LANGUAGE UndecidableInstances #-}+--------------------------------------------------------------------------------+-- |+-- Module : Algorithms.BinarySearch+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Algorithms.BinarySearch where++import Control.Applicative ((<|>))+import Data.Kind+import Data.Sequence (Seq, ViewL(..),ViewR(..))+import qualified Data.Sequence as Seq+import Data.Set (Set)+import qualified Data.Set.Internal as Set+import qualified Data.Vector.Generic as V+--------------------------------------------------------------------------------++-- | Given a monotonic predicate p, a lower bound l, and an upper bound u, with:+-- p l = False+-- p u = True+-- l < u.+--+-- Get the index h such that everything strictly smaller than h has: p i =+-- False, and all i >= h, we have p h = True+--+-- running time: \(O(\log(u - l))\)+{-# SPECIALIZE binarySearch :: (Int -> Bool) -> Int -> Int -> Int #-}+{-# SPECIALIZE binarySearch :: (Word -> Bool) -> Word -> Word -> Word #-}+binarySearch :: Integral a => (a -> Bool) -> a -> a -> a+binarySearch p = go+ where+ go l u = let d = u - l+ m = l + (d `div` 2)+ in if d == 1 then u else if p m then go l m+ else go m u++-- | Given a value \(\varepsilon\), a monotone predicate \(p\), and two values \(l\) and+-- \(u\) with:+--+-- - \(p l\) = False+-- - \(p u\) = True+-- - \(l < u\)+--+-- we find a value \(h\) such that:+--+-- - \(p h\) = True+-- - \(p (h - \varepsilon)\) = False+--+-- >>> binarySearchUntil (0.1) (>= 0.5) 0 (1 :: Double)+-- 0.5+-- >>> binarySearchUntil (0.1) (>= 0.51) 0 (1 :: Double)+-- 0.5625+-- >>> binarySearchUntil (0.01) (>= 0.51) 0 (1 :: Double)+-- 0.515625+binarySearchUntil :: (Fractional r, Ord r)+ => r+ -> (r -> Bool) -> r -> r -> r+binarySearchUntil eps p = go+ where+ go l u | u - l < eps = u+ | otherwise = let m = (l + u) / 2+ in if p m then go l m else go m u+++--------------------------------------------------------------------------------+-- * Binary Searching in some data structure+++class BinarySearch v where+ type Index v :: Type+ type Elem v :: Type++ -- | Given a monotonic predicate p and a data structure v, find the+ -- element v[h] such that that+ --+ -- for every index i < h we have p v[i] = False, and+ -- for every inedx i >= h we have p v[i] = True+ --+ -- returns Nothing if no element satisfies p+ --+ -- running time: \(O(T*\log n)\), where \(T\) is the time to execute the+ -- predicate.+ binarySearchIn :: (Elem v -> Bool) -> v -> Maybe (Elem v)++ -- | Given a monotonic predicate p and a data structure v, find the+ -- index h such that that+ --+ -- for every index i < h we have p v[i] = False, and+ -- for every inedx i >= h we have p v[i] = True+ --+ -- returns Nothing if no element satisfies p+ --+ -- running time: \(O(T*\log n)\), where \(T\) is the time to execute the+ -- predicate.+ binarySearchIdxIn :: (Elem v -> Bool) -> v -> Maybe (Index v)++--------------------------------------------------------------------------------+-- * Searching on a Sequence++instance BinarySearch (Seq a) where+ type Index (Seq a) = Int+ type Elem (Seq a) = a++ -- ^ runs in \(O(T*\log^2 n)\) time.+ binarySearchIn p s = Seq.index s <$> binarySearchIdxIn p s++ -- ^ runs in \(O(T*\log^2 n)\) time.+ binarySearchIdxIn p s = case Seq.viewr s of+ EmptyR -> Nothing+ (_ :> x) | p x -> Just $ case Seq.viewl s of+ (y :< _) | p y -> 0+ _ -> binarySearch p' 0 u+ | otherwise -> Nothing+ where+ p' = p . Seq.index s+ u = Seq.length s - 1++instance {-# OVERLAPPABLE #-} V.Vector v a => BinarySearch (v a) where+ type Index (v a) = Int+ type Elem (v a) = a++ binarySearchIdxIn p' v | V.null v = Nothing+ | not $ p n' = Nothing+ | otherwise = Just $ if p 0 then 0 else binarySearch p 0 n'+ where+ n' = V.length v - 1+ p = p' . (v V.!)++ binarySearchIn p v = (v V.!) <$> binarySearchIdxIn p v++instance BinarySearch (Set a) where+ type Index (Set a) = Int+ type Elem (Set a) = a++ binarySearchIn p = go+ where+ go = \case+ Set.Tip -> Nothing+ Set.Bin _ k l r | p k -> go l <|> Just k+ | otherwise -> go r++ binarySearchIdxIn p = go+ where+ go = \case+ Set.Tip -> Nothing+ Set.Bin _ k l r | p k -> go l <|> Just (Set.size l)+ | otherwise -> (+ (1 + Set.size l)) <$> go r
src/Algorithms/DivideAndConquer.hs view
@@ -1,3 +1,10 @@+--------------------------------------------------------------------------------+-- |+-- Module : Algorithms.DivideAndConquer+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Algorithms.DivideAndConquer( divideAndConquer , divideAndConquer1 , divideAndConquer1With@@ -7,59 +14,68 @@ , mergeSortedListsBy ) where +import qualified Data.Foldable as F import Data.List.NonEmpty (NonEmpty(..),(<|)) import qualified Data.List.NonEmpty as NonEmpty-+import Data.Semigroup.Foldable -- | Divide and conquer strategy ----- the running time is: O(n*L) + T(n) = 2T(n/2) + M(n)+-- the running time satifies T(n) = 2T(n/2) + M(n), ----- where M(n) is the time corresponding to the semigroup operation of s+-- where M(n) is the time corresponding to the semigroup operation of s on n elements. ---divideAndConquer1 :: Semigroup s => (a -> s) -> NonEmpty a -> s+--+divideAndConquer1 :: (Foldable1 f, Semigroup s) => (a -> s) -> f a -> s divideAndConquer1 = divideAndConquer1With (<>) ---- | Divide and conquer for-divideAndConquer :: Monoid s => (a -> s) -> [a] -> s-divideAndConquer g = maybe mempty (divideAndConquer1 g) . NonEmpty.nonEmpty+-- | Divide and conquer strategy. See 'divideAndConquer1'.+divideAndConquer :: (Foldable f, Monoid s) => (a -> s) -> f a -> s+divideAndConquer g = maybe mempty (divideAndConquer1 g) . NonEmpty.nonEmpty . F.toList +{- HLINT ignore divideAndConquer1With -} -- | Divide and conquer strategy ----- the running time is: O(n*L) + T(n) = 2T(n/2) + M(n)+-- the running time satifies T(n) = 2T(n/2) + M(n), ----- where M(n) is the time corresponding to the merge operation s+-- where M(n) is the time corresponding to the semigroup operation of s on n elements. ---divideAndConquer1With :: (s -> s -> s) -> (a -> s) -> NonEmpty a -> s-divideAndConquer1With (<.>) g = repeatedly merge . fmap g+divideAndConquer1With :: Foldable1 f => (s -> s -> s) -> (a -> s) -> f a -> s+divideAndConquer1With (<.>) g = repeatedly merge . fmap g . toNonEmpty where repeatedly _ (t :| []) = t repeatedly f ts = repeatedly f $ f ts merge ts@(_ :| []) = ts merge (l :| r : []) = l <.> r :| []- merge (l :| r : ts) = l <.> r <| (merge $ NonEmpty.fromList ts)+ merge (l :| r : ts) = l <.> r <| merge (NonEmpty.fromList ts) -------------------------------------------------------------------------------- -- * Merging NonEmpties/Sorted lists +-- | Merges two sorted non-Empty lists in linear time. mergeSorted :: Ord a => NonEmpty a -> NonEmpty a -> NonEmpty a mergeSorted = mergeSortedBy compare +-- | Merges two sorted lists in linear time. mergeSortedLists :: Ord a => [a] -> [a] -> [a] mergeSortedLists = mergeSortedListsBy compare -- | Given an ordering and two nonempty sequences ordered according to that--- ordering, merge them+-- ordering, merge them.+--+-- running time: \(O(n*T)\), where \(n\) is the length of the list,+-- and \(T\) the time required to compare two elements. mergeSortedBy :: (a -> a -> Ordering) -> NonEmpty a -> NonEmpty a -> NonEmpty a mergeSortedBy cmp ls rs = NonEmpty.fromList $ mergeSortedListsBy cmp (NonEmpty.toList ls) (NonEmpty.toList rs) - -- | Given an ordering and two nonempty sequences ordered according to that -- ordering, merge them+--+-- running time: \(O(n*T)\), where \(n\) is the length of the list,+-- and \(T\) the time required to compare two elements. mergeSortedListsBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a] mergeSortedListsBy cmp = go where
+ src/Algorithms/FloydWarshall.hs view
@@ -0,0 +1,56 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.Geometry.Polygon.Core+-- Copyright : (C) David Himmelstrup+-- License : see the LICENSE file+-- Maintainer : David Himmelstrup+--+-- Implementation of Floyd-Warshall shortest path algorithm.+--+-- See Wikipedia article for details: https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm+--+--------------------------------------------------------------------------------+module Algorithms.FloydWarshall+ ( mkIndex+ , mkGraph+ , floydWarshall+ ) where++import Control.Monad (forM_, when)+import Control.Monad.ST (ST)+import Data.Vector.Unboxed.Mutable as V (MVector, length, replicate, unsafeRead,+ unsafeWrite, Unbox)++-- | \( O(n^3) \)+floydWarshall :: (Unbox a, Fractional a, Ord a) => Int -> MVector s (a, Int) -> ST s ()+floydWarshall n graph = do+ let nSq = V.length graph+ when (n*n /= nSq) $ error "Bad bounds"+ forM_ [0 .. n-1] $ \k ->+ forM_ [0 .. n-1] $ \i ->+ forM_ [0 .. n-1] $ \j -> do+ (distIJ, _) <- access (i,j)+ (distIK, pathIK) <- access (i,k)+ (distKJ, _) <- access (k,j)+ let indirectDist = distIK + distKJ+ when (distIJ > indirectDist+indirectDist*eps && distIJ > distIK && distIJ > distKJ) $+ put (i,j) (indirectDist, pathIK)+ where+ access idx = V.unsafeRead graph (mkIndex n idx)+ put idx e = V.unsafeWrite graph (mkIndex n idx) e+ eps = 1e-10 -- When two paths are nearly the same length, pick the one with the fewest segments.++-- | Compute the index of an element in a given range.+mkIndex :: Num a => a -> (a, a) -> a+mkIndex n (i,j) = i*n+j++-- | Construct a weighted graph from \(n\) vertices, a max bound, and a list of weighted edges.+mkGraph :: (Unbox a, Num a) => Int -> a -> [(Int,Int,a)] -> ST s (MVector s (a, Int))+mkGraph n maxValue edges = do+ graph <- V.replicate (n*n) (maxValue, maxBound)+ forM_ [0..n-1] $ \v -> do+ unsafeWrite graph (mkIndex n (v,v)) (0, v)+ forM_ edges $ \(i,j,cost) -> do+ unsafeWrite graph (mkIndex n (i,j)) (cost, j)+ unsafeWrite graph (mkIndex n (j,i)) (cost, i)+ return graph
+ src/Algorithms/Graph/BFS.hs view
@@ -0,0 +1,66 @@+{-# LANGUAGE ScopedTypeVariables #-}+--------------------------------------------------------------------------------+-- |+-- Module : Algorithms.Graph.BFS+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Algorithms.Graph.BFS+ ( bfs+ , bfs'+ ) where++import Control.Monad.ST.Strict+import qualified Data.Foldable as F+import Data.Sequence (Seq(..))+import qualified Data.Sequence as Seq+import Data.Tree+import qualified Data.Vector as V+import qualified Data.Vector.Mutable as MV+import qualified Data.Vector.Unboxed.Mutable as UMV+import Witherable++--------------------------------------------------------------------------------++-- | Runs a BFS from the first vertex in the graph. The graph is given+-- in adjacency list representation.+--+-- running time: \(O(V + E)\)+bfs :: Foldable f => Int -> V.Vector (v, f Int) -> Tree v+bfs s gr = fmap (fst . (gr V.!)) . bfs' s . fmap snd $ gr++-- | Runs a BFS from the first vertex in the graph. The graph is given+-- in adjacency list representation.+--+-- running time: \(O(V + E)\)+bfs' :: Foldable f => Int -> V.Vector (f Int) -> Tree Int+bfs' s gr = extract s $ V.create+ $ do st <- UMV.replicate n False+ out <- MV.new n+ go0 st out (s :<| mempty)+ pure out+ where+ n = V.length gr+ go0 :: forall s. UMV.MVector s Bool -> MV.MVector s [Int]+ -> Seq Int -> ST s ()+ go0 st out = go+ where+ visit i = do b <- UMV.read st i+ UMV.write st i True -- mark i as visited+ pure $ if b then Nothing else Just i++ go :: Seq Int -> ST s ()+ go = \case+ Empty -> pure ()+ (u:<|queue) -> do ns <- wither visit . F.toList $ gr V.! u+ MV.write out u ns -- write that u's children are ns+ go (queue <> Seq.fromList ns)+++-- | Give na root index and a vector s.t. v[i] lists the children of+-- node i, builds the acutal tree.+extract :: Int -> V.Vector [Int] -> Tree Int+extract s v = go s+ where+ go i = Node i (map go $ v V.! i)
src/Algorithms/Graph/DFS.hs view
@@ -1,14 +1,21 @@ {-# LANGUAGE ScopedTypeVariables #-}+--------------------------------------------------------------------------------+-- |+-- Module : Algorithms.Graph.DFS+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Algorithms.Graph.DFS where -import Control.Monad.ST (ST,runST)+import Control.Monad.ST (ST, runST) import Data.Maybe import Data.PlanarGraph import Data.Tree-import qualified Data.Vector as V-import qualified Data.Vector.Generic as GV+import qualified Data.Vector as V+import qualified Data.Vector.Generic as GV import qualified Data.Vector.Unboxed.Mutable as UMV-+import qualified Data.IntSet as IntSet -- | DFS on a planar graph. --@@ -51,3 +58,20 @@ False -> do visit bv u Just . Node u . catMaybes <$> mapM (dfs'' bv) (neighs u)++-- | DFS, from a given vertex, on a graph in AdjacencyLists representation. Cycles are not removed.+-- If your graph may contain cycles, see 'dfsFilterCycles'.+--+-- Running time: \(O(k)\), where \(k\) is the number of nodes consumed.+dfsSensitive :: forall s w. (VertexId s w -> [VertexId s w]) -> VertexId s w -> Tree (VertexId s w)+dfsSensitive neighs u = Node u $ map (dfsSensitive neighs) (neighs u)++-- | Remove infinite cycles from a DFS search tree.+dfsFilterCycles :: Tree (VertexId s w) -> Tree (VertexId s w)+dfsFilterCycles = worker IntSet.empty+ where+ worker seen (Node root forest) = Node root+ [ Node (VertexId v) (map (worker (IntSet.insert v seen)) sub)+ | Node (VertexId v) sub <- forest+ , v `IntSet.notMember` seen+ ]
src/Algorithms/Graph/MST.hs view
@@ -1,4 +1,11 @@ {-# LANGUAGE ScopedTypeVariables #-}+--------------------------------------------------------------------------------+-- |+-- Module : Algorithms.Graph.MST+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Algorithms.Graph.MST( mst , mstEdges , makeTree
+ src/Algorithms/LogarithmicMethod.hs view
@@ -0,0 +1,151 @@+{-# LANGUAGE DefaultSignatures #-}+--------------------------------------------------------------------------------+-- |+-- Module : Algorithms.LogarithmicMethod+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Algorithms.LogarithmicMethod+ ( InsertionOnly(..)+ , empty+ , LogarithmicMethodDS(..)+ , insert+ , queryWith+ )+ where++import Data.List.NonEmpty (NonEmpty(..))+import Data.Maybe (mapMaybe)+import Data.Semigroup.Foldable++--------------------------------------------------------------------------------++-- | Represents an insertion-only data structure built from static+-- data structures.+--+-- In particular, we maintain \(O(\log n)\) static data structures of+-- sizes \(2^i\), for \(i \in [0..c\log n]\).+newtype InsertionOnly static a = InsertionOnly [Maybe (static a)]+ deriving (Show,Eq,Ord)++-- | Builds an empty structure+empty :: InsertionOnly static a+empty = InsertionOnly []++instance Functor static => Functor (InsertionOnly static) where+ fmap f (InsertionOnly dss) = InsertionOnly $ map (fmap (fmap f)) dss++instance Traversable static => Traversable (InsertionOnly static) where+ traverse f (InsertionOnly dss) = InsertionOnly <$> traverse (traverse (traverse f)) dss++instance Foldable static => Foldable (InsertionOnly static) where+ foldMap f = queryWith (foldMap f)+ length = sum . mapMaybe (uncurry (<$)) . withSizes++instance LogarithmicMethodDS static a => Semigroup (InsertionOnly static a) where+ (InsertionOnly ds1) <> (InsertionOnly ds2) = InsertionOnly $ runMergeWith Nothing ds1 0 ds2 0++instance LogarithmicMethodDS static a => Monoid (InsertionOnly static a) where+ mempty = empty+++class LogarithmicMethodDS static a where+ {-# MINIMAL build #-}+ -- | Create a new static data structure storing only one value.+ singleton :: a -> static a+ singleton = build . (:| [])++ -- | Given a NonEmpty list of a's build a static a.+ build :: NonEmpty a -> static a++ -- | Merges two structurs of the same size. Has a default+ -- implementation via build in case the static structure is Foldable1.+ merge :: static a -> static a -> static a+ default merge :: Foldable1 static => static a -> static a -> static a+ merge as bs = build $ toNonEmpty as <> toNonEmpty bs+++type Power = Word++-- | 2^h, for whatever value h.+pow2 :: Integral i => Power -> i+pow2 h = 2 ^ h++-- | Annotate the data structures with their sizes+withSizes :: Integral i => InsertionOnly static a -> [(i,Maybe (static a))]+withSizes (InsertionOnly dss) = zipWith (\i ds -> (pow2 i,ds)) [0..] dss++-- | Inserts an element into the data structure+--+-- running time: \(O(M(n)\log n / n)\), where \(M(n)\) is the time+-- required to merge two data structures of size \(n\).+insert :: LogarithmicMethodDS static a+ => a -> InsertionOnly static a -> InsertionOnly static a+insert x (InsertionOnly dss) = InsertionOnly $ runMerge (singleton x) 0 0 dss++-- | Runs the merging procedure. If there are two data structures of+-- the same size they are merged.+runMerge :: LogarithmicMethodDS static a+ => static a -- ^ ds1+ -> Power -- ^ ds1 has size 2^i+ -> Power -- ^ the first entry in the next list corresponds to size 2^j+ -> [Maybe (static a)] -> [Maybe (static a)]+runMerge ds1 i j = \case+ [] -> [Just ds1]+ dss@(Nothing : dss') | i == j -> Just ds1 : dss' -- replace+ | otherwise -> Just ds1 : dss -- cons+ dss@(Just ds2 : dss') | i == j -> Nothing : runMerge (ds1 `merge` ds2) (i+1) (j+1) dss'+ | otherwise -> Just ds1 : dss -- cons -- I don't think insert can ever+ -- trigger this scenario.++-- | merges two structures (potentially with a carry)+--+-- invariant: size carry == size ds1 <= size ds2+runMergeWith :: LogarithmicMethodDS static a+ => Maybe (static a) -- ^ carry, if it exists+ -> [Maybe (static a)] -> Power+ -- ^ size of the first ds+ -> [Maybe (static a)] -> Power+ -- ^ size of the second ds+ -> [Maybe (static a)]+runMergeWith mc ds1 i ds2 j = case (ds1,ds2) of+ ([],_) -> case mc of+ Nothing -> ds2+ Just c -> runMerge c i j ds2+ (_,[]) -> case mc of+ Nothing -> ds1+ Just c -> runMerge c i i ds1+ (m1:ds1',m2:ds2') -> case (m1,m2) of+ (Nothing,Nothing) -> mc : runMergeWith Nothing ds1' (i+1) ds2' (j+1)+ (Nothing,Just d2) -> case mc of+ Nothing | i == j -> m2 : runMergeWith Nothing ds1' (i+1) ds2' (j+1)+ | otherwise -> m1 : runMergeWith Nothing ds1' (i+1) ds2 j+ Just c | i == j -> Nothing : runMergeWith (Just $ c `merge` d2) ds1' (i+1) ds2' (j+1)+ | otherwise -> mc : runMergeWith Nothing ds1' (i+1) ds2 j+ -- i < j, so invariant (i+1) <= j again holds holds++ (Just d1,Nothing) -> case mc of+ Nothing -> m1 : runMergeWith Nothing ds1' (i+1) ds2' (j+1)+ Just c -> Nothing : runMergeWith (Just $ c `merge` d1) ds1' (i+1) ds2' (j+1)++ (Just d1,Just d2) -> case mc of+ Nothing | i == j -> Nothing : runMergeWith (Just $ d1 `merge` d2) ds1' (i+1) ds2' (j+1)+ | otherwise -> m1 : runMergeWith Nothing ds1' (i+1) ds2 j++ Just c | i == j -> mc : runMergeWith (Just $ d1 `merge` d2) ds1' (i+1) ds2' (j+1)+ | otherwise -> Nothing : runMergeWith (Just $ c `merge` d1) ds1' (i+1) ds2 j+ -- i < j, so invariant holds++-- | Given a decomposable query algorithm for the static structure,+-- lift it to a query algorithm on the insertion only structure.+--+-- pre: (As indicated by the Monoid constraint), the query answer+-- should be decomposable. I.e. we should be able to anser the query+-- on a set \(A \cup B\) by answering the query on \(A\) and \(B\)+-- separately, and combining their results.+--+-- running time: \(O(Q(n)\log n)\), where \(Q(n)\) is the query time+-- on the static structure.+queryWith :: Monoid m => (static a -> m) -> InsertionOnly static a -> m+queryWith query (InsertionOnly dss) = foldMap (foldMap query) dss
+ src/Control/CanAquire.hs view
@@ -0,0 +1,87 @@+{-# LANGUAGE FunctionalDependencies #-}+--------------------------------------------------------------------------------+-- |+-- Module : Control.CanAquire+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Control.CanAquire(+ runAcquire+ , CanAquire(..)+ , HasIndex(..)++ , replaceByIndex, labelWithIndex+ , I+ ) where++import Control.Monad.ST.Strict+import Control.Monad.State.Strict+import Data.Reflection+import qualified Data.Vector as V+import qualified Data.Vector.Mutable as MV+import Unsafe.Coerce(unsafeCoerce)++--------------------------------------------------------------------------------++-- | Run a computation on something that can aquire i's.+runAcquire :: forall t a b. Traversable t+ => (forall s. CanAquire (I s a) a => t (I s a) -> b)+ -> t a -> b+runAcquire alg pts = reify v $ \px -> alg (coerceTS px ts)+ where+ (v,ts) = replaceByIndex pts++ coerceTS :: proxy s -> t Int -> t (I s a)+ coerceTS _ = unsafeCoerce -- fmap I+ -- Ideally this would just be a coerce. But GHC doesn't want to do that.++class HasIndex i Int => CanAquire i a where+ -- | A value of type i can obtain something of type @\'a\'@+ aquire :: i -> a++class HasIndex t i | t -> i where+ -- | Types that have an instance of this class can act as indices.+ indexOf :: t -> i++--------------------------------------------------------------------------------++-- | Replaces every element by an index. Returns the new traversable+-- containing only these indices, as well as a vector with the+-- values. (such that indexing in this value gives the original+-- value).+replaceByIndex :: forall t a. Traversable t => t a -> (V.Vector a, t Int)+replaceByIndex ts' = runST $ do+ v <- MV.new n+ t <- traverse (lbl v) ts+ (,t) <$> V.unsafeFreeze v+ where+ (ts, n) = labelWithIndex ts'++ lbl :: MV.MVector s' a -> (Int,a) -> ST s' Int+ lbl v (i,x) = MV.write v i x >> pure i++-- | Label each element with its index. Returns the new collection as+-- well as its size.+labelWithIndex :: Traversable t => t a -> (t (Int, a), Int)+labelWithIndex = flip runState 0 . traverse lbl+ where+ lbl :: a -> State Int (Int,a)+ lbl x = do i <- get+ put $ i+1+ pure (i,x)+++--------------------------------------------------------------------------------++-- | A type that can act as an Index.+newtype I (s :: *) a = I Int deriving (Eq, Ord, Enum)++instance Show (I s a) where+ showsPrec i (I j) = showsPrec i j++instance HasIndex (I s a) Int where+ indexOf (I i) = i++instance Reifies s (V.Vector a) => I s a `CanAquire` a where+ aquire (I i) = let v = reflect @s undefined in v V.! i
src/Control/Monad/State/Persistent.hs view
@@ -1,3 +1,10 @@+--------------------------------------------------------------------------------+-- |+-- Module : Control.Monad.State.Persistent+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Control.Monad.State.Persistent( PersistentStateT , PersistentState , store@@ -32,7 +39,7 @@ put (s' :| os) return x --- | run a persistentStateT, returns a triplet with the value, the last state+-- | Run a persistentStateT, returns a triplet with the value, the last state -- and a list of all states (including the last one) in chronological order runPersistentStateT :: Functor m => PersistentStateT s m a -> s -> m (a,s,[s]) runPersistentStateT (PersistentStateT act) initS = f <$> runStateT act (initS :| [])@@ -42,7 +49,10 @@ -------------------------------------------------------------------------------- +-- | A State monad that can store earlier versions of the state. type PersistentState s = PersistentStateT s Identity +-- | Run a persistentStateT, returns a triplet with the value, the last state+-- and a list of all states (including the last one) in chronological order runPersistentState :: PersistentState s a -> s -> (a,s,[s]) runPersistentState act = runIdentity . runPersistentStateT act
− src/Data/BalBST.hs
@@ -1,378 +0,0 @@-{-# LANGUAGE RecordWildCards #-}-module Data.BalBST where--import Control.Applicative((<|>))-import Data.Bifunctor-import Data.Function (on)-import Data.Functor.Contravariant-import qualified Data.List as L-import Data.Maybe-import qualified Data.Tree as T-import Prelude hiding (lookup,null)-------------------------------------------------------------------------------------- | Describes how to search in a tree-data TreeNavigator k a = Nav { goLeft :: a -> k -> Bool- , extractKey :: a -> a -> k- }--instance Contravariant (TreeNavigator k) where- contramap f (Nav gL eK) = Nav (\a k -> gL (f a) k) (\x y -> eK (f x) (f y))---ordNav :: Ord a => TreeNavigator a a-ordNav = Nav (<=) min---ordNavBy :: Ord b => (a -> b) -> TreeNavigator b a-ordNavBy f = Nav (\x k -> f x <= k) (min `on` f)----- instance Functor (TreeNavigator k) where--- fmap f Nav{..} = Nav (\b k -> )------ | A balanced binary search tree-data BalBST k a = BalBST { nav :: !(TreeNavigator k a)- , toTree :: !(Tree k a)- }--instance (Show k, Show a) => Show (BalBST k a) where- show (BalBST _ t) = "BalBST (" ++ show t ++ ")"---data Color = Red | Black deriving (Show,Read,Eq,Ord)--type Height = Int---- Red-Black tree with values in the leaves-data Tree k a = Empty- | Leaf !a- | Node !Color !Height (Tree k a) !k (Tree k a) deriving (Show,Eq)-------------------------------------------------------------------------------------- | Creates an empty BST-empty :: TreeNavigator k a -> BalBST k a-empty n = BalBST n Empty----- | \(O(n\log n)\)-fromList :: TreeNavigator k a -> [a] -> BalBST k a-fromList n = foldr insert (empty n)--fromList' :: Ord a => [a] -> BalBST a a-fromList' = fromList ordNav----- -- | \(O(n)\)--- fromAscList :: TreeNavigator k a -> [a] -> BalBST k a--- fromAscList = undefined--------------------------------------------------------------------------------------- | Check if the tree is empty-null :: BalBST k a -> Bool-null (BalBST _ Empty) = True-null _ = False---- | Test if an element occurs in the BST.--- \(O(\log n)\)-lookup :: Eq a => a -> BalBST k a -> Maybe a-lookup x (BalBST Nav{..} t) = lookup' t- where- lookup' Empty = Nothing- lookup' (Leaf y) = if x == y then Just y else Nothing- lookup' (Node _ _ l k r)- | goLeft x k = lookup' l- | otherwise = lookup' r---- | \(O(\log n)\)-member :: Eq a => a -> BalBST k a -> Bool-member x = isJust . lookup x---- | Search for the Predecessor--- \(O(\log n)\)-lookupLE :: Ord k => k -> BalBST k a -> Maybe a-lookupLE kx (BalBST n@Nav{..} t) = lookup' t- where- lookup' Empty = Nothing- lookup' (Leaf y) = if goLeft y kx then Just y else Nothing- lookup' (Node _ _ l k r)- | kx <= k = lookup' l- | otherwise = lookup' r <|> lookupMax (BalBST n l)----- | Insert an element in the BST.------ \(O(\log n)\)-insert :: a -> BalBST k a -> BalBST k a-insert x (BalBST n@Nav{..} t) = BalBST n (blacken $ insert' t)- where- insert' Empty = Leaf x- insert' (Leaf y) = let k = extractKey x y- (l,r) = if goLeft x k then (x,y) else (y,x)- in red 2 (Leaf l) k (Leaf r)- insert' (Node c h l k r)- | goLeft x k = balance c h (insert' l) k r- | otherwise = balance c h l k (insert' r)------ delete = undefined---- | Delete (one occurance of) an element.--- \(O(\log n)\)-delete :: Eq a => a -> BalBST k a -> BalBST k a-delete x t = let Split l _ r = split x t- n = nav t- in BalBST n $ joinWith n l r----- (BalBST n@Nav{..} t) = delete' t--- where--- delete' Empty = Empty--- delete' l@(Leaf y) = if x == y then Empty else l--- delete' (Node c h l k r)--- | goLeft x k =---------------------------------------------------------------------------------------- | Extract the minimum from the tree--- \(O(\log n)\)-minView :: BalBST k a -> Maybe (a, Tree k a)-minView (BalBST n t) = minView' t- where- minView' Empty = Nothing- minView' (Leaf x) = Just (x,Empty)- minView' (Node _ _ l _ r) = fmap (flip (joinWith n) r) <$> minView' l--lookupMin :: BalBST k b -> Maybe b-lookupMin = fmap fst . maxView---- | Extract the maximum from the tree--- \(O(\log n)\)-maxView :: BalBST k a -> Maybe (a, Tree k a)-maxView (BalBST n t) = maxView' t- where- maxView' Empty = Nothing- maxView' (Leaf x) = Just (x,Empty)- maxView' (Node _ _ l _ r) = fmap (joinWith n l) <$> maxView' r--lookupMax :: BalBST k b -> Maybe b-lookupMax = fmap fst . maxView----- | Joins two BSTs. Assumes that the ranges are disjoint. It takes the left Tree nav------ \(O(\log n)\)-join :: BalBST k a -> BalBST k a -> BalBST k a-join (BalBST n l) (BalBST _ r) = BalBST n $ joinWith n l r---- | Joins two BSTs' with a specific Tree Navigator------ \(O(\log n)\)-joinWith :: TreeNavigator k a -> Tree k a -> Tree k a -> Tree k a-joinWith Nav{..} tl tr- | lh >= rh = blacken $ joinL tl tr- | otherwise = blacken $ joinR tl tr- where- rh = height tr- lh = height tl-- joinL Empty _ = Empty- joinL l Empty = l- joinL l@(Leaf x) r@(Leaf y) = red 2 l (extractKey x y) r- joinL l@(Node c h ll k lr) r- | h == rh = let lm = unsafeMax lr- rm = unsafeMin r- in balance Red (h+1) l (extractKey lm rm) r- | otherwise = balance c h ll k (joinL lr r)- -- lh >= rh- joinL _ _ = error "joinL. absurd"--- joinR _ Empty = Empty- joinR Empty r = r-- joinR l@(Leaf x) r@(Leaf y) = red 2 l (extractKey x y) r- joinR l r@(Node c h rl k rr)- | h == lh = let lm = unsafeMax l- rm = unsafeMin rl- in balance Red (h+1) l (extractKey lm rm) r- | otherwise = balance c h (joinR l rl) k rr- -- lh >= rh- joinR _ _ = error "joinR absurd"-------------------------------------------------------------------------------------- | Splitting and extracting---- | A pair that is strict in its first argument and lazy in the second.-data Pair a b = Pair { fst' :: !a- , snd' :: b- } deriving (Show,Eq,Functor,Foldable,Traversable)---collect :: b -> [Pair a b] -> Pair [a] b-collect def [] = Pair [] def-collect _ xs = Pair (map fst' xs) (snd' $ last xs)----- | Extract a prefix from the tree, i.e. a repeated 'minView'------ \(O(\log n +k)\), where \(k\) is the size of the extracted part-extractPrefix :: BalBST k a -> [Pair a (Tree k a)]-extractPrefix (BalBST n@Nav{..} t) = extractPrefix' t- where- extractPrefix' Empty = []- extractPrefix' (Leaf x) = [Pair x Empty]- extractPrefix' (Node _ _ l _ r) = ls ++ extractPrefix' r- where- ls = map (fmap $ flip (joinWith n) r) $ extractPrefix' l---- | Extract a suffix from the tree, i.e. a repeated 'minView'------ \(O(\log n +k)\), where \(k\) is the size of the extracted part-extractSuffix :: BalBST k a -> [Pair a (Tree k a)]-extractSuffix (BalBST n@Nav{..} t) = extract t- where- extract Empty = []- extract (Leaf x) = [Pair x Empty]- extract (Node _ _ l _ r) = rs ++ extract l- where- rs = map (fmap $ joinWith n l) $ extract r---- | Result of splititng a tree-data Split a b = Split a !b a deriving (Show,Eq)---- | Splits the tree at x. Note that if x occurs more often, no guarantees are--- given which one is found.------ \(O(\log n)\)-split :: Eq a => a -> BalBST k a -> Split (Tree k a) (Maybe a)-split x (BalBST n@Nav{..} t) = split' t- where- split' Empty = Split Empty Nothing Empty- split' l@(Leaf y)- | x == y = Split Empty (Just y) Empty- | goLeft x (extractKey x y) = Split l Nothing Empty- | otherwise = Split Empty Nothing l- split' (Node _ _ l k r)- | goLeft x k = let Split l' mx r' = split' l- in Split l' mx (joinWith n r' r)- | otherwise = let Split l' mx r' = split' r- in Split (joinWith n l l') mx r'---- | split based on a monotonic predicate------ \(O(\log n)\)-splitMonotone :: (a -> Bool) -> BalBST k a- -> (BalBST k a, BalBST k a)-splitMonotone p (BalBST n@Nav{..} t) = bimap (BalBST n) (BalBST n) $ split' t- where- split' Empty = (Empty,Empty)- split' l@(Leaf y)- | p y = (Empty,l)- | otherwise = (l,Empty)- split' (Node _ _ l _ r)- | p (unsafeMin r) = let (l',m) = split' l in (l',joinWith n m r)- | otherwise = let (m,r') = split' r in (joinWith n l m, r')----- | Splits at a given monotone predicate p, and then selects everything that--- satisfies the predicate sel.-splitExtract :: (a -> Bool) -> (a -> Bool) -> BalBST k a- -> Split (BalBST k a) ([a],[a])-splitExtract p sel bst = Split (BalBST n before) (reverse mid1,mid2) (BalBST n after)- where- n = nav bst- (before',after') = splitMonotone p bst-- extract def = collect def . L.takeWhile (sel . fst')-- Pair mid1 before = extract (toTree before') $ extractSuffix before'- Pair mid2 after = extract (toTree after') $ extractPrefix after'--------------------------------------------------------------------------------------data T k a = Internal !Color !Height !k | Val !a deriving (Show,Eq,Ord)--toRoseTree :: Tree k a -> Maybe (T.Tree (T k a))-toRoseTree Empty = Nothing-toRoseTree (Leaf x) = Just $ T.Node (Val x) []-toRoseTree (Node c h l k r) = Just $ T.Node (Internal c h k) (mapMaybe toRoseTree [l,r])---showTree :: (Show k, Show a) => BalBST k a -> String-showTree = maybe "Empty" T.drawTree . fmap (fmap show) . toRoseTree . toTree---- | Get the minimum in the tree. Errors when the tree is empty------ \(O(\log n)\)-unsafeMin :: Tree k a -> a-unsafeMin (Leaf x) = x-unsafeMin (Node _ _ l _ _) = unsafeMin l-unsafeMin _ = error "unsafeMin: Empty"---- | Get the maximum in the tree. Errors when the tree is empty------ \(O(\log n)\)-unsafeMax :: Tree k a -> a-unsafeMax (Leaf x) = x-unsafeMax (Node _ _ _ _ r) = unsafeMax r-unsafeMax _ = error "unsafeMax: Empty"---- | Extract all elements in the tree------ \(O(n)\)-toList :: BalBST k a -> [a]-toList = toList' . toTree---- | Extract all elements in the tree------ \(O(n)\)-toList' :: Tree k a -> [a]-toList' Empty = []-toList' (Leaf x) = [x]-toList' (Node _ _ l _ r) = toList' l ++ toList' r-------------------------------------------------------------------------------------- * Helper stuff--black :: Height -> Tree k a -> k -> Tree k a -> Tree k a-black = Node Black--red :: Height -> Tree k a -> k -> Tree k a -> Tree k a-red = Node Red---blacken :: Tree k a -> Tree k a-blacken (Node Red h l k r) = Node Black h l k r-blacken t = t---- | rebalance the tree-balance :: Color -> Height -> Tree k a -> k -> Tree k a -> Tree k a-balance Black h (Node Red _ (Node Red _ a x b) y c) z d = mkNode h a x b y c z d-balance Black h (Node Red _ a x (Node Red _ b y c)) z d = mkNode h a x b y c z d-balance Black h a x (Node Red _ (Node Red _ b y c) z d) = mkNode h a x b y c z d-balance Black h a x (Node Red _ b y (Node Red _ c z d)) = mkNode h a x b y c z d-balance co h a x b = Node co h a x b--mkNode :: Height- -> Tree k a -> k -> Tree k a -> k -> Tree k a -> k -> Tree k a- -> Tree k a-mkNode h a x b y c z d = red h (black h a x b) y (black h c z d)--height :: Tree k a -> Height-height Empty = 0-height (Leaf _) = 1-height (Node _ h _ _ _) = h
src/Data/BinaryTree.hs view
@@ -1,5 +1,4 @@ {-# Language DeriveFunctor#-}-{-# Language FunctionalDependencies #-} -------------------------------------------------------------------------------- -- | -- Module : Data.BinaryTree@@ -17,12 +16,14 @@ import Data.Bifunctor.Apply import Data.List.NonEmpty (NonEmpty) import Data.Maybe (mapMaybe)+import Data.Measured.Class+import Data.Measured.Size import Data.Semigroup.Foldable import qualified Data.Tree as Tree+import Data.Tree.Util (TreeNode(..)) import qualified Data.Vector as V import GHC.Generics (Generic) import Test.QuickCheck- -------------------------------------------------------------------------------- -- | Binary tree that stores its values (of type a) in the leaves. Internal@@ -33,9 +34,6 @@ instance (NFData v, NFData a) => NFData (BinLeafTree v a) -class Semigroup v => Measured v a | a -> v where- measure :: a -> v- -- | smart constructor node :: Measured v a => BinLeafTree v a -> BinLeafTree v a -> BinLeafTree v a node l r = Node l (measure l <> measure r) r@@ -116,50 +114,19 @@ zipExactWith _ _ _ _ = error "zipExactWith: tree structures not the same " -newtype Size = Size Int deriving (Show,Read,Eq,Num,Integral,Enum,Real,Ord,Generic,NFData) -instance Semigroup Size where- x <> y = x + y -instance Monoid Size where- mempty = Size 0- mappend = (<>)--newtype Elem a = Elem { _unElem :: a }- deriving (Show,Read,Eq,Ord,Functor,Foldable,Traversable)--instance Measured Size (Elem a) where- measure _ = 1---data Sized a = Sized !Size a- deriving (Show,Eq,Ord,Functor,Foldable,Traversable,Generic)-instance NFData a => NFData (Sized a)--instance Semigroup a => Semigroup (Sized a) where- (Sized i a) <> (Sized j b) = Sized (i <> j) (a <> b)--instance Monoid a => Monoid (Sized a) where- mempty = Sized mempty mempty- (Sized i a) `mappend` (Sized j b) = Sized (i <> j) (a `mappend` b)---- instance Semigroup a => Measured Size (Sized a) where--- measure (Sized i _) = i-- -------------------------------------------------------------------------------- -- * Converting into a Data.Tree -data RoseElem v a = InternalNode v | LeafNode a deriving (Show,Eq,Functor)--toRoseTree :: BinLeafTree v a -> Tree.Tree (RoseElem v a)+-- | \( O(n) \) Convert binary tree to a rose tree, aka 'Tree.Tree'.+toRoseTree :: BinLeafTree v a -> Tree.Tree (TreeNode v a) toRoseTree (Leaf x) = Tree.Node (LeafNode x) [] toRoseTree (Node l v r) = Tree.Node (InternalNode v) (map toRoseTree [l,r]) -+-- | 2-dimensional ASCII drawing of a tree. drawTree :: (Show v, Show a) => BinLeafTree v a -> String drawTree = Tree.drawTree . fmap show . toRoseTree- -------------------------------------------------------------------------------- -- * Internal Node Tree
− src/Data/BinaryTree/Zipper.hs
@@ -1,64 +0,0 @@-module Data.BinaryTree.Zipper where--import Data.BinaryTree------------------------------------------------------------------------------------data Ctx a = Top | L (Ctx a) a (BinaryTree a) | R (BinaryTree a) a (Ctx a)- deriving (Show,Read,Eq,Ord,Functor,Foldable,Traversable)--data BinaryTreeZipper a = Loc (BinaryTree a) (Ctx a)- deriving (Show,Read,Eq,Ord,Functor,Foldable,Traversable)---- | Focus on the root-top :: BinaryTree a -> BinaryTreeZipper a-top t = Loc t Top---- | Go to the left child-left :: BinaryTreeZipper a -> Maybe (BinaryTreeZipper a)-left (Loc (Internal l x r) ctx) = Just $ Loc l (L ctx x r)-left (Loc Nil _) = Nothing---- | Go to the right child-right :: BinaryTreeZipper a -> Maybe (BinaryTreeZipper a)-right (Loc (Internal l x r) ctx) = Just $ Loc r (R l x ctx)-right (Loc Nil _) = Nothing---- | Move to the parent-up :: BinaryTreeZipper a -> Maybe (BinaryTreeZipper a)-up (Loc _ Top) = Nothing-up (Loc l (L ctx x r)) = Just $ Loc (Internal l x r) ctx-up (Loc r (R l x ctx)) = Just $ Loc (Internal l x r) ctx---- | Navigate to the root-toRoot :: BinaryTreeZipper a -> BinaryTreeZipper a-toRoot z = toRoot' z (Just z)- where- toRoot' z' Nothing = z'- toRoot' _ (Just z') = toRoot' z' (up z')----- | Returns a list of zippers; one focussed on each node in the tree-visitAll :: BinaryTree a -> [BinaryTreeZipper a]-visitAll t = visitAll' (top t)- where- f = maybe [] visitAll'- visitAll' z = z : f (left z) <> f (right z)---- | Get the value stored at the current node-accessZ :: BinaryTreeZipper a -> Maybe a-accessZ (Loc t _) = access t----- | Returns all subtrees; i.e. every node with all its decendents-subTrees :: BinaryTree a -> [BinaryTree a]-subTrees t = Nil : subTrees' t- where- subTrees' Nil = []- subTrees' tt@(Internal l _ r) = tt : subTrees' l <> subTrees' r----- | Splits the tree here, returns a pair (innerTree,outerTree)-splitTree :: BinaryTreeZipper a -> (BinaryTree a, BinaryTree a)-splitTree (Loc t ctx) = let (Loc r _) = toRoot $ Loc Nil ctx- in (t, r)
src/Data/CircularList/Util.hs view
@@ -1,3 +1,10 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.CircularList.Util+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Data.CircularList.Util where import Control.Lens@@ -43,14 +50,14 @@ insertOrdBy' :: (a -> a -> Ordering) -> a -> [a] -> [a] insertOrdBy' cmp x xs = case (rest, x `cmp` head rest) of ([], _) -> L.insertBy cmp x pref- (z:zs, GT) -> (z : L.insertBy cmp x zs) ++ pref- (_:_, EQ) -> (x : xs) -- == x : rest ++ pref+ (z:zs, GT) -> z : L.insertBy cmp x zs ++ pref+ (_:_, EQ) -> x : xs -- == x : rest ++ pref (_:_, LT) -> rest ++ L.insertBy cmp x pref where -- split the list at its maximum. (pref,rest) = splitIncr cmp xs --- given a list of elements that is supposedly a a cyclic-shift of a list of+-- | Given a list of elements that is supposedly a a cyclic-shift of a list of -- increasing items, find the splitting point. I.e. returns a pair of lists -- (ys,zs) such that xs = zs ++ ys, and ys ++ zs is (supposedly) in sorted -- order.
src/Data/CircularSeq.hs view
@@ -1,3 +1,10 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.CircularSeq+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Data.CircularSeq( CSeq , cseq , singleton@@ -15,6 +22,7 @@ , rightElements , leftElements , asSeq+ , withIndices , reverseDirection , allRotations@@ -32,18 +40,20 @@ import Algorithms.StringSearch.KMP (isSubStringOf) import Control.DeepSeq-import Control.Lens (lens, Lens', bimap)+import Control.Lens (Lens', bimap, lens)+import Data.Ext import qualified Data.Foldable as F import qualified Data.List as L import qualified Data.List.NonEmpty as NonEmpty-import Data.Maybe (listToMaybe, isJust)+import Data.Maybe (isJust) import Data.Semigroup.Foldable-import Data.Sequence ((|>),(<|),ViewL(..),ViewR(..),Seq)+import Data.Sequence (Seq, ViewL (..), ViewR (..), (<|),+ (|>)) import qualified Data.Sequence as S import qualified Data.Traversable as T import Data.Tuple (swap) import GHC.Generics (Generic)-import Test.QuickCheck(Arbitrary(..))+import Test.QuickCheck (Arbitrary (..)) import Test.QuickCheck.Instances () --------------------------------------------------------------------------------@@ -67,6 +77,11 @@ showString (("CSeq " <>) . show . F.toList . rightElements $ s) where app_prec = 10 +instance Read a => Read (CSeq a) where+ readsPrec d = readParen (d > app_prec) $ \r ->+ [ (fromList lst, t) | ("CSeq", s) <- lex r, (lst, t) <- reads s ]+ where app_prec = 10+ -- traverses starting at the focus, going to the right. instance T.Traversable CSeq where traverse f (CSeq l x r) = (\x' r' l' -> CSeq l' x' r')@@ -87,15 +102,18 @@ instance Arbitrary a => Arbitrary (CSeq a) where arbitrary = CSeq <$> arbitrary <*> arbitrary <*> arbitrary +-- | /O(1)/ CSeq with exactly one element. singleton :: a -> CSeq a singleton x = CSeq S.empty x S.empty --- | Gets the focus of the CSeq+-- | Gets the focus of the CSeq.+-- -- running time: O(1) focus :: CSeq a -> a focus (CSeq _ x _) = x --- | Access the i^th item (w.r.t the focus) in the CSeq (indices modulo n).+-- | Access the i^th item (w.r.t the focus; elements numbered in+-- increasing order towards the right) in the CSeq (indices modulo n). -- -- running time: \(O(\log (i \mod n))\) --@@ -120,6 +138,15 @@ else if i - 1 < rn then S.index r (i - 1) else S.index l (i - rn - 1) +-- | Label the elements with indices.+--+-- >>> withIndices $ fromList [0..5]+-- CSeq [0 :+ 0,1 :+ 1,2 :+ 2,3 :+ 3,4 :+ 4,5 :+ 5]+withIndices :: CSeq a -> CSeq (Int :+ a)+withIndices (CSeq l x r) = let s = 1 + length r in+ CSeq (S.mapWithIndex (\i y -> i + s :+ y) l) (0 :+ x) (S.mapWithIndex (\i y -> i+1 :+ y) r)++ -- | Adjusts the i^th element w.r.t the focus in the CSeq -- -- running time: \(O(\log (i \mod n))\)@@ -135,9 +162,9 @@ else CSeq (S.adjust f (i - rn - 1) l) x r --- | Access te ith item in the CSeq (w.r.t the focus) as a lens+-- | Access the ith item in the CSeq (w.r.t the focus) as a lens item :: Int -> Lens' (CSeq a) a-item i = lens (flip index i) (\s x -> adjust (const x) i s)+item i = lens (`index` i) (\s x -> adjust (const x) i s) resplit :: Seq a -> (Seq a, Seq a)@@ -194,8 +221,8 @@ rotateL :: CSeq a -> CSeq a rotateL s@(CSeq l x r) = case S.viewr l of EmptyR -> case S.viewr r of- EmptyR -> s- (r' :> y) -> cseq r' y (S.singleton x)+ EmptyR -> s+ (r' :> y) -> cseq r' y (S.singleton x) (l' :> y) -> cseq l' y (x <| r) @@ -223,6 +250,11 @@ fromNonEmpty :: NonEmpty.NonEmpty a -> CSeq a fromNonEmpty (x NonEmpty.:| xs) = withFocus x $ S.fromList xs +{- HLINT ignore fromList -}+-- | /O(n)/ Convert from a list to a CSeq.+--+-- Warning: the onus is on the user to ensure that their list+-- is not empty, otherwise all bets are off! fromList :: [a] -> CSeq a fromList (x:xs) = withFocus x $ S.fromList xs fromList [] = error "fromList: Empty list"@@ -266,7 +298,7 @@ S.EmptyR -> let (y :< r') = S.viewl r in cseq l' y r' --- | Reversres the direction of the CSeq+-- | Reverses the direction of the CSeq -- -- running time: \(O(n)\) --@@ -283,9 +315,9 @@ -- >>> findRotateTo (== 7) $ fromList [1..5] -- Nothing findRotateTo :: (a -> Bool) -> CSeq a -> Maybe (CSeq a)-findRotateTo p = listToMaybe . filter (p . focus) . allRotations'-+findRotateTo p = L.find (p . focus) . allRotations' +-- | Rotate to a specific element in the CSeq. rotateTo :: Eq a => a -> CSeq a -> Maybe (CSeq a) rotateTo x = findRotateTo (== x) @@ -354,8 +386,8 @@ insertOrdBy' :: (a -> a -> Ordering) -> a -> [a] -> [a] insertOrdBy' cmp x xs = case (rest, x `cmp` head rest) of ([], _) -> L.insertBy cmp x pref- (z:zs, GT) -> (z : L.insertBy cmp x zs) ++ pref- (_:_, EQ) -> (x : xs) -- == x : rest ++ pref+ (z:zs, GT) -> z : L.insertBy cmp x zs ++ pref+ (_:_, EQ) -> x : xs -- == x : rest ++ pref (_:_, LT) -> rest ++ L.insertBy cmp x pref where -- split the list at its maximum.
+ src/Data/Double/Approximate.hs view
@@ -0,0 +1,83 @@+{-# LANGUAGE GADTs #-}+{-# LANGUAGE MagicHash #-}+{-# LANGUAGE ScopedTypeVariables #-}+-- | See: https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/+module Data.Double.Approximate+ ( SafeDouble+ , DoubleRelAbs(..)+ ) where++import Control.DeepSeq+import Data.Proxy+import GHC.TypeLits+import Numeric.MathFunctions.Comparison+import Numeric.MathFunctions.Constants+import System.Random+import Text.Read++-- | Relatively safe double floating-point type with a relative error+-- margin of 10 <https://en.wikipedia.org/wiki/Unit_in_the_last_place ULPs>+-- and an absolute margin around zero of+-- @10*<https://en.wikipedia.org/wiki/Machine_epsilon epsilon>@.+--+-- Warning: All numbers within+-- @10*<https://en.wikipedia.org/wiki/Machine_epsilon epsilon>@ of zero will be considered zero.+--+-- >>> m_epsilon * 10+-- 2.220446049250313e-15+--+-- >>> realToFrac (m_epsilon * 10) == (0::SafeDouble)+-- False+--+-- >>> realToFrac (m_epsilon * 9) == (0::SafeDouble)+-- True+--+-- >>> 1e-20 == (5e-20 :: Double)+-- False+-- >>> 1e-20 == (5e-20 :: SafeDouble)+-- True+--+-- 'pi' and 'sin' are approximations:+--+-- >>> sin pi+-- 1.2246467991473532e-16+--+-- >>> sin pi == (0 :: Double)+-- False+--+-- >>> sin pi == (0 :: SafeDouble)+-- True+--+type SafeDouble = DoubleRelAbs 10 10++-- | Custom double floating-point type with a relative error margin of+-- @rel@ number of+-- <https://en.wikipedia.org/wiki/Unit_in_the_last_place ULPs> and an+-- absolute error margin of @abs@ times+-- <https://en.wikipedia.org/wiki/Machine_epsilon epsilon>.+--+-- The relative error margin is the primary tool for good numerical+-- robustness and can relatively safely be set to a high number such+-- as 100. The absolute error margin is a last ditch attempt at fixing+-- broken algorithms and dramatically limits the resolution around zero.+-- If possible, use a low absolute error margin.+newtype DoubleRelAbs (abs :: Nat) (rel :: Nat) = DoubleRelAbs Double+ deriving (Num, Enum, Floating, Fractional, Real, RealFloat, RealFrac, Random, NFData)++instance (KnownNat abs, KnownNat rel) => Eq (DoubleRelAbs abs rel) where+ DoubleRelAbs d1 == DoubleRelAbs d2 =+ within (fromIntegral (natVal @rel Proxy)) d1 d2 ||+ (abs d1 < m_epsilon * fromIntegral (natVal @abs Proxy) &&+ abs d2 < m_epsilon * fromIntegral (natVal @abs Proxy))++instance (KnownNat abs, KnownNat rel) => Ord (DoubleRelAbs abs rel) where+ lhs@(DoubleRelAbs d1) `compare` rhs@(DoubleRelAbs d2)+ | lhs == rhs = EQ+ | otherwise = d1 `compare` d2++instance Show (DoubleRelAbs abs rel) where+ showsPrec i (DoubleRelAbs d) = showsPrec i d++instance Read (DoubleRelAbs abs rel) where+ readPrec = DoubleRelAbs <$> readPrec+
+ src/Data/Double/Shaman.hs view
@@ -0,0 +1,295 @@+-- https://tel.archives-ouvertes.fr/tel-03116750/document+{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE RecordWildCards #-}+module Data.Double.Shaman+ ( Shaman+ , significativeBits+ , significativeDigits+ , SDouble+ ) where++import Numeric.MathFunctions.Comparison ( addUlps)+import Numeric.MathFunctions.Constants+import GHC.TypeLits+import Data.Double.Approximate++-- | Double-precision floating point numbers that throw exceptions if+-- the accumulated errors grow large enough to cause unstable branching.+--+-- If @SDouble n@ works without throwing any exceptions, it'll be safe to+-- use @DoubleRelAbs n 0@ instead for a sizable performance boost.+--+-- >>> sin pi == (0 :: SDouble 0)+-- *** Exception: Insufficient precision.+-- ...+--+-- @SDouble 0@ failed so @DoubleRelAbs 0 0@ will lead to an unstable branch. In+-- other words, it'll return @False@ when it should have returned @True@:+--+-- >>> sin pi == (0 :: DoubleRelAbs 0 0)+-- False+--+-- Comparing to within 1 ULP stabalizes the branch:+--+-- >>> sin pi == (0 :: SDouble 1)+-- True+--+-- >>> sin pi == (0 :: DoubleRelAbs 1 0)+-- True+--+newtype SDouble (n::Nat) = SDouble Shaman+ deriving (Num, Fractional, Floating, Real, RealFrac, RealFloat)++instance Show (SDouble n) where+ showsPrec d (SDouble s) = showsPrec d s++instance Read (SDouble n) where+ readsPrec d inp = [ (SDouble v, r) | (v, r) <- readsPrec d inp ]+++-- shamanUlpDistance :: Shaman -> Word64+-- shamanUlpDistance (Shaman n e) = ulpDistance n (n+e)++compareSDouble :: KnownNat n => SDouble n -> SDouble n -> Ordering+compareSDouble a@(SDouble a') b@(SDouble b')+ | a == b = EQ+ | otherwise = shamanValue a' `compare` shamanValue b'++toDoubleRelAbs :: SDouble n -> DoubleRelAbs n 0+toDoubleRelAbs (SDouble (Shaman v _e)) = DoubleRelAbs v++-- If (a :: DoubleRelAbs n 0) == (b :: DoubleRelAbs n 0)+instance KnownNat n => Eq (SDouble n) where+ a@(SDouble a') == b@(SDouble b')+ | blessedResult == approxResult = blessedResult+ | otherwise = error "Insufficient precision."+ where+ blessedResult = a' == b'+ approxResult = toDoubleRelAbs a == toDoubleRelAbs b++instance KnownNat n => Ord (SDouble n) where+ compare = compareSDouble++++++-- | Double-precision floating point numbers with error-bounds.+--+-- Some digits can be represented exactly and have essentially an infinitely number of significant digits:+--+-- >>> significativeDigits 1+-- Infinity+--+-- Some fractional numbers can also be represented exactly:+--+-- >>> significativeDigits 0.5+-- Infinity+--+-- Other numbers are merely approximations:+--+-- >>> significativeDigits 0.1+-- 16.255619765854984+--+-- Pi is an irrational number so we can't represent it with infinite precision:+--+-- >>> significativeDigits pi+-- 15.849679651557175+--+-- @sin pi@ should theoretically be zero but we cannot do better than saying it is near zero:+--+-- >>> sin pi+-- 1.2246467991473532e-16+--+-- The error margins are greater than value itself so we have no significant digits:+--+-- >>> significativeDigits (sin pi)+-- 0.0+--+-- Since 'near zero' is not zero, the following fails when using Doubles:+--+-- >>> sin pi == (0 :: Double)+-- False+--+-- Equality testing for Shaman numbers tests whether the two intervals+-- overlap:+--+-- >>> sin pi == (0 :: Shaman)+-- True+data Shaman = Shaman+ { shamanValue :: {-# UNPACK #-} !Double+ , shamanError :: {-# UNPACK #-} !Double+ }++instance Show Shaman where+ showsPrec d Shaman{..} = showParen (d > 10) $+ shows shamanValue . showChar '±' . shows shamanError++instance Read Shaman where+ readsPrec d = readParen (d > app_prec) $ \r ->+ [ (Shaman{..}, t')+ | (shamanValue, '±':t) <- reads r+ , (shamanError, t') <- reads t]+ where app_prec = 10++-- | Number of significant bits (base 2).+significativeBits :: Shaman -> Double+significativeBits v = significativeValue v / log 2++-- | Number of significant digits (base 10).+significativeDigits :: Shaman -> Double+significativeDigits v = significativeValue v / log 10++significativeValue :: Shaman -> Double+significativeValue (Shaman v e)+ | e == 0 = m_pos_inf+ | isNaN e = 0+ | v == 0 = max 0 (log (abs e - 1))+ | otherwise =+ let relError = abs (e / v) in+ if relError >= 1+ then 0+ else negate $ log relError++instance Num Shaman where+ Shaman x dx + Shaman y dy =+ case x+y of+ !xy -> Shaman xy (dx+dy+twoSum x y xy)++ Shaman x dx * Shaman y dy =+ case x*y of+ !z -> Shaman z (dx * y + dy * x + fma x y (-z))+ + abs (Shaman x dx) = Shaman (abs x) dx++ signum (Shaman x dx) = Shaman (signum x) dx++ negate (Shaman x dx) = Shaman (negate x) dx++ fromInteger i =+ let d = fromInteger i+ in Shaman d (abs $ realToFrac $ i - round d)++instance Fractional Shaman where+ Shaman x dx / Shaman y dy =+ let z = x/y+ numerator = dx - fma y z (-x) - z * dy+ denominator = y + dy+ in Shaman z (numerator / denominator)+ fromRational r =+ let d = fromRational r+ in Shaman d (abs $ realToFrac $ r - realToFrac d)++instance Floating Shaman where+ pi = Shaman pi (addUlps 1 pi - pi)+ sqrt (Shaman x dx)+ | z == 0, dx == 0 =+ Shaman z 0+ | z == 0 =+ Shaman z (sqrt (abs dx)) -- FIXME: Use long double.+ | otherwise =+ Shaman z ((r + dx) / (z+z))+ where+ r = negate $ fma z z (negate x)+ z = sqrt x+ log = foreignOp erf_log log+ exp = foreignOp erf_exp exp+ (**) = foreignBinOp erf_pow (**)+ sin = foreignOp erf_sin sin+ cos = foreignOp erf_cos cos+ tan = foreignOp erf_tan tan+ asin = foreignOp erf_asin asin+ acos = foreignOp erf_acos acos+ atan = foreignOp erf_atan atan+ sinh = foreignOp erf_sinh sinh+ cosh = foreignOp erf_cosh cosh+ tanh = foreignOp erf_tanh tanh+ asinh = foreignOp erf_asinh asinh+ acosh = foreignOp erf_acosh acosh+ atanh = foreignOp erf_atanh atanh++instance Real Shaman where+ toRational (Shaman v _) = toRational v++instance RealFrac Shaman where+ properFraction (Shaman v e) =+ case properFraction v of+ (i, v') -> (i, Shaman v' e)+ truncate (Shaman v _e) = truncate v+ round (Shaman v _e) = round v+ ceiling (Shaman v e) = ceiling (v+e)+ floor (Shaman v e) = floor (v-e)++instance RealFloat Shaman where+ floatRadix = floatRadix . shamanValue+ floatDigits = floatDigits . shamanValue+ floatRange = floatRange . shamanValue+ decodeFloat = decodeFloat . shamanValue+ encodeFloat m e = Shaman (encodeFloat m e) 0 -- FIXME: 1 ULP error bound?+ exponent = exponent . shamanValue+ significand s = Shaman (significand $ shamanValue s) 0+ scaleFloat p (Shaman v e) = Shaman (scaleFloat p v) e+ isNaN = isNaN . shamanValue+ isInfinite = isInfinite . shamanValue+ isDenormalized = isDenormalized . shamanValue+ isNegativeZero = isNegativeZero . shamanValue+ isIEEE = isIEEE . shamanValue+ atan2 = foreignBinOp erf_atan2 atan2+++instance Eq Shaman where+ x == y = compareShaman x y == EQ++instance Ord Shaman where+ compare = compareShaman++-- Returns EQ iff the two numbers overlap.+compareShaman :: Shaman -> Shaman -> Ordering+compareShaman (Shaman x dx) (Shaman y dy)+ | abs (x-y) < abs dx+ abs dy = EQ+ | x < y = LT+ | otherwise = GT++twoSum :: Double -> Double -> Double -> Double+twoSum x y xy = abs (x-x') + abs (y-y')+ where+ x' = xy-y+ y' = xy-x++foreignOp :: (Double -> Double -> Double -> Double) -> (Double -> Double) -> Shaman -> Shaman+foreignOp mkDelta fn (Shaman x dx) =+ let !z = fn x+ in Shaman z (abs $ mkDelta x dx z)++foreignBinOp ::+ (Double -> Double -> Double -> Double -> Double -> Double) ->+ (Double -> Double -> Double) ->+ Shaman -> Shaman -> Shaman+foreignBinOp mkDelta fn (Shaman x dx) (Shaman y dy) =+ let !z = fn x y+ in Shaman z (mkDelta x dx y dy z)++foreign import ccall unsafe "fma" fma :: Double -> Double -> Double -> Double++foreign import ccall unsafe "erf_log" erf_log :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_exp" erf_exp :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_pow" erf_pow :: Double -> Double -> Double -> Double -> Double -> Double++foreign import ccall unsafe "erf_sin" erf_sin :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_cos" erf_cos :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_tan" erf_tan :: Double -> Double -> Double -> Double++foreign import ccall unsafe "erf_asin" erf_asin :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_acos" erf_acos :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_atan" erf_atan :: Double -> Double -> Double -> Double++foreign import ccall unsafe "erf_sinh" erf_sinh :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_cosh" erf_cosh :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_tanh" erf_tanh :: Double -> Double -> Double -> Double++foreign import ccall unsafe "erf_asinh" erf_asinh :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_acosh" erf_acosh :: Double -> Double -> Double -> Double+foreign import ccall unsafe "erf_atanh" erf_atanh :: Double -> Double -> Double -> Double++foreign import ccall unsafe "erf_atan2" erf_atan2 :: Double -> Double -> Double -> Double -> Double -> Double
src/Data/DynamicOrd.hs view
@@ -1,6 +1,14 @@ {-# LANGUAGE UndecidableInstances #-}+--------------------------------------------------------------------------------+-- |+-- Module : Data.DynamicOrd+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Data.DynamicOrd where +import Data.Kind import Data.Proxy import Data.Reflection import Unsafe.Coerce@@ -10,8 +18,8 @@ -- Implementation from -- https://www.schoolofhaskell.com/user/thoughtpolice/using-reflection --- | Values of type 'a' in our dynamically constructed 'Ord' instance-newtype O (s :: *) (a :: *) = O { runO :: a } deriving (Show)+-- | Values of type '@a@' in our dynamically constructed 'Ord' instance+newtype O (s :: Type) (a :: Type) = O { runO :: a } deriving (Show) -- | An Ord Dictionary newtype OrdDict a = OrdDict { compare_ :: a -> a -> Ordering }@@ -37,35 +45,35 @@ -- * Introducing and removing the dynamic order type -- Note that all of these may be unsafe if used incorrectly --- | Lifts a container f whose values (of type a) depend on 's' into a--- more general computation in that produces a 'f a' (depending on s).+-- | Lifts a container f whose values (of type a) depend on '@s@' into a+-- more general computation in that produces a '@f a@' (depending on s). -- -- running time: \(O(1)\) extractOrd1 :: f (O s a) -> O s (f a) extractOrd1 = unsafeCoerce --- | Introduce dynamic order in a container 'f'.+-- | Introduce dynamic order in a container '@f@'. -- -- running time: \(O(1)\) introOrd1 :: f a -> f (O s a) introOrd1 = unsafeCoerce --- | Lifts a function that works on a container 'f' of+-- | Lifts a function that works on a container '@f@' of -- orderable-things into one that works on dynamically ordered ones.-liftOrd1 :: (f (O s a) -> f (O s a))- -> f a -> O s (f a)+liftOrd1 :: (f (O s a) -> g (O s a))+ -> f a -> O s (g a) liftOrd1 f = extractOrd1 . f . introOrd1 --- | Lifts a container f whose keys (of type k) depend on 's' into a--- more general computation in that produces a 'f k v' (depending on s).+-- | Lifts a container f whose keys (of type k) depend on '@s@' into a+-- more general computation in that produces a @`f k v`@ (depending on s). -- -- running time: \(O(1)\) extractOrd2 :: f (O s k) v -> O s (f k v) extractOrd2 = unsafeCoerce --- | Introduce dynamic order in a container 'f' that has keys of type+-- | Introduce dynamic order in a container '@f@' that has keys of type -- k. -- -- running time: \(O(1)\)
src/Data/Ext.hs view
@@ -21,6 +21,7 @@ import Data.Bifoldable import Data.Bifunctor.Apply import Data.Bitraversable+-- import Data.Default import Data.Functor.Apply (liftF2) import Data.Semigroup.Bifoldable import Data.Semigroup.Bitraversable@@ -74,17 +75,30 @@ instance (Arbitrary c, Arbitrary e) => Arbitrary (c :+ e) where arbitrary = (:+) <$> arbitrary <*> arbitrary +-- instance (Default a, Default b) => Default (a :+ b) where+-- def = def :+ def++-- | Access the core of an extended value. _core :: (core :+ extra) -> core _core (c :+ _) = c+{-# INLINABLE _core #-} +-- | Access the extra part of an extended value. _extra :: (core :+ extra) -> extra _extra (_ :+ e) = e+{-# INLINABLE _extra #-} +-- | Lens access to the core of an extended value. core :: Lens (core :+ extra) (core' :+ extra) core core'-core = lens _core (\(_ :+ e) c -> (c :+ e))+core = lens _core (\(_ :+ e) c -> c :+ e)+{-# INLINABLE core #-} +-- | Lens access to the extra part of an extended value. extra :: Lens (core :+ extra) (core :+ extra') extra extra'-extra = lens _extra (\(c :+ _) e -> (c :+ e))+extra = lens _extra (\(c :+ _) e -> c :+ e)+{-# INLINABLE extra #-} +-- | Tag a value with the unit type. ext :: a -> a :+ () ext x = x :+ ()+{-# INLINABLE ext #-}
+ src/Data/IndexedDoublyLinkedList.hs view
@@ -0,0 +1,216 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.IndexedDoublyLinkedList+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.IndexedDoublyLinkedList( DLList(..)+ , Cell(..), emptyCell+ , DLListMonad, runDLListMonad+ , Index++ , singletons+ , writeList+ , valueAt, getNext, getPrev+ , toListFrom, toListFromR, toListContains+ , toListFromK, toListFromRK+ , insertAfter, insertBefore+ , delete+ , dump+ ) where++import Control.Monad.Primitive (PrimMonad(..))+import Control.Monad.Reader (ReaderT, runReaderT)+import Control.Monad.Reader.Class+import Control.Monad.ST+import Data.Foldable (forM_)+import Data.List.NonEmpty (NonEmpty(..))+import qualified Data.List.NonEmpty as NonEmpty+import Data.Util+import qualified Data.Vector as V+import qualified Data.Vector.Mutable as MV++--------------------------------------------------------------------------------++-- | Cell indices. Must be non-negative.+type Index = Int++-- TODO: Switch to unobxed sums for these!++-- | Cells in the Linked List+data Cell = Cell { prev :: Maybe Index+ , next :: Maybe Index+ } deriving (Show,Eq)++-- | Empty cell with no next or prev cells.+emptyCell :: Cell+emptyCell = Cell Nothing Nothing++-- | Doubly linked list implemented by a mutable vector. So actually+-- this data type can represent a collection of Linked Lists that can+-- efficiently be concatenated and split.+--+-- Supports O(1) indexing, and O(1) insertions, deletions+data DLList s a = DLList { values :: !(V.Vector a)+ , llist :: !(MV.MVector s Cell)+ }++instance Functor (DLList s) where+ fmap f (DLList v l) = DLList (fmap f v) l+++--------------------------------------------------------------------------------++-- | Monad in which we can use the IndexedDoublyLinkedList.+newtype DLListMonad s b a = DLListMonad { runDLListMonad' :: ReaderT (DLList s b) (ST s) a }+ deriving (Functor,Applicative,Monad)++instance PrimMonad (DLListMonad s b) where+ type PrimState (DLListMonad s b) = s+ primitive = DLListMonad . primitive++instance MonadReader (DLList s b) (DLListMonad s b) where+ local f = DLListMonad . local f . runDLListMonad'+ ask = DLListMonad ask++-- | Runs a DLList Computation, starting with singleton values, crated+-- from the input vector.+runDLListMonad :: V.Vector b -> (forall s. DLListMonad s b a) -> a+runDLListMonad vs comp = runST $ singletons vs >>= runReaderT (runDLListMonad' comp)++----------------------------------------++-- | Constructs a new DoublyLinkedList. Every element is its own singleton list+singletons :: (PrimMonad m, s ~ PrimState m) => V.Vector b -> m (DLList s b)+singletons vs = DLList vs <$> MV.replicate (V.length vs) emptyCell++-- | Sets the DoublyLinkedList to the given List.+--+-- Indices that do not occur in the list are not touched.+writeList :: NonEmpty Index -> DLListMonad s b ()+writeList h = do v <- asks llist+ forM_ (withNeighs h) $ \(STR p i s) ->+ modify v i $ \c -> c { prev = p , next = s }+ where+ withNeighs (x:|xs) = let l = x:xs+ in zipWith3 STR (Nothing : map Just l) l (map Just xs ++ [Nothing])++----------------------------------------+-- * Queries++-- | Gets the value at Index i+valueAt :: Index -> DLListMonad s b b+valueAt i = asks ((V.! i) . values)++-- | Next element in the List+getNext :: Index -> DLListMonad s b (Maybe Index)+getNext i = do v <- asks llist+ next <$> MV.read v i++-- | Previous Element in the List+getPrev :: Index -> DLListMonad s b (Maybe Index)+getPrev i = do v <- asks llist+ prev <$> MV.read v i++-- | Computes a maximal length list starting from the Given index+--+-- running time: \(O(k)\), where \(k\) is the length of the output list+toListFrom :: Index -> DLListMonad s b (NonEmpty Index)+toListFrom i = (i :|) <$> iterateM getNext i++-- | Takes the current element and its k next's+toListFromK :: Index -> Int -> DLListMonad s b (NonEmpty Index)+toListFromK i k = (i :|) <$> replicateM k getNext i++-- | Computes a maximal length list by walking backwards in the+-- DoublyLinkedList, starting from the Given index+--+-- running time: \(O(k)\), where \(k\) is the length of the output list+toListFromR :: Index -> DLListMonad s b (NonEmpty Index)+toListFromR i = (i :|) <$> iterateM getPrev i++-- | Takes the current element and its k prev's+toListFromRK :: Index -> Int -> DLListMonad s b (NonEmpty Index)+toListFromRK i k = (i :|) <$> replicateM k getPrev i++-- | Computes a maximal length list that contains the element i.+--+-- running time: \(O(k)\), where \(k\) is the length of the output+-- list+toListContains :: Index -> DLListMonad s b (NonEmpty Index)+toListContains i = f <$> toListFromR i <*> toListFrom i+ where+ f l r = NonEmpty.fromList $ reverse (NonEmpty.toList l) <> NonEmpty.tail r+++----------------------------------------+-- * Updates++-- | Inserts the second argument after the first one into the linked list+insertAfter :: Index -> Index -> DLListMonad s b ()+insertAfter i j = do v <- asks llist+ mr <- getNext i+ modify v i $ \c -> c { next = Just j }+ modify v j $ \c -> c { prev = Just i , next = mr }+ mModify v mr $ \c -> c { prev = Just j }++-- | Inserts the second argument before the first one into the linked list+insertBefore :: Index -> Index -> DLListMonad s b ()+insertBefore i h = do v <- asks llist+ ml <- getPrev i+ mModify v ml $ \c -> c { next = Just h }+ modify v h $ \c -> c { prev = ml , next = Just i }+ modify v i $ \c -> c { prev = Just h }++-- | Deletes the element from the linked list. This element thus+-- essentially becomes a singleton list. Returns the pair of indices+-- that now have become neighbours (i.e. the predecessor and successor+-- of j just before we deleted j).+delete :: Index -> DLListMonad s b (Maybe Index, Maybe Index)+delete j = do v <- asks llist+ ml <- getPrev j+ mr <- getNext j+ modify v j $ \c -> c { prev = Nothing, next = Nothing }+ mModify v ml $ \c -> c { next = mr }+ mModify v mr $ \c -> c { prev = ml }+ pure (ml,mr)+++++----------------------------------------+-- * Helper functions++-- | Applies the action at most n times.+replicateM :: Monad m => Int -> (a -> m (Maybe a)) -> a -> m [a]+replicateM n f = go n+ where+ go 0 _ = pure []+ go k x = f x >>= \case+ Nothing -> pure []+ Just y -> (y:) <$> go (k-1) y++iterateM :: Monad m => (a -> m (Maybe a)) -> a -> m [a]+iterateM f = go+ where+ go x = f x >>= \case+ Nothing -> pure []+ Just y -> (y:) <$> go y++mModify :: PrimMonad m => MV.MVector (PrimState m) a -> Maybe Int -> (a -> a) -> m ()+mModify v mi f = case mi of+ Nothing -> pure ()+ Just i -> modify v i f++modify :: PrimMonad m => MV.MVector (PrimState m) a -> Int -> (a -> a) -> m ()+modify v i f = MV.modify v f i+++--------------------------------------------------------------------------------++-- | For debugging purposes, dump the values and the cells+dump :: DLListMonad s a (V.Vector a, V.Vector Cell)+dump = do DLList v cs <- ask+ cs' <- V.freeze cs+ pure (v,cs')
+ src/Data/IndexedDoublyLinkedList/Bare.hs view
@@ -0,0 +1,197 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.IndexedDoublyLinkedList.Bare+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.IndexedDoublyLinkedList.Bare(+ IDLList(..)+ , Cell(..), emptyCell+ , IDLListMonad, runIDLListMonad+ , Index++ , singletons+ , writeList+ , getNext, getPrev+ , toListFrom, toListFromR, toListContains+ , toListFromK, toListFromRK+ , insertAfter, insertBefore+ , delete+ , dump+ ) where++import Control.Monad.Primitive (PrimMonad(..))+import Control.Monad.Reader (ReaderT, runReaderT)+import Control.Monad.Reader.Class+import Control.Monad.ST+import Data.Foldable (forM_)+import Data.List.NonEmpty (NonEmpty(..))+import qualified Data.List.NonEmpty as NonEmpty+import Data.Util+import qualified Data.Vector as V+import qualified Data.Vector.Mutable as MV++--------------------------------------------------------------------------------++-- | Cell indices. Must be non-negative.+type Index = Int++-- | Cells in the Linked List+data Cell = Cell { prev :: !(Maybe Index)+ , next :: !(Maybe Index)+ } deriving (Show,Eq)++-- | Empty cell with no next or prev cells.+emptyCell :: Cell+emptyCell = Cell Nothing Nothing++-- | Doubly linked list implemented by a mutable vector. So actually+-- this data type can represent a collection of Linked Lists that can+-- efficiently be concatenated and split.+--+-- Supports O(1) indexing, and O(1) insertions, deletions+newtype IDLList s = IDLList { llist :: MV.MVector s Cell }++--------------------------------------------------------------------------------++-- | Monad in which we can use the IndexedDoublyLinkedList.+newtype IDLListMonad s a = IDLListMonad { runIDLListMonad' :: ReaderT (IDLList s) (ST s) a }+ deriving (Functor,Applicative,Monad)++instance PrimMonad (IDLListMonad s) where+ type PrimState (IDLListMonad s) = s+ primitive = IDLListMonad . primitive++instance MonadReader (IDLList s) (IDLListMonad s) where+ local f = IDLListMonad . local f . runIDLListMonad'+ ask = IDLListMonad ask++-- | Runs a DLList Computation, starting with n singleton values+runIDLListMonad :: Int -> (forall s. IDLListMonad s a) -> a+runIDLListMonad n comp = runST $ singletons n >>= runReaderT (runIDLListMonad' comp)++----------------------------------------++-- | Constructs a new DoublyLinkedList, of size at most n+singletons :: (PrimMonad m, s ~ PrimState m) => Int -> m (IDLList s)+singletons n = IDLList <$> MV.replicate n emptyCell++-- | Sets the DoublyLinkedList to the given List.+--+-- Indices that do not occur in the list are not touched.+writeList :: NonEmpty Index -> IDLListMonad s ()+writeList h = do v <- asks llist+ forM_ (withNeighs h) $ \(STR p i s) ->+ modify v i $ \c -> c { prev = p , next = s }+ where+ withNeighs (x:|xs) = let l = x:xs+ in zipWith3 STR (Nothing : map Just l) l (map Just xs ++ [Nothing])++----------------------------------------+-- * Queries++-- | Next element in the List+getNext :: Index -> IDLListMonad s (Maybe Index)+getNext i = do v <- asks llist+ next <$> MV.read v i++-- | Previous Element in the List+getPrev :: Index -> IDLListMonad s (Maybe Index)+getPrev i = do v <- asks llist+ prev <$> MV.read v i++-- | Computes a maximal length list starting from the Given index+--+-- running time: \(O(k)\), where \(k\) is the length of the output list+toListFrom :: Index -> IDLListMonad s (NonEmpty Index)+toListFrom i = (i :|) <$> iterateM getNext i++-- | Takes the current element and its k next's+toListFromK :: Index -> Int -> IDLListMonad s (NonEmpty Index)+toListFromK i k = (i :|) <$> replicateM k getNext i++-- | Computes a maximal length list by walking backwards in the+-- DoublyLinkedList, starting from the Given index+--+-- running time: \(O(k)\), where \(k\) is the length of the output list+toListFromR :: Index -> IDLListMonad s (NonEmpty Index)+toListFromR i = (i :|) <$> iterateM getPrev i++-- | Takes the current element and its k prev's+toListFromRK :: Index -> Int -> IDLListMonad s (NonEmpty Index)+toListFromRK i k = (i :|) <$> replicateM k getPrev i++-- | Computes a maximal length list that contains the element i.+--+-- running time: \(O(k)\), where \(k\) is the length of the output+-- list+toListContains :: Index -> IDLListMonad s (NonEmpty Index)+toListContains i = f <$> toListFromR i <*> toListFrom i+ where+ f l r = NonEmpty.fromList $ reverse (NonEmpty.toList l) <> NonEmpty.tail r+++----------------------------------------+-- * Updates++-- | Inserts the second argument after the first one into the linked list+insertAfter :: Index -> Index -> IDLListMonad s ()+insertAfter i j = do v <- asks llist+ mr <- getNext i+ modify v i $ \c -> c { next = Just j }+ modify v j $ \c -> c { prev = Just i , next = mr }+ mModify v mr $ \c -> c { prev = Just j }++-- | Inserts the second argument before the first one into the linked list+insertBefore :: Index -> Index -> IDLListMonad s ()+insertBefore i h = do v <- asks llist+ ml <- getPrev i+ mModify v ml $ \c -> c { next = Just h }+ modify v h $ \c -> c { prev = ml , next = Just i }+ modify v i $ \c -> c { prev = Just h }++-- | Deletes the element from the linked list. This element thus+-- essentially becomes a singleton list.+delete :: Index -> IDLListMonad s ()+delete j = do v <- asks llist+ ml <- getPrev j+ mr <- getNext j+ modify v j $ \c -> c { prev = Nothing, next = Nothing }+ mModify v ml $ \c -> c { next = mr }+ mModify v mr $ \c -> c { prev = ml }++----------------------------------------+-- * Helper functions++-- | Applies the action at most n times.+replicateM :: Monad m => Int -> (a -> m (Maybe a)) -> a -> m [a]+replicateM n f = go n+ where+ go 0 _ = pure []+ go k x = f x >>= \case+ Nothing -> pure []+ Just y -> (y:) <$> go (k-1) y++iterateM :: Monad m => (a -> m (Maybe a)) -> a -> m [a]+iterateM f = go+ where+ go x = f x >>= \case+ Nothing -> pure []+ Just y -> (y:) <$> go y++mModify :: PrimMonad m => MV.MVector (PrimState m) a -> Maybe Int -> (a -> a) -> m ()+mModify v mi f = case mi of+ Nothing -> pure ()+ Just i -> modify v i f++modify :: PrimMonad m => MV.MVector (PrimState m) a -> Int -> (a -> a) -> m ()+modify v i f = MV.modify v f i+++--------------------------------------------------------------------------------++-- | For debugging purposes, dump the values and the cells+dump :: IDLListMonad s (V.Vector Cell)+dump = do IDLList cs <- ask+ V.freeze cs
src/Data/Intersection.hs view
@@ -35,16 +35,19 @@ coRec :: (a ∈ as) => a -> CoRec Identity as coRec = CoRec . Identity -class IsIntersectableWith g h where- intersect :: g -> h -> Intersection g h-+class HasIntersectionWith g h where -- | g `intersects` h <=> The intersection of g and h is non-empty. -- -- The default implementation computes the intersection of g and h, -- and uses nonEmptyIntersection to determine if the intersection is -- non-empty. intersects :: g -> h -> Bool+ default intersects :: IsIntersectableWith g h => g -> h -> Bool g `intersects` h = nonEmptyIntersection (Identity g) (Identity h) $ g `intersect` h++-- | Class relationship between intersectable geometric objects.+class HasIntersectionWith g h => IsIntersectableWith g h where+ intersect :: g -> h -> Intersection g h -- | Helper to implement `intersects`. nonEmptyIntersection :: proxy g -> proxy h -> Intersection g h -> Bool
src/Data/LSeq.hs view
@@ -1,4 +1,5 @@ {-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE BangPatterns #-} -------------------------------------------------------------------------------- -- | -- Module : Data.LSeq@@ -8,7 +9,7 @@ -- Description : Wrapper around Data.Sequence with type level length annotation. -- ---------------------------------------------------------------------------------module Data.LSeq( LSeq+module Data.LSeq( LSeq( EmptyL, (:<|), (:<<), (:|>) ) , toSeq , empty , fromList@@ -17,7 +18,7 @@ , (<|), (|>) , (><)- , eval+ , eval, eval' , index , adjust@@ -26,39 +27,38 @@ , take , drop , unstableSort, unstableSortBy- , head, last+ , head, tail, last, init , append+ , reverse , ViewL(..) , viewl- , pattern (:<|) - , pattern (:<<)- , pattern EmptyL- , ViewR(..) , viewr- , pattern (:|>) + , zipWith , promise , forceLSeq ) where import Control.DeepSeq-import Control.Lens ((%~), (&), (<&>), (^?), bimap)+import Control.Lens ((%~), (&), (<&>), (^?!), bimap) import Control.Lens.At (Ixed(..), Index, IxValue) import Data.Aeson+import Data.Coerce(coerce) import qualified Data.Foldable as F+import Data.Functor.Apply import qualified Data.List.NonEmpty as NonEmpty-import Data.Maybe (fromJust) import Data.Proxy import Data.Semigroup.Foldable+import Data.Semigroup.Traversable import qualified Data.Sequence as S import qualified Data.Traversable as Tr import GHC.Generics (Generic) import GHC.TypeLits-import Prelude hiding (drop,take,head,last)+import Prelude hiding (drop,take,head,last,tail,init,zipWith,reverse) import Test.QuickCheck (Arbitrary(..),vector) --------------------------------------------------------------------------------@@ -75,6 +75,7 @@ deriving (Show,Read,Eq,Ord,Foldable,Functor,Traversable ,Generic,NFData) +-- | \( O(1) \) Convert to a sequence by dropping the type-level size. toSeq :: LSeq n a -> S.Seq a toSeq (LSeq s) = s @@ -103,108 +104,156 @@ | otherwise = pure s instance (1 <= n) => Foldable1 (LSeq n)+instance (1 <= n) => Traversable1 (LSeq n) where+ traverse1 f (LSeq xs) = case runMaybeApply $ traverse (MaybeApply . Left . f) xs of+ Left xs' -> LSeq <$> xs'+ Right _ -> error "Data.LSeq.traverse1: impossible" +-- | \( O(1) \) The empty sequence. empty :: LSeq 0 a empty = LSeq S.empty +-- | \( O(1) \) Add an element to the left end of a sequence.+-- Mnemonic: a triangle with the single element at the pointy end. (<|) :: a -> LSeq n a -> LSeq (1 + n) a x <| xs = LSeq (x S.<| toSeq xs) +-- | \( O(1) \) Add an element to the right end of a sequence.+-- Mnemonic: a triangle with the single element at the pointy end. (|>) :: LSeq n a -> a -> LSeq (1 + n) a xs |> x = LSeq (toSeq xs S.|> x) infixr 5 <| infixl 5 |> +-- | \( O(log(min(n,m))) \) Concatenate two sequences. (><) :: LSeq n a -> LSeq m a -> LSeq (n + m) a xs >< ys = LSeq (toSeq xs <> toSeq ys) infix 5 >< +-- | \( O(1) \) Prove a sequence has at least @n@ elements.+--+-- >>> eval @3 (fromList [1,2,3])+-- Just (LSeq (fromList [1,2,3]))+-- >>> eval @3 (fromList [1,2])+-- Nothing+-- >>> eval @3 (fromList [1..10])+-- Just (LSeq (fromList [1,2,3,4,5,6,7,8,9,10]))+eval :: forall n m a. KnownNat n => LSeq m a -> Maybe (LSeq n a)+eval = eval' (Proxy @n) -eval :: forall proxy n m a. KnownNat n => proxy n -> LSeq m a -> Maybe (LSeq n a)-eval n (LSeq xs)+-- | Implementatio nof eval' that takes an explicit proxy.+eval' :: forall proxy n m a. KnownNat n => proxy n -> LSeq m a -> Maybe (LSeq n a)+eval' n (LSeq xs) | toInteger (S.length xs) >= natVal n = Just $ LSeq xs | otherwise = Nothing --- -- | Promises that the length of this LSeq is actually n. This is not -- checked. -- -- This function should be a noop-promise :: LSeq m a -> LSeq n a-promise = LSeq . toSeq-+promise :: forall n m a. LSeq m a -> LSeq n a+promise = coerce -- | Forces the first n elements of the LSeq forceLSeq :: KnownNat n => proxy n -> LSeq m a -> LSeq n a forceLSeq n = promise . go (fromInteger $ natVal n) where -- forces the Lseq for n' positions- go :: Int -> LSeq m a -> LSeq m a- go n' s | n' <= l = s- | otherwise = error msg+ go :: Int -> LSeq m a -> LSeq m a+ go !n' s | n' <= l = s+ | otherwise = error msg where- l = S.length . S.take n' . toSeq $ s+ !l = S.length . S.take n' . toSeq $ s msg = "forceLSeq: too few elements. expected " <> show n' <> " but found " <> show l -- | appends two sequences. -- append :: LSeq n a -> LSeq m a -> LSeq (n + m) a-sa `append` sb = LSeq $ (toSeq sa) <> toSeq sb+sa `append` sb = LSeq $ toSeq sa <> toSeq sb -------------------------------------------------------------------------------- --- | get the element with index i, counting from the left and starting at 0.--- O(log(min(i,n-i)))+-- | \( O(log(min(i,n-i))) \)+-- Get the element with index i, counting from the left and starting at 0. index :: LSeq n a -> Int -> a-index s i = fromJust $ s^?ix i+index s i = s^?!ix i +-- | \( O(log(min(i,n−i))) \) Update the element at the specified position. If the+-- position is out of range, the original sequence is returned. adjust can lead+-- to poor performance and even memory leaks, because it does not force the new+-- value before installing it in the sequence. adjust' should usually be preferred. adjust :: (a -> a) -> Int -> LSeq n a -> LSeq n a adjust f i s = s&ix i %~ f -+-- | \( O(n) \) The partition function takes a predicate p and a sequence xs and+-- returns sequences of those elements which do and do not satisfy the predicate. partition :: (a -> Bool) -> LSeq n a -> (LSeq 0 a, LSeq 0 a) partition p = bimap LSeq LSeq . S.partition p . toSeq +-- | A generalization of 'fmap', 'mapWithIndex' takes a mapping+-- function that also depends on the element's index, and applies it to every+-- element in the sequence. mapWithIndex :: (Int -> a -> b) -> LSeq n a -> LSeq n b mapWithIndex f = wrapUnsafe (S.mapWithIndex f) +-- | \( O(\log(\min(i,n-i))) \). The first @i@ elements of a sequence.+-- If @i@ is negative, @'take' i s@ yields the empty sequence.+-- If the sequence contains fewer than @i@ elements, the whole sequence+-- is returned. take :: Int -> LSeq n a -> LSeq 0 a take i = wrapUnsafe (S.take i) +-- | \( O(\log(\min(i,n-i))) \). Elements of a sequence after the first @i@.+-- If @i@ is negative, @'drop' i s@ yields the whole sequence.+-- If the sequence contains fewer than @i@ elements, the empty sequence+-- is returned. drop :: Int -> LSeq n a -> LSeq 0 a drop i = wrapUnsafe (S.drop i) -+-- | \( O(n \log n) \). A generalization of 'unstableSort', 'unstableSortBy'+-- takes an arbitrary comparator and sorts the specified sequence.+-- The sort is not stable. This algorithm is frequently faster and+-- uses less memory than 'Data.Sequence.sortBy'. unstableSortBy :: (a -> a -> Ordering) -> LSeq n a -> LSeq n a unstableSortBy f = wrapUnsafe (S.unstableSortBy f) +-- | \( O(n \log n) \). 'unstableSort' sorts the specified 'LSeq' by+-- the natural ordering of its elements, but the sort is not stable.+-- This algorithm is frequently faster and uses less memory than 'Data.Sequence.sort'. unstableSort :: Ord a => LSeq n a -> LSeq n a-unstableSort = wrapUnsafe (S.unstableSort)+unstableSort = wrapUnsafe S.unstableSort wrapUnsafe :: (S.Seq a -> S.Seq b) -> LSeq n a -> LSeq m b wrapUnsafe f = LSeq . f . toSeq +-- | Reverses the sequence.+reverse :: LSeq n a -> LSeq n a+reverse = wrapUnsafe S.reverse++ -------------------------------------------------------------------------------- +-- | \( O(1) \). Create an l-sequence from a sequence of elements. fromSeq :: S.Seq a -> LSeq 0 a fromSeq = LSeq +-- | \( O(n) \). Create an l-sequence from a finite list of elements. fromList :: Foldable f => f a -> LSeq 0 a fromList = LSeq . S.fromList . F.toList +-- | \( O(n) \). Create an l-sequence from a non-empty list. fromNonEmpty :: NonEmpty.NonEmpty a -> LSeq 1 a fromNonEmpty = LSeq . S.fromList . F.toList -------------------------------------------------------------------------------- +-- | View of the left end of a sequence. data ViewL n a where (:<) :: a -> LSeq n a -> ViewL (1 + n) a @@ -220,12 +269,21 @@ foldMap = Tr.foldMapDefault instance Traversable (ViewL n) where traverse f (x :< xs) = (:<) <$> f x <*> traverse f xs+instance (1 <= n) => Foldable1 (ViewL n)+instance (1 <= n) => Traversable1 (ViewL n) where+ traverse1 f (a :< LSeq as) = (\(b :< bs) -> b :< promise bs) <$> go a as+ where+ go x = \case+ S.Empty -> (:< empty) <$> f x+ (y S.:<| ys) -> (\x' (y' :< ys') -> x' :< promise @0 (y' :<| ys'))+ <$> f x <.> go y ys+ instance Eq a => Eq (ViewL n a) where s == s' = F.toList s == F.toList s' instance Ord a => Ord (ViewL n a) where s `compare` s' = F.toList s `compare` F.toList s' -+-- | \( O(1) )\. Analyse the left end of a sequence. viewl :: LSeq (1 + n) a -> ViewL (1 + n) a viewl xs = let ~(x S.:< ys) = S.viewl $ toSeq xs in x :< LSeq ys @@ -234,6 +292,8 @@ infixr 5 :<| +-- | A bidirectional pattern synonym viewing the front of a non-empty+-- sequence. pattern (:<|) :: a -> LSeq n a -> LSeq (1 + n) a pattern x :<| xs <- (viewl' -> (x,xs)) -- we need the coerce unfortunately where@@ -244,9 +304,12 @@ infixr 5 :<< +-- | A unidirectional pattern synonym viewing the front of a non-empty+-- sequence. pattern (:<<) :: a -> LSeq 0 a -> LSeq n a pattern x :<< xs <- (viewLSeq -> Just (x,xs)) +-- | The empty sequence. pattern EmptyL :: LSeq n a pattern EmptyL <- (viewLSeq -> Nothing) @@ -258,6 +321,7 @@ -------------------------------------------------------------------------------- +-- | View of the right end of a sequence. data ViewR n a where (:>) :: LSeq n a -> a -> ViewR (1 + n) a @@ -278,6 +342,7 @@ instance Ord a => Ord (ViewR n a) where s `compare` s' = F.toList s `compare` F.toList s' +-- | \( O(1) \). Analyse the right end of a sequence. viewr :: LSeq (1 + n) a -> ViewR (1 + n) a viewr xs = let ~(ys S.:> x) = S.viewr $ toSeq xs in LSeq ys :> x @@ -286,6 +351,8 @@ infixl 5 :|> +-- | A bidirectional pattern synonym viewing the rear of a non-empty+-- sequence. pattern (:|>) :: forall n a. LSeq n a -> a -> LSeq (1 + n) a pattern xs :|> x <- (viewr' -> (xs,x)) where@@ -301,6 +368,12 @@ head :: LSeq (1 + n) a -> a head (x :<| _) = x +-- | Get the LSeq without its first element+-- -- >>> head $ forceLSeq (Proxy :: Proxy 3) $ fromList [1,2,3]+-- LSeq (fromList [2,3])+tail :: LSeq (1 + n) a -> LSeq n a+tail (_ :<| s) = s+ -- s = let (x :< _) = viewl s in x -- | Get the last element of the LSeq@@ -310,6 +383,14 @@ last :: LSeq (1 + n) a -> a last (_ :|> x) = x ++-- | The sequence without its last element+--+-- >>> init $ forceLSeq (Proxy :: Proxy 3) $ fromList [1,2,3]+-- LSeq (fromList [1,2])+init :: LSeq (1 + n) a -> LSeq n a+init (s :|> _) = s+ -- testL = (eval (Proxy :: Proxy 2) $ fromList [1..5]) -- testL' :: LSeq 2 Integer@@ -317,3 +398,10 @@ -- test :: Show a => LSeq (1 + n) a -> String -- test (x :<| xs) = show x ++ show xs+++--------------------------------------------------------------------------------++-- | Zips two equal length LSeqs+zipWith :: (a -> b -> c) -> LSeq n a -> LSeq n b -> LSeq n c+zipWith f sa sb = LSeq $ S.zipWith f (toSeq sa) (toSeq sb)
+ src/Data/List/Alternating.hs view
@@ -0,0 +1,93 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.List.Alternating+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.List.Alternating(+ Alternating(..)+ , withNeighbours+ , mergeAlternating+ , insertBreakPoints+ , reverse+ ) where++import Prelude hiding (reverse)+import Control.Lens+import Data.Bifoldable+import Data.Bitraversable+import Data.Ext+import qualified Data.List as List++--------------------------------------------------------------------------------++-- | A (non-empty) alternating list of @a@\'s and @b@\'s+data Alternating a b = Alternating a [b :+ a] deriving (Show,Eq,Ord)++instance Bifunctor Alternating where+ bimap = bimapDefault+instance Bifoldable Alternating where+ bifoldMap = bifoldMapDefault+instance Bitraversable Alternating where+ bitraverse f g (Alternating a xs) = Alternating <$> f a <*> traverse (bitraverse g f) xs+++-- | Computes a b with all its neighbours+--+-- >>> withNeighbours (Alternating 0 ['a' :+ 1, 'b' :+ 2, 'c' :+ 3])+-- [(0,'a' :+ 1),(1,'b' :+ 2),(2,'c' :+ 3)]+withNeighbours :: Alternating a b -> [(a,b :+ a)]+withNeighbours (Alternating a0 xs) = let as = a0 : map (^.extra) xs+ in zip as xs++++-- | Generic merging scheme that merges two Alternatings and applies+-- the function '@f@', with the current/new value at every event. So+-- note that if the alternating consists of 'Alternating a0 [t1 :++-- a1]' then the function is applied to a1, not to a0 (i.e. every+-- value ai is considered alive on the interval [ti,t(i+1))+--+-- >>> let odds = Alternating "a" [3 :+ "c", 5 :+ "e", 7 :+ "g"]+-- >>> let evens = Alternating "b" [4 :+ "d", 6 :+ "f", 8 :+ "h"]+-- >>> mergeAlternating (\_ a b -> a <> b) odds evens+-- [3 :+ "cb",4 :+ "cd",5 :+ "ed",6 :+ "ef",7 :+ "gf",8 :+ "gh"]+-- >>> mergeAlternating (\t a b -> if t `mod` 2 == 0 then a else b) odds evens+-- [3 :+ "b",4 :+ "c",5 :+ "d",6 :+ "e",7 :+ "f",8 :+ "g"]+-- >>> mergeAlternating (\_ a b -> a <> b) odds (Alternating "b" [0 :+ "d", 5 :+ "e", 8 :+ "h"])+-- [0 :+ "ad",3 :+ "cd",5 :+ "ee",7 :+ "ge",8 :+ "gh"]+mergeAlternating :: Ord t+ => (t -> a -> b -> c)+ -> Alternating a t -> Alternating b t -> [t :+ c]+mergeAlternating f (Alternating a00 as0)+ (Alternating b00 bs0) = go a00 b00 as0 bs0+ where+ go a _ [] bs = map (\(t :+ b) -> t :+ f t a b) bs+ go _ b as [] = map (\(t :+ a) -> t :+ f t a b) as+ go a0 b0 as@((t :+ a):as') bs@((t' :+ b):bs') = case t `compare` t' of+ LT -> (t :+ f t a b0) : go a b0 as' bs+ EQ -> (t :+ f t a b) : go a b as' bs'+ GT -> (t' :+ f t' a0 b) : go a0 b as bs'+++-- | Adds additional t-values in the alternating, (in sorted order). I.e. if we insert a+-- "breakpoint" at time t the current '@a@' value is used at that time.+--+-- >>> insertBreakPoints [0,2,4,6,8,10] $ Alternating "a" [3 :+ "c", 5 :+ "e", 7 :+ "g"]+-- Alternating "a" [0 :+ "a",2 :+ "a",3 :+ "c",4 :+ "c",5 :+ "e",6 :+ "e",7 :+ "g",8 :+ "g",10 :+ "g"]+insertBreakPoints :: Ord t => [t] -> Alternating a t -> Alternating a t+insertBreakPoints ts a@(Alternating a0 _) =+ Alternating a0 $ mergeAlternating (\_ _ a' -> a') (Alternating undefined (ext <$> ts)) a+++-- | Reverses an alternating list.+--+-- >>> reverse $ Alternating "a" [3 :+ "c", 5 :+ "e", 7 :+ "g"]+-- Alternating "g" [7 :+ "e",5 :+ "c",3 :+ "a"]+reverse :: Alternating a b -> Alternating a b+reverse p@(Alternating s xs) = case xs of+ [] -> p+ ((e1 :+ _):tl) -> let ys = (e1 :+ s) : List.zipWith (\(_ :+ v) (e :+ _) -> e :+ v) xs tl+ t = last xs ^. extra+ in Alternating t (List.reverse ys)
+ src/Data/List/Set.hs view
@@ -0,0 +1,70 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.List.Set+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.List.Set( Set, singleton+ , insert, delete+ , union, intersection, difference+ , fromList, insertAll+ ) where++import qualified Data.List as List++--------------------------------------------------------------------------------++-- | A Set of @a@\'s, implemented using a simple list. The only+-- advantage of this implementation over 'Data.Set' from containers is+-- that most operations require only @'Eq a'@ rather than @'Ord a'@.+newtype Set a = Set { toList :: [a] }+ deriving (Show,Read,Functor,Foldable,Traversable)++instance Eq a => Eq (Set a) where+ (Set xs) == (Set ys) = all (`elem` ys) xs && all (`elem` xs) ys+++instance Eq a => Semigroup (Set a) where+ (Set xs) <> s = insertAll xs s++instance Eq a => Monoid (Set a) where+ mempty = Set []++-- | Creates a singleton set.+singleton :: a -> Set a+singleton x = Set [x]++-- | \(O(n)\) Inserts an element in the set+insert :: Eq a => a -> Set a -> Set a+insert x s@(Set xs) | x `elem` s = s+ | otherwise = Set (x:xs)++-- | \( O(n^2) \) Insert an element in a set.+insertAll :: Eq a => [a] -> Set a -> Set a+insertAll xs s = List.foldl' (flip insert) s xs++-- | \( O(n^2) \) Create a set from a finite list of elements.+fromList :: Eq a => [a] -> Set a+fromList = flip insertAll mempty++-- | \(O(n)\) Deletes an element from the set+delete :: Eq a => a -> Set a -> Set a+delete x (Set xs) = Set $ go xs+ where+ go = \case+ [] -> []+ (y:ys) | x == y -> ys -- found the element, no need to continue looking+ | otherwise -> y:go ys++-- | \(O(n^2)\) Computes the union of two sets+union :: Eq a => Set a -> Set a -> Set a+union = (<>)++-- | \(O(n^2)\) Computes the intersection of two sets+intersection :: Eq a => Set a -> Set a -> Set a+(Set xs) `intersection` (Set ys) = Set (xs `List.intersect` ys)++-- | \(O(n^2)\) Computes the difference of two sets+difference :: Eq a => Set a -> Set a -> Set a+(Set xs) `difference` (Set ys) = Set $ xs List.\\ ys
+ src/Data/List/Util.hs view
@@ -0,0 +1,144 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.List.Util+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.List.Util where++import Data.Bifunctor+import Data.Ext+import qualified Data.Foldable as F+import qualified Data.List as List+import Data.List.NonEmpty (NonEmpty(..))+import qualified Data.List.NonEmpty as NonEmpty+import Data.List.Zipper (allNonEmptyNexts, extractNext)+import qualified Data.List.Zipper as Zipper+import Data.Maybe+import Data.Ord (comparing)++--------------------------------------------------------------------------------++-- | Given an input list, computes all lists in which just one element is missing.+--+-- >>> mapM_ print $ leaveOutOne [1..5]+-- (1,[2,3,4,5])+-- (2,[1,3,4,5])+-- (3,[1,2,4,5])+-- (4,[1,2,3,5])+-- (5,[1,2,3,4])+-- >>> leaveOutOne []+-- []+-- >>> leaveOutOne [1]+-- [(1,[])]+leaveOutOne :: [a] -> [(a,[a])]+leaveOutOne xs = second F.toList . fromJust . extractNext+ <$> allNonEmptyNexts (Zipper.fromList xs)+++--------------------------------------------------------------------------------+-- * Improved functions for minima and maxima++-- | Safe variant of Prelude.minimum.+--+-- >>> minimum1 [] :: Maybe ()+-- Nothing+-- >>> minimum1 [1,2,3]+-- Just 1+minimum1 :: Ord a => [a] -> Maybe a+minimum1 = minimum1By compare++-- | Safe variant of Prelude.maximum.+--+-- >>> maximum1 [] :: Maybe ()+-- Nothing+-- >>> maximum1 [1,2,3]+-- Just 3+maximum1 :: Ord a => [a] -> Maybe a+maximum1 = minimum1By (flip compare)++-- | Total variant of Data.List.minimumBy.+--+-- >>> minimum1By (comparing abs) [] :: Maybe Int+-- Nothing+-- >>> minimum1By (comparing abs) [1,-2,3]+-- Just 1+minimum1By :: (a -> a -> Ordering) -> [a] -> Maybe a+minimum1By cmp = \case+ [] -> Nothing+ xs -> Just $ List.minimumBy cmp xs++-- | Computes all minima by comparing some property.+--+-- >>> minimaOn (max 2) [1,2,3,4,5,-1]+-- [-1,2,1]+minimaOn :: Ord b => (a -> b) -> [a] -> [a]+minimaOn f = minimaBy (comparing f)++-- | Computes all minima.+--+-- >>> minimaBy (comparing abs) [1,2,3,2,1,-1]+-- [-1,1,1]+minimaBy :: (a -> a -> Ordering) -> [a] -> [a]+minimaBy cmp = \case+ [] -> []+ (x:xs) -> NonEmpty.toList $ List.foldl' (\mins@(m:|_) y -> case m `cmp` y of+ LT -> mins+ EQ -> y NonEmpty.<| mins+ GT -> y:|[]+ ) (x:|[]) xs++-- | extracts all minima from the list. The result consists of the+-- list of minima, and all remaining points. Both lists are returned+-- in the order in which they occur in the input.+--+-- >>> extractMinimaBy compare [1,2,3,0,1,2,3,0,1,2,0,2]+-- [0,0,0] :+ [2,3,1,2,3,1,2,1,2]+extractMinimaBy :: (a -> a -> Ordering) -> [a] -> [a] :+ [a]+extractMinimaBy cmp = \case+ [] -> [] :+ []+ (x:xs) -> first NonEmpty.toList $ foldr (\y (mins@(m:|_) :+ rest) ->+ case m `cmp` y of+ LT -> mins :+ y:rest+ EQ -> (y NonEmpty.<| mins) :+ rest+ GT -> (y:|[]) :+ NonEmpty.toList mins <> rest+ ) ((x:|[]) :+ []) xs+ -- TODO: This is actually a good scenario for testing how much slower :+ is compared+ -- to doing nothing. i..e compare minimaBy and extractMinimaBy+ -- note that I'm using foldr here, and foldl' before+++--------------------------------------------------------------------------------+-- * Partitioning and Grouping++-- | Given a function f, partitions the list into three lists+-- (lts,eqs,gts) such that:+--+-- - f x == LT for all x in lts+-- - f x == EQ for all x in eqs+-- - f x == gt for all x in gts+--+-- >>> partition3 (compare 4) [0,1,2,2,3,4,5,5,6,6,7,7,7,7,7,8]+-- ([5,5,6,6,7,7,7,7,7,8],[4],[0,1,2,2,3])+--+partition3 :: Foldable f => (a -> Ordering) -> f a -> ([a],[a],[a])+partition3 f = foldr g ([],[],[])+ where+ g x (lts,eqs,gts) = case f x of+ LT -> (x:lts, eqs, gts)+ EQ -> ( lts, x:eqs, gts)+ GT -> ( lts, eqs,x:gts)++-- | A version of groupBy that uses the given Ordering to group+-- consecutive Equal items+--+-- >>> groupBy' compare [0,1,2,2,3,4,5,5,6,6,7,7,7,7,7,8]+-- [0 :| [],1 :| [],2 :| [2],3 :| [],4 :| [],5 :| [5],6 :| [6],7 :| [7,7,7,7],8 :| []]+groupBy' :: (a -> a -> Ordering) -> [a] -> [NonEmpty a]+groupBy' cmp = go+ where+ go = \case+ [] -> []+ (x:xs) -> let (pref,rest) = List.span (\y -> x `cmp` y == EQ) xs+ in (x :| pref) : go rest
+ src/Data/List/Zipper.hs view
@@ -0,0 +1,79 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.List.Zipper+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.List.Zipper where++import qualified Data.List as List++--------------------------------------------------------------------------------++-- | Simple Zipper for Lists.+data Zipper a = Zipper [a] [a] deriving (Show,Eq,Functor)++instance Foldable Zipper where+ -- Folds like it it is a normal list+ foldMap f (Zipper ls rs) = foldMap f (reverse ls) <> foldMap f rs+++-- | Construct a Zipper from a list+--+-- running time: \(O(1)\)+fromList :: [a] -> Zipper a+fromList = Zipper []++-- | Go to the Next Element+--+-- running time: \(O(1)\)+goNext :: Zipper a -> Maybe (Zipper a)+goNext (Zipper xs ys) = case ys of+ [] -> Nothing+ x:ys' -> Just $ Zipper (x:xs) ys'++-- | Go to the previous Element+--+-- running time: \(O(1)\)+goPrev :: Zipper a -> Maybe (Zipper a)+goPrev (Zipper xs ys) = case xs of+ [] -> Nothing+ x:xs' -> Just $ Zipper xs' (x:ys)++-- | Computes all nexts, even one that has no elements initially or at+-- the end.+--+-- >>> mapM_ print $ allNexts $ fromList [1..5]+-- Zipper [] [1,2,3,4,5]+-- Zipper [1] [2,3,4,5]+-- Zipper [2,1] [3,4,5]+-- Zipper [3,2,1] [4,5]+-- Zipper [4,3,2,1] [5]+-- Zipper [5,4,3,2,1] []+allNexts :: Zipper a -> [Zipper a]+allNexts = List.unfoldr (fmap (\z -> (z,goNext z))) . Just++-- | Returns the next element, and the zipper without it+extractNext :: Zipper a -> Maybe (a, Zipper a)+extractNext (Zipper xs ys) = case ys of+ [] -> Nothing+ (y:ys') -> Just (y,Zipper xs ys')+++-- | Drops the next element in the zipper.+--+-- running time: \(O(1)\)+dropNext :: Zipper a -> Maybe (Zipper a)+dropNext = fmap snd . extractNext++-- | Computes all list that still have next elements.+--+-- >>> mapM_ print $ allNonEmptyNexts $ fromList [1..5]+-- Zipper [] [1,2,3,4,5]+-- Zipper [1] [2,3,4,5]+-- Zipper [2,1] [3,4,5]+-- Zipper [3,2,1] [4,5]+-- Zipper [4,3,2,1] [5]+allNonEmptyNexts :: Zipper a -> [Zipper a]+allNonEmptyNexts = List.unfoldr (\z -> (z,) <$> goNext z)
+ src/Data/Measured.hs view
@@ -0,0 +1,11 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.Measured+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.Measured( module Data.Measured.Class+ ) where++import Data.Measured.Class
+ src/Data/Measured/Class.hs view
@@ -0,0 +1,21 @@+{-# Language FunctionalDependencies #-}+--------------------------------------------------------------------------------+-- |+-- Module : Data.Measured.Class+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.Measured.Class where++-- | Things that can be measured.+class Semigroup v => Measured v a | a -> v where+ measure :: a -> v++-- | Things that can be inserted.+class Measured v a => CanInsert v a where+ insertA :: a -> v -> v++-- | Things that can be deleted.+class Measured v a => CanDelete v a where+ deleteA :: a -> v -> Maybe v
+ src/Data/Measured/Size.hs view
@@ -0,0 +1,48 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.Measured.Size+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.Measured.Size where++import Control.DeepSeq+import Data.Measured.Class+import GHC.Generics (Generic)++--------------------------------------------------------------------------------++-- | Measured size. Always non-negative.+newtype Size = Size Word deriving (Show,Read,Eq,Num,Integral,Enum,Real,Ord,Generic,NFData)++instance Semigroup Size where+ x <> y = x + y++instance Monoid Size where+ mempty = Size 0++--------------------------------------------------------------------------------++-- | Newtype wrapper for things for which we can measure the size+newtype Elem a = Elem { _unElem :: a }+ deriving (Show,Read,Eq,Ord,Functor,Foldable,Traversable)++instance Measured Size (Elem a) where+ measure _ = 1++--------------------------------------------------------------------------------++-- | Things that have a size+data Sized a = Sized {-# UNPACK #-} !Size a+ deriving (Show,Eq,Ord,Functor,Foldable,Traversable,Generic)+instance NFData a => NFData (Sized a)++instance Semigroup a => Semigroup (Sized a) where+ (Sized i a) <> (Sized j b) = Sized (i <> j) (a <> b)++instance Monoid a => Monoid (Sized a) where+ mempty = Sized mempty mempty++-- instance Semigroup a => Measured Size (Sized a) where+-- measure (Sized i _) = i
src/Data/OrdSeq.hs view
@@ -1,12 +1,41 @@-module Data.OrdSeq where+--------------------------------------------------------------------------------+-- |+-- Module : Data.OrdSeq+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.OrdSeq+ ( OrdSeq+ , Compare+ , insertBy+ , insert+ , splitBy+ , splitOn+ , splitMonotonic+ , deleteAll+ , deleteAllBy+ , fromListBy+ , fromListByOrd+ , fromAscList+ , lookupBy+ , memberBy+ , mapMonotonic+ , viewl+ , viewr+ , minView+ , lookupMin+ , maxView+ , lookupMax+ ) where -import Control.Lens (bimap)-import qualified Data.FingerTree as FT+import Control.Lens (bimap) import Data.FingerTree hiding (null, viewl, viewr)-import qualified Data.Foldable as F-import Data.Maybe-import Test.QuickCheck+import qualified Data.FingerTree as FT+import qualified Data.Foldable as F+import Data.Maybe (fromJust, isJust, listToMaybe)+import Test.QuickCheck (Arbitrary (arbitrary)) -------------------------------------------------------------------------------- @@ -28,15 +57,18 @@ -newtype Elem a = Elem { getElem :: a } deriving (Eq,Ord,Traversable,Foldable,Functor)+newtype Elem a = Elem a deriving (Eq,Ord,Traversable,Foldable,Functor) instance Show a => Show (Elem a) where show (Elem x) = "Elem " <> show x -+-- | Sequence of ordered elements. newtype OrdSeq a = OrdSeq { _asFingerTree :: FingerTree (Key a) (Elem a) }- deriving (Show,Eq)+ deriving (Eq) +instance Show a => Show (OrdSeq a) where+ show s = "fromAscList " ++ show (F.toList s)+ instance Semigroup (OrdSeq a) where (OrdSeq s) <> (OrdSeq t) = OrdSeq $ s `mappend` t @@ -57,7 +89,7 @@ instance Measured (Key a) (Elem a) where measure (Elem x) = Key x -+-- | Signature for functions that give the ordering of two values. type Compare a = a -> a -> Ordering -- | Insert into a monotone OrdSeq.@@ -76,6 +108,7 @@ insert :: Ord a => a -> OrdSeq a -> OrdSeq a insert = insertBy compare +-- | \( O(\log n) \). Delete all elements that compare as equal to @x@. deleteAllBy :: Compare a -> a -> OrdSeq a -> OrdSeq a deleteAllBy cmp x s = l <> r where@@ -93,18 +126,18 @@ (m',r) = split (\v -> liftCmp cmp v (Key x) == GT) m +{- HLINT ignore splitOn -} -- | Given a monotonic function f that maps a to b, split the sequence s -- depending on the b values. I.e. the result (l,m,r) is such that--- * all (< x) . fmap f $ l--- * all (== x) . fmap f $ m--- * all (> x) . fmap f $ r ----- >>> splitOn id 3 $ fromAscList' [1..5]--- (OrdSeq {_asFingerTree = fromList [Elem 1,Elem 2]},OrdSeq {_asFingerTree = fromList [Elem 3]},OrdSeq {_asFingerTree = fromList [Elem 4,Elem 5]})--- >>> splitOn fst 2 $ fromAscList' [(0,"-"),(1,"A"),(2,"B"),(2,"C"),(3,"D"),(4,"E")]--- (OrdSeq {_asFingerTree = fromList [Elem (0,"-"),Elem (1,"A")]},OrdSeq {_asFingerTree = fromList [Elem (2,"B"),Elem (2,"C")]},OrdSeq {_asFingerTree = fromList [Elem (3,"D"),Elem (4,"E")]})+-- * @all (< x) . fmap f $ l@+-- * @all (== x) . fmap f $ m@+-- * @all (> x) . fmap f $ r@ ----- \(O(\log n)\)+-- >>> splitOn id 3 $ fromAscList [1..5]+-- (fromAscList [1,2],fromAscList [3],fromAscList [4,5])+-- >>> splitOn fst 2 $ fromAscList [(0,"-"),(1,"A"),(2,"B"),(2,"C"),(3,"D"),(4,"E")]+-- (fromAscList [(0,"-"),(1,"A")],fromAscList [(2,"B"),(2,"C")],fromAscList [(3,"D"),(4,"E")]) splitOn :: Ord b => (a -> b) -> b -> OrdSeq a -> (OrdSeq a, OrdSeq a, OrdSeq a) splitOn f x (OrdSeq s) = (OrdSeq l, OrdSeq m', OrdSeq r) where@@ -119,7 +152,7 @@ splitMonotonic p = bimap OrdSeq OrdSeq . split (p . getKey) . _asFingerTree --- Deletes all elements from the OrdDeq+-- | Deletes all elements from the OrdDeq -- -- \(O(n\log n)\) deleteAll :: Ord a => a -> OrdSeq a -> OrdSeq a@@ -136,58 +169,56 @@ fromListByOrd :: Ord a => [a] -> OrdSeq a fromListByOrd = fromListBy compare --- | O(n)-fromAscList' :: [a] -> OrdSeq a-fromAscList' = OrdSeq . fromList . fmap Elem+-- | \( O(n) \)+fromAscList :: [a] -> OrdSeq a+fromAscList = OrdSeq . fromList . fmap Elem -- | \(O(\log n)\) lookupBy :: Compare a -> a -> OrdSeq a -> Maybe a lookupBy cmp x s = let (_,m,_) = splitBy cmp x s in listToMaybe . F.toList $ m +-- | \(O(\log n)\). Queries for the existance of any elements that compare as equal to @x@. memberBy :: Compare a -> a -> OrdSeq a -> Bool memberBy cmp x = isJust . lookupBy cmp x --- | Fmap, assumes the order does not change--- O(n)+-- | \( O(n) \) Fmap, assumes the order does not change mapMonotonic :: (a -> b) -> OrdSeq a -> OrdSeq b-mapMonotonic f = fromAscList' . map f . F.toList+mapMonotonic f = fromAscList . map f . F.toList --- | Gets the first element from the sequence--- \(O(1)\)+-- | \(O(1)\) Gets the first element from the sequence viewl :: OrdSeq a -> ViewL OrdSeq a viewl = f . FT.viewl . _asFingerTree where- f EmptyL = EmptyL- f (Elem x :< s) = x :< OrdSeq s+ f EmptyL = EmptyL+ f (Elem x :< s) = x :< OrdSeq s --- Last element--- \(O(1)\)+-- | \(O(1)\) Gets the last element from the sequence viewr :: OrdSeq a -> ViewR OrdSeq a viewr = f . FT.viewr . _asFingerTree where- f EmptyR = EmptyR- f (s :> Elem x) = OrdSeq s :> x+ f EmptyR = EmptyR+ f (s :> Elem x) = OrdSeq s :> x --- \(O(1)\)+-- | \(O(1)\) minView :: OrdSeq a -> Maybe (a, OrdSeq a) minView s = case viewl s of EmptyL -> Nothing (x :< t) -> Just (x,t) --- \(O(1)\)+-- | \(O(1)\) lookupMin :: OrdSeq a -> Maybe a lookupMin = fmap fst . minView --- \(O(1)\)+-- | \(O(1)\) maxView :: OrdSeq a -> Maybe (a, OrdSeq a) maxView s = case viewr s of EmptyR -> Nothing (t :> x) -> Just (x,t) --- \(O(1)\)+-- | \(O(1)\) lookupMax :: OrdSeq a -> Maybe a lookupMax = fmap fst . maxView
src/Data/PlanarGraph.hs view
@@ -1,6 +1,4 @@-{-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE ScopedTypeVariables #-}-{-# LANGUAGE OverloadedStrings #-} -------------------------------------------------------------------------------- -- | -- Module : Data.PlanarGraph@@ -47,6 +45,7 @@ , tailOf, headOf, endPoints , incidentEdges, incomingEdges, outgoingEdges, neighboursOf , nextIncidentEdge, prevIncidentEdge+ , nextIncidentEdgeFrom, prevIncidentEdgeFrom -- * Associated Data @@ -71,10 +70,12 @@ -------------------------------------------------------------------------------- -- $setup+-- >>> import qualified Data.Vector as V+-- >>> import Control.Lens -- >>> :{ -- let dart i s = Dart (Arc i) (read s) -- (aA:aB:aC:aD:aE:aG:_) = take 6 [Arc 0..]--- myGraph :: PlanarGraph () Primal () String ()+-- myGraph :: PlanarGraph () Primal String String String -- myGraph = planarGraph [ [ (Dart aA Negative, "a-") -- , (Dart aC Positive, "c+") -- , (Dart aB Positive, "b+")@@ -91,7 +92,10 @@ -- ] -- , [ (Dart aG Negative, "g-") -- ]--- ]+-- ] & vertexData .~ V.fromList ["u","v","w","x"]+-- & faceData .~ V.fromList ["f_3", "f_infty","f_1","f_2"]+-- showWithData :: HasDataOf s i => s -> i -> (i, DataOf s i)+-- showWithData g i = (i, g^.dataOf i) -- :} -- --@@ -99,8 +103,6 @@ -- arrows are just to indicate what the Positive direction of the darts is. -- -- -- --------------------------------------------------------------------------------
src/Data/PlanarGraph/AdjRep.hs view
@@ -11,16 +11,17 @@ -------------------------------------------------------------------------------- module Data.PlanarGraph.AdjRep where -import Data.Aeson-import GHC.Generics (Generic)-import Control.Lens(Bifunctor(..))+import Control.Lens (Bifunctor (..))+import Data.Aeson+import Data.Bifunctor (second)+import GHC.Generics (Generic) -------------------------------------------------------------------------------- -- | Data type representing the graph in its JSON/Yaml format data Gr v f = Gr { adjacencies :: [v] , faces :: [f]- } deriving (Generic)+ } deriving (Generic, Show, Eq) instance Bifunctor Gr where bimap f g (Gr vs fs) = Gr (map f vs) (map g fs)@@ -43,10 +44,10 @@ -- vertices. This is not (yet) -- enforced by the data type. , vData :: v- } deriving (Generic)+ } deriving (Generic, Show, Eq) instance Bifunctor Vtx where- bimap f g (Vtx i as x) = Vtx i (map (\(j,y) -> (j,g y)) as) (f x)+ bimap f g (Vtx i as x) = Vtx i (map (second g) as) (f x) instance (ToJSON v, ToJSON e) => ToJSON (Vtx v e) where toEncoding = genericToEncoding defaultOptions@@ -58,7 +59,7 @@ data Face f = Face { incidentEdge :: (Int,Int) -- ^ an edge (u,v) s.t. the face -- is right from (u,v) , fData :: f- } deriving (Generic,Functor)+ } deriving (Generic,Functor, Show, Eq) instance ToJSON f => ToJSON (Face f) where toEncoding = genericToEncoding defaultOptions
src/Data/PlanarGraph/Core.hs view
@@ -1,4 +1,3 @@-{-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE ScopedTypeVariables #-} -------------------------------------------------------------------------------- -- |@@ -13,18 +12,19 @@ import Control.DeepSeq-import Control.Lens hiding ((.=))+import Control.Lens hiding ((.=)) import Control.Monad.State.Strict import Data.Aeson-import qualified Data.Foldable as F+import qualified Data.Foldable as F import Data.Permutation import Data.PlanarGraph.Dart-import Data.Type.Equality (gcastWith, (:~:)(..))-import qualified Data.Vector as V-import qualified Data.Vector.Mutable as MV-import GHC.Generics (Generic)-import Unsafe.Coerce (unsafeCoerce)+import Data.Type.Equality (gcastWith)+import qualified Data.Vector as V+import qualified Data.Vector.Mutable as MV+import GHC.Generics (Generic)+import Unsafe.Coerce (unsafeCoerce) + -------------------------------------------------------------------------------- --------------------------------------------------------------------------------@@ -32,7 +32,7 @@ -- >>> :{ -- let dart i s = Dart (Arc i) (read s) -- (aA:aB:aC:aD:aE:aG:_) = take 6 [Arc 0..]--- myGraph :: PlanarGraph () Primal () String ()+-- myGraph :: PlanarGraph () Primal String String String -- myGraph = planarGraph [ [ (Dart aA Negative, "a-") -- , (Dart aC Positive, "c+") -- , (Dart aB Positive, "b+")@@ -49,7 +49,10 @@ -- ] -- , [ (Dart aG Negative, "g-") -- ]--- ]+-- ] & vertexData .~ V.fromList ["u","v","w","x"]+-- & faceData .~ V.fromList ["f_3", "f_infty","f_1","f_2"]+-- showWithData :: HasDataOf s i => s -> i -> (i, DataOf s i)+-- showWithData g i = (i, g^.dataOf i) -- :} -- --@@ -90,6 +93,7 @@ -- | Shorthand for vertices in the primal. type VertexId' s = VertexId s Primal +-- | Getter for a VertexId's unique number. unVertexId :: Getter (VertexId s w) Int unVertexId = to _unVertexId @@ -99,7 +103,7 @@ -------------------------------------------------------------------------------- -- * FaceId's --- | The type to reprsent FaceId's+-- | The type to represent FaceId's newtype FaceId s w = FaceId { _unFaceId :: VertexId s (DualOf w) } deriving (Eq,Ord,Enum,ToJSON,FromJSON) @@ -145,19 +149,22 @@ -- ** lenses and getters --- | Get the embedding, reprsented as a permutation of the darts, of this+-- | Get the embedding, represented as a permutation of the darts, of this -- graph. embedding :: Getter (PlanarGraph s w v e f) (Permutation (Dart s)) embedding = to _embedding +-- | O\(1\) access, \( O(n) \) update. vertexData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v' e f) (V.Vector v) (V.Vector v') vertexData = lens _vertexData (\g vD -> updateData (const vD) id id g) +-- | O\(1\) access, \( O(n) \) update. rawDartData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v e' f) (V.Vector e) (V.Vector e') rawDartData = lens _rawDartData (\g dD -> updateData id (const dD) id g) +-- | O\(1\) access, \( O(n) \) update. faceData :: Lens (PlanarGraph s w v e f) (PlanarGraph s w v e f') (V.Vector f) (V.Vector f') faceData = lens _faceData (\g fD -> updateData id id (const fD) g)@@ -182,6 +189,9 @@ (V.Vector (Dart s, e)) (V.Vector (Dart s, e')) edgeData = dartData +++ -- | Helper function to update the data in a planar graph. Takes care to update -- both the data in the original graph as well as in the dual. updateData :: forall s w v e f v' e' f'@@ -222,18 +232,18 @@ -- | Traverse the vertices ----- (^.vertexData) <$> traverseVertices (\i x -> Just (i,x)) myGraph--- Just [(VertexId 0,()),(VertexId 1,()),(VertexId 2,()),(VertexId 3,())]+-- >>> (^.vertexData) <$> traverseVertices (\i x -> Just (i,x)) myGraph+-- Just [(VertexId 0,"u"),(VertexId 1,"v"),(VertexId 2,"w"),(VertexId 3,"x")] -- >>> traverseVertices (\i x -> print (i,x)) myGraph >> pure ()--- (VertexId 0,())--- (VertexId 1,())--- (VertexId 2,())--- (VertexId 3,())+-- (VertexId 0,"u")+-- (VertexId 1,"v")+-- (VertexId 2,"w")+-- (VertexId 3,"x") traverseVertices :: Applicative m => (VertexId s w -> v -> m v') -> PlanarGraph s w v e f -> m (PlanarGraph s w v' e f)-traverseVertices f = itraverseOf (vertexData.itraversed) (\i -> f (VertexId i))+traverseVertices f = itraverseOf (vertexData.itraversed) (f . VertexId) -- | Traverses the darts --@@ -254,15 +264,15 @@ => (Dart s -> e -> m e') -> PlanarGraph s w v e f -> m (PlanarGraph s w v e' f)-traverseDarts f = itraverseOf (rawDartData.itraversed) (\i -> f (toEnum i))+traverseDarts f = itraverseOf (rawDartData.itraversed) (f . toEnum) -- | Traverses the faces -- -- >>> traverseFaces (\i x -> print (i,x)) myGraph >> pure ()--- (FaceId 0,())--- (FaceId 1,())--- (FaceId 2,())--- (FaceId 3,())+-- (FaceId 0,"f_3")+-- (FaceId 1,"f_infty")+-- (FaceId 2,"f_1")+-- (FaceId 3,"f_2") traverseFaces :: Applicative m => (FaceId s w -> f -> m f') -> PlanarGraph s w v e f@@ -294,7 +304,7 @@ -- -- running time: \(O(n)\). planarGraph :: [[(Dart s,e)]] -> PlanarGraph s Primal () e ()-planarGraph ds = (planarGraph' perm)&dartData .~ (V.fromList . concat $ ds)+planarGraph ds = planarGraph' perm & dartData .~ (V.fromList . concat $ ds) where n = sum . map length $ ds perm = toCycleRep n $ map (map fst) ds@@ -405,75 +415,155 @@ -- | The tail of a dart, i.e. the vertex this dart is leaving from --+-- >>> showWithData myGraph $ tailOf (Dart (Arc 3) Positive) myGraph+-- (VertexId 2,"w")+-- -- running time: \(O(1)\) tailOf :: Dart s -> PlanarGraph s w v e f -> VertexId s w tailOf d g = VertexId . fst $ lookupIdx (g^.embedding) d -- | The vertex this dart is heading in to --+-- showWithData myGraph $ headOf (Dart (Arc 3) Positive) myGraph+-- (VertexId 1,"v")+-- -- running time: \(O(1)\) headOf :: Dart s -> PlanarGraph s w v e f -> VertexId s w headOf d = tailOf (twin d) -- | endPoints d g = (tailOf d g, headOf d g) --+-- >>> endPoints (Dart (Arc 3) Positive) myGraph+-- (VertexId 2,VertexId 1)+-- -- running time: \(O(1)\) endPoints :: Dart s -> PlanarGraph s w v e f -> (VertexId s w, VertexId s w) endPoints d g = (tailOf d g, headOf d g) - -- | All edges incident to vertex v, in counterclockwise order around v. -----+-- >>> incidentEdges (VertexId 1) myGraph+-- [Dart (Arc 4) -1,Dart (Arc 1) -1,Dart (Arc 3) -1,Dart (Arc 5) +1]+-- >>> mapM_ (print . showWithData myGraph) $ incidentEdges (VertexId 1) myGraph+-- (Dart (Arc 4) -1,"e-")+-- (Dart (Arc 1) -1,"b-")+-- (Dart (Arc 3) -1,"d-")+-- (Dart (Arc 5) +1,"g+")+-- >>> mapM_ (print . showWithData myGraph) $ incidentEdges (VertexId 3) myGraph+-- (Dart (Arc 5) -1,"g-") -- -- running time: \(O(k)\), where \(k\) is the output size incidentEdges :: VertexId s w -> PlanarGraph s w v e f -> V.Vector (Dart s) incidentEdges (VertexId v) g = g^?!embedding.orbits.ix v- -- TODO: The Delaunay triang. stuff seems to produce these in clockwise order instead --- | All incoming edges incident to vertex v, in counterclockwise order around v.+-- | All edges incident to vertex v in incoming direction+-- (i.e. pointing into v) in counterclockwise order around v.+--+-- >>> incomingEdges (VertexId 1) myGraph+-- [Dart (Arc 4) +1,Dart (Arc 1) +1,Dart (Arc 3) +1,Dart (Arc 5) -1]+-- >>> mapM_ (print . showWithData myGraph) $ incomingEdges (VertexId 1) myGraph+-- (Dart (Arc 4) +1,"e+")+-- (Dart (Arc 1) +1,"b+")+-- (Dart (Arc 3) +1,"d+")+-- (Dart (Arc 5) -1,"g-")+--+-- running time: \(O(k)\), where \(k) is the total number of incident edges of v incomingEdges :: VertexId s w -> PlanarGraph s w v e f -> V.Vector (Dart s)-incomingEdges v g = V.filter (not . isPositive) $ incidentEdges v g+incomingEdges v g = orient <$> incidentEdges v g+ where+ orient d = if headOf d g == v then d else twin d --- | All outgoing edges incident to vertex v, in counterclockwise order around v.+-- | All edges incident to vertex v in outgoing direction+-- (i.e. pointing away from v) in counterclockwise order around v.+--+-- running time: \(O(k)\), where \(k) is the total number of incident edges of v outgoingEdges :: VertexId s w -> PlanarGraph s w v e f -> V.Vector (Dart s)-outgoingEdges v g = V.filter isPositive $ incidentEdges v g+outgoingEdges v g = orient <$> incidentEdges v g+ where+ orient d = if tailOf d g == v then d else twin d -- | Gets the neighbours of a particular vertex, in counterclockwise order -- around the vertex. --+-- >>> mapM_ (print . showWithData myGraph) $ neighboursOf (VertexId 1) myGraph -- around v+-- (VertexId 2,"w")+-- (VertexId 0,"u")+-- (VertexId 2,"w")+-- (VertexId 3,"x")+-- >>> mapM_ (print . showWithData myGraph) $ neighboursOf (VertexId 3) myGraph -- around x+-- (VertexId 1,"v")+-- -- running time: \(O(k)\), where \(k\) is the output size neighboursOf :: VertexId s w -> PlanarGraph s w v e f -> V.Vector (VertexId s w)-neighboursOf v g = otherVtx <$> incidentEdges v g- where- otherVtx d = let u = tailOf d g in if u == v then headOf d g else u+neighboursOf v g = flip tailOf g <$> incomingEdges v g -- | Given a dart d that points into some vertex v, report the next dart in the--- cyclic order around v.+-- cyclic (counterclockwise) order around v. --+-- >>> nextIncidentEdge (dart 3 "+1") myGraph+-- Dart (Arc 5) +1+-- >>> showWithData myGraph $ nextIncidentEdge (dart 3 "+1") myGraph+-- (Dart (Arc 5) +1,"g+")+-- >>> showWithData myGraph $ nextIncidentEdge (dart 1 "+1") myGraph+-- (Dart (Arc 3) -1,"d-")+-- -- running time: \(O(1)\)-nextIncidentEdge :: Dart s -> PlanarGraph s w v e f -> Dart s-nextIncidentEdge d g = let perm = g^.embedding- (i,j) = lookupIdx perm d- in next (perm^?!orbits.ix i) j+nextIncidentEdge :: Dart s -> PlanarGraph s w v e f -> Dart s+nextIncidentEdge d = nextIncidentEdgeFrom (twin d) +-- | Given a dart d that points into some vertex v, report the previous dart in the+-- cyclic (counterclockwise) order around v.+--+-- >>> prevIncidentEdge (dart 3 "+1") myGraph+-- Dart (Arc 1) -1+-- >>> showWithData myGraph $ prevIncidentEdge (dart 3 "+1") myGraph+-- (Dart (Arc 1) -1,"b-")+--+-- running time: \(O(1)\)+prevIncidentEdge :: Dart s -> PlanarGraph s w v e f -> Dart s+prevIncidentEdge d = prevIncidentEdgeFrom (twin d) --- | Given a dart d that points into some vertex v, report the next dart in the--- cyclic order around v.++-- | Given a dart d that points away from some vertex v, report the+-- next dart in the cyclic (counterclockwise) order around v. --+-- >>> nextIncidentEdgeFrom (Dart (Arc 3) Positive) myGraph+-- Dart (Arc 2) -1+-- >>> showWithData myGraph $ nextIncidentEdgeFrom (Dart (Arc 3) Positive) myGraph+-- (Dart (Arc 2) -1,"c-")+-- >>> showWithData myGraph $ nextIncidentEdgeFrom (dart 1 "+1") myGraph+-- (Dart (Arc 0) +1,"a+")+-- -- running time: \(O(1)\)-prevIncidentEdge :: Dart s -> PlanarGraph s w v e f -> Dart s-prevIncidentEdge d g = let perm = g^.embedding- (i,j) = lookupIdx perm d- in previous (perm^?!orbits.ix i) j+nextIncidentEdgeFrom :: Dart s -> PlanarGraph s w v e f -> Dart s+nextIncidentEdgeFrom d g = let perm = g^.embedding+ (i,j) = lookupIdx perm d+ in next (perm^?!orbits.ix i) j +-- | Given a dart d that points into away from vertex v, report the previous dart in the+-- cyclic (counterclockwise) order around v.+--+-- >>> prevIncidentEdgeFrom (Dart (Arc 3) Positive) myGraph+-- Dart (Arc 4) +1+-- >>> showWithData myGraph $ prevIncidentEdgeFrom (Dart (Arc 3) Positive) myGraph+-- (Dart (Arc 4) +1,"e+")+-- >>> showWithData myGraph $ prevIncidentEdgeFrom (Dart (Arc 1) Positive) myGraph+-- (Dart (Arc 2) +1,"c+")+--+-- running time: \(O(1)\)+prevIncidentEdgeFrom :: Dart s -> PlanarGraph s w v e f -> Dart s+prevIncidentEdgeFrom d g = let perm = g^.embedding+ (i,j) = lookupIdx perm d+ in previous (perm^?!orbits.ix i) j++ -------------------------------------------------------------------------------- -- * Access data -+-- | General interface to accessing vertex data, dart data, and face data. class HasDataOf g i where type DataOf g i -- | get the data associated with the value i.@@ -495,6 +585,9 @@ -- | Data corresponding to the endpoints of the dart+--+-- >>> myGraph^.endPointDataOf (Dart (Arc 3) Positive)+-- ("w","v") endPointDataOf :: Dart s -> Getter (PlanarGraph s w v e f) (v,v) endPointDataOf d = to $ endPointData d @@ -540,3 +633,35 @@ (g^.rawDartData) (g^.vertexData) g++++--------------------------------------------------------------------------------++-- myGraph :: PlanarGraph () Primal String String String+-- myGraph = planarGraph [ [ (Dart aA Negative, "a-")+-- , (Dart aC Positive, "c+")+-- , (Dart aB Positive, "b+")+-- , (Dart aA Positive, "a+")+-- ]+-- , [ (Dart aE Negative, "e-")+-- , (Dart aB Negative, "b-")+-- , (Dart aD Negative, "d-")+-- , (Dart aG Positive, "g+")+-- ]+-- , [ (Dart aE Positive, "e+")+-- , (Dart aD Positive, "d+")+-- , (Dart aC Negative, "c-")+-- ]+-- , [ (Dart aG Negative, "g-")+-- ]+-- ]+-- & vertexData .~ V.fromList ["u","v","w","x"]+-- & faceData .~ V.fromList ["f_3", "f_infty","f_1","f_2"]+-- where+-- (aA:aB:aC:aD:aE:aG:_) = take 6 [Arc 0..]++-- dart i s = Dart (Arc i) (read s)++-- showWithData :: HasDataOf s i => s -> i -> (i, DataOf s i)+-- showWithData g i = (i, g^.dataOf i)
src/Data/PlanarGraph/Dart.hs view
@@ -62,7 +62,16 @@ data Dart s = Dart { _arc :: !(Arc s) , _direction :: !Direction } deriving (Eq,Ord,Generic)-makeLenses ''Dart++-- | Arc lens.+arc :: Lens' (Dart s) (Arc s)+arc = lens _arc (\d a -> d{_arc = a})++-- | Direction lens.+direction :: Lens' (Dart s) Direction+direction = lens _direction (\d dir -> d{_direction = dir})++-- makeLenses ''Dart instance NFData (Dart s)
src/Data/PlanarGraph/Dual.hs view
@@ -24,7 +24,7 @@ -- >>> :{ -- let dart i s = Dart (Arc i) (read s) -- (aA:aB:aC:aD:aE:aG:_) = take 6 [Arc 0..]--- myGraph :: PlanarGraph () Primal () String ()+-- myGraph :: PlanarGraph () Primal String String String -- myGraph = planarGraph [ [ (Dart aA Negative, "a-") -- , (Dart aC Positive, "c+") -- , (Dart aB Positive, "b+")@@ -41,7 +41,10 @@ -- ] -- , [ (Dart aG Negative, "g-") -- ]--- ]+-- ] & vertexData .~ V.fromList ["u","v","w","x"]+-- & faceData .~ V.fromList ["f_3", "f_infty","f_1","f_2"]+-- showWithData :: HasDataOf s i => s -> i -> (i, DataOf s i)+-- showWithData g i = (i, g^.dataOf i) -- :} -- --@@ -61,14 +64,17 @@ -- | The face to the left of the dart --+-- -- >>> leftFace (dart 1 "+1") myGraph -- FaceId 1+-- >>> showWithData myGraph $ leftFace (dart 1 "+1") myGraph+-- (FaceId 1,"f_infty") -- >>> leftFace (dart 1 "-1") myGraph -- FaceId 2--- >>> leftFace (dart 2 "+1") myGraph--- FaceId 2--- >>> leftFace (dart 0 "+1") myGraph--- FaceId 0+-- >>> showWithData myGraph $ leftFace (dart 1 "-1") myGraph+-- (FaceId 2,"f_1")+-- >>> showWithData myGraph $ leftFace (dart 0 "+1") myGraph+-- (FaceId 0,"f_3") -- -- running time: \(O(1)\). leftFace :: Dart s -> PlanarGraph s w v e f -> FaceId s w@@ -77,50 +83,95 @@ -- | The face to the right of the dart --+-- -- >>> rightFace (dart 1 "+1") myGraph -- FaceId 2+-- >>> showWithData myGraph $ rightFace (dart 1 "+1") myGraph+-- (FaceId 2,"f_1") -- >>> rightFace (dart 1 "-1") myGraph -- FaceId 1--- >>> rightFace (dart 2 "+1") myGraph--- FaceId 1--- >>> rightFace (dart 0 "+1") myGraph--- FaceId 1+-- >>> showWithData myGraph $ rightFace (dart 1 "-1") myGraph+-- (FaceId 1,"f_infty")+-- >>> showWithData myGraph $ rightFace (dart 0 "+1") myGraph+-- (FaceId 1,"f_infty") -- -- running time: \(O(1)\). rightFace :: Dart s -> PlanarGraph s w v e f -> FaceId s w rightFace d g = FaceId . tailOf d $ _dual g --- | Get the next edge along the face+-- | Get the next edge (in clockwise order) along the face that is to+-- the right of this dart. --+-- >> showWithData myGraph $ nextEdge (dart 1 "+1") myGraph+-- (Dart (Arc 3) -1,"d-")+-- >> showWithData myGraph $ nextEdge (dart 2 "+1") myGraph+-- (Dart (Arc 4) +1,"e+")+-- -- running time: \(O(1)\). nextEdge :: Dart s -> PlanarGraph s w v e f -> Dart s-nextEdge d = nextIncidentEdge d . _dual+nextEdge d = nextIncidentEdgeFrom d . _dual+ -- prevIncidentEdge (twin d) (_dual g)+ -- where+ -- f = rightFace d g --- | Get the previous edge along the face+-- | Get the previous edge (in clockwise order) along the face that is+-- to the right of this dart. --+-- >>> showWithData myGraph $ prevEdge (dart 1 "+1") myGraph+-- (Dart (Arc 2) -1,"c-")+-- >>> showWithData myGraph $ prevEdge (dart 3 "-1") myGraph+-- (Dart (Arc 1) +1,"b+")+-- -- running time: \(O(1)\).-prevEdge :: Dart s -> PlanarGraph s w v e f -> Dart s-prevEdge d = prevIncidentEdge d . _dual-+prevEdge :: Dart s -> PlanarGraph s w v e f -> Dart s+prevEdge d = prevIncidentEdgeFrom d . _dual -- | Gets a dart bounding this face. I.e. a dart d such that the face lies to -- the right of the dart.+--+-- >>> boundaryDart (FaceId $ VertexId 2) myGraph+-- Dart (Arc 1) +1+-- >>> showWithData myGraph $ boundaryDart (FaceId $ VertexId 2) myGraph+-- (Dart (Arc 1) +1,"b+")+-- >>> showWithData myGraph $ boundaryDart (FaceId $ VertexId 1) myGraph+-- (Dart (Arc 2) +1,"c+") boundaryDart :: FaceId s w -> PlanarGraph s w v e f -> Dart s boundaryDart f = V.head . boundary f--- TODO: make sure that this is indeed to the right. --- | The darts bounding this face, for internal faces in clockwise order, for--- the outer face in counter clockwise order.+-- | The darts bounding this face. The darts are reported in order+-- along the face. This means that for internal faces the darts are+-- reported in *clockwise* order along the boundary, whereas for the+-- outer face the darts are reported in counter clockwise order. --+-- >>> boundary (FaceId $ VertexId 2) myGraph+-- [Dart (Arc 1) +1,Dart (Arc 3) -1,Dart (Arc 2) -1]+-- >>> mapM_ (print . showWithData myGraph) $ boundary (FaceId $ VertexId 2) myGraph+-- (Dart (Arc 1) +1,"b+")+-- (Dart (Arc 3) -1,"d-")+-- (Dart (Arc 2) -1,"c-")+-- >>> boundary (FaceId $ VertexId 1) myGraph+-- [Dart (Arc 2) +1,Dart (Arc 4) +1,Dart (Arc 1) -1,Dart (Arc 0) +1]+-- >>> mapM_ (print . showWithData myGraph) $ boundary (FaceId $ VertexId 1) myGraph+-- (Dart (Arc 2) +1,"c+")+-- (Dart (Arc 4) +1,"e+")+-- (Dart (Arc 1) -1,"b-")+-- (Dart (Arc 0) +1,"a+") -- -- running time: \(O(k)\), where \(k\) is the output size. boundary :: FaceId s w -> PlanarGraph s w v e f -> V.Vector (Dart s) boundary (FaceId v) g = incidentEdges v $ _dual g ---- | Generates the darts incident to a face, starting with the given dart.+-- | Given a dart d, generates the darts bounding the face that is to+-- the right of the given dart. The darts are reported in order along+-- the face. This means that for internal faces the darts are reported+-- in *clockwise* order along the boundary, whereas for the outer face+-- the darts are reported in counter clockwise order. --+-- >>> mapM_ (print . showWithData myGraph) $ boundary' (dart 1 "+1") myGraph+-- (Dart (Arc 1) +1,"b+")+-- (Dart (Arc 3) -1,"d-")+-- (Dart (Arc 2) -1,"c-") -- -- \(O(k)\), where \(k\) is the number of darts reported boundary' :: Dart s -> PlanarGraph s w v e f -> V.Vector (Dart s)@@ -132,13 +183,22 @@ f i = let (a,b) = V.splitAt i v in b <> a --- | The vertices bounding this face, for internal faces in clockwise order, for--- the outer face in counter clockwise order.+-- | The vertices bounding this face, for internal faces in clockwise+-- order, for the outer face in counter clockwise order. --+-- >>> mapM_ (print . showWithData myGraph) $ boundaryVertices (FaceId $ VertexId 2) myGraph+-- (VertexId 0,"u")+-- (VertexId 1,"v")+-- (VertexId 2,"w")+-- >>> mapM_ (print . showWithData myGraph) $ boundaryVertices (FaceId $ VertexId 1) myGraph+-- (VertexId 0,"u")+-- (VertexId 2,"w")+-- (VertexId 1,"v")+-- (VertexId 0,"u") -- -- running time: \(O(k)\), where \(k\) is the output size. boundaryVertices :: FaceId s w -> PlanarGraph s w v e f -> V.Vector (VertexId s w)-boundaryVertices f g = fmap (flip tailOf g) $ boundary f g+boundaryVertices f g = flip tailOf g <$> boundary f g -- -- | Gets the next dart along the face -- nextDart :: Dart s -> PlanarGraph s w v e f -> Dart s
src/Data/PlanarGraph/IO.hs view
@@ -13,22 +13,20 @@ module Data.PlanarGraph.IO where import Control.Lens-import Control.Monad (forM_) import Control.Monad.State.Strict import Data.Aeson import Data.Bifunctor import Data.Ext-import qualified Data.Foldable as F-import Data.Maybe (fromJust)+import qualified Data.Foldable as F+import Data.Maybe (fromJust) import Data.Permutation-import Data.PlanarGraph.AdjRep (Face(Face), Vtx(Vtx),Gr(Gr))+import Data.PlanarGraph.AdjRep (Face (Face), Gr (Gr), Vtx (Vtx)) import Data.PlanarGraph.Core import Data.PlanarGraph.Dart import Data.PlanarGraph.Dual import Data.PlanarGraph.EdgeOracle-import Data.Proxy-import qualified Data.Vector as V-import qualified Data.Vector.Mutable as MV+import qualified Data.Vector as V+import qualified Data.Vector.Mutable as MV -------------------------------------------------------------------------------- @@ -37,7 +35,7 @@ toJSON = toJSON . toAdjRep instance (FromJSON v, FromJSON e, FromJSON f) => FromJSON (PlanarGraph s Primal v e f) where- parseJSON v = fromAdjRep (Proxy :: Proxy s) <$> parseJSON v+ parseJSON v = fromAdjRep @s <$> parseJSON v -------------------------------------------------------------------------------- @@ -72,13 +70,13 @@ -- should be in counter clockwise order. -- -- running time: \(O(n)\)-fromAdjRep :: proxy s -> Gr (Vtx v e) (Face f) -> PlanarGraph s Primal v e f-fromAdjRep px gr@(Gr as fs) = g&vertexData .~ reorder vs' _unVertexId- &dartData .~ ds- &faceData .~ reorder fs' (_unVertexId._unFaceId)+fromAdjRep :: forall s v e f. Gr (Vtx v e) (Face f) -> PlanarGraph s Primal v e f+fromAdjRep (Gr as fs) = g&vertexData .~ reorder vs' _unVertexId+ &dartData .~ ds+ &faceData .~ reorder fs' (_unVertexId._unFaceId) where -- build the actual graph using the adjacencies- g = buildGraph px gr+ g = buildGraph as -- build an edge oracle so that we can quickly lookup the dart corresponding to a -- pair of vertices. oracle = edgeOracle g@@ -96,14 +94,40 @@ -- TODO: Properly handle graphs with self-loops +-- | Read a planar graph, given by its adjacencylists in counter clockwise order.+--+-- pre: no self-loops and no multiedges+--+-- running time: \(O(n)\)+fromAdjRep' :: forall s v e. [Vtx v e] -> PlanarGraph s Primal v e ()+fromAdjRep' as = g&vertexData .~ reorder vs' _unVertexId+ &dartData .~ ds+ where+ -- build the actual graph using the adjacencies+ g = buildGraph as+ -- build an edge oracle so that we can quickly lookup the dart corresponding to a+ -- pair of vertices.+ oracle = edgeOracle g+ -- function to lookup a given dart+ findEdge' u v = fromJust $ findDart u v oracle++ vs' = V.fromList [ VertexId vi :+ v | Vtx vi _ v <- as ]+ ds = V.fromList $ concatMap (\(Vtx vi us _) ->+ [(findEdge' (VertexId vi) (VertexId ui), x) | (ui,x) <- us]+ ) as++ -- TODO: Properly handle graphs with self-loops++ -- | Builds the graph from the adjacency lists (but ignores all associated data)-buildGraph :: proxy s -> Gr (Vtx v e) (Face f) -> PlanarGraph s Primal () () ()-buildGraph _ (Gr as' _) = fromAdjacencyLists as+buildGraph :: forall s v e. [Vtx v e] -> PlanarGraph s Primal () () ()+buildGraph as' = fromAdjacencyLists as where as = [ (VertexId vi, V.fromList [VertexId ui | (ui,_) <- us]) | Vtx vi us _ <- as' ] + -- make sure we order the data values appropriately reorder :: V.Vector (i :+ a) -> (i -> Int) -> V.Vector a reorder v f = V.create $ do@@ -126,7 +150,7 @@ fromAdjacencyLists adjM = planarGraph' . toCycleRep n $ perm where n = sum . fmap length $ perm- perm = map toOrbit $ adjM'+ perm = map toOrbit adjM' adjM' = fmap (second F.toList) adjM @@ -142,7 +166,9 @@ toOrbit (u,adjU) = concatMap (toDart u) adjU -- if u = v we have a self-loop, so we add both a positive and a negative dart- toDart u v = let Just a = findEdge u v oracle+ toDart u v = let a = case findEdge u v oracle of+ Nothing -> error $ "edge not found? " <> show (u,v)+ Just a' -> a' in case u `compare` v of LT -> [Dart (Arc a) Positive] EQ -> [Dart (Arc a) Positive, Dart (Arc a) Negative]
+ src/Data/PlanarGraph/Immutable.hs view
@@ -0,0 +1,1404 @@+{-# LANGUAGE RecordWildCards #-}+--------------------------------------------------------------------------------+-- |+-- Module : Data.PlanarGraph.Immutable+-- Copyright : (C) David Himmelstrup+-- License : see the LICENSE file+-- Maintainer : David Himmelstrup+--+-- A graph is planar if it can be drawn on a flat piece of+-- paper without any crossing edges. More theory is explained on wikipedia:+-- <https://en.wikipedia.org/wiki/Planar_graph>+--+-- This module describes the connectivity of planar graphs without knowing+-- the 2D coordinates of each vertex. Algorithms that require the vertex+-- positions (such as planar point locators or mesh smoothers) have to store+-- that information somewhere else. Vertices are identified by dense, consecutive+-- integers and can be efficiently used with arrays or finite maps.+-- +-- A planar graph consists of directed edges (also called half-edges or darts),+-- vertices, and faces. If a face lies on the outside of a set of vertices, this+-- face is called a boundary.+--+-- The simplest planar graph has just three vertices and three edges:+--+-- @'pgFromFaces' [[0,1,2]]@+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- The above pictures shows three vertices (named @'0'@, @'1'@, and @'2'@), a single face+-- (named @'0'@ with an underscore), and 6 half-edges (named @'0'@ through @'5'@).+-- Vertices, faces, and half-edges can be efficiently queried and traversed.+--+-- >>> let pg = pgFromFaces [[0,1,2]]+-- >>> pgFaces pg+-- [Face 0]+-- >>> faceBoundary (Face 0) pg+-- [Vertex 1,Vertex 2,Vertex 0]+--+--+-- == Planar graph examples:+--+-- Faces in planar graphs do not have to be triangular:+--+-- @'pgFromFaces' [[0,1,2,3]]@+--+-- <<docs/Data/PlanarGraph/planargraph-2506803680640023584.svg>>+--+-- Vertices may be interior or lie on a boundary:+--+-- @'pgFromFaces' [[0,1,2,3],[4,3,2,1]]@+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+-- >>> pgFaces pg+-- [Face 0,Face 1]+-- >>> vertexIsBoundary (Vertex 0) pg+-- True+-- >>> vertexIsBoundary (Vertex 2) pg+-- False+--+-- Planar graphs may have multiple boundaries. Notice how the area between vertices+-- @'1'@, @'2'@ and @'3'@ does not have a face ID:+--+-- @'pgFromFaces' [[0,4,1],[0,1,2],[4,3,1],[4,5,3],[3,5,2],[2,5,0]]@+--+-- <<docs/Data/PlanarGraph/planargraph-2635031442529484236.compact.svg>>+--+-- >>> let pg = pgFromFaces [[0,4,1],[0,1,2],[4,3,1],[4,5,3],[3,5,2],[2,5,0]]+-- >>> pgFaces pg+-- [Face 0,Face 1,Face 2,Face 3,Face 4,Face 5]+-- >>> pgBoundaries pg+-- [Boundary 0,Boundary 1]+-- >>> faceBoundary (Boundary 0) pg {- Outer boundary -}+-- [Vertex 0,Vertex 4,Vertex 5]+-- >>> faceBoundary (Boundary 1) pg {- Inner boundary -}+-- [Vertex 1,Vertex 2,Vertex 3]+--+-- Planar graphs may also have multiple unconnected components but they cannot be+-- automatically rendered:+--+-- >>> let pg = pgFromFaces [[0,1,2], [3,4,5]]+-- >>> pgFaces pg+-- [Face 0,Face 1]+-- >>> pgBoundaries pg+-- [Boundary 0,Boundary 1]+-- >>> faceBoundary (Boundary 0) pg+-- [Vertex 0,Vertex 1,Vertex 2]+-- >>> faceBoundary (Boundary 1) pg+-- [Vertex 3,Vertex 4,Vertex 5]+--+-- == Big-O Notation+--+-- When describing runtime complexity, @n@ refers to the size of the graph+-- (vertices, half-edges, faces, etcs). Some functions are output-sensitive+-- and use @k@ to indicate the amount of data consumed. For example,+-- 'vertexNeighbours' runs in \( O(k) \) and taking the first neighbour is therefore+-- an \( O(1) \) operation (because k=1).+--------------------------------------------------------------------------------+module Data.PlanarGraph.Immutable+ ( -- * Planar graphs+ PlanarGraph+ , pgFromFaces -- :: [[VertexId]] -> PlanarGraph+ , pgFromFacesCV -- :: [CircularVector VertexId] -> PlanarGraph+ , pgVertices -- :: PlanarGraph -> [Vertex]+ , pgEdges -- :: PlanarGraph -> [Edge]+ , pgHalfEdges -- :: PlanarGraph -> [HalfEdge]+ , pgFaces -- :: PlanarGraph -> [Face]+ , pgBoundaries -- :: PlanarGraph -> [Face]++ -- * Elements+ -- ** Vertices+ , Vertex(..)+ , vertexHalfEdge -- :: Vertex -> PlanarGraph -> HalfEdge+ , vertexIsInterior -- :: Vertex -> PlanarGraph -> Bool+ , vertexIsBoundary -- :: Vertex -> PlanarGraph -> Bool+ , vertexOutgoingHalfEdges -- :: Vertex -> PlanarGraph -> [HalfEdge]+ , vertexIncomingHalfEdges -- :: Vertex -> PlanarGraph -> [HalfEdge]+ , vertexNeighbours -- :: Vertex -> PlanarGraph -> [Vertex]++ -- ** Edges+ , Edge(..)+ , edgeHalfEdges -- :: Edge -> (HalfEdge, HalfEdge)++ -- ** Half-edges+ , HalfEdge(..)+ , halfEdgeNext -- :: HalfEdge -> PlanarGraph -> HalfEdge+ , halfEdgePrev -- :: HalfEdge -> PlanarGraph -> HalfEdge+ , halfEdgeTwin -- :: HalfEdge -> HalfEdge+ , halfEdgeNextOutgoing -- :: HalfEdge -> PlanarGraph -> HalfEdge+ , halfEdgeNextIncoming -- :: HalfEdge -> PlanarGraph -> HalfEdge+ , halfEdgeVertex -- :: HalfEdge -> PlanarGraph -> Vertex+ , halfEdgeTailVertex -- :: HalfEdge -> PlanarGraph -> Vertex+ , halfEdgeTipVertex -- :: HalfEdge -> PlanarGraph -> Vertex+ , halfEdgeFace -- :: HalfEdge -> PlanarGraph -> Face+ , halfEdgeIsInterior -- :: HalfEdge -> PlanarGraph -> Bool+ , halfEdgeIsBoundary -- :: HalfEdge -> PlanarGraph -> Bool++ -- ** Faces+ , Face(..), FaceId+ , faceMember -- :: Face -> PlanarGraph -> Bool+ , faceId -- :: Face -> FaceId+ , faceHalfEdge -- :: Face -> PlanarGraph -> HalfEdge+ , faceIsInterior -- :: Face -> Bool+ , faceIsBoundary -- :: Face -> Bool+ , faceHalfEdges -- :: Face -> PlanarGraph -> CircularVector HalfEdge+ , faceBoundary -- :: Face -> PlanarGraph -> CircularVector Vertex++ -- * Mutation+ , pgMutate -- :: PlanarGraph -> (forall s. Mut.PlanarGraph s -> ST s ()) -> PlanarGraph+ , pgCreate -- :: (forall s. ST s (Mut.PlanarGraph s)) -> PlanarGraph+ , pgThaw -- :: PlanarGraph -> ST s (Mut.PlanarGraph s)+ , pgFreeze -- :: Mut.PlanarGraph s -> ST s PlanarGraph+ , pgUnsafeThaw -- :: PlanarGraph -> ST s (Mut.PlanarGraph s)+ , pgUnsafeFreeze -- :: Mut.PlanarGraph s -> ST s PlanarGraph++ -- * Misc+ , tutteEmbedding -- :: PlanarGraph -> Vector.Vector (V2 Double)+ )+ where++import Control.Monad+import Control.Monad.ST+import Data.Bits+import Data.Coerce+import Data.Hashable+import Data.PlanarGraph.Internal (FaceId, HalfEdgeId, VertexId)+import qualified Data.PlanarGraph.Internal as Mut+import qualified Data.PlanarGraph.Mutable as Mut+import Data.Proxy+import Data.STRef+import Data.Vector (Vector)+import qualified Data.Vector as Vector+import Data.Vector.Circular (CircularVector)+import qualified Data.Vector.Circular as CV+import qualified Data.Vector.Mutable as V+import GHC.Exts+import Linear.Matrix (luSolve)+import Linear.V+import Linear.V2++-- import Debug.Trace++-------------------------------------------------------------------------------+-- Elements: Half-edges, vertices, faces.+++-- | Half-edges are directed edges between vertices. All Half-edge have a twin+-- in the opposite direction. Half-edges have individual identity but are always+-- created in pairs.+newtype HalfEdge = HalfEdge {halfEdgeId :: Int}+ deriving (Eq, Hashable)++instance Show HalfEdge where+ showsPrec d (HalfEdge v) = showParen (d > 10) $+ showString "HalfEdge " . shows v++instance Read HalfEdge where+ readsPrec d = readParen (d > app_prec) $ \r ->+ [ (HalfEdge v, t)+ | ("HalfEdge", s) <- lex r, (v, t) <- reads s ]+ where app_prec = 10++-- | Edges are bidirectional and connect two vertices. No two edges are allowed+-- to cross.+newtype Edge = Edge {edgeId :: Int}+ deriving (Eq, Hashable)++instance Show Edge where+ showsPrec d (Edge v) = showParen (d > 10) $+ showString "Edge " . shows v++instance Read Edge where+ readsPrec d = readParen (d > app_prec) $ \r ->+ [ (Edge v, t)+ | ("Edge", s) <- lex r, (v, t) <- reads s ]+ where app_prec = 10++-- | Graph vertices. For best performance, make sure to use consecutive numbers.+newtype Vertex = Vertex {vertexId :: Int}+ deriving (Eq, Hashable)++instance Show Vertex where+ showsPrec d (Vertex v) = showParen (d > 10) $+ showString "Vertex " . shows v++instance Read Vertex where+ readsPrec d = readParen (d > app_prec) $ \r ->+ [ (Vertex v, t)+ | ("Vertex", s) <- lex r, (v, t) <- reads s ]+ where app_prec = 10++-- | Faces are the areas divided by edges. If a face is not surrounded by a set of vertices,+-- it is called a boundary.+data Face = Face FaceId | Boundary FaceId+ deriving (Eq, Read, Show)++-------------------------------------------------------------------------------+-- Planar graph++-- PlanarGraphs have vertices, edges, and faces.+-- Invariant: The half-edge of a boundary vertex is interior, twin is exterior.++-- FIXME: Use STRefU ?+-- PlanarGraph with 0 vertices: No edges, no vertices, no faces.+-- PlanarGraph with 1 vertex: No edges, no interior faces.+-- PlanarGraph with 2 vertices: One edge, no interior faces.+-- PlanarGraph with 3+ vertices: Usual properties hold.+-- | Immutable planar graph.+data PlanarGraph = PlanarGraph+ { pgHalfEdgeNext :: !(Vector HalfEdgeId) -- HalfEdge indexed+ , pgHalfEdgePrev :: !(Vector HalfEdgeId) -- HalfEdge indexed+ , pgHalfEdgeVertex :: !(Vector VertexId) -- HalfEdge indexed+ , pgHalfEdgeFace :: !(Vector FaceId) -- HalfEdge indexed+ , pgVertexEdges :: !(Vector HalfEdgeId) -- Vertex indexed+ , pgFaceEdges :: !(Vector HalfEdgeId) -- Face indexed+ , pgBoundaryEdges :: !(Vector HalfEdgeId) -- Boundary faces+ } deriving Eq++panic :: String -> String -> a+panic tag msg = error $ "Data.PlanarGraph.Immutable." ++ tag ++ ": " ++ msg+++-- Disabled since hashes are not stable across different versions of hashable.+-- // $setup+--+-- >>> hash $ pgFromFaces [[0,1,2]]+-- 2959979592048325618+-- >>> hash $ pgFromFaces [[1,2,3]]+-- 2486673127436488352+-- >>> hash $ pgFromFaces [[0,1,2,3]]+-- 2506803680640023584+-- >>> hash $ pgFromFaces [[0,1,2,3],[4,3,2,1]]+-- 1711135548958680232+--++-- | \( O(n \log n) \)+--+-- Construct a planar graph from a list of faces. Vertices are assumed to be dense+-- (ie without gaps) but this only affects performance, not correctness. Memory+-- usage is defined by the largest vertex ID. That means @'pgFromFaces' [[0,1,2]]@+-- has the same connectivity as @'pgFromFaces' [[7,8,9]]@ but uses three times less+-- memory.+--+-- ==== __Examples:__+-- @+-- 'pgFromFaces' [[0,1,2]]+-- @+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- @+-- 'pgFromFaces' [[0,1,2,3]]+-- @+-- <<docs/Data/PlanarGraph/planargraph-2506803680640023584.svg>>+--+-- @+-- 'pgFromFaces' [[1,2,3]]+-- @+-- <<docs/Data/PlanarGraph/planargraph-2486673127436488352.svg>>+--+-- @since 0.12.0.0+pgFromFaces :: [[VertexId]] -> PlanarGraph+pgFromFaces = pgFromFacesCV . map CV.unsafeFromList++-- | \( O(n \log n) \)+--+-- Construct a planar graph from a list of faces. This is a slightly more+-- efficient version of 'pgFromFacesCV'.+-- +-- @since 0.12.0.0+pgFromFacesCV :: [CircularVector VertexId] -> PlanarGraph+pgFromFacesCV faces = pgCreate $ Mut.pgFromFacesCV faces++-- fromFaces' :: Int -> Int -> Int -> [CircularVector VertexId] -> ST s (PlanarGraph)+-- fromFaces' nFaces nHalfEdges maxVertexId faces = do+-- undefined++-- dualTree :: Face -> ST s (Tree Face)+-- dualTree = undefined++instance Hashable PlanarGraph where+ hashWithSalt salt = hashWithSalt salt . pgHash+ hash = pgHash++-- | O(n)+-- +-- @since 0.12.0.0+pgHash :: PlanarGraph -> Int+pgHash pg =+ let loop [] salt = salt+ loop (edgeId:rest) salt =+ let he = HalfEdge (edgeId*2)+ vTail = halfEdgeTailVertex he pg+ vTip = halfEdgeTipVertex he pg+ in loop rest (hashWithSalt salt (vTail, vTip))+ in abs $ loop [0..Vector.length (pgHalfEdgeNext pg)`div`2-1] 0++-------------------------------------------------------------------------------+-- Vertices++-- | O(1)+vertexCheck :: String -> Vertex -> PlanarGraph -> a -> a+vertexCheck tag (Vertex vId) pg _val+ | vId >= Vector.length (pgVertexEdges pg) || vId < 0 =+ panic tag ("Out-of-bounds vertex access: " ++ show vId)+ | not (halfEdgeIsValid (HalfEdge (pgVertexEdges pg Vector.! vId))) =+ panic tag ("Tried to access deleted vertex: " ++ show vId)+vertexCheck _tag _face _pg val = val++-- | \( O(k) \)+-- +-- List all vertices in a graph.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> pgVertices pg+-- [Vertex 0,Vertex 1,Vertex 2]+--+-- @since 0.12.0.0+pgVertices :: PlanarGraph -> [Vertex]+pgVertices pg =+ [ Vertex v+ | v <- [0 .. Vector.length (pgVertexEdges pg)-1 ]+ , halfEdgeIsValid (HalfEdge $ pgVertexEdges pg Vector.! v)+ ]++-- -- | \( O(1) \)+-- vertexFromId :: VertexId -> Vertex+-- vertexFromId vId = Vertex vId++-- -- | \( O(1) \)+-- vertexId :: Vertex -> VertexId+-- vertexId (Vertex vId) = vId++-- Disabled since hashes are not stable across different versions of hashable.+-- // $hidden+--+-- >>> hash $ pgFromFaces [[0,1,2]]+-- 2959979592048325618++-- | \( O(1) \)+--+-- Each vertex has an assigned half-edge with the following properties:+--+-- @'halfEdgeVertex' ('vertexHalfEdge' vertex pg) pg = vertex@+--+-- @'faceIsInterior' ('halfEdgeFace' ('vertexHalfEdge' vertex pg) pg) = True@+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> vertexHalfEdge (Vertex 0) pg+-- HalfEdge 4+--+-- >>> vertexHalfEdge (Vertex 1) pg+-- HalfEdge 0+--+-- >>> vertexHalfEdge (Vertex 6) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexHalfEdge: Out-of-bounds vertex access: 6+-- ...+--+-- >>> vertexHalfEdge (Vertex (-10)) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexHalfEdge: Out-of-bounds vertex access: -10+-- ...+--+-- >>> halfEdgeVertex (vertexHalfEdge (Vertex 2) pg) pg+-- Vertex 2+--+-- >>> halfEdgeFace (vertexHalfEdge (Vertex 0) pg) pg+-- Face 0+--+-- @since 0.12.0.0+vertexHalfEdge :: Vertex -> PlanarGraph -> HalfEdge+vertexHalfEdge vertex pg | vertexCheck "vertexHalfEdge" vertex pg False = undefined+vertexHalfEdge (Vertex vId) pg = HalfEdge $ pgVertexEdges pg Vector.! vId+++-- Disabled since hashes are not stable across different versions of hashable.+-- // $hidden+--+-- >>> hash $ pgFromFaces [[0,1,2,3],[4,3,2,1]]+-- 1711135548958680232++-- | \( O(1) \)+--+-- Returns @True@ iff the vertex lies on a boundary.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> vertexIsBoundary (Vertex 0) pg+-- True+--+-- >>> vertexIsBoundary (Vertex 2) pg+-- False+--+-- >>> vertexIsBoundary (Vertex 4) pg+-- True+--+-- >>> vertexIsBoundary (Vertex 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexIsBoundary: Out-of-bounds vertex access: 12+-- ...+--+-- @since 0.12.0.0+vertexIsBoundary :: Vertex -> PlanarGraph -> Bool+vertexIsBoundary vertex pg | vertexCheck "vertexIsBoundary" vertex pg False = undefined+vertexIsBoundary vertex pg =+ faceIsBoundary $ halfEdgeFace (halfEdgeTwin $ vertexHalfEdge vertex pg) pg++-- | \( O(1) \)+--+-- Returns @True@ iff the vertex is interior, ie. does not lie on a boundary.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> vertexIsInterior (Vertex 0) pg+-- False+--+-- >>> vertexIsInterior (Vertex 2) pg+-- True+--+-- >>> vertexIsInterior (Vertex 4) pg+-- False+--+-- >>> vertexIsInterior (Vertex 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexIsInterior: Out-of-bounds vertex access: 12+-- ...+--+-- @since 0.12.0.0+vertexIsInterior :: Vertex -> PlanarGraph -> Bool+vertexIsInterior vertex pg | vertexCheck "vertexIsInterior" vertex pg False = undefined+vertexIsInterior vertex pg = not $ vertexIsBoundary vertex pg++-- | \( O(k) \)+--+-- Query outgoing half-edges from a given vertex in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> vertexOutgoingHalfEdges (Vertex 1) pg+-- [HalfEdge 0,HalfEdge 11,HalfEdge 3]+--+-- Each half-edge will point out from the origin vertex:+--+-- >>> map (`halfEdgeVertex` pg) $ vertexOutgoingHalfEdges (Vertex 1) pg+-- [Vertex 1,Vertex 1,Vertex 1]+--+-- >>> map (`halfEdgeTipVertex` pg) $ vertexOutgoingHalfEdges (Vertex 1) pg+-- [Vertex 0,Vertex 4,Vertex 2]+--+-- >>> vertexOutgoingHalfEdges (Vertex 2) pg+-- [HalfEdge 2,HalfEdge 5]+--+-- >>> vertexOutgoingHalfEdges (Vertex 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexOutgoingHalfEdges: Out-of-bounds vertex access: 12+-- ...+--+-- @since 0.12.0.0+vertexOutgoingHalfEdges :: Vertex -> PlanarGraph -> [HalfEdge]+vertexOutgoingHalfEdges vertex pg | vertexCheck "vertexOutgoingHalfEdges" vertex pg False = undefined+vertexOutgoingHalfEdges vertex pg = first : build (g (advance first))+ where+ advance he = halfEdgeNext (halfEdgeTwin he) pg+ first = vertexHalfEdge vertex pg+ g :: HalfEdge -> (HalfEdge -> b -> b) -> b -> b+ g he cons nil+ | he == first = nil+ | otherwise = cons he (g (advance he) cons nil)++-- Disabled since hashes are not stable across different versions of hashable.+-- // $hidden+--+-- >>> hash $ pgFromFaces [[0,1,2,3],[4,3,2,1]]+-- 1711135548958680232++-- | \( O(k) \)+--+-- Query incoming half-edges from a given vertex in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> vertexIncomingHalfEdges (Vertex 1) pg+-- [HalfEdge 1,HalfEdge 10,HalfEdge 2]+--+-- >>> map (`halfEdgeVertex` pg) $ vertexIncomingHalfEdges (Vertex 1) pg+-- [Vertex 0,Vertex 4,Vertex 2]+--+-- >>> map (`halfEdgeTipVertex` pg) $ vertexIncomingHalfEdges (Vertex 1) pg+-- [Vertex 1,Vertex 1,Vertex 1]+--+-- >>> vertexIncomingHalfEdges (Vertex 2) pg+-- [HalfEdge 3,HalfEdge 4]+--+-- >>> vertexIncomingHalfEdges (Vertex 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexIncomingHalfEdges: Out-of-bounds vertex access: 12+-- ...+--+-- @since 0.12.0.0+vertexIncomingHalfEdges :: Vertex -> PlanarGraph -> [HalfEdge]+vertexIncomingHalfEdges vertex pg | vertexCheck "vertexIncomingHalfEdges" vertex pg False = undefined+vertexIncomingHalfEdges vertex pg = map halfEdgeTwin $ vertexOutgoingHalfEdges vertex pg++-- | \( O(k) \)+--+-- Query vertex neighbours in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> vertexNeighbours (Vertex 0) pg+-- [Vertex 3,Vertex 1]+--+-- >>> vertexNeighbours (Vertex 1) pg+-- [Vertex 0,Vertex 4,Vertex 2]+--+-- >>> vertexNeighbours (Vertex 2) pg+-- [Vertex 1,Vertex 3]+--+-- >>> vertexNeighbours (Vertex 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.vertexNeighbours: Out-of-bounds vertex access: 12+-- ...+--+-- @since 0.12.0.0+vertexNeighbours :: Vertex -> PlanarGraph -> [Vertex]+vertexNeighbours vertex pg | vertexCheck "vertexNeighbours" vertex pg False = undefined+vertexNeighbours vertex pg = map (`halfEdgeVertex` pg) $ vertexIncomingHalfEdges vertex pg++-- vertexAdjacentVertices :: Vertex -> PlanarGraph -> [Vertex]+-- vertexAdjacentFaces :: Vertex -> PlanarGraph -> [Face]++-------------------------------------------------------------------------------+-- Edges++-- | \( O(k) \)+-- +-- List all edges in a graph.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> pgEdges pg+-- [Edge 0,Edge 1,Edge 2]+--+-- >>> map edgeHalfEdges $ pgEdges pg+-- [(HalfEdge 0,HalfEdge 1),(HalfEdge 2,HalfEdge 3),(HalfEdge 4,HalfEdge 5)]+--+-- @since 0.12.0.0+pgEdges :: PlanarGraph -> [Edge]+pgEdges pg =+ [ Edge e+ | e <- [0 .. Vector.length (pgHalfEdgeNext pg) `div` 2 -1]+ , let he = e*2+ , halfEdgeIsValid (HalfEdge he)+ ]++-- | \( O(1) \)+--+-- Split a bidirectional edge into directed half-edges.+--+-- @since 0.12.0.0+edgeHalfEdges :: Edge -> (HalfEdge, HalfEdge)+edgeHalfEdges (Edge e) = (HalfEdge $ e*2, HalfEdge $ e*2+1)++-------------------------------------------------------------------------------+-- Half-edges++-- | O(1)+halfEdgeCheck :: String -> HalfEdgeId -> PlanarGraph -> a -> a+halfEdgeCheck tag eId pg _val+ | eId >= Vector.length (pgHalfEdgeVertex pg) || eId < 0 =+ panic tag ("Out-of-bounds half-edge access: " ++ show eId)+ | pgHalfEdgeVertex pg Vector.! eId < 0 =+ panic tag ("Tried to access deleted half-edge: " ++ show eId)+halfEdgeCheck _tag _face _pg val = val++-- | \( O(k) \)+-- +-- List all half-edges in a graph.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> pgHalfEdges pg+-- [HalfEdge 0,HalfEdge 1,HalfEdge 2,HalfEdge 3,HalfEdge 4,HalfEdge 5]+--+-- @since 0.12.0.0+pgHalfEdges :: PlanarGraph -> [HalfEdge]+pgHalfEdges pg =+ [ he+ | he <- map HalfEdge [0 .. Vector.length (pgHalfEdgeNext pg)-1 ]+ , halfEdgeIsValid he+ ]+++-- | O(1)+--+-- @since 0.12.0.0+halfEdgeIsValid :: HalfEdge -> Bool+halfEdgeIsValid (HalfEdge eId) = eId >= 0++-- -- | O(1)+-- halfEdgeFromId :: HalfEdgeId -> HalfEdge+-- halfEdgeFromId eId = HalfEdge eId++-- -- | O(1)+-- halfEdgeId :: HalfEdge -> HalfEdgeId+-- halfEdgeId (HalfEdge eId) = eId++-- Disabled since hashes are not stable across different versions of hashable.+-- // $hidden+--+-- >>> hash $ pgFromFaces [[0,1,2,3],[4,3,2,1]]+-- 1711135548958680232++-- | \( O(1) \)+--+-- Query the half-edge in the pointed direction. Internal half-edges+-- are arranged clockwise and external half-edges go counter-clockwise.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> halfEdgeNext (HalfEdge 4) pg {- clockwise -}+-- HalfEdge 2+--+-- >>> halfEdgeNext (HalfEdge 3) pg {- clockwise -}+-- HalfEdge 5+--+-- >>> halfEdgeNext (HalfEdge 1) pg {- counter-clockwise -}+-- HalfEdge 11+--+-- >>> halfEdgeNext (HalfEdge 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeNext: Out-of-bounds half-edge access: 12+-- ...+--+-- @since 0.12.0.0+halfEdgeNext :: HalfEdge -> PlanarGraph -> HalfEdge+halfEdgeNext (HalfEdge eId) pg = halfEdgeCheck "halfEdgeNext" eId pg $+ HalfEdge $ pgHalfEdgeNext pg Vector.! eId++-- | \( O(1) \)+--+-- Query the half-edge opposite the pointed direction. This means counter-clockwise+-- for internal half-edges and clockwise for external half-edges.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> halfEdgePrev (HalfEdge 4) pg {- counter-clockwise -}+-- HalfEdge 6+--+-- >>> halfEdgePrev (HalfEdge 3) pg {- counter-clockwise -}+-- HalfEdge 10+--+-- >>> halfEdgePrev (HalfEdge 1) pg {- clockwise -}+-- HalfEdge 7+--+-- >>> halfEdgePrev (HalfEdge 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgePrev: Out-of-bounds half-edge access: 12+-- ...+--+-- @since 0.12.0.0+halfEdgePrev :: HalfEdge -> PlanarGraph -> HalfEdge+halfEdgePrev (HalfEdge eId) pg = halfEdgeCheck "halfEdgePrev" eId pg $+ HalfEdge $ pgHalfEdgePrev pg Vector.! eId++-- | \( O(1) \)+--+-- Next half-edge with the same vertex in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- @HalfEdge 0@ is poiting out from @Vertex 1@. Moving counter-clockwise+-- around @Vertex 1@ yields @HalfEdge 11@ and @HalfEdge 3@.+--+-- >>> halfEdgeNextOutgoing (HalfEdge 0) pg+-- HalfEdge 11+--+-- >>> halfEdgeNextOutgoing (HalfEdge 11) pg+-- HalfEdge 3+--+-- >>> halfEdgeNextOutgoing (HalfEdge 3) pg+-- HalfEdge 0+--+-- >>> halfEdgeNextOutgoing (HalfEdge 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeNextOutgoing: Out-of-bounds half-edge access: 12+-- ...+--+-- @since 0.12.0.0+halfEdgeNextOutgoing :: HalfEdge -> PlanarGraph -> HalfEdge+halfEdgeNextOutgoing e pg = halfEdgeCheck "halfEdgeNextOutgoing" (halfEdgeId e) pg $+ halfEdgeNext (halfEdgeTwin e) pg++-- | \( O(1) \)+--+-- Next half-edge with the same vertex in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- @HalfEdge 6@ is poiting towards @Vertex 3@. Moving clockwise+-- around @Vertex 3@ yields @HalfEdge 11@ and @HalfEdge 3@.+--+-- >>> halfEdgeNextIncoming (HalfEdge 6) pg+-- HalfEdge 5+--+-- >>> halfEdgeNextIncoming (HalfEdge 5) pg+-- HalfEdge 9+--+-- >>> halfEdgeNextIncoming (HalfEdge 9) pg+-- HalfEdge 6+--+-- >>> halfEdgeNextIncoming (HalfEdge 12) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeNextIncoming: Out-of-bounds half-edge access: 12+-- ...+--+-- @since 0.12.0.0+halfEdgeNextIncoming :: HalfEdge -> PlanarGraph -> HalfEdge+halfEdgeNextIncoming e pg = halfEdgeCheck "halfEdgeNextIncoming" (halfEdgeId e) pg $+ halfEdgeTwin (halfEdgeNext e pg)++-- | \( O(1) \)+--+-- @+-- 'halfEdgeTwin' . 'halfEdgeTwin' == id+-- @+--+-- @since 0.12.0.0+halfEdgeTwin :: HalfEdge -> HalfEdge+halfEdgeTwin (HalfEdge idx) = HalfEdge (idx `xor` 1)+++-- | \( O(1) \)+--+-- Tail-end of a half-edge. Synonym of 'halfEdgeTailVertex'.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> halfEdgeVertex (HalfEdge 1) pg+-- Vertex 0+--+-- >>> halfEdgeVertex (HalfEdge 2) pg+-- Vertex 2+--+-- >>> halfEdgeVertex (HalfEdge 6) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeVertex: Out-of-bounds half-edge access: 6+-- ...+--+-- @since 0.12.0.0+halfEdgeVertex :: HalfEdge -> PlanarGraph -> Vertex+halfEdgeVertex (HalfEdge idx) pg = halfEdgeCheck "halfEdgeVertex" idx pg $+ Vertex $ pgHalfEdgeVertex pg Vector.! idx++-- | O(1)+--+-- Tail-end of a half-edge. Synonym of 'halfEdgeVertex'.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> halfEdgeTailVertex (HalfEdge 1) pg+-- Vertex 0+--+-- >>> halfEdgeTailVertex (HalfEdge 2) pg+-- Vertex 2+--+-- @since 0.12.0.0+halfEdgeTailVertex :: HalfEdge -> PlanarGraph -> Vertex+halfEdgeTailVertex e pg = halfEdgeVertex e pg++-- | O(1)+--+-- Tip-end of a half-edge. This is the tail-end vertex of the twin half-edge.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> halfEdgeTipVertex (HalfEdge 1) pg+-- Vertex 1+--+-- >>> halfEdgeTipVertex (HalfEdge 5) pg+-- Vertex 0+--+-- @since 0.12.0.0+halfEdgeTipVertex :: HalfEdge -> PlanarGraph -> Vertex+halfEdgeTipVertex e pg = halfEdgeVertex (halfEdgeTwin e) pg++-- Disabled since hashes are not stable across different versions of hashable.+-- // $hidden+--+-- >>> hash $ pgFromFaces [[0,1,2]]+-- 2959979592048325618++-- | \( O(1) \)+--+-- Query the face of a half-edge.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> halfEdgeFace (HalfEdge 0) pg+-- Face 0+--+-- >>> halfEdgeFace (HalfEdge 1) pg+-- Boundary 0+--+-- >>> halfEdgeFace (HalfEdge 6) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeFace: Out-of-bounds half-edge access: 6+-- ...+--+-- @since 0.12.0.0+halfEdgeFace :: HalfEdge -> PlanarGraph -> Face+halfEdgeFace (HalfEdge eId) pg = halfEdgeCheck "halfEdgeFace" eId pg $+ faceFromId $ pgHalfEdgeFace pg Vector.! eId++-- | \( O(1) \)+--+-- Check if a half-edge's face is on a boundary.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> halfEdgeIsBoundary (HalfEdge 0) pg+-- False+--+-- >>> halfEdgeIsBoundary (HalfEdge 1) pg+-- True+--+-- >>> halfEdgeIsBoundary (HalfEdge 2) pg+-- False+--+-- >>> halfEdgeIsBoundary (HalfEdge 3) pg+-- True+--+-- >>> halfEdgeIsBoundary (HalfEdge 6) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeIsBoundary: Out-of-bounds half-edge access: 6+-- ...+--+-- @since 0.12.0.0+halfEdgeIsBoundary :: HalfEdge -> PlanarGraph -> Bool+halfEdgeIsBoundary edge pg = halfEdgeCheck "halfEdgeIsBoundary" (halfEdgeId edge) pg $+ faceIsBoundary $ halfEdgeFace edge pg++-- | \( O(1) \)+--+-- Check if a half-edge's face is interior.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> halfEdgeIsInterior (HalfEdge 0) pg+-- True+--+-- >>> halfEdgeIsInterior (HalfEdge 1) pg+-- False+--+-- >>> halfEdgeIsInterior (HalfEdge 2) pg+-- True+--+-- >>> halfEdgeIsInterior (HalfEdge 3) pg+-- False+--+-- >>> halfEdgeIsInterior (HalfEdge 6) pg+-- ... Exception: Data.PlanarGraph.Immutable.halfEdgeIsInterior: Out-of-bounds half-edge access: 6+-- ...+--+-- @since 0.12.0.0+halfEdgeIsInterior :: HalfEdge -> PlanarGraph -> Bool+halfEdgeIsInterior edge pg = halfEdgeCheck "halfEdgeIsInterior" (halfEdgeId edge) pg $+ faceIsInterior $ halfEdgeFace edge pg++-------------------------------------------------------------------------------+-- Faces++-- | \( O(k) \)+-- +-- List all faces in a graph.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,4,1],[0,1,2],[4,3,1],[4,5,3],[3,5,2],[2,5,0]]+--+-- <<docs/Data/PlanarGraph/planargraph-2635031442529484236.compact.svg>>+--+-- >>> pgFaces pg+-- [Face 0,Face 1,Face 2,Face 3,Face 4,Face 5]+--+-- @since 0.12.0.0+pgFaces :: PlanarGraph -> [Face]+pgFaces pg =+ [ Face fId+ | fId <- [0 .. Vector.length (pgFaceEdges pg)-1 ]+ , halfEdgeIsValid (faceHalfEdge (Face fId) pg)+ ]++-- | \( O(k) \)+-- +-- List all boundaries (ie external faces) in a graph. There may be+-- multiple boundaries and they may or may not be reachable from each other.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,4,1],[0,1,2],[4,3,1],[4,5,3],[3,5,2],[2,5,0]]+--+-- <<docs/Data/PlanarGraph/planargraph-2635031442529484236.compact.svg>>+--+-- >>> pgBoundaries pg+-- [Boundary 0,Boundary 1]+--+-- >>> faceBoundary (Boundary 0) pg+-- [Vertex 0,Vertex 4,Vertex 5]+--+-- >>> faceBoundary (Boundary 1) pg+-- [Vertex 1,Vertex 2,Vertex 3]+--+-- @since 0.12.0.0+pgBoundaries :: PlanarGraph -> [Face]+pgBoundaries pg =+ [ Boundary fId+ | fId <- [0 .. Vector.length (pgBoundaryEdges pg)-1 ]+ , halfEdgeIsValid (faceHalfEdge (Boundary fId) pg)+ ]++-- | O(1)+faceCheck :: String -> Face -> PlanarGraph -> a -> a+faceCheck tag (Face fId) pg _val+ | fId >= Vector.length (pgFaceEdges pg) || fId < 0 =+ panic tag ("Out-of-bounds face access: " ++ show fId)+ | pgFaceEdges pg Vector.! fId < 0 =+ panic tag ("Tried to access deleted face: " ++ show fId)+faceCheck tag (Boundary fId) pg _val+ | fId >= Vector.length (pgBoundaryEdges pg) || fId < 0 =+ panic tag ("Out-of-bounds boundary access: " ++ show fId)+ | pgBoundaryEdges pg Vector.! fId < 0 =+ panic tag ("Tried to access deleted boundary: " ++ show fId)+faceCheck _tag _face _pg val = val++-- | \( O(1) \)+--+-- Returns @True@ iff a face or boundary is part of the planar graph.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2]]+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> faceMember (Face 0) pg+-- True+--+-- >>> faceMember (Face 1) pg+-- False+--+-- >>> faceMember (Face 100) pg+-- False+--+-- >>> faceMember (Face (-100)) pg+-- False+--+-- >>> faceMember (Boundary 0) pg+-- True+--+-- >>> faceMember (Boundary 1) pg+-- False+--+-- @since 0.12.0.0+faceMember :: Face -> PlanarGraph -> Bool+faceMember face@(Face fId) pg =+ fId < Vector.length (pgFaceEdges pg) &&+ fId >= 0 &&+ halfEdgeIsValid (faceHalfEdge face pg)+faceMember face@(Boundary fId) pg =+ fId < Vector.length (pgFaceEdges pg) &&+ fId >= 0 &&+ halfEdgeIsValid (faceHalfEdge face pg)+++-- -- | O(1)+-- faceInvalid :: Face+-- faceInvalid = faceFromId maxBound++-- -- | O(1)+-- faceIsValid :: Face -> Bool+-- faceIsValid = not . faceIsInvalid++-- -- | O(1)+-- faceIsInvalid :: Face -> Bool+-- faceIsInvalid (Face fId) = fId == maxBound+-- faceIsInvalid (Boundary fId) = fId == maxBound++-- | O(1)+--+-- @since 0.12.0.0+faceFromId :: FaceId -> Face+faceFromId fId | fId < 0 = Boundary (negate fId - 1)+faceFromId fId = Face fId++-- | \( O(1) \)+--+-- Maps interior faces to positive integers and boundary faces to negative integers.+--+-- ==== __Examples:__+--+-- >>> faceId (Face 0)+-- 0+--+-- >>> faceId (Face 10)+-- 10+--+-- >>> faceId (Boundary 0)+-- -1+--+-- >>> faceId (Boundary 10)+-- -11+--+-- @since 0.12.0.0+faceId :: Face -> FaceId+faceId (Face fId) = fId+faceId (Boundary fId) = negate fId - 1+++-- | \( O(1) \)+--+-- Query the half-edge associated with a face or boundary.+--+-- ==== __Examples:__+--+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> faceHalfEdge (Face 0) pg+-- HalfEdge 0+--+-- >>> faceHalfEdge (Face 1) pg+-- HalfEdge 8+--+-- >>> faceHalfEdge (Boundary 0) pg+-- HalfEdge 1+--+-- >>> faceHalfEdge (Face 10) pg {- Invalid face -}+-- ... Exception: Data.PlanarGraph.Immutable.faceHalfEdge: Out-of-bounds face access: 10+-- ...+--+-- @since 0.12.0.0+faceHalfEdge :: Face -> PlanarGraph -> HalfEdge+faceHalfEdge face pg = faceCheck "faceHalfEdge" face pg $+ case face of+ Face fId -> HalfEdge $ pgFaceEdges pg Vector.! fId+ Boundary fId -> HalfEdge $ pgBoundaryEdges pg Vector.! fId++-- | \( O(1) \)+--+-- Returns @True@ iff a face is interior. Does not check if the face actually exists.+--+-- ==== __Examples:__+--+-- >>> faceIsInterior (Face 0)+-- True+--+-- >>> faceIsInterior (Face 10000)+-- True+--+-- >>> faceIsInterior (Boundary 0)+-- False+--+-- @since 0.12.0.0+faceIsInterior :: Face -> Bool+faceIsInterior = not . faceIsBoundary++-- | \( O(1) \)+--+-- Returns @True@ iff a face is a boundary. Does not check if the face actually exists.+--+-- ==== __Examples:__+--+-- >>> faceIsBoundary (Face 0)+-- False+--+-- >>> faceIsBoundary (Face 10000)+-- False+--+-- >>> faceIsBoundary (Boundary 0)+-- True+--+-- @since 0.12.0.0+faceIsBoundary :: Face -> Bool+faceIsBoundary Face{} = False+faceIsBoundary Boundary{} = True++-- faceVertices :: Face -> ST s (CircularVector Vertex)++-- | \( O(k) \)+--+-- Query the half-edges around a face in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> faceHalfEdges (Face 0) pg+-- [HalfEdge 0,HalfEdge 2,HalfEdge 4,HalfEdge 6]+--+-- >>> faceHalfEdges (Face 1) pg+-- [HalfEdge 8,HalfEdge 5,HalfEdge 3,HalfEdge 10]+--+-- >>> faceHalfEdges (Boundary 0) pg+-- [HalfEdge 1,HalfEdge 11,HalfEdge 9,HalfEdge 7]+--+-- >>> faceHalfEdges (Face 10) pg+-- ... Exception: Data.PlanarGraph.Immutable.faceHalfEdges: Out-of-bounds face access: 10+-- ...+--+-- @since 0.12.0.0+faceHalfEdges :: Face -> PlanarGraph -> [HalfEdge]+faceHalfEdges face pg | faceCheck "faceHalfEdges" face pg False = undefined+faceHalfEdges face pg+ | faceIsBoundary face = first : build (worker halfEdgeNext (halfEdgeNext first pg))+ | otherwise = first : build (worker halfEdgePrev (halfEdgePrev first pg))+ where+ first = faceHalfEdge face pg+ worker :: (HalfEdge -> PlanarGraph -> HalfEdge) -> HalfEdge -> (HalfEdge -> b -> b) -> b -> b+ worker advance he cons nil+ | he == first = nil+ | otherwise = cons he (worker advance (advance he pg) cons nil)++-- | \( O(k) \)+--+-- Query the vertices of a face in counter-clockwise order.+--+-- ==== __Examples:__+-- >>> let pg = pgFromFaces [[0,1,2,3],[4,3,2,1]]+--+-- <<docs/Data/PlanarGraph/planargraph-1711135548958680232.svg>>+--+-- >>> faceBoundary (Face 0) pg+-- [Vertex 1,Vertex 2,Vertex 3,Vertex 0]+--+-- >>> faceBoundary (Face 1) pg+-- [Vertex 3,Vertex 2,Vertex 1,Vertex 4]+--+-- >>> faceBoundary (Boundary 0) pg+-- [Vertex 0,Vertex 1,Vertex 4,Vertex 3]+--+-- >>> faceBoundary (Face 10) pg+-- ... Exception: Data.PlanarGraph.Immutable.faceBoundary: Out-of-bounds face access: 10+-- ...+--+-- @since 0.12.0.0+faceBoundary :: Face -> PlanarGraph -> [Vertex]+faceBoundary face pg = faceCheck "faceBoundary" face pg $+ map (`halfEdgeVertex` pg) $ faceHalfEdges face pg++-- faceAdjacentFaces :: Face -> ST s (CircularVector Face)++-------------------------------------------------------------------------------+-- Mutation++-- | \( O(n) \)+--+-- @since 0.12.0.0+pgMutate :: PlanarGraph -> (forall s. Mut.PlanarGraph s -> ST s ()) -> PlanarGraph+pgMutate pg action = runST $ do+ mutPG <- pgThaw pg+ action mutPG+ pgUnsafeFreeze mutPG++-- | \( O(1) \)+--+-- @since 0.12.0.0+pgCreate :: (forall s. ST s (Mut.PlanarGraph s)) -> PlanarGraph+pgCreate action = runST (action >>= pgUnsafeFreeze)++-- | \( O(n) \)+--+-- @since 0.12.0.0+pgThaw :: PlanarGraph -> ST s (Mut.PlanarGraph s)+pgThaw pg = do+ pgNextHalfEdgeId <- newSTRef $ Vector.length (pgHalfEdgeNext pg) `div` 2+ pgNextVertexId <- newSTRef $ Vector.length $ pgVertexEdges pg+ pgNextFaceId <- newSTRef $ Vector.length $ pgFaceEdges pg+ pgNextBoundaryId <- newSTRef $ Vector.length $ pgBoundaryEdges pg++ pgHalfEdgeNext <- Mut.thawVector $ pgHalfEdgeNext pg+ pgHalfEdgePrev <- Mut.thawVector $ pgHalfEdgePrev pg+ pgHalfEdgeFace <- Mut.thawVector $ pgHalfEdgeFace pg+ pgHalfEdgeVertex <- Mut.thawVector $ pgHalfEdgeVertex pg+ pgVertexEdges <- Mut.thawVector $ pgVertexEdges pg+ pgFaceEdges <- Mut.thawVector $ pgFaceEdges pg+ pgBoundaryEdges <- Mut.thawVector $ pgBoundaryEdges pg+ pure Mut.PlanarGraph {..}++-- | \( O(1) \)+--+-- @since 0.12.0.0+pgUnsafeThaw :: PlanarGraph -> ST s (Mut.PlanarGraph s)+pgUnsafeThaw pg = do+ pgNextHalfEdgeId <- newSTRef $ Vector.length $ pgHalfEdgeNext pg+ pgNextVertexId <- newSTRef $ Vector.length $ pgVertexEdges pg+ pgNextFaceId <- newSTRef $ Vector.length $ pgFaceEdges pg+ pgNextBoundaryId <- newSTRef $ Vector.length $ pgBoundaryEdges pg++ pgHalfEdgeNext <- Mut.unsafeThawVector $ pgHalfEdgeNext pg+ pgHalfEdgePrev <- Mut.unsafeThawVector $ pgHalfEdgePrev pg+ pgHalfEdgeFace <- Mut.unsafeThawVector $ pgHalfEdgeFace pg+ pgHalfEdgeVertex <- Mut.unsafeThawVector $ pgHalfEdgeVertex pg+ pgVertexEdges <- Mut.unsafeThawVector $ pgVertexEdges pg+ pgFaceEdges <- Mut.unsafeThawVector $ pgFaceEdges pg+ pgBoundaryEdges <- Mut.unsafeThawVector $ pgBoundaryEdges pg+ pure Mut.PlanarGraph {..}++-- | \( O(n) \)+--+-- @since 0.12.0.0+pgFreeze :: Mut.PlanarGraph s -> ST s PlanarGraph+pgFreeze pg = do+ maxEdgeId <- readSTRef (Mut.pgNextHalfEdgeId pg)+ maxVertexId <- readSTRef (Mut.pgNextVertexId pg)+ maxFaceId <- readSTRef (Mut.pgNextFaceId pg)+ maxBoundaryId <- readSTRef (Mut.pgNextBoundaryId pg)++ pgHalfEdgeNext <- Vector.take (maxEdgeId*2) <$> Mut.freezeVector (Mut.pgHalfEdgeNext pg)+ pgHalfEdgePrev <- Vector.take (maxEdgeId*2) <$> Mut.freezeVector (Mut.pgHalfEdgePrev pg)+ pgHalfEdgeFace <- Vector.take (maxEdgeId*2) <$> Mut.freezeVector (Mut.pgHalfEdgeFace pg)+ pgHalfEdgeVertex <- Vector.take (maxEdgeId*2) <$> Mut.freezeVector (Mut.pgHalfEdgeVertex pg)+ pgVertexEdges <- Vector.take maxVertexId <$> Mut.freezeVector (Mut.pgVertexEdges pg)+ pgFaceEdges <- Vector.take maxFaceId <$> Mut.freezeVector (Mut.pgFaceEdges pg)+ pgBoundaryEdges <- Vector.take maxBoundaryId <$> Mut.freezeVector (Mut.pgBoundaryEdges pg)+ pure PlanarGraph { .. }++-- | \( O(1) \)+--+-- @since 0.12.0.0+pgUnsafeFreeze :: Mut.PlanarGraph s -> ST s PlanarGraph+pgUnsafeFreeze pg = do+ maxEdgeId <- readSTRef (Mut.pgNextHalfEdgeId pg)+ maxVertexId <- readSTRef (Mut.pgNextVertexId pg)+ maxFaceId <- readSTRef (Mut.pgNextFaceId pg)+ maxBoundaryId <- readSTRef (Mut.pgNextBoundaryId pg)++ pgHalfEdgeNext <- Vector.take (maxEdgeId*2) <$> Mut.unsafeFreezeVector (Mut.pgHalfEdgeNext pg)+ pgHalfEdgePrev <- Vector.take (maxEdgeId*2) <$> Mut.unsafeFreezeVector (Mut.pgHalfEdgePrev pg)+ pgHalfEdgeFace <- Vector.take (maxEdgeId*2) <$> Mut.unsafeFreezeVector (Mut.pgHalfEdgeFace pg)+ pgHalfEdgeVertex <- Vector.take (maxEdgeId*2) <$> Mut.unsafeFreezeVector (Mut.pgHalfEdgeVertex pg)+ pgVertexEdges <- Vector.take maxVertexId <$> Mut.unsafeFreezeVector (Mut.pgVertexEdges pg)+ pgFaceEdges <- Vector.take maxFaceId <$> Mut.unsafeFreezeVector (Mut.pgFaceEdges pg)+ pgBoundaryEdges <- Vector.take maxBoundaryId <$> Mut.unsafeFreezeVector (Mut.pgBoundaryEdges pg)+ pure PlanarGraph { .. }++-------------------------------------------------------------------------------+-- Tutte embedding++-- | \( O(n^3) \)+--+-- @since 0.12.0.0+tutteEmbedding :: PlanarGraph -> Vector.Vector (V2 Double)+tutteEmbedding pg = runST $ do+ let nVertices = Vector.length (pgVertexEdges pg)+ -- trace ("nVertices: " ++ show nVertices) $ return ()+ m <- Vector.replicateM nVertices (V.replicate nVertices 0)+ vx <- V.replicate nVertices 0+ vy <- V.replicate nVertices 0++ let boundary = faceBoundary (Boundary 0) pg+ let nBoundary = length boundary+ -- trace ("Vectors: " ++ show boundary) $+ forM_ (zip boundary (regularPolygon nBoundary)) $ \(vertex,(x,y)) -> do+ let valid = halfEdgeIsValid $ vertexHalfEdge vertex pg+ when valid $ do+ V.write (m Vector.! vertexId vertex) (vertexId vertex) (1::Double)+ V.write vx (vertexId vertex) x+ V.write vy (vertexId vertex) y++ forM_ [0..nVertices-1] $ \vId -> -- trace ("Vertex: " ++ show vId) $+ do+ let valid = halfEdgeIsValid $ vertexHalfEdge (Vertex vId) pg+ unless valid $ do+ V.write (m Vector.! vId) vId (1::Double)+ when valid $ do+ let onOuterBoundary =+ Boundary 0 == halfEdgeFace (halfEdgeTwin $ vertexHalfEdge (Vertex vId) pg) pg+ unless onOuterBoundary $ do+ let vertex = Vertex vId+ let neighbours = vertexNeighbours vertex pg+ forM_ neighbours $ \neighbour ->+ V.write (m Vector.! vId) (vertexId neighbour) (1::Double)+ V.write (m Vector.! vId) vId (negate $ fromIntegral $ length neighbours)++ mi <- mapM Vector.freeze m+ vxi <- Vector.freeze vx+ vyi <- Vector.freeze vy++ let xPos = reifyMatrix mi vxi luSolve+ yPos = reifyMatrix mi vyi luSolve++ pure $ Vector.zipWith V2 xPos yPos++reifyMatrix :: forall a. Vector.Vector (Vector.Vector a) ->+ Vector.Vector a ->+ (forall (n :: *). Dim n => V n (V n a) -> V n a -> V n a) ->+ Vector.Vector a+reifyMatrix m v f = reifyDim (Vector.length m) $ \(Proxy :: Proxy n) ->+ toVector (f (coerce m :: (V n (V n a))) (coerce v))++regularPolygon :: Int -> [(Double, Double)]+regularPolygon n =+ [ (cos ang, sin ang)+ | i <- [0 .. n-1]+ , let ang = fromIntegral i * frac + pi/2]+ where+ frac = 2*pi / fromIntegral n
+ src/Data/PlanarGraph/Internal.hs view
@@ -0,0 +1,92 @@+module Data.PlanarGraph.Internal where++import Control.Monad.ST+import Data.STRef+import qualified Data.Vector as V (unsafeFreeze)+import qualified Data.Vector as Vector+import Data.Vector.Circular (CircularVector)+import qualified Data.Vector.Circular as CV+import Data.Vector.Mutable (STVector)+import qualified Data.Vector.Mutable as V++-------------------------------------------------------------------------------+-- Resizeable vector++type GrowVector s v = STRef s (STVector s v)++newVector :: Int -> ST s (GrowVector s v)+newVector n = newSTRef =<< V.new n++setVector :: GrowVector s v -> v -> ST s ()+setVector ref val = do+ vec <- readSTRef ref+ V.set vec val++readVector :: GrowVector s v -> Int -> ST s v+readVector ref idx = do+ v <- readSTRef ref+ V.read v idx++writeVector :: GrowVector s v -> Int -> v -> ST s ()+writeVector ref idx val = do+ v <- readSTRef ref+ let l = V.length v+ if idx >= l+ then {-trace ("Growing: " ++ show (idx, l)) $ -} do+ v' <- V.grow v ((idx+1)*2)+ V.write v' idx val+ writeSTRef ref v'+ else -- trace ("Writing: " ++ show (idx, l)) $+ V.write v idx val++freezeVector :: GrowVector s v -> ST s (Vector.Vector v)+freezeVector ref = Vector.freeze =<< readSTRef ref++unsafeFreezeVector :: GrowVector s v -> ST s (Vector.Vector v)+unsafeFreezeVector ref = Vector.unsafeFreeze =<< readSTRef ref++thawVector :: Vector.Vector v -> ST s (GrowVector s v)+thawVector v = newSTRef =<< Vector.thaw v++unsafeThawVector :: Vector.Vector v -> ST s (GrowVector s v)+unsafeThawVector v = newSTRef =<< Vector.unsafeThaw v+++freezeCircularVector :: Int -> GrowVector s v -> ST s (CircularVector v)+freezeCircularVector n ref =+ (CV.unsafeFromVector . Vector.take n) <$> (V.unsafeFreeze =<< readSTRef ref)+++-------------------------------------------------------------------------------+-- Planar graph++type EdgeId = Int+type HalfEdgeId = Int+type VertexId = Int++-- | Numerical face identifier. Negative numbers indicate boundaries, non-negative numbers+-- are internal faces.+type FaceId = Int++-- PlanarGraphs have vertices, edges, and faces.+-- Invariant: The half-edge of a boundary vertex is interior, twin is exterior.++-- FIXME: Use STRefU ?+-- PlanarGraph with 0 vertices: No edges, no vertices, no faces.+-- PlanarGraph with 1 vertex: No edges, no interior faces.+-- PlanarGraph with 2 vertices: One edge, no interior faces.+-- PlanarGraph with 3+ vertices: Usual properties hold.+data PlanarGraph s = PlanarGraph+ { pgNextHalfEdgeId :: !(STRef s HalfEdgeId)+ , pgNextVertexId :: !(STRef s VertexId)+ , pgNextFaceId :: !(STRef s FaceId)+ , pgNextBoundaryId :: !(STRef s FaceId)+ , pgHalfEdgeNext :: !(GrowVector s HalfEdgeId) -- HalfEdge indexed+ , pgHalfEdgePrev :: !(GrowVector s HalfEdgeId) -- HalfEdge indexed+ , pgHalfEdgeVertex :: !(GrowVector s VertexId) -- HalfEdge indexed+ , pgHalfEdgeFace :: !(GrowVector s FaceId) -- HalfEdge indexed+ , pgVertexEdges :: !(GrowVector s HalfEdgeId) -- Vertex indexed+ , pgFaceEdges :: !(GrowVector s HalfEdgeId) -- Face indexed+ , pgBoundaryEdges :: !(GrowVector s HalfEdgeId) -- Boundary faces+ } deriving Eq+
+ src/Data/PlanarGraph/Mutable.hs view
@@ -0,0 +1,692 @@+module Data.PlanarGraph.Mutable+ ( -- * Planar graphs+ PlanarGraph+ , pgFromFaces -- :: [[VertexId]] -> ST s (PlanarGraph s)+ , pgFromFacesCV -- :: [CircularVector VertexId] -> ST s (PlanarGraph s)+ , pgClone -- :: PlanarGraph s -> ST s (PlanarGraph s)+ , pgHash -- :: PlanarGraph s -> ST s Int++ -- * Elements+ -- ** Vertices+ , Vertex, VertexId+ , vertexFromId -- :: VertexId -> PlanarGraph s -> Vertex s+ , vertexToId -- :: Vertex s -> VertexId+ , vertexHalfEdge -- :: Vertex s -> ST s (HalfEdge s)+ , vertexIsBoundary -- :: Vertex s -> ST s Bool+ , vertexOutgoingHalfEdges -- :: Vertex s -> ST s (CircularVector (HalfEdge s))+ , vertexWithOutgoingHalfEdges -- :: Vertex s -> (HalfEdge s -> ST s ()) -> ST s ()+ , vertexIncomingHalfEdges -- :: Vertex s -> ST s (CircularVector (HalfEdge s))+ , vertexWithIncomingHalfEdges -- :: Vertex s -> (HalfEdge s -> ST s ()) -> ST s ()+ , vertexNeighbours -- :: Vertex s -> ST s (CircularVector (Vertex s))+ -- , vertexNew -- :: PlanarGraph s -> ST s (Vertex s)+ -- , vertexSetHalfEdge -- :: Vertex s -> HalfEdge s -> ST s ()++ -- ** Edges+ , Edge, EdgeId+ , edgeFromId -- :: EdgeId -> PlanarGraph s -> Edge s+ , edgeToId -- :: Edge s -> EdgeId+ , edgeFromHalfEdge -- :: HalfEdge s -> Edge s++ -- ** Half-edges+ , HalfEdge, HalfEdgeId+ , halfEdgeFromId -- :: HalfEdgeId -> PlanarGraph s -> HalfEdge s+ , halfEdgeToId -- :: HalfEdge s -> HalfEdgeId+ , halfEdgeNext -- :: HalfEdge s -> ST s (HalfEdge s)+ , halfEdgePrev -- :: HalfEdge s -> ST s (HalfEdge s)+ , halfEdgeNextOutgoing -- :: HalfEdge s -> ST s (HalfEdge s)+ , halfEdgeNextIncoming -- :: HalfEdge s -> ST s (HalfEdge s)+ , halfEdgeVertex -- :: HalfEdge s -> ST s (Vertex s)+ , halfEdgeTwin -- :: HalfEdge s -> HalfEdge s+ , halfEdgeTailVertex -- :: HalfEdge s -> ST s (Vertex s)+ , halfEdgeTipVertex -- :: HalfEdge s -> ST s (Vertex s)+ , halfEdgeFace -- :: HalfEdge s -> ST s (Face s)+ , halfEdgeIsInterior -- :: HalfEdge s -> ST s Bool+ -- , halfEdgeNew -- :: PlanarGraph s -> ST s (HalfEdge s)+ -- , halfEdgeSetNext -- :: HalfEdge s -> HalfEdge s -> ST s ()+ -- , halfEdgeSetPrev -- :: HalfEdge s -> HalfEdge s -> ST s ()+ -- , halfEdgeSetFace -- :: HalfEdge s -> Face s -> ST s ()+ -- , halfEdgeSetVertex -- :: HalfEdge s -> Vertex s -> ST s ()++ -- ** Faces+ , Face, FaceId+ , faceInvalid -- :: PlanarGraph s -> Face s+ , faceIsValid -- :: Face s -> Bool+ , faceIsInvalid -- :: Face s -> Bool+ , faceFromId -- :: FaceId -> PlanarGraph s -> Face s+ , faceToId -- :: Face s -> FaceId+ , faceHalfEdge -- :: Face s -> ST s (HalfEdge s)+ , faceIsInterior -- :: Face s -> Bool+ , faceIsBoundary -- :: Face s -> Bool+ , faceHalfEdges -- :: Face s -> ST s (CircularVector (HalfEdge s))+ , faceBoundary -- :: Face s -> ST s (CircularVector (Vertex s))+ -- , faceNew :: PlanarGraph s -> ST s (Face s)+ -- , faceNewBoundary :: PlanarGraph s -> ST s (Face s)+ -- , faceSetHalfEdge :: Face s -> HalfEdge s -> ST s ()++ -- * Mutation+ , pgConnectVertices -- :: HalfEdge s -> HalfEdge s -> ST s (Edge s)+-- pgSplitHalfEdge :: HalfEdge s -> ST s (Vertex s)++-- pgRemoveFace :: Face s -> ST s ()+-- pgRemoveHalfEdge :: HalfEdge s -> ST s ()+-- pgRemoveVertex :: Vertex s -> ST s ()+ -- * Misc+ -- , tutteEmbedding -- :: PlanarGraph s -> ST s (Vector.Vector (Double, Double))+ )+ where++import Control.Monad (forM_, unless, when)+import Control.Monad.ST (ST)+import Data.Bits (Bits (xor))+import qualified Data.HashMap.Strict as HM+import Data.Hashable (Hashable (hashWithSalt))+import Data.PlanarGraph.Internal+import Data.STRef (modifySTRef', newSTRef, readSTRef, writeSTRef)+import Data.Vector.Circular (CircularVector)+import qualified Data.Vector.Circular as CV++import Debug.Trace++-------------------------------------------------------------------------------+-- Elements: Half-edges, vertices, faces.++data HalfEdge s = HalfEdge HalfEdgeId (PlanarGraph s)+ deriving Eq+instance Show (HalfEdge s) where+ showsPrec d (HalfEdge s _) = showsPrec d s+instance Hashable (HalfEdge s) where+ hashWithSalt salt (HalfEdge eId _) = hashWithSalt salt eId+++data Edge s = Edge EdgeId (PlanarGraph s)+ deriving Eq++data Vertex s = Vertex VertexId (PlanarGraph s)+ deriving Eq+instance Show (Vertex s) where+ showsPrec d (Vertex v _) = showsPrec d v+instance Hashable (Vertex s) where+ hashWithSalt salt (Vertex vId _) = hashWithSalt salt vId++data Face s = Face FaceId (PlanarGraph s) | Boundary FaceId (PlanarGraph s)+ deriving Eq+instance Show (Face s) where+ showsPrec _ (Face fId _) = showString "Face " . shows fId+ showsPrec _ (Boundary fId _) = showString "Boundary " . shows fId++-------------------------------------------------------------------------------+-- Planar graph++panic :: String -> String -> a+panic tag msg = error $ "Data.PlanarGraph.Mutable." ++ tag ++ ": " ++ msg++eqCheck :: String -> PlanarGraph s -> PlanarGraph s -> a -> a+eqCheck tag pg1 pg2 v+ | pg1 == pg2 = v+ | otherwise = panic tag "Invalid cross reference."++empty :: Int -> Int -> Int -> ST s (PlanarGraph s)+empty nFaces nVertices nEdges = PlanarGraph+ <$> newSTRef 0+ <*> newSTRef 0+ <*> newSTRef 0+ <*> newSTRef 0+ <*> newVector (nEdges*2)+ <*> newVector (nEdges*2)+ <*> newVector (nEdges*2)+ <*> newVector (nEdges*2)+ <*> newVector nVertices+ <*> newVector nFaces+ <*> newVector 0++-- {-+-- For all boundary vertices:+-- vertex.half-edge.face == interior+-- vertex.half-edge.twin.face == exterior+-- Boundary face: 0++-- create N+-- -}+-- -- | O(n)+-- -- Create a planar graph with N boundary vertices.+-- new :: Int -> ST s (PlanarGraph s)+-- new n | n < 0 = panic "new" "Cannot contain negative vertices."+-- new 0 = empty 0 0 0+-- new 1 = undefined+-- new 2 = undefined+-- new n = pgFromFaces [[0..n-1]]++-- $setup+--+-- >>> import Control.Monad.ST++-- Disabled since hashes are not stable across different versions of hashable.+-- >>> runST $ pgFromFaces [[0,1,2]] >>= pgHash+-- 2959979592048325618+-- >>> runST $ pgFromFaces [[0,1,2,3]] >>= pgHash+-- 2506803680640023584+-- >>> runST $ pgFromFaces [[0,1,2,3],[4,3,2,1]] >>= pgHash+-- 1711135548958680232++-- | \( O(n \log n) \)+--+--+--+-- ==== __Examples:__+-- @+-- 'pgFromFaces' [[0,1,2]]+-- @+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- @+-- 'pgFromFaces' [[0,1,2,3]]+-- @+-- <<docs/Data/PlanarGraph/planargraph-2506803680640023584.svg>>+pgFromFaces :: [[VertexId]] -> ST s (PlanarGraph s)+pgFromFaces = pgFromFacesCV . map CV.unsafeFromList++pgFromFacesCV :: [CircularVector VertexId] -> ST s (PlanarGraph s)+pgFromFacesCV [] = empty 0 0 0+pgFromFacesCV faces = do+ let maxVertexId = maximum (map CV.maximum faces)+ nFaces = length faces+ nHalfEdges = sum (map length faces)+ pg <- empty nFaces (maxVertexId+1) (nHalfEdges `div` 2)+ setVector (pgVertexEdges pg) (-1)+ writeSTRef (pgNextVertexId pg) (maxVertexId+1)+ edgeMap <- newSTRef HM.empty+ let getHalfEdge (vTail, vTip) = do+ hm <- readSTRef edgeMap+ case HM.lookup (vTail, vTip) hm of+ Just{} -> panic "fromFaces" "Duplicate half-edge."+ Nothing ->+ case HM.lookup (vTip, vTail) hm of+ Just twin -> pure (halfEdgeTwin twin)+ Nothing -> {-trace ("Creating new half-edge: " ++ show (vTip, vTail)) $ -} do+ halfEdge <- halfEdgeNew pg+ halfEdgeSetFace (halfEdgeTwin halfEdge) (faceInvalid pg)+ vertexSetHalfEdge (vertexFromId vTip pg) halfEdge+ writeSTRef edgeMap $ HM.insert (vTail, vTip) halfEdge hm+ halfEdgeSetVertex halfEdge (vertexFromId vTip pg)+ halfEdgeSetVertex (halfEdgeTwin halfEdge) (vertexFromId vTail pg)+ pure halfEdge+ addFace face | length face < 3 = panic "fromFaces" "Faces must have at least 3 vertices."+ addFace face = {- trace "Adding face" $ -} do+ fId <- faceNew pg+ let edges = CV.zip face (CV.rotateRight 1 face)+ halfEdges <- {- trace ("getHalfEdge") $ -} mapM getHalfEdge edges+ faceSetHalfEdge fId (CV.head halfEdges)+ setNextPrevFace fId (CV.reverse halfEdges)+ forM_ faces addFace++ maxHalfEdgeId <- readSTRef (pgNextHalfEdgeId pg)+ -- For each half-edge:+ -- If face is invalid:+ -- Find loop and add it as a boundary.+ forM_ (map (`halfEdgeFromId` pg) [0..maxHalfEdgeId*2-1]) $ \he -> {- trace ("Scan halfedge: " ++ show he) $ -} do+ -- f <- halfEdgeFace he+ validFace <- faceIsValid <$> halfEdgeFace he+ unless validFace $ {- trace ("Found invalid face: " ++ show f) $ -} do+ face <- faceNewBoundary pg+ boundary <- halfEdgeConstructBoundary he+ -- trace ("Boundary: " ++ show (face, boundary)) $ return ()+ faceSetHalfEdge face (CV.head boundary)+ setNextPrevFace face boundary+ pure pg+ where+ setNextPrevFace fId halfEdges = do+ let edgeTriples = CV.zip3 (CV.rotateLeft 1 halfEdges) halfEdges (CV.rotateRight 1 halfEdges)+ forM_ (edgeTriples) $ \(prev, edge, next) -> do+ halfEdgeSetNext edge next+ halfEdgeSetPrev edge prev+ halfEdgeSetFace edge fId++-- fromFaces' :: Int -> Int -> Int -> [CircularVector VertexId] -> ST s (PlanarGraph s)+-- fromFaces' nFaces nHalfEdges maxVertexId faces = do+-- undefined++-- | \( O(n) \)+pgClone :: PlanarGraph s -> ST s (PlanarGraph s)+pgClone = undefined++-- dualTree :: Face s -> ST s (Tree (Face s))+-- dualTree = undefined++pgHash :: PlanarGraph s -> ST s Int+pgHash pg = do+ eMax <- readSTRef (pgNextHalfEdgeId pg)+ let loop [] salt = pure salt+ loop (edgeId:rest) salt = do+ let he = halfEdgeFromId (edgeId*2) pg+ vTail <- halfEdgeTailVertex he+ vTip <- halfEdgeTipVertex he+ loop rest (hashWithSalt salt (vTail, vTip))+ abs <$> loop [0..eMax-1] 0++-------------------------------------------------------------------------------+-- Vertices++-- | \( O(1) \)+vertexFromId :: VertexId -> PlanarGraph s -> Vertex s+vertexFromId vId pg = Vertex vId pg++-- | \( O(1) \)+vertexToId :: Vertex s -> VertexId+vertexToId (Vertex vId _pg) = vId++-- | \( O(1) \)+vertexHalfEdge :: Vertex s -> ST s (HalfEdge s)+vertexHalfEdge (Vertex vId pg) = do+ eId <- readVector (pgVertexEdges pg) vId+ pure $ HalfEdge eId pg++-- | \( O(1) \)+vertexIsBoundary :: Vertex s -> ST s Bool+vertexIsBoundary vertex = faceIsBoundary <$> (halfEdgeFace =<< (halfEdgeTwin <$> vertexHalfEdge vertex))++-- | O(k)+vertexOutgoingHalfEdges :: Vertex s -> ST s (CircularVector (HalfEdge s))+vertexOutgoingHalfEdges vertex = do+ tmp <- newVector 10+ iRef <- newSTRef 0+ vertexWithOutgoingHalfEdges vertex $ \edge -> do+ i <- readSTRef iRef+ modifySTRef' iRef succ+ writeVector tmp i edge+ i <- readSTRef iRef+ freezeCircularVector i tmp++-- | O(k), more efficient than 'vertexOutgoingHalfEdges'.+vertexWithOutgoingHalfEdges :: Vertex s -> (HalfEdge s -> ST s ()) -> ST s ()+vertexWithOutgoingHalfEdges vertex cb = do+ first <- vertexHalfEdge vertex+ cb first+ let loop edge | edge == first = return ()+ loop edge = trace ("At edge: "++ show (first, edge)) $ do+ cb edge+ loop =<< halfEdgeNext (halfEdgeTwin edge)+ loop =<< halfEdgeNext (halfEdgeTwin first)++-- | O(k)+vertexIncomingHalfEdges :: Vertex s -> ST s (CircularVector (HalfEdge s))+vertexIncomingHalfEdges vertex = CV.map halfEdgeTwin <$> vertexOutgoingHalfEdges vertex++-- | O(k)+vertexWithIncomingHalfEdges :: Vertex s -> (HalfEdge s -> ST s ()) -> ST s ()+vertexWithIncomingHalfEdges = undefined++-- | O(k)+vertexNeighbours :: Vertex s -> ST s (CircularVector (Vertex s))+vertexNeighbours vertex = CV.mapM halfEdgeVertex =<< vertexIncomingHalfEdges vertex++-- vertexAdjacentVertices :: Vertex -> PlanarGraph -> [Vertex]+-- vertexAdjacentFaces :: Vertex -> PlanarGraph -> [Face]++-- -- O(1), internal function.+-- vertexNew :: PlanarGraph s -> ST s (Vertex s)+-- vertexNew pg = do+-- vId <- readSTRef (pgNextVertexId pg)+-- writeSTRef (pgNextVertexId pg) (vId+1)+-- return (Vertex vId pg)++vertexSetHalfEdge :: Vertex s -> HalfEdge s -> ST s ()+vertexSetHalfEdge (Vertex vId pg) (HalfEdge eId pg') = eqCheck "vertexSetHalfEdge" pg pg' $+ writeVector (pgVertexEdges pg) vId eId++-------------------------------------------------------------------------------+-- Edges++-- | O(1)+edgeFromId :: EdgeId -> PlanarGraph s -> Edge s+edgeFromId = Edge++-- | O(1)+edgeToId :: Edge s -> EdgeId+edgeToId (Edge e _) = e++-- | O(1)+edgeFromHalfEdge :: HalfEdge s -> Edge s+edgeFromHalfEdge (HalfEdge he pg) = Edge (he `div` 2) pg++-- -- | O(1)+-- edgeToHalfEdges :: Edge s -> (HalfEdge s, HalfEdge s)+-- edgeToHalfEdges (Edge e pg) = (HalfEdge (e*2) pg, HalfEdge (e*2+1) pg)++-------------------------------------------------------------------------------+-- Half-edges++-- | O(1)+halfEdgePlanarGraph :: HalfEdge s -> PlanarGraph s+halfEdgePlanarGraph (HalfEdge _ pg) = pg++-- -- | O(1)+-- halfEdgeIsValid :: HalfEdge s -> Bool+-- halfEdgeIsValid (HalfEdge eId _) = eId >= 0++-- | O(1)+halfEdgeFromId :: HalfEdgeId -> PlanarGraph s -> HalfEdge s+halfEdgeFromId eId pg = HalfEdge eId pg++-- | O(1)+halfEdgeToId :: HalfEdge s -> HalfEdgeId+halfEdgeToId (HalfEdge eId _pg) = eId++-- | O(1)+halfEdgeNext :: HalfEdge s -> ST s (HalfEdge s)+halfEdgeNext (HalfEdge eId pg) = do+ next <- readVector (pgHalfEdgeNext pg) eId+ pure $ HalfEdge next pg++-- | O(1)+halfEdgePrev :: HalfEdge s -> ST s (HalfEdge s)+halfEdgePrev (HalfEdge eId pg) = do+ prev <- readVector (pgHalfEdgePrev pg) eId+ pure $ HalfEdge prev pg++-- | O(1)+-- Next half-edge with the same vertex.+halfEdgeNextOutgoing :: HalfEdge s -> ST s (HalfEdge s)+halfEdgeNextOutgoing = halfEdgeNext . halfEdgeTwin++-- | O(1)+-- Next half-edge with the same vertex.+halfEdgeNextIncoming :: HalfEdge s -> ST s (HalfEdge s)+halfEdgeNextIncoming = halfEdgePrev . halfEdgeTwin++-- | O(1)+halfEdgeVertex :: HalfEdge s -> ST s (Vertex s)+halfEdgeVertex (HalfEdge idx pg) = do+ v <- readVector (pgHalfEdgeVertex pg) idx+ pure $ Vertex v pg++-- | O(1)+halfEdgeTwin :: HalfEdge s -> HalfEdge s+halfEdgeTwin (HalfEdge idx graph) = HalfEdge (idx `xor` 1) graph++-- | O(1)+-- Tail vertex. IE. the vertex of the twin edge.+halfEdgeTailVertex :: HalfEdge s -> ST s (Vertex s)+halfEdgeTailVertex = halfEdgeVertex++-- | O(1)+-- Synonym of `halfEdgeVertex`.+halfEdgeTipVertex :: HalfEdge s -> ST s (Vertex s)+halfEdgeTipVertex = halfEdgeVertex . halfEdgeTwin++-- | \( O(1) \)+--+-- ==== __Examples:__+-- @+-- 'pgFromFaces' [[0,1,2]]+-- @+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> runST $ do pg <- pgFromFaces [[0,1,2]]; show <$> halfEdgeFace (halfEdgeFromId 0 pg)+-- "Face 0"+--+-- >>> runST $ do pg <- pgFromFaces [[0,1,2]]; show <$> halfEdgeFace (halfEdgeFromId 1 pg)+-- "Boundary 0"+--+halfEdgeFace :: HalfEdge s -> ST s (Face s)+halfEdgeFace (HalfEdge eId pg) = do+ fId <- readVector (pgHalfEdgeFace pg) eId+ pure $ faceFromId fId pg++-- | O(n)+-- Scan boundary half-edges without using 'next' or 'prev'.+halfEdgeConstructBoundary :: HalfEdge s -> ST s (CircularVector (HalfEdge s))+halfEdgeConstructBoundary halfEdge = {- trace ("mkBoundary from: " ++ show halfEdge) $ -} do+ tmp <- newVector 10+ writeVector tmp 0 halfEdge+ let loop i edge | edge == halfEdge = {- trace "Done" $ -} return i+ loop i edge = {- trace ("Going to: " ++ show edge) $ -} do+ face <- halfEdgeFace edge+ if faceIsInvalid face+ then do+ writeVector tmp i edge+ loop (i+1) =<< (halfEdgeTwin <$> halfEdgeNextIncoming edge)+ else+ loop i =<< (halfEdgeTwin <$> halfEdgePrev edge)+ i <- loop 1 =<< (halfEdgeTwin <$> halfEdgeNextIncoming halfEdge)+ cv <- freezeCircularVector i tmp+ -- trace ("Boundary: " ++ show cv) $ pure cv+ pure cv++-- | O(k)+halfEdgeWithLoop :: HalfEdge s -> (HalfEdge s -> ST s ()) -> ST s ()+halfEdgeWithLoop he cb = worker =<< halfEdgeNext he+ where+ worker edge+ | edge == he = return ()+ | otherwise = do cb edge; worker =<< halfEdgeNext edge++-- $setup+-- >>> let genPG = pgFromFaces [[0,1,2]]++-- | \( O(1) \)+-- Check if a half-edge's face is interior or exterior.+--+-- ==== __Examples:__+-- @+-- 'pgFromFaces' [[0,1,2]]+-- @+--+-- <<docs/Data/PlanarGraph/planargraph-2959979592048325618.svg>>+--+-- >>> runST $ do pg <- pgFromFaces [[0,1,2]]; halfEdgeIsInterior (halfEdgeFromId 0 pg)+-- True+--+-- >>> runST $ do pg <- pgFromFaces [[0,1,2]]; halfEdgeIsInterior (halfEdgeFromId 1 pg)+-- False+--+-- >>> runST $ do pg <- pgFromFaces [[0,1,2]]; halfEdgeIsInterior (halfEdgeFromId 2 pg)+-- True+--+-- >>> runST $ do pg <- pgFromFaces [[0,1,2]]; halfEdgeIsInterior (halfEdgeFromId 3 pg)+-- False+halfEdgeIsInterior :: HalfEdge s -> ST s Bool+halfEdgeIsInterior edge = faceIsInterior <$> halfEdgeFace edge++-- O(1) Allocate new half-edge pair.+halfEdgeNew :: PlanarGraph s -> ST s (HalfEdge s)+halfEdgeNew pg = do+ eId <- readSTRef (pgNextHalfEdgeId pg)+ writeSTRef (pgNextHalfEdgeId pg) (eId+1)+ return (HalfEdge (eId*2) pg)++halfEdgeSetNext :: HalfEdge s -> HalfEdge s -> ST s ()+halfEdgeSetNext (HalfEdge e pg) (HalfEdge next pg') = eqCheck "halfEdgeSetNext" pg pg' $+ -- trace ("Set next: " ++ show (e, next)) $+ writeVector (pgHalfEdgeNext pg) e next++halfEdgeSetPrev :: HalfEdge s -> HalfEdge s -> ST s ()+halfEdgeSetPrev (HalfEdge e pg) (HalfEdge prev pg') = eqCheck "halfEdgeSetPrev" pg pg' $+ -- trace ("Set prev: " ++ show (e, prev)) $+ writeVector (pgHalfEdgePrev pg) e prev++halfEdgeSetFace :: HalfEdge s -> Face s -> ST s ()+halfEdgeSetFace (HalfEdge e pg) face =+ -- trace ("Set face: " ++ show (e, face)) $+ writeVector (pgHalfEdgeFace pg) e (faceToId face)++halfEdgeSetVertex :: HalfEdge s -> Vertex s -> ST s ()+halfEdgeSetVertex (HalfEdge e pg) vertex =+ -- trace ("Set vertex: " ++ show (e, vertex)) $+ writeVector (pgHalfEdgeVertex pg) e (vertexToId vertex)++-------------------------------------------------------------------------------+-- Faces++-- | O(1)+faceInvalid :: PlanarGraph s -> Face s+faceInvalid = faceFromId maxBound++-- | O(1)+faceIsValid :: Face s -> Bool+faceIsValid = not . faceIsInvalid++-- | O(1)+faceIsInvalid :: Face s -> Bool+faceIsInvalid (Face fId _) = fId == maxBound+faceIsInvalid (Boundary fId _) = fId == maxBound++-- | O(1)+faceFromId :: FaceId -> PlanarGraph s -> Face s+faceFromId fId pg | fId < 0 = Boundary (negate fId - 1) pg+faceFromId fId pg = Face fId pg++-- | O(1)+faceToId :: Face s -> FaceId+faceToId (Face fId _) = fId+faceToId (Boundary fId _) = negate fId - 1++-- | O(1)+faceHalfEdge :: Face s -> ST s (HalfEdge s)+faceHalfEdge (Face fId pg) = do+ eId <- readVector (pgFaceEdges pg) fId+ pure $ HalfEdge eId pg+faceHalfEdge (Boundary fId pg) = do+ eId <- readVector (pgBoundaryEdges pg) fId+ pure $ HalfEdge eId pg++-- | O(1)+faceIsInterior :: Face s -> Bool+faceIsInterior = not . faceIsBoundary++-- | O(1)+faceIsBoundary :: Face s -> Bool+faceIsBoundary Face{} = False+faceIsBoundary Boundary{} = True++-- faceVertices :: Face s -> ST s (CircularVector (Vertex s))++-- | O(k)+-- Counterclockwise vector of edges.+faceHalfEdges :: Face s -> ST s (CircularVector (HalfEdge s))+faceHalfEdges face+ | faceIsBoundary face = worker halfEdgeNext+ | otherwise = worker halfEdgePrev+ where+ worker advance = do+ first <- faceHalfEdge face+ tmp <- newVector 10+ writeVector tmp 0 first+ let loop i edge | edge == first = return i+ loop i edge = do+ writeVector tmp i edge+ loop (i+1) =<< advance edge+ i <- loop 1 =<< advance first+ freezeCircularVector i tmp++-- | O(k)+faceBoundary :: Face s -> ST s (CircularVector (Vertex s))+faceBoundary face = CV.mapM halfEdgeVertex =<< faceHalfEdges face++-- faceAdjacentFaces :: Face s -> ST s (CircularVector (Face s))++faceNew :: PlanarGraph s -> ST s (Face s)+faceNew pg = do+ fId <- readSTRef (pgNextFaceId pg)+ writeSTRef (pgNextFaceId pg) (fId+1)+ return (Face fId pg)++faceNewBoundary :: PlanarGraph s -> ST s (Face s)+faceNewBoundary pg = do+ fId <- readSTRef (pgNextBoundaryId pg)+ writeSTRef (pgNextBoundaryId pg) (fId+1)+ return (Boundary fId pg)++faceSetHalfEdge :: Face s -> HalfEdge s -> ST s ()+faceSetHalfEdge (Boundary fId pg) (HalfEdge eId pg') = eqCheck "faceSetHalfEdge" pg pg' $+ -- trace ("faceSetHalfEdge: " ++ show (fId, eId)) $+ writeVector (pgBoundaryEdges pg) fId eId+faceSetHalfEdge (Face fId pg) (HalfEdge eId pg') = eqCheck "faceSetHalfEdge" pg pg' $+ writeVector (pgFaceEdges pg) fId eId++-------------------------------------------------------------------------------+-- Mutation++-- | O(k) where @k@ is the number of edges in new face.+--+-- The two half-edges must be different, must have the same face, and may not be+-- consecutive. The first half-edge will stay in the original face. The second+-- half-edge will be in the newly created face.+--+-- ==== __Examples:__+--+-- @+-- 'pgFromFaces' [[0,1,2,3]]+-- @+--+-- <<docs/Data/PlanarGraph/planargraph-2506803680640023584.svg>>+--+-- @+-- do pg <- 'pgFromFaces' [[0,1,2,3]]+-- let he0 = 'halfEdgeFromId' 0 pg'+-- he4 = 'halfEdgeFromId' 4 pg'+-- 'pgConnectVertices' he0 he4+-- @+--+-- <<docs/Data/PlanarGraph/planargraph-1902492848341357096.svg>>+pgConnectVertices :: HalfEdge s -> HalfEdge s -> ST s (Edge s)+pgConnectVertices e1 e2 =+ eqCheck "pgConnectVertices" (halfEdgePlanarGraph e1) (halfEdgePlanarGraph e2) $ do+ let pg = halfEdgePlanarGraph e1+ when (e1 == e2) $ fail "Edges must be different"+ f1 <- halfEdgeFace e1+ f2 <- halfEdgeFace e2+ unless (f1==f2) $ fail "Faces must be the same"+ e1' <- halfEdgeNext e1+ e2' <- halfEdgeNext e2+ when (e1' == e2 || e2' == e1) $ fail "Edges must not be consecutive"++ e1_prev <- halfEdgePrev e1+ e2_prev <- halfEdgePrev e2++ he <- halfEdgeNew pg+ halfEdgeSetFace he f1+ let he' = halfEdgeTwin he+ + halfEdgeSetVertex he =<< halfEdgeVertex e2+ halfEdgeSetVertex he' =<< halfEdgeVertex e1++ halfEdgeSetNext he e1+ halfEdgeSetPrev he e2_prev++ halfEdgeSetNext he' e2+ halfEdgeSetPrev he' =<< halfEdgePrev e1++ halfEdgeSetPrev e1 he+ halfEdgeSetNext e2_prev he++ halfEdgeSetNext e1_prev he'+ halfEdgeSetPrev e2 he'++ face <- faceNew pg+ faceSetHalfEdge face he'+ halfEdgeWithLoop he' (`halfEdgeSetFace` face)++ pure $ Edge (halfEdgeToId he `div` 2) pg++-- pgInsertVertex :: HalfEdge s -> ST s (Vertex s)++-- pgRemoveEdge :: Edge s -> ST s ()+-- pgRemoveEdges :: [Edge s] -> ST s ()+-- pgRemoveVertex :: Vertex s -> ST s ()+-- pgRemoveBorder :: Edge s -> ST s ()++-------------------------------------------------------------------------------+-- Use cases++-- Use cases:+-- Triangulate polygon.+-- Create PlanarGraph from polygon. Holes have unique faces.+-- Update with [LineSegment 2 Vertex r]+-- Update Face ids at the end.+-- Cut planar graph in two.+-- Re-triangulate part of graph.+-- Mesh smoothing.+-- 1. Keep vertex positions separate. Can update without changing the graph.+-- 2. Swap edges. HalfEdge+Twin. Find next of each. Delete original half-edges.+-- Then insert half-edges to next.
+ src/Data/PlanarGraph/Persistent.hs view
@@ -0,0 +1,71 @@+module Data.PlanarGraph.Persistent where++import Data.HashMap.Strict+import Control.Monad.State++type HalfEdge = Int+type Vertex = Int+type Face = Int++-- PlanarGraphs have vertices, edges, and faces.+-- Invariant: The half-edge of a boundary vertex is interior, twin is exterior.+data PlanarGraph = PlanarGraph+ { pgNextHalfEdgeId :: HalfEdge+ , pgNextVertexId :: Vertex+ , pgNextFaceId :: Face+ , pgNext :: HashMap HalfEdge HalfEdge+ , pgVertex :: HashMap HalfEdge Vertex+ , pgFace :: HashMap HalfEdge Face+ , pgHalfEdgeFromVertex :: HashMap Vertex HalfEdge+ , pgHalfEdgeFromFace :: HashMap Face HalfEdge+ }++-- data PlaneGraph r = PlaneGraph PlanarGraph (HashMap Vertex (Point 2 r))++new :: Int -> PlanarGraph+new = undefined++-- O(log n)+-- vertexHalfEdge :: Vertex -> PlanarGraph -> HalfEdge+-- O(k log n)+-- vertexOutgoingHalfEdges :: Vertex -> PlanarGraph -> [HalfEdge]+-- O(k log n)+-- vertexIncomingHalfEdges :: Vertex -> PlanarGraph -> [HalfEdge]+-- vertexAdjacentVertices :: Vertex -> PlanarGraph -> [Vertex]+-- vertexAdjacentFaces :: Vertex -> PlanarGraph -> [Face]++halfEdgeNext :: HalfEdge -> PlanarGraph -> HalfEdge+halfEdgeNext = undefined++halfEdgeNextM :: MonadState PlanarGraph m => HalfEdge -> m HalfEdge+halfEdgeNextM = gets . halfEdgeNext++-- halfEdgeNext :: HalfEdge -> PlanarGraph -> HalfEdge+-- halfEdgeVertex :: HalfEdge -> PlanarGraph -> Vertex+-- halfEdgeTwin :: HalfEdge -> PlanarGraph -> HalfEdge+-- halfEdgeTailVertex :: HalfEdge -> PlanarGraph -> Vertex+-- halfEdgeTipVertex :: HalfEdge -> PlanarGraph -> Vertex+-- halfEdgeFace :: HalfEdge -> PlanarGraph -> Face+-- halfEdgeIsInterior++-- faceHalfEdge :: Face -> PlanarGraph -> HalfEdge+-- faceIsInterior+-- faceIsBoundary+-- faceAdjacentVertices :: +-- faceAdjaventFaces :: Face -> PlanarGraph -> [Face]++-- connectVertices :: HalfEdge -> HalfEdge -> PlanarGraph -> PlanarGraph+-- splitHalfEdge :: HalfEdge -> PlanarGraph -> (PlanarGraph, Vertex)++-- Use cases:+-- Triangulate polygon.+-- Create PlanarGraph from polygon. Holes have unique faces.+-- Update with [LineSegment 2 Vertex r]+-- Update Face ids at the end.+-- Cut planar graph in two.+-- Re-triangulate part of graph.+-- Mesh smoothing.+-- 1. Keep vertex positions separate. Can update without changing the graph.+-- 2. Swap edges. HalfEdge+Twin. Find next of each. Delete original half-edges.+-- Then insert half-edges to next.+
src/Data/Range.hs view
@@ -14,23 +14,25 @@ module Data.Range( EndPoint(..) , isOpen, isClosed , unEndPoint- , Range(..)+ , Range(.., OpenRange, ClosedRange, Range') , prettyShow , lower, upper- , pattern OpenRange, pattern ClosedRange, pattern Range' , inRange, width, clipLower, clipUpper, midPoint, clampTo- , isValid, covers+ , isValidRange, covers , shiftLeft, shiftRight ) where +import Control.Monad((<=<)) import Control.DeepSeq import Control.Lens+import Control.Applicative import Data.Intersection import Data.Vinyl.CoRec import GHC.Generics (Generic) import Test.QuickCheck-import Text.Printf (printf)+import Data.Functor.Classes+import Text.Read -------------------------------------------------------------------------------- -- * Representing Endpoints of a Range@@ -38,8 +40,26 @@ -- | Endpoints of a range may either be open or closed. data EndPoint a = Open !a | Closed !a- deriving (Show,Read,Eq,Functor,Foldable,Traversable,Generic,NFData)+ deriving (Eq,Functor,Foldable,Traversable,Generic,NFData) +instance (Show a) => Show (EndPoint a) where+ showsPrec = liftShowsPrec showsPrec showList++instance Show1 EndPoint where+ liftShowsPrec sp _sl d (Open a) = showsUnaryWith sp "Open" d a+ liftShowsPrec sp _sl d (Closed a) = showsUnaryWith sp "Closed" d a++instance (Read a) => Read (EndPoint a) where+ readPrec = liftReadPrec readPrec readListPrec+ readListPrec = readListPrecDefault++instance Read1 EndPoint where+ liftReadPrec rp _rl = readData $+ readUnaryWith rp "Open" Open <|>+ readUnaryWith rp "Closed" Closed+ liftReadListPrec = liftReadListPrecDefault++ instance Ord a => Ord (EndPoint a) where -- | order on the actual value, and Open before Closed a `compare` b = f a `compare` f b@@ -56,6 +76,14 @@ _unEndPoint (Open a) = a _unEndPoint (Closed a) = a +-- | Access lens for EndPoint value regardless of whether it is open or closed.+--+-- >>> Open 5 ^. unEndPoint+-- 5+-- >>> Closed 10 ^. unEndPoint+-- 10+-- >>> Open 4 & unEndPoint .~ 0+-- Open 0 unEndPoint :: Lens (EndPoint a) (EndPoint b) a b unEndPoint = lens _unEndPoint f where@@ -63,10 +91,12 @@ f (Closed _) a = Closed a {-# INLINE unEndPoint #-} +-- | True iff EndPoint is open. isOpen :: EndPoint a -> Bool-isOpen (Open _) = True-isOpen _ = False+isOpen Open{} = True+isOpen _ = False +-- | True iff EndPoint is closed. isClosed :: EndPoint a -> Bool isClosed = not . isOpen @@ -79,12 +109,35 @@ , _upper :: !(EndPoint a) } deriving (Eq,Functor,Foldable,Traversable,Generic,NFData)-makeLenses ''Range -instance Show a => Show (Range a) where- show (Range l u) = printf "Range (%s) (%s)" (show l) (show u)+-- | Lens access for the lower part of a range.+lower :: Lens' (Range a) (EndPoint a)+lower = lens _lower (\r l -> r{_lower=l}) +-- | Lens access for the upper part of a range.+upper :: Lens' (Range a) (EndPoint a)+upper = lens _upper (\r u -> r{_upper=u}) +-- instance Show a => Show (Range a) where+-- show (Range l u) = printf "Range (%s) (%s)" (show l) (show u)++instance (Show a) => Show (Range a) where+ showsPrec = liftShowsPrec showsPrec showList++instance Show1 Range where+ liftShowsPrec sp sl d (Range l u) =+ showsBinaryWith (liftShowsPrec sp sl) (liftShowsPrec sp sl) "Range" d l u++instance (Read a) => Read (Range a) where+ readPrec = liftReadPrec readPrec readListPrec+ readListPrec = readListPrecDefault++instance Read1 Range where+ liftReadPrec rp rl = readData $+ readBinaryWith (liftReadPrec rp rl) (liftReadPrec rp rl) "Range" Range+ liftReadListPrec = liftReadListPrecDefault++ pattern OpenRange :: a -> a -> Range a pattern OpenRange l u = Range (Open l) (Open u) @@ -156,14 +209,16 @@ type instance IntersectionOf (Range a) (Range a) = [ NoIntersection, Range a] -instance Ord a => (Range a) `IsIntersectableWith` (Range a) where+instance Ord a => Range a `HasIntersectionWith` Range a+instance Ord a => Range a `IsIntersectableWith` Range a where nonEmptyIntersection = defaultNonEmptyIntersection -- The intersection is empty, if after clipping, the order of the end points is inverted -- or if the endpoints are the same, but both are open.- (Range l u) `intersect` s = let i = clipLower' l . clipUpper' u $ s- in if isValid i then coRec i else coRec NoIntersection+ (Range l u) `intersect` s = case (clipLower l <=< clipUpper u $ s) of+ Nothing -> coRec NoIntersection+ Just i -> coRec i -- | Get the width of the interval --@@ -174,6 +229,7 @@ width :: Num r => Range r -> r width i = i^.upper.unEndPoint - i^.lower.unEndPoint +-- | Compute the halfway point between the start and end of a range. midPoint :: Fractional r => Range r -> r midPoint r = let w = width r in r^.lower.unEndPoint + (w / 2) @@ -204,63 +260,45 @@ -- | Clip the interval from below. I.e. intersect with the interval {l,infty), -- where { is either open, (, orr closed, [. clipLower :: Ord a => EndPoint a -> Range a -> Maybe (Range a)-clipLower l r = let r' = clipLower' l r in if isValid r' then Just r' else Nothing+clipLower p rr@(Range l r) = case (p^.unEndPoint) `compare` (r^.unEndPoint) of+ GT -> Nothing+ EQ | isOpen r || isOpen p -> Nothing+ _ -> Just $+ case (p^.unEndPoint) `compare` (l^.unEndPoint) of+ LT -> rr+ EQ -> if isOpen p then Range p r else rr+ GT -> Range p r -- | Clip the interval from above. I.e. intersect with (-\infty, u}, where } is -- either open, ), or closed, ], clipUpper :: Ord a => EndPoint a -> Range a -> Maybe (Range a)-clipUpper u r = let r' = clipUpper' u r in if isValid r' then Just r' else Nothing+clipUpper p (Range l r) = case (p^.unEndPoint) `compare` (l^.unEndPoint) of+ LT -> Nothing+ EQ | isOpen l || isOpen p -> Nothing+ _ -> Just $ Range l (p `min` r) + -- | Wether or not the first range completely covers the second one covers :: forall a. Ord a => Range a -> Range a -> Bool-x `covers` y = maybe False (== y) . asA @(Range a) $ x `intersect` y-+x `covers` y = (== Just y) . asA @(Range a) $ x `intersect` y -- | Check if the range is valid and nonEmpty, i.e. if the lower endpoint is -- indeed smaller than the right endpoint. Note that we treat empty open-ranges -- as invalid as well.-isValid :: Ord a => Range a -> Bool-isValid (Range l u) = case (_unEndPoint l) `compare` (_unEndPoint u) of- LT -> True- EQ | isClosed l || isClosed u -> True- _ -> False---- operation is unsafe, as it may produce an invalid range (where l > u)-clipLower' :: Ord a => EndPoint a -> Range a -> Range a-clipLower' l' r@(Range l u) = case l' `cmpLower` l of- GT -> Range l' u- _ -> r--- operation is unsafe, as it may produce an invalid range (where l > u)-clipUpper' :: Ord a => EndPoint a -> Range a -> Range a-clipUpper' u' r@(Range l u) = case u' `cmpUpper` u of- LT -> Range l u'- _ -> r---- | Compare end points, Closed < Open-cmpLower :: Ord a => EndPoint a -> EndPoint a -> Ordering-cmpLower a b = case (_unEndPoint a) `compare` (_unEndPoint b) of- LT -> LT- GT -> GT- EQ -> case (a,b) of- (Open _, Open _) -> EQ -- if both are same type, report EQ- (Closed _, Closed _) -> EQ- (Open _, _) -> GT -- otherwise, choose the Closed one- (Closed _,_) -> LT -- is the *smallest*----- | Compare the end points, Open < Closed-cmpUpper :: Ord a => EndPoint a -> EndPoint a -> Ordering-cmpUpper a b = case (_unEndPoint a) `compare` (_unEndPoint b) of- LT -> LT- GT -> GT- EQ -> case (a,b) of- (Open _, Open _) -> EQ -- if both are same type, report EQ- (Closed _, Closed _) -> EQ- (Open _, _) -> LT -- otherwise, choose the Closed one- (Closed _,_) -> GT -- is the *largest*---+--+-- >>> isValidRange $ Range (Open 4) (Closed 4)+-- False+-- >>> isValidRange $ Range (Open 5) (Closed 4)+-- False+-- >>> isValidRange $ Range (Open 4) (Closed 5)+-- True+-- >>> isValidRange $ Range (Closed 5) (Closed 40)+-- True+isValidRange :: Ord a => Range a -> Bool+isValidRange (Range l u) = case _unEndPoint l `compare` _unEndPoint u of+ LT -> True+ EQ | isClosed l && isClosed u -> True+ _ -> False --------------------------------------------------------------------------------
+ src/Data/RealNumber/Rational.hs view
@@ -0,0 +1,101 @@+{-# LANGUAGE DeriveDataTypeable #-}+--------------------------------------------------------------------------------+-- |+-- Module : Data.RealNumber.Rational+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--------------------------------------------------------------------------------+module Data.RealNumber.Rational(RealNumber(..)++ -- * Converting to and from RealNumber's+ , AsFixed(..), asFixed+ , toFixed, fromFixed+ , Nat+ ) where++import Data.Aeson+import Data.Data+import Data.Fixed+import Data.Hashable+import Data.List (dropWhileEnd)+import GHC.Generics (Generic (..))+import GHC.TypeLits+import Test.QuickCheck (Arbitrary (..))+import Control.Monad.Random+import Data.Ratio+import Control.DeepSeq++--------------------------------------------------------------------------------++-- | Real Numbers represented using Rational numbers. The number type+-- itself is exact in the sense that we can represent any rational+-- number.+--+-- The parameter, a natural number, represents the precision (in+-- number of decimals behind the period) with which we display the+-- numbers when printing them (using Show).+--+-- If the number cannot be displayed exactly a '~' is printed after+-- the number.+newtype RealNumber (p :: Nat) = RealNumber Rational+ deriving (Eq,Ord,Data,Num,Fractional,Real,RealFrac,Generic,Hashable,ToJSON,FromJSON,NFData)++data NatPrec (p :: Nat) = NatPrec++instance KnownNat p => HasResolution (NatPrec p) where+ resolution _ = 10 ^ (natVal (NatPrec @p))+++instance KnownNat p => Show (RealNumber p) where+ showsPrec d r = showParen (d > app_prec && r < 0) $+ case asFixed r of+ Exact p -> showString (dropWhileEnd (== '.') . dropWhileEnd (== '0') . show $ p)+ Lossy p -> shows p . showChar '~'+ where+ app_prec = 10++instance KnownNat p => Read (RealNumber p) where+ readsPrec i = map wrap . readsPrec @(Fixed (NatPrec p)) i+ where+ wrap (RealNumber . realToFrac -> x,s') = case s' of+ '~':s'' -> (x,s'')+ _ -> (x,s')++instance KnownNat p => Arbitrary (RealNumber p) where+ arbitrary = fromFixed <$> arbitrary+++instance Random (RealNumber p) where+ -- Generate a random number between a and b with 'maxBound `div` 2 :: Int' discrete increments.+ randomR (a,b) = runRand $ do+ v <- getRandom+ pure $ (b-a)*abs v + a+ -- Generate a random number between -1 and +1 with 'maxBound::Int' discrete increments.+ random = runRand $ do+ v <- getRandom+ let fromInt :: Int -> Integer; fromInt = fromIntegral+ pure $ RealNumber $ fromInt v % fromInt maxBound++--------------------------------------------------------------------------------++++-- | Fixed-precision representation of a 'RealNumber'. If there's insufficient+-- precision to accurately represent the 'RealNumber' then the 'Lossy' constructor+-- will be used.+data AsFixed p = Exact !(Fixed p) | Lossy !(Fixed p) deriving (Show,Eq)++-- | Cast 'RealNumber' to a fixed-precision number. Data is silently lost if there's+-- insufficient precision.+toFixed :: KnownNat p => RealNumber p -> Fixed (NatPrec p)+toFixed = realToFrac++-- | Cast a fixed-precision number to a 'RealNumber'.+fromFixed :: KnownNat p => Fixed (NatPrec p) -> RealNumber p+fromFixed = realToFrac++-- | Cast 'RealNumber' to a fixed-precision number. Data-loss caused by insufficient+-- precision will be marked by the 'Lossy' constructor.+asFixed :: KnownNat p => RealNumber p -> AsFixed (NatPrec p)+asFixed r = let p = toFixed r in if r == fromFixed p then Exact p else Lossy p
src/Data/Sequence/Util.hs view
@@ -1,47 +1,18 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.Sequence.Util+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Data.Sequence.Util where -import Data.Sequence(Seq, ViewL(..),ViewR(..))+import Algorithms.BinarySearch import qualified Data.Sequence as S-import qualified Data.Vector.Generic as V+import Data.Sequence (Seq) -------------------------------------------------------------------------------- --- | Given a monotonic predicate, Get the index h such that everything strictly--- smaller than h has: p i = False, and all i >= h, we have p h = True------ returns Nothing if no element satisfies p------ running time: \(O(\log^2 n + T*\log n)\), where \(T\) is the time to execute the--- predicate.-binarySearchSeq :: (a -> Bool) -> Seq a -> Maybe Int-binarySearchSeq p s = case S.viewr s of- EmptyR -> Nothing- (_ :> x) | p x -> Just $ case S.viewl s of- (y :< _) | p y -> 0- _ -> binarySearch p' 0 u- | otherwise -> Nothing- where- p' = p . S.index s- u = S.length s - 1---- | Given a monotonic predicate, get the index h such that everything strictly--- smaller than h has: p i = False, and all i >= h, we have p h = True------ returns Nothing if no element satisfies p------ running time: \(O(T*\log n)\), where \(T\) is the time to execute the--- predicate.-binarySearchVec :: V.Vector v a- => (a -> Bool) -> v a -> Maybe Int-binarySearchVec p' v | V.null v = Nothing- | not $ p n' = Nothing- | otherwise = Just $ if p 0 then 0- else binarySearch p 0 n'- where- n' = V.length v - 1- p = p' . (v V.!)-- -- | Partition the seq s given a monotone predicate p into (xs,ys) such that -- -- all elements in xs do *not* satisfy the predicate p@@ -52,25 +23,6 @@ -- running time: \(O(\log^2 n + T*\log n)\), where \(T\) is the time to execute the -- predicate. splitMonotone :: (a -> Bool) -> Seq a -> (Seq a, Seq a)-splitMonotone p s = case binarySearchSeq p s of+splitMonotone p s = case binarySearchIdxIn p s of Nothing -> (s,S.empty) Just i -> S.splitAt i s----- | Given a monotonic predicate p, a lower bound l, and an upper bound u, with:--- p l = False--- p u = True--- l < u.------ Get the index h such that everything strictly smaller than h has: p i =--- False, and all i >= h, we have p h = True------ running time: \(O(\log(u - l))\)-{-# SPECIALIZE binarySearch :: (Int -> Bool) -> Int -> Int -> Int #-}-{-# SPECIALIZE binarySearch :: (Word -> Bool) -> Word -> Word -> Word #-}-binarySearch :: Integral a => (a -> Bool) -> a -> a -> a-binarySearch p l u = let d = u - l- m = l + (d `div` 2)- in if d == 1 then u else- if p m then binarySearch p l m- else binarySearch p m u
src/Data/Set/Util.hs view
@@ -1,16 +1,23 @@+--------------------------------------------------------------------------------+-- |+-- Module : Data.Set.Util+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+-------------------------------------------------------------------------------- module Data.Set.Util where import Data.DynamicOrd-import qualified Data.Set as Set import Data.Set (Set)+import qualified Data.Set as Set import qualified Data.Set.Internal as Internal --- import Data.Ord(comparing)+import Data.Ord (comparing) --- data S = S String deriving Show--- cmpS :: S -> S -> Ordering--- cmpS = comparing (\(S s) -> length s)+data S = S String deriving Show+cmpS :: S -> S -> Ordering+cmpS = comparing (\(S s) -> length s) -- $setup@@ -32,6 +39,18 @@ g c y = y `compare` x == c in (l,m,r) +-- | Given a monotonic function f that orders @a@, split the sequence @s@+-- into three parts. I.e. the result (lt,eq,gt) is such that+-- * all (\x -> f x == LT) . fmap f $ lt+-- * all (\x -> f x == EQ) . fmap f $ eq+-- * all (\x -> f x == GT) . fmap f $ gt+--+-- running time: \(O(\log n)\)+splitBy :: (a -> Ordering) -> Set a -> (Set a, Set a, Set a)+splitBy f s = let (l,s') = Set.spanAntitone ((==) LT . f) s+ (m,r) = Set.spanAntitone ((==) EQ . f) s'+ in (l,m,r)+ -- | Constructs a Set using the given Order. -- -- Note that this is dangerous as the resulting set may not abide the@@ -78,3 +97,44 @@ -- running time: \(O(\log n)\) deleteAllBy :: (a -> a -> Ordering) -> a -> Set a -> Set a deleteAllBy cmp x s = withOrd cmp $ liftOrd1 (Set.delete $ O x) s++-- | Run a query, eg. lookupGE, on the set with the given ordering.+--+-- Note: The 'Algorithms.BinarySearch.binarySearchIn' function may be+-- a useful alternative to 'queryBy'+--+-- >>> queryBy cmpS Set.lookupGE (S "22") $ fromListBy cmpS [S "a" , S "bbb" , S "ddddddd"]+-- Just (S "bbb")+-- >>> queryBy cmpS Set.lookupLE (S "22") $ fromListBy cmpS [S "a" , S "bbb" , S "ddddddd"]+-- Just (S "a")+-- >>> queryBy cmpS Set.lookupGE (S "333") $ fromListBy cmpS [S "a" , S "bbb" , S "ddddddd"]+-- Just (S "bbb")+queryBy :: (a -> a -> Ordering)+ -> (forall b. Ord b => b -> Set b -> t b)+ -> a -> Set a -> t a+queryBy cmp fs q s = withOrd cmp $ liftOrd1 (fs $ O q) s+++++-- queryBy' :: Ord r+-- => (a -> r)+-- -> r+-- -> (forall b. Ord b => b -> Set b -> t b)+-- -> a -> Set a -> t a+-- queryBy' g fs q s = queryBy+-- where++++-- withOrd cmp $ liftOrd1 (fs $ O q) s++++ -- withOrd cmp $ liftOrd1 (Set.lookupGE $ O q) s+++++-- test = queryBy cmpS Set.lookupGE (S "22") $ fromListBy cmpS [S "a" , S "bbb" , S "ddddddd"]+-- test = succBy cmpS (S "22") $ fromListBy cmpS [S "a" , S "bbb" , S "ddddddd"]
− src/Data/SlowSeq.hs
@@ -1,205 +0,0 @@-module Data.SlowSeq where---import Control.Lens (bimap)--- import qualified Data.FingerTree as FT--- import Data.FingerTree hiding (null, viewl, viewr)-import Data.FingerTree(ViewL(..),ViewR(..))-import qualified Data.Foldable as F-import Data.Maybe-import qualified Data.Sequence as S-import qualified Data.Sequence.Util as SU--------------------------------------------------------------------------------------data Key a = NoKey | Key { getKey :: a } deriving (Show,Eq,Ord)--instance Semigroup (Key a) where- k <> NoKey = k- _ <> k = k--instance Monoid (Key a) where- mempty = NoKey- k `mappend` k' = k <> k'--liftCmp :: (a -> a -> Ordering) -> Key a -> Key a -> Ordering-liftCmp _ NoKey NoKey = EQ-liftCmp _ NoKey (Key _) = LT-liftCmp _ (Key _) NoKey = GT-liftCmp cmp (Key x) (Key y) = x `cmp` y------ newtype Elem a = Elem { getElem :: a } deriving (Eq,Ord,Traversable,Foldable,Functor)---- instance Show a => Show (Elem a) where--- show (Elem x) = "Elem " <> show x---newtype OrdSeq a = OrdSeq { _asSeq :: S.Seq a }- deriving (Show,Eq)--instance Semigroup (OrdSeq a) where- (OrdSeq s) <> (OrdSeq t) = OrdSeq $ s `mappend` t--instance Monoid (OrdSeq a) where- mempty = OrdSeq mempty- mappend = (<>)--instance Foldable OrdSeq where- foldMap f = foldMap f . _asSeq- null = null . _asSeq- length = length . _asSeq- minimum = fromJust . lookupMin- maximum = fromJust . lookupMax---- instance Measured (Key a) (Elem a) where--- measure (Elem x) = Key x---type Compare a = a -> a -> Ordering---- | Insert into a monotone OrdSeq.------ pre: the comparator maintains monotonicity------ \(O(\log^2 n)\)-insertBy :: Compare a -> a -> OrdSeq a -> OrdSeq a-insertBy cmp x (OrdSeq s) = OrdSeq $ l `mappend` (x S.<| r)- where- (l,r) = split (\v -> cmp v x `elem` [EQ, GT]) s--------- | Insert into a sorted OrdSeq------ \(O(\log^2 n)\)-insert :: Ord a => a -> OrdSeq a -> OrdSeq a-insert = insertBy compare--deleteAllBy :: Compare a -> a -> OrdSeq a -> OrdSeq a-deleteAllBy cmp x s = l <> r- where- (l,_,r) = splitBy cmp x s-- -- (l,m) = split (\v -> liftCmp cmp v (Key x) `elem` [EQ,GT]) s- -- (_,r) = split (\v -> liftCmp cmp v (Key x) == GT) m----- | \(O(\log^2 n)\)-splitBy :: Compare a -> a -> OrdSeq a -> (OrdSeq a, OrdSeq a, OrdSeq a)-splitBy cmp x (OrdSeq s) = (OrdSeq l, OrdSeq m', OrdSeq r)- where- (l, m) = split (\v -> cmp v x `elem` [EQ,GT]) s- (m',r) = split (\v -> cmp v x == GT) m----- | Given a monotonic function f that maps a to b, split the sequence s--- depending on the b values. I.e. the result (l,m,r) is such that--- * all (< x) . fmap f $ l--- * all (== x) . fmap f $ m--- * all (> x) . fmap f $ r------ >>> splitOn id 3 $ fromAscList' [1..5]--- (OrdSeq {_asSeq = fromList [Elem 1,Elem 2]},OrdSeq {_asSeq = fromList [Elem 3]},OrdSeq {_asSeq = fromList [Elem 4,Elem 5]})--- >>> splitOn fst 2 $ fromAscList' [(0,"-"),(1,"A"),(2,"B"),(2,"C"),(3,"D"),(4,"E")]--- (OrdSeq {_asSeq = fromList [Elem (0,"-"),Elem (1,"A")]},OrdSeq {_asSeq = fromList [Elem (2,"B"),Elem (2,"C")]},OrdSeq {_asSeq = fromList [Elem (3,"D"),Elem (4,"E")]})------ \(O(\log^2 n)\)-splitOn :: Ord b => (a -> b) -> b -> OrdSeq a -> (OrdSeq a, OrdSeq a, OrdSeq a)-splitOn f x (OrdSeq s) = (OrdSeq l, OrdSeq m', OrdSeq r)- where- (l, m) = split (\v -> compare (f v) x `elem` [EQ,GT]) s- (m',r) = split (\v -> compare (f v) x == GT) m---- | Given a monotonic predicate p, splits the sequence s into two sequences--- (as,bs) such that all (not p) as and all p bs------ \(O(\log^2 n)\)-splitMonotonic :: (a -> Bool) -> OrdSeq a -> (OrdSeq a, OrdSeq a)-splitMonotonic p = bimap OrdSeq OrdSeq . split p . _asSeq----- monotonic split for Sequences------ \(O(\log^2 n)\)-split :: (a -> Bool) -> S.Seq a -> (S.Seq a, S.Seq a)-split = SU.splitMonotone---- Deletes all elements from the OrdDeq------ \(O(\log^2 n)\)-deleteAll :: Ord a => a -> OrdSeq a -> OrdSeq a-deleteAll = deleteAllBy compare----- | inserts all eleements in order--- \(O(n\log n)\)-fromListBy :: Compare a -> [a] -> OrdSeq a-fromListBy cmp = foldr (insertBy cmp) mempty---- | inserts all eleements in order--- \(O(n\log n)\)-fromListByOrd :: Ord a => [a] -> OrdSeq a-fromListByOrd = fromListBy compare---- | O(n)-fromAscList' :: [a] -> OrdSeq a-fromAscList' = OrdSeq . S.fromList----- | \(O(\log^2 n)\)-lookupBy :: Compare a -> a -> OrdSeq a -> Maybe a-lookupBy cmp x s = let (_,m,_) = splitBy cmp x s in listToMaybe . F.toList $ m--memberBy :: Compare a -> a -> OrdSeq a -> Bool-memberBy cmp x = isJust . lookupBy cmp x----- | Fmap, assumes the order does not change--- \(O(n)\)-mapMonotonic :: (a -> b) -> OrdSeq a -> OrdSeq b-mapMonotonic f = fromAscList' . map f . F.toList----- | Gets the first element from the sequence--- \(O(1)\)-viewl :: OrdSeq a -> ViewL OrdSeq a-viewl = f . S.viewl . _asSeq- where- f S.EmptyL = EmptyL- f (x S.:< s) = x :< OrdSeq s---- Last element--- \(O(1)\)-viewr :: OrdSeq a -> ViewR OrdSeq a-viewr = f . S.viewr . _asSeq- where- f S.EmptyR = EmptyR- f (s S.:> x) = OrdSeq s :> x----- \(O(1)\)-minView :: OrdSeq a -> Maybe (a, OrdSeq a)-minView s = case viewl s of- EmptyL -> Nothing- (x :< t) -> Just (x,t)---- \(O(1)\)-lookupMin :: OrdSeq a -> Maybe a-lookupMin = fmap fst . minView---- \(O(1)\)-maxView :: OrdSeq a -> Maybe (a, OrdSeq a)-maxView s = case viewr s of- EmptyR -> Nothing- (t :> x) -> Just (x,t)---- \(O(1)\)-lookupMax :: OrdSeq a -> Maybe a-lookupMax = fmap fst . maxView
src/Data/Tree/Util.hs view
@@ -1,10 +1,16 @@+-- | Tree-related utilities. module Data.Tree.Util where -import Data.Maybe(listToMaybe,maybeToList)-import Control.Lens-import Control.Monad((>=>))-import Data.Tree+import Data.Bifoldable+import Data.Bifunctor+import Data.Bitraversable+import Control.Lens+import Control.Monad ((>=>)) import qualified Data.List as List+import qualified Data.List.NonEmpty as NonEmpty+import Data.List.NonEmpty (NonEmpty(..))+import Data.Maybe (listToMaybe,maybeToList)+import Data.Tree -------------------------------------------------------------------------------- @@ -16,7 +22,31 @@ -- ] -- :} + --------------------------------------------------------------------------------++-- | Nodes in a tree are typically either an internal node or a leaf node+data TreeNode v a = InternalNode v | LeafNode a deriving (Show,Eq)++instance Bifunctor TreeNode where+ bimap = bimapDefault+instance Bifoldable TreeNode where+ bifoldMap = bifoldMapDefault+instance Bitraversable TreeNode where+ bitraverse f g = \case+ InternalNode v -> InternalNode <$> f v+ LeafNode l -> LeafNode <$> g l++-- | A TreeNode is isomorphic to Either+_TreeNodeEither :: Iso' (TreeNode v p) (Either v p)+_TreeNodeEither = iso tne etn+ where+ tne = \case+ InternalNode v -> Left v+ LeafNode l -> Right l+ etn = either InternalNode LeafNode++-------------------------------------------------------------------------------- -- * Zipper on rose trees -- | Zipper for rose trees@@ -50,16 +80,16 @@ -- Just (Zipper {focus = Node {rootLabel = 2, subForest = []}, ancestors = [([Node {rootLabel = 1, subForest = []}],0,[Node {rootLabel = 3, subForest = [Node {rootLabel = 4, subForest = []}]}])]}) nextSibling :: Zipper a -> Maybe (Zipper a) nextSibling (Zipper t as) = case as of- [] -> Nothing -- no parent- ((_,_,[]):_) -> Nothing -- no next sibling- ((ls,p,(r:rs)):as') -> Just $ Zipper r ((t:ls,p,rs):as')+ [] -> Nothing -- no parent+ ((_,_,[]):_) -> Nothing -- no next sibling+ ((ls,p,r:rs):as') -> Just $ Zipper r ((t:ls,p,rs):as') -- | Move the focus to the next sibling of this node prevSibling :: Zipper a -> Maybe (Zipper a) prevSibling (Zipper t as) = case as of- [] -> Nothing -- no parent- (([],_,_):_) -> Nothing -- no prev sibling- (((l:ls),p,rs):as') -> Just $ Zipper l ((ls,p,t:rs):as')+ [] -> Nothing -- no parent+ (([],_,_):_) -> Nothing -- no prev sibling+ ((l:ls,p,rs):as') -> Just $ Zipper l ((ls,p,t:rs):as') -- | Given a zipper that focussses on some subtree t, construct a list with -- zippers that focus on each child.@@ -103,15 +133,15 @@ -- running time: \(O(nT(n))\) where \(n\) is the size of the tree, and \(T(m)\) is -- the time to evaluate a predicate on a subtree of size \(m\). findEvert' :: (Tree a -> Bool) -> Tree a -> Maybe (Tree a)-findEvert' p = fmap unZipperLocal . listToMaybe . filter (p . focus) . allTrees . root+findEvert' p = fmap unZipperLocal . List.find (p . focus) . allTrees . root -- | Function to extract a path between a start node and an end node (if such a --path exists). If there are multiple paths, no guarantees are given about --which one is returned. -- -- running time: \(O(n(T_p+T_s)\), where \(n\) is the size of the tree, and--- \(T_p\) and \(T_s\) are the times it takes to evaluate the 'isStartingNode'--- and 'isEndingNode' predicates.+-- \(T_p\) and \(T_s\) are the times it takes to evaluate the @isStartingNode@+-- and @isEndingNode@ predicates. -- -- -- >>> findPath (== 1) (==4) myTree@@ -150,5 +180,29 @@ findNodes :: (Tree a -> Bool) -> Tree a -> [[a]] findNodes p = go where- go t = let mh = if p t then [[]] else []+ go t = let mh = [ [] | p t ] -- [[]] iff 'p t' in map (rootLabel t:) $ mh <> concatMap go (children t)+++-- | BFS Traversal of the rose tree that decomposes it into levels.+--+-- running time: \(O(n)\)+levels :: Tree a -> NonEmpty (NonEmpty a)+levels = go1 . (:| [])+ where+ go0 :: [Tree a] -> [NonEmpty a]+ go0 q = case NonEmpty.nonEmpty q of+ Nothing -> []+ Just q1 -> NonEmpty.toList $ go1 q1+ {-# INLINE go0 #-}++ -- all work essentially happens here: given a bunch of trees whose+ -- root elements all have the same level, extract the values+ -- stored at these root nodes, collect all children in a big list,+ -- and explore those recursively.+ go1 :: NonEmpty (Tree a) -> NonEmpty (NonEmpty a)+ go1 qs = fmap root' qs :| go0 (concatMap children' qs)+ {-# INLINE go1 #-}++ root' (Node x _) = x+ children' (Node _ chs) = chs
src/Data/UnBounded.hs view
@@ -1,33 +1,47 @@-{-# LANGUAGE TemplateHaskell #-}-module Data.UnBounded( Top, topToMaybe- , pattern ValT, pattern Top- , _ValT, _Top+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE TemplateHaskell #-}+--------------------------------------------------------------------------------+-- |+-- Module : Data.UnBounded+-- Copyright : (C) Frank Staals+-- License : see the LICENSE file+-- Maintainer : Frank Staals+--+-- Add an unbounded/infintity element to a data type. Essentially,+-- t'Bottom' adds \(-\infty\) (and is pretty much identical to Maybe),+-- whereas t'Top' adds \(\infty\). The 'UnBounded' type adds both.+--+--------------------------------------------------------------------------------+module Data.UnBounded( Top( ValT, Top), topToMaybe+ , _ValT, _Top, _TopMaybe - , Bottom, bottomToMaybe- , pattern Bottom, pattern ValB- , _ValB, _Bottom+ , Bottom(Bottom, ValB), bottomToMaybe+ , _ValB, _Bottom, _BottomMaybe , UnBounded(..)- , unUnBounded- , _MinInfinity, _Val, _MaxInfinity+ , _Val , unBoundedToMaybe ) where import Control.Lens-import qualified Data.Foldable as F-import qualified Data.Traversable as T+import qualified Data.Foldable as F import Data.Functor.Classes+import qualified Data.Traversable as T -------------------------------------------------------------------------------- -- * Top and Bottom --- | `Top a` represents the type a, together with a 'Top' element, i.e. an element+-- | @Top a@ represents the type a, together with a v'Top' element, i.e. an element -- that is greater than any other element. We can think of `Top a` being defined as: -- -- >>> data Top a = ValT a | Top-newtype Top a = GTop { topToMaybe :: Maybe a }+newtype Top a = GTop (Maybe a) deriving (Eq,Functor,F.Foldable,T.Traversable,Applicative,Monad,Eq1) +-- | @Top a@ values are isomorphing to @Maybe a@ values.+topToMaybe :: Top a -> Maybe a+topToMaybe (GTop mb) = mb+ pattern ValT :: a -> Top a pattern ValT x = GTop (Just x) @@ -50,22 +64,49 @@ show Top = "Top" show ~(ValT x) = "ValT " ++ show x +-- | 'ValT' prism. Can be used to access the non-bottom element if it exists:+--+-- >>> ValT True & _ValT %~ not+-- ValT False+--+-- >>> Top & _ValT %~ not+-- Top _ValT :: Prism (Top a) (Top b) a b-_ValT = prism ValT (\ta -> case ta of Top -> Left Top ; ValT x -> Right x)+_ValT = prism ValT (\case Top -> Left Top ; ValT x -> Right x) +-- | t'Top' prism. _Top :: Prism' (Top a) ()-_Top = prism' (const Top) (\ta -> case ta of Top -> Just () ; ValT _ -> Nothing)+_Top = prism' (const Top) (\case Top -> Just () ; ValT _ -> Nothing) +-- | Iso between a @Top a@ and a @Maybe a@, interpreting a v'Top' as a+-- 'Nothing' and vice versa. Note that this reverses the ordering of+-- the elements.+--+-- >>> ValT 5 ^. _TopMaybe+-- Just 5+-- >>> Just 5 ^.re _TopMaybe+-- ValT 5+-- >>> Top ^. _TopMaybe+-- Nothing+-- >>> Nothing ^.re _TopMaybe+-- Top+_TopMaybe :: Iso' (Top a) (Maybe a)+_TopMaybe = iso topToMaybe GTop+ -------------------------------------------------------------------------------- --- | `Bottom a` represents the type a, together with a 'Bottom' element,+-- | @`Bottom a`@ represents the type a, together with a v'Bottom' element, -- i.e. an element that is smaller than any other element. We can think of--- `Bottom a` being defined as:+-- @`Bottom a`@ being defined as: -- -- >>> data Bottom a = Bottom | ValB a-newtype Bottom a = GBottom { bottomToMaybe :: Maybe a }+newtype Bottom a = GBottom (Maybe a) deriving (Eq,Ord,Functor,F.Foldable,T.Traversable,Applicative,Monad,Eq1,Ord1) +-- | `Bottom a` values are isomorphing to `Maybe a` values.+bottomToMaybe :: Bottom a -> Maybe a+bottomToMaybe (GBottom mb) = mb+ pattern Bottom :: Bottom a pattern Bottom = GBottom Nothing @@ -78,12 +119,34 @@ show Bottom = "Bottom" show ~(ValB x) = "ValB " ++ show x +-- | 'ValB' prism. Can be used to access the non-bottom element if it exists:+--+-- >>> ValB True & _ValB %~ not+-- ValB False+--+-- >>> Bottom & _ValB %~ not+-- Bottom _ValB :: Prism (Bottom a) (Bottom b) a b-_ValB = prism ValB (\ba -> case ba of Bottom -> Left Bottom ; ValB x -> Right x)+_ValB = prism ValB (\case Bottom -> Left Bottom ; ValB x -> Right x) +-- | t'Bottom' prism. _Bottom :: Prism' (Bottom a) ()-_Bottom = prism' (const Bottom) (\ba -> case ba of Bottom -> Just () ; ValB _ -> Nothing)+_Bottom = prism' (const Bottom) (\case Bottom -> Just () ; ValB _ -> Nothing) +-- | Iso between a 'Bottom a' and a 'Maybe a', interpreting a Bottom as a+-- Nothing and vice versa.+--+-- >>> ValB 5 ^. _BottomMaybe+-- Just 5+-- >>> Just 5 ^.re _BottomMaybe+-- ValB 5+-- >>> Bottom ^. _BottomMaybe+-- Nothing+-- >>> Nothing ^.re _BottomMaybe+-- Bottom+_BottomMaybe :: Iso' (Bottom a) (Maybe a)+_BottomMaybe = iso bottomToMaybe GBottom+ -------------------------------------------------------------------------------- -- | `UnBounded a` represents the type a, together with an element@@ -91,8 +154,26 @@ -- smaller than any other element. data UnBounded a = MinInfinity | Val { _unUnBounded :: a } | MaxInfinity deriving (Eq,Ord,Functor,F.Foldable,T.Traversable)-makeLenses ''UnBounded-makePrisms ''UnBounded++-- | Prism to access unbounded value if it exists.+--+-- >>> Val True ^? _Val+-- Just True+--+-- >>> MinInfinity ^? _Val :: Maybe Bool+-- Nothing+--+-- >>> Val True & _Val %~ not+-- Val False+--+-- >>> MaxInfinity & _Val %~ not+-- MaxInfinity+_Val :: Prism (UnBounded a) (UnBounded b) a b+_Val = prism Val fromUnBounded+ where+ fromUnBounded MinInfinity = Left MinInfinity+ fromUnBounded MaxInfinity = Left MaxInfinity+ fromUnBounded (Val v) = Right v instance Show a => Show (UnBounded a) where show MinInfinity = "MinInfinity"
src/Data/Util.hs view
@@ -10,17 +10,18 @@ -------------------------------------------------------------------------------- module Data.Util where -import Control.DeepSeq-import Control.Lens-import GHC.Generics (Generic)+import Control.DeepSeq+import Control.Lens import qualified Data.List as List+import GHC.Generics (Generic)+import Linear.V2 (V2(..))+import Linear.V3 (V3(..)) -------------------------------------------------------------------------------- -- * Strict Triples -- | strict triple-data STR a b c = STR { fst' :: !a, snd' :: !b , trd' :: !c}- deriving (Show,Eq,Ord,Functor,Generic)+data STR a b c = STR !a !b !c deriving (Show,Eq,Ord,Functor,Generic) instance (Semigroup a, Semigroup b, Semigroup c) => Semigroup (STR a b c) where (STR a b c) <> (STR d e f) = STR (a <> d) (b <> e) (c <> f)@@ -33,22 +34,29 @@ instance (NFData a, NFData b, NFData c) => NFData (STR a b c) instance Field1 (STR a b c) (STR d b c) a d where- _1 = lens fst' (\(STR _ b c) d -> STR d b c)+ _1 = lens (\(STR a _ _) -> a) (\(STR _ b c) d -> STR d b c) instance Field2 (STR a b c) (STR a d c) b d where- _2 = lens snd' (\(STR a _ c) d -> STR a d c)+ _2 = lens (\(STR _ b _) -> b) (\(STR a _ c) d -> STR a d c) instance Field3 (STR a b c) (STR a b d) c d where- _3 = lens trd' (\(STR a b _) d -> STR a b d)---- | Generate All unique unordered triplets.----uniqueTriplets :: [a] -> [STR a a a]-uniqueTriplets xs = [ STR x y z | (x:ys) <- nonEmptyTails xs, SP y z <- uniquePairs ys]+ _3 = lens (\(STR _ _ c) -> c) (\(STR a b _) d -> STR a b d) +-------------------------------------------------------------------------------- +--------------------------------------------------------------------------------+-- | Strict Triple with all items the same+type Three = V3 +-- | Pattern synonym for strict triples.+pattern Three :: a -> a -> a -> Three a+pattern Three a b c = V3 a b c+{-# COMPLETE Three #-} +-- | Generate All unique unordered triplets.+--+uniqueTriplets :: [a] -> [Three a]+uniqueTriplets xs = [ Three x y z | (x:ys) <- nonEmptyTails xs, Two y z <- uniquePairs ys] -------------------------------------------------------------------------------- -- * Strict Pairs@@ -80,10 +88,11 @@ -- | * Strict pair whose elements are of the same type. -- | Strict pair with both items the same-type Two a = SP a a+type Two = V2 +-- | Pattern synonym for strict pairs. pattern Two :: a -> a -> Two a-pattern Two a b = SP a b+pattern Two a b = V2 a b {-# COMPLETE Two #-} -- | Given a list xs, generate all unique (unordered) pairs.@@ -91,14 +100,6 @@ -- uniquePairs :: [a] -> [Two a] uniquePairs xs = [ Two x y | (x:ys) <- nonEmptyTails xs, y <- ys ]------------------------------------------------------------------------------------- | Strict Triple with all items the same-type Three a = STR a a a--pattern Three :: a -> a -> a -> Three a-pattern Three a b c = STR a b c-{-# COMPLETE Three #-} --------------------------------------------------------------------------------
+ src/Data/Vector/Circular/Util.hs view
@@ -0,0 +1,74 @@+{-# OPTIONS_GHC -fno-warn-orphans #-}+--------------------------------------------------------------------------------+-- |+-- Module : Data.Vector.Circular.Util+-- Copyright : (C) Frank Staals, David Himmelstrup+-- License : see the LICENSE file+-- Maintainer : David Himmelstrup+--------------------------------------------------------------------------------+module Data.Vector.Circular.Util where++import Algorithms.StringSearch.KMP (isSubStringOf)+import Control.Lens+import Data.Ext+import Data.Maybe+import Data.Semigroup.Foldable+import qualified Data.Vector as V+import Data.Vector.Circular as CV+import qualified Data.Vector.NonEmpty as NV+import Test.QuickCheck (Arbitrary (..), NonEmptyList (..))+++-- FIXME: Upstream this to the non-empty vector library?+instance Foldable1 NV.NonEmptyVector++-- | Access the ith item in the CircularVector (w.r.t the rotation) as a lens+item :: Int -> Lens' (CircularVector a) a+item i = lens (`CV.index` i) (\s x -> unsafeFromVector (toVector s V.// [(i,x)]))++-- | All elements, starting with the focus, going to the right+--+-- >>> rightElements $ unsafeFromList [3,4,5,1,2]+-- [3,4,5,1,2]+rightElements :: CircularVector a -> NV.NonEmptyVector a+rightElements = toNonEmptyVector++-- | All elements, starting with the focus, going to the left+--+-- >>> leftElements $ unsafeFromList [3,4,5,1,2]+-- [3,2,1,5,4]+leftElements :: CircularVector a -> NV.NonEmptyVector a+leftElements v = NV.generate1 (length v) (CV.index v . negate)++-- | Finds an element in the CircularVector+--+-- >>> findRotateTo (== 3) $ unsafeFromList [1..5]+-- Just (CircularVector {vector = [1,2,3,4,5], rotation = 2})+-- >>> findRotateTo (== 7) $ unsafeFromList [1..5]+-- Nothing+findRotateTo :: (a -> Bool) -> CircularVector a -> Maybe (CircularVector a)+findRotateTo p (CircularVector v _rot) = CircularVector v <$> NV.findIndex p v++-- | Test if the circular list is a cyclic shift of the second+-- list.+--+-- Running time: \(O(n+m)\), where \(n\) and \(m\) are the sizes of+-- the lists.+isShiftOf :: Eq a => CircularVector a -> CircularVector a -> Bool+xs `isShiftOf` ys = let twice zs = let zs' = leftElements zs in zs' <> zs'+ once = leftElements+ check as bs = isJust $ once as `isSubStringOf` twice bs+ in length xs == length ys && check xs ys++instance Arbitrary a => Arbitrary (CircularVector a) where+ arbitrary = unsafeFromList <$> (getNonEmpty <$> arbitrary)++-- | label the circular vector with indices, starting from zero at the+-- current focus, going right.+--+-- Running time: \(O(n)\)+withIndicesRight :: CircularVector a -> CircularVector (Int :+ a)+withIndicesRight (CircularVector v s) = CircularVector v' s+ where+ n = length v+ v' = NV.imap (\i x -> ((i-s) `mod` n) :+ x) v
src/Data/Yaml/Util.hs view
@@ -66,6 +66,7 @@ , content :: a } deriving (Show,Read,Generic,Eq,Functor,Foldable,Traversable) +-- | Unpack versioned data type. unversioned :: Versioned a -> a unversioned = content
test/Algorithms/DivideAndConquerSpec.hs view
@@ -1,10 +1,11 @@ module Algorithms.DivideAndConquerSpec where import Algorithms.DivideAndConquer- import Test.Hspec import Test.QuickCheck import qualified Data.List as List++-------------------------------------------------------------------------------- spec = describe "divide and conquer strategy tests" $ do it "mergeSort" $ property $
+ test/Algorithms/Graph/BFSSpec.hs view
@@ -0,0 +1,26 @@+module Algorithms.Graph.BFSSpec (spec) where++import Algorithms.Graph.BFS+import Data.Tree+import qualified Data.Vector as V+import Test.Hspec++--------------------------------------------------------------------------------++spec :: Spec+spec = it "BFS test" $+ bfs' 0 testGr `shouldBe` answer++testGr :: V.Vector [Int]+testGr = V.fromList [ [1,3, 6]+ , [2]+ , [3, 5]+ , [2 ]+ , []+ , [4, 5]+ , [7]+ , [8,4]+ , [2]+ ]+answer :: Tree Int+answer = Node {rootLabel = 0, subForest = [Node {rootLabel = 1, subForest = [Node {rootLabel = 2, subForest = [Node {rootLabel = 5, subForest = []}]}]},Node {rootLabel = 3, subForest = []},Node {rootLabel = 6, subForest = [Node {rootLabel = 7, subForest = [Node {rootLabel = 8, subForest = []},Node {rootLabel = 4, subForest = []}]}]}]}
+ test/Algorithms/Graph/DFSSpec.hs view
@@ -0,0 +1,29 @@+module Algorithms.Graph.DFSSpec (spec) where+++import Algorithms.Graph.DFS (dfsSensitive)+import Control.DeepSeq (NFData (rnf))+import Control.Exception (evaluate)+import qualified Data.Foldable as F+import Data.PlanarGraph (VertexId (VertexId), World (Primal))+import qualified Data.Set as S+import Data.Tree (Tree (rootLabel, subForest))+import Test.Hspec (Spec, anyErrorCall, describe, it, shouldBe, shouldThrow)++{-+ 0+ / \+1 2+-}+tree1 :: Tree (VertexId () Primal)+tree1 = dfsSensitive (\i -> case i of VertexId 0 -> [VertexId 1, VertexId 2]; _ -> error "fail!") (VertexId 0)++spec :: Spec+spec = do+ describe "DFS output sensitivity" $ do+ it "fails when forced" $+ evaluate (rnf tree1) `shouldThrow` anyErrorCall+ it "outputs root label lazily" $+ rootLabel tree1 `shouldBe` VertexId 0+ it "outputs forest lazily" $+ length (subForest tree1) `shouldBe` 2
+ test/Algorithms/LogarithmicMethodSpec.hs view
@@ -0,0 +1,45 @@+module Algorithms.LogarithmicMethodSpec where++import Algorithms.LogarithmicMethod+import Data.List.NonEmpty (NonEmpty(..))+import qualified Data.List.NonEmpty as NonEmpty+import Data.Maybe (mapMaybe)+import Data.Semigroup+import Data.Semigroup.Foldable+import Data.List.Util+import Test.Hspec+import Test.QuickCheck++--------------------------------------------------------------------------------++spec :: Spec+spec = describe "Logarithmic method successor test" $ do+ it "successor test" $ property $+ \q (xs :: [Int]) ->+ successor q (fromList xs)+ `shouldBe`+ minimum1 [ x | x <- xs, x >= q]++ it "merge test" $ property $+ \q (xs :: [Int]) (ys :: [Int]) ->+ successor q ((fromList xs) <> (fromList ys))+ `shouldBe`+ successor q (fromList $ xs <> ys)+++newtype DummySucc a = Dummy (NonEmpty a)+ deriving (Show,Eq,Functor,Foldable,Foldable1,Traversable)++instance Ord a => LogarithmicMethodDS DummySucc a where+ build = Dummy . NonEmpty.sort++successor' :: Ord a => a -> DummySucc a -> Maybe (Min a)+successor' q (Dummy xs) = case NonEmpty.dropWhile (< q) xs of+ [] -> Nothing+ (s:_) -> Just (Min s)++successor :: Ord a => a -> InsertionOnly DummySucc a -> Maybe a+successor q = fmap getMin . queryWith (successor' q)++fromList :: Ord a => [a] -> InsertionOnly DummySucc a+fromList = foldr insert empty
test/Data/CircularSeqSpec.hs view
@@ -39,6 +39,9 @@ -- let cs = fromNonEmpty xs -- cs' = rotateNR i cs -- in+ it "read . show = id" $ do+ property $ \(lst :: CSeq Rational) ->+ read (show lst) == lst
test/Data/EdgeOracleSpec.hs view
@@ -3,7 +3,7 @@ import Control.Arrow import Data.Ext import Data.PlanarGraph.EdgeOracle-import Data.PlanarGraph.Core+import Data.PlanarGraph import Data.Semigroup import qualified Data.Set as S import Test.Hspec
+ test/Data/IndexedDoublyLinkedListSpec.hs view
@@ -0,0 +1,36 @@+module Data.IndexedDoublyLinkedListSpec where++import Control.Monad.ST+import Data.IndexedDoublyLinkedList+import Data.List.NonEmpty (NonEmpty(..))+import qualified Data.Vector as V+import Test.Hspec++--------------------------------------------------------------------------------++spec :: Spec+spec = do+ describe "IndexedDoublyLinkedList tests" $ do+ it "myTest" $+ runT myProg `shouldBe` (4 :| [2,1,0],4 :| [5,8])+ it "myTest'" $+ runT myProg' `shouldBe` ('e' :| "cba",'e' :| "fi")+++runT :: (forall s. DLListMonad s Char a) -> a+runT c = runDLListMonad (V.fromList "abcdefghi") c++myProg :: DLListMonad s b (NonEmpty Index, NonEmpty Index)+myProg = do writeList (0 :| [2,4,6,8])+ delete 6+ insertBefore 2 1+ insertAfter 4 5+ as <- toListFromR 4+ bs <- toListFrom 4+ pure (as,bs)++myProg' :: DLListMonad s b (NonEmpty b, NonEmpty b)+myProg' = do (as,bs) <- myProg+ as' <- mapM valueAt as+ bs' <- mapM valueAt bs+ pure (as',bs')
test/Data/PlanarGraphSpec.hs view
@@ -1,7 +1,7 @@ {-# LANGUAGE ScopedTypeVariables #-} module Data.PlanarGraphSpec where -+import Control.Lens(view,_3) import Data.Bifunctor import qualified Data.ByteString.Char8 as B import qualified Data.Foldable as F@@ -90,7 +90,7 @@ fromAdjacencyListsOld adjM = planarGraph' . toCycleRep n $ perm where n = sum . fmap length $ perm- perm = trd' . foldr toOrbit (STR mempty 0 mempty) $ adjM+ perm = view (_3) . foldr toOrbit (STR mempty 0 mempty) $ adjM -- | Given a vertex with its adjacent vertices (u,vs) (in CCW order) convert this
test/Data/RangeSpec.hs view
@@ -18,6 +18,11 @@ it "closed cap open, disjoint" $ do ((ClosedRange (1::Int) 10) `intersect` (OpenRange 50 (60 :: Int))) `shouldBe` (coRec NoIntersection)+ it "endpoints overlap but open/closed" $ do+ let r1, r2 :: Range Int+ r1 = ClosedRange 3 6+ r2 = Range (Open 1) (Open 3)+ in (r1 `intersects` r2) `shouldBe` False -- it "closed intersect open" $ -- ((OpenRange 1 (10 :: Int)) `intersect` (ClosedRange 10 (12 :: Int))) -- `shouldBe` (coRec NoIntersection)
+ test/Data/RealNumber/RationalSpec.hs view
@@ -0,0 +1,25 @@+{-# LANGUAGE DataKinds #-}+module Data.RealNumber.RationalSpec where++import Data.RealNumber.Rational+import Test.Hspec+import Test.QuickCheck++type R = RealNumber 5++spec :: Spec+spec = do+ describe "Read/Show" $ do+ it "read basic" $ do+ read (show (1::R)) `shouldBe` (1::R)+ read (show (negate 1::R)) `shouldBe` negate (1::R)+ it "read nested" $ do+ read (show (Just (1::R))) `shouldBe` Just (1::R)+ read (show (Just (negate 1::R))) `shouldBe` Just (negate (1::R))+ specify "significant digits" $ do+ show (0.12345::RealNumber 2) `shouldBe` "0.12~"+ show (0.12345::RealNumber 5) `shouldBe` "0.12345"+ it "should discard tail" $ do+ read (show (0.12345::RealNumber 2)) `shouldBe` (0.12 ::R)+ reads "0.12345~" `shouldBe` [(0.12::RealNumber 2, "")]+