completeness(scale): add support for scale

diff --git a/literate-phylomemy.cabal b/literate-phylomemy.cabal
index acf42881156c7a52012d62b1d966e2033284a457..16d9415594c1ef7f012a120ace0fd9937d8b1227 100644 (file)
--- a/literate-phylomemy.cabal
+++ b/literate-phylomemy.cabal
@@ -77,6 +77,18 @@ extra-source-files:
   tests/Clustering/FrequentItemSet/LCM/closedFrequentItemSets/db=4.minSupp=1.minSize=2.golden
   tests/Clustering/FrequentItemSet/LCM/closedFrequentItemSets/db=4.minSupp=2.minSize=1.golden
   tests/Clustering/FrequentItemSet/LCM/closedFrequentItemSets/db=4.minSupp=2.minSize=2.golden
   tests/Clustering/FrequentItemSet/LCM/closedFrequentItemSets/db=4.minSupp=1.minSize=2.golden
   tests/Clustering/FrequentItemSet/LCM/closedFrequentItemSets/db=4.minSupp=2.minSize=1.golden
   tests/Clustering/FrequentItemSet/LCM/closedFrequentItemSets/db=4.minSupp=2.minSize=2.golden

+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.00.scale=0.3333333333333333333.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.00.scale=0.5000000000000000000.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.00.scale=0.6666666666666666667.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.00.scale=1.0000000000000000000.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.30.scale=0.3333333333333333333.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.30.scale=0.5000000000000000000.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.30.scale=0.6666666666666666667.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=0.30.scale=1.0000000000000000000.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=1.00.scale=0.3333333333333333333.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=1.00.scale=0.5000000000000000000.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=1.00.scale=0.6666666666666666667.golden
+  tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningForest/docs=docs0.minSupp=1.minSize=2.lambda=1.00.scale=1.0000000000000000000.golden

   tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.00.golden
   tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.30.golden
   tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=1.00.golden
   tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.00.golden
   tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.30.golden
   tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=1.00.golden

diff --git a/src/Numeric/Probability.hs b/src/Numeric/Probability.hs
index 1314d4da7e23e63ff022fda6180332095c0f31f5..dcbde146105eaec182618af073459bb18a8c7ba2 100644 (file)
--- a/src/Numeric/Probability.hs
+++ b/src/Numeric/Probability.hs
@@ -17,7 +17,7 @@ where
 
 import Control.Monad (Monad (..))
 import Data.Bool (Bool)
 
 import Control.Monad (Monad (..))
 import Data.Bool (Bool)

-import Data.Eq (Eq(..))
+import Data.Eq (Eq (..))

 import Data.Function (id, on, (.))
 import Data.Maybe (Maybe (..), fromJust)
 import Data.Monoid (Monoid (..))
 import Data.Function (id, on, (.))
 import Data.Maybe (Maybe (..), fromJust)
 import Data.Monoid (Monoid (..))


@@ -27,7 +27,7 @@ import Data.Semigroup (Semigroup (..))
 import Data.Validity (Validity (..), declare)
 import Data.Word (Word64)
 import GHC.Generics (Generic)
 import Data.Validity (Validity (..), declare)
 import Data.Word (Word64)
 import GHC.Generics (Generic)

-import GHC.Real (RealFrac(..))
+import GHC.Real (RealFrac (..))

 import GHC.Stack (HasCallStack)
 import GHC.TypeNats (Natural, natVal)
 import Logic
 import GHC.Stack (HasCallStack)
 import GHC.TypeNats (Natural, natVal)
 import Logic


@@ -37,7 +37,7 @@ import Numeric.Decimal (Decimal (..), MonadThrow (..))
 import Numeric.Decimal qualified as Decimal
 import System.Random (Random)
 import Text.Show (Show (show))
 import Numeric.Decimal qualified as Decimal
 import System.Random (Random)
 import Text.Show (Show (show))

-import Prelude (Bounded (..), Enum, Fractional (..), Integral, Num (..), Rational, Real(..), error, (^))
+import Prelude (Bounded (..), Enum, Fractional (..), Integral, Num (..), Rational, Real (..), error, (^))

 
 type Probability = Decimal Decimal.RoundHalfEven ProbabilityScale ProbabilityBounded
 instance Validity Probability where
 
 type Probability = Decimal Decimal.RoundHalfEven ProbabilityScale ProbabilityBounded
 instance Validity Probability where


@@ -76,12 +76,14 @@ instance Fractional (Decimal.Arith Probability) where
   (/) = Decimal.bindM2 Decimal.divideDecimalBoundedWithRounding
   fromRational = probability
 
   (/) = Decimal.bindM2 Decimal.divideDecimalBoundedWithRounding
   fromRational = probability
 

+{- HasCallStack does not work well for those
+

 instance Eq (Decimal.Arith Probability) where
 instance Eq (Decimal.Arith Probability) where

-  --(==) :: HasCallStack => Decimal.Arith Probability -> Decimal.Arith Probability -> Bool
+  (==) :: HasCallStack => Decimal.Arith Probability -> Decimal.Arith Probability -> Bool

   (==) = (==) `on` Decimal.arithError
 
 instance Ord (Decimal.Arith Probability) where
   (==) = (==) `on` Decimal.arithError
 
 instance Ord (Decimal.Arith Probability) where

-  --compare :: HasCallStack => Decimal.Arith Probability -> Decimal.Arith Probability -> Ordering
+  compare :: HasCallStack => Decimal.Arith Probability -> Decimal.Arith Probability -> Ordering

   compare = compare `on` Decimal.arithError
 
 instance Real (Decimal.Arith Probability) where
   compare = compare `on` Decimal.arithError
 
 instance Real (Decimal.Arith Probability) where


@@ -91,6 +93,7 @@ instance RealFrac (Decimal.Arith Probability) where
   properFraction p = (n, return (assertProbability f))
     where
     (n,f) = properFraction (Decimal.toRationalDecimal (Decimal.arithError p))
   properFraction p = (n, return (assertProbability f))
     where
     (n,f) = properFraction (Decimal.toRationalDecimal (Decimal.arithError p))

+-}

 
 -- >>> 10^19 <= (fromIntegral (maxBound :: Word64) :: Integer
 -- True
 
 -- >>> 10^19 <= (fromIntegral (maxBound :: Word64) :: Integer
 -- True

diff --git a/src/Phylomemy/DOT.hs b/src/Phylomemy/DOT.hs
index 8f03ab6a94d67b6558d1104d3b8eb4478e2d09f8..5edfe3725de783208d6b6454d9891c32f603bf00 100644 (file)
--- a/src/Phylomemy/DOT.hs
+++ b/src/Phylomemy/DOT.hs
@@ -2,35 +2,38 @@
 
 module Phylomemy.DOT where
 
 
 module Phylomemy.DOT where
 

--- import Debug.Pretty.Simple (pTraceShow, pTraceShowM)

 import Control.Applicative (Applicative (..))
 import Control.Monad (Monad (..), foldM_, forM_, mapM_, when, zipWithM_)
 import Control.Monad.Trans.Class qualified as MT
 import Control.Monad.Trans.Reader qualified as MT
 import Control.Monad.Trans.Writer.CPS qualified as MT
 import Control.Applicative (Applicative (..))
 import Control.Monad (Monad (..), foldM_, forM_, mapM_, when, zipWithM_)
 import Control.Monad.Trans.Class qualified as MT
 import Control.Monad.Trans.Reader qualified as MT
 import Control.Monad.Trans.Writer.CPS qualified as MT

-import Data.Bool (otherwise)
+import Data.Bool (otherwise, (&&))

 import Data.ByteString.Builder qualified as BS
 import Data.ByteString.Short qualified as BSh
 import Data.Eq (Eq (..))
 import Data.Foldable (foldMap', toList)
 import Data.ByteString.Builder qualified as BS
 import Data.ByteString.Short qualified as BSh
 import Data.Eq (Eq (..))
 import Data.Foldable (foldMap', toList)

-import Data.Function (on, ($), (&), (.))
+import Data.Function (id, on, ($), (&), (.))

 import Data.Functor ((<&>))
 import Data.Int (Int)
 import Data.List qualified as List
 import Data.Map.Strict qualified as Map
 import Data.Functor ((<&>))
 import Data.Int (Int)
 import Data.List qualified as List
 import Data.Map.Strict qualified as Map

-import Data.Maybe (Maybe (..), maybe)
+import Data.Maybe (Maybe (..), fromMaybe)

 import Data.Monoid (Monoid (..))
 import Data.Ord (Ord (..))
 import Data.Monoid (Monoid (..))
 import Data.Ord (Ord (..))

-import Data.Semigroup (Semigroup (..))
+import Data.Semigroup (Min (..), Semigroup (..))

 import Data.Set (Set)
 import Data.Set qualified as Set
 import Data.String (String)
 import Data.Set (Set)
 import Data.Set qualified as Set
 import Data.String (String)

+import Data.Text.Lazy qualified as LazyText
+import Data.Text.Lazy.Encoding qualified as LazyText

 import Data.Text.Short qualified as TS
 import Data.Tree qualified as Tree
 import Data.Text.Short qualified as TS
 import Data.Tree qualified as Tree

-import Data.Tuple (snd)
+import Debug.Pretty.Simple (pTraceShow)

 import GHC.Real (floor)
 import GHC.Real (floor)

+import GHC.Stack (HasCallStack)

 import Numeric (showFFloat)
 import Numeric.Probability
 import Numeric (showFFloat)
 import Numeric.Probability

+import Text.Pretty.Simple (pShow)

 import Text.Printf (printf)
 import Text.Show (Show (..))
 import Prelude
 import Text.Printf (printf)
 import Text.Show (Show (..))
 import Prelude


@@ -38,11 +41,21 @@ import Prelude
 import Phylomemy.Indexation
 import Phylomemy.TemporalMatching
 
 import Phylomemy.Indexation
 import Phylomemy.TemporalMatching
 

--- | @(`dotMaximalSpanningForest` msf)@
+type MST = Int
+type ClusterGroup = Int
+
+-- | @(`dotMaximalSpanningForest` scaleToMsf)@

 -- returns a graph of the given `MaximalSpanningForest`
 -- in [DOT](https://graphviz.org/doc/info/lang.html) format.
 -- returns a graph of the given `MaximalSpanningForest`
 -- in [DOT](https://graphviz.org/doc/info/lang.html) format.

+--
+-- Each maximal spanning tree is here pruned of its edges
+-- from the lowest `Similarity` it contains, to the highest,
+-- each level is called a `Scale`, and groups `(range, cluster)` differently,
+-- hence this actually returns a `Map.Map` of `Scale` to graph.

 dotMaximalSpanningForest ::
   forall range cluster.
 dotMaximalSpanningForest ::
   forall range cluster.

+  HasCallStack =>
+  cluster ~ Cluster =>

   Show range =>
   Show cluster =>
   Ord range =>
   Show range =>
   Show cluster =>
   Ord range =>


@@ -50,105 +63,148 @@ dotMaximalSpanningForest ::
   ShowHuman range =>
   ShowHuman cluster =>
   MaximalSpanningForest range cluster ->
   ShowHuman range =>
   ShowHuman cluster =>
   MaximalSpanningForest range cluster ->

-  BS.Builder
-dotMaximalSpanningForest msf = runDOT do
-  let sortedMSF = msf & List.sortBy (compare `on` mstNodeRangeCluster . Tree.rootLabel)
-  let rangeToMSTToClusters :: range :-> {-mstI-} Int :-> (Maybe Similarity, Set cluster) =
-        let merge = Map.unionWith \(minSimil, x) (_minSimil, y) -> (minSimil, Set.union x y)
+  Int :-> BS.Builder
+dotMaximalSpanningForest msf =
+  -- pTraceShow ("scaleToRangeToMstToGroupToClusters", Map.findMin scaleToRangeToMstToGroupToClusters) $
+  scaleToRangeToMstToGroupToClusters
+    & Map.mapWithKey \scaleI rangeToMstToGroupToClusters -> runDOT do
+      -- forM_ (similToRangeToMstToGroupToClusters & Map.toList) \(minSimil, rangeToMstToGroupToClusters) -> do
+      dotComments [(BS.lazyByteString $ LazyText.encodeUtf8 $ pShow $ rangeToMstToGroupToClusters & Map.map Map.keys)]
+      -- pTraceShow ("num of nodes", Map.size nodeToBranch, "num of branches", Map.size msf) $
+      dotLine "digraph g"
+      dotBlock do
+        dotLine "splines=\"ortho\""
+        indexFrom1M_ (rangeToMstToGroupToClusters & Map.toList) \(srcR, mstToGroupToClusters) srcRI -> do
+          let srcRB = "r" <> BS.intDec srcRI
+          dotLine $ "subgraph cluster_" <> srcRB
+          dotBlock do
+            dotComments ["Create a node for the range " <> srcRB]
+            dotNode
+              srcRB
+              [ ("shape", "box")
+              , ("label", builderQuotedString (showHuman srcR))
+              , ("color", "gray")
+              , ("style", "filled")
+              , ("fillcolor", "gray")
+              ]
+            dotLine "color=gray"
+            dotBlock do
+              dotLine "rank=same"
+              dotComments ["Create the cluster nodes within the range " <> srcRB]
+              forM_ (mstToGroupToClusters & Map.toList) \(mstI, groupToClusters) -> do
+                forM_ (groupToClusters & Map.toList) \(srcGroup, srcClusters) -> do
+                  dotNodeCluster
+                    srcRI
+                    mstI
+                    srcGroup
+                    [
+                      ( "label"
+                      , builderQuotedString $
+                          (srcClusters & toList <&> showHuman & List.unlines)
+                            <> "\nT"
+                            <> printf "%03d" mstI
+                            <> "\nS"
+                            <> show scaleI
+                            -- <> {-maybe ""-} (("\n" <>) . showSimilarity) minSimil
+                      )
+                    , ("style", "filled")
+                    , -- , minSimil & {-maybe ("", "")-} (\s -> ("fillcolor", 1 + ((floor (runProbability s * 10)) `mod` 10) & BS.intDec))
+                      ("colorscheme", "ylorrd9")
+                    , ("shape", "box")
+                    ]
+              dotComments ["Horizontally align the cluster nodes within the same range"]
+              let row =
+                    [ (mstI, group)
+                    | (mstI, groupToClusters) <- mstToGroupToClusters & Map.toList
+                    , (group, _clusters) <- groupToClusters & Map.toList
+                    ]
+              case row of
+                [] -> return ()
+                c@(firstMst, firstGroup) : cs -> do
+                  dotEdges
+                    [srcRB, srcRB <> "t" <> BS.intDec firstMst <> "c" <> BS.intDec firstGroup]
+                    [ ("style", "invis")
+                    ]
+                  cs & (`foldM_` c) \(srcMst, srcGroup) dst@(dstMst, dstGroup) -> do
+                    dotEdgesCluster
+                      [(srcRI, srcMst, srcGroup), (srcRI, dstMst, dstGroup)]
+                      [ ("weight", "10")
+                      , ("style", "invis")
+                      ]
+                    return dst
+        indexFrom1M_ sortedMSF \mst mstI -> do
+          dotComments ["Create the edges of the MST " <> BS.intDec mstI]
+          -- pTraceShowM (mstI, List.length (Tree.flatten mst))
+          let loop (Tree.Node MSTNode{mstNodeRangeCluster = src} dsts) = do
+                forM_ dsts \dstNode@(Tree.Node MSTNode{mstNodeRangeCluster = dst, mstNodeSimilarity = simil} _) -> do
+                  -- let similB = BS.stringUtf8 $ showFFloat (Just 2) (simil & runProbability & fromRational @Double) ""
+                  let indexRangeCluster (r, c) =
+                        let clusterToGroup :: cluster :-> ClusterGroup =
+                              Map.fromList
+                                [ (cluster, group)
+                                | (group, clusters) <-
+                                    rangeToMstToGroupToClusters
+                                      & Map.lookup r
+                                      & fromMaybe Map.empty
+                                      & Map.lookup mstI
+                                      & fromMaybe Map.empty
+                                      & Map.toList
+                                , cluster <- clusters & Set.toList
+                                ]
+                        in ( 1 + Map.findIndex r rangeToMstToGroupToClusters
+                           , mstI
+                           , Map.lookup c clusterToGroup
+                              & fromMaybe (error (LazyText.unpack (pShow ("r", r, "c", c {-, "clusterToGroup", clusterToGroup, "rangeToMstToGroupToClusters", rangeToMstToGroupToClusters-}))))
+                           )
+                  dotEdgesCluster
+                    [ indexRangeCluster src
+                    , indexRangeCluster dst
+                    ]
+                    [ ("constraint", "false")
+                    , ("color", (floor (runProbability simil * 10)) `mod` 10 & BS.intDec)
+                    , ("colorscheme", "ylorrd9")
+                    , -- , ("label", similB)
+                      ("fontcolor", "blue")
+                    , ("dir", "both")
+                    , ("arrowhead", "dot")
+                    , ("arrowtail", "dot")
+                    ]
+                  loop dstNode
+          loop mst
+        dotRanges rangeToMstToGroupToClusters
+  where
+    -- TODO: improve this, this is just a quick attempt to stabilize the DOT
+    sortedMSF = msf & List.sortBy (compare `on` mstNodeRangeCluster . Tree.rootLabel)
+    -- Deep remapping of the `msf` to something more suitable for generating the DOT
+    scaleToRangeToMstToGroupToClusters ::
+      {-scale-} Int :-> range :-> MST :-> ClusterGroup :-> Set cluster =
+        let merge = Map.unionWith (Map.unionWith (Map.unionWith Set.union))

         in Map.unionsWith
             merge
         in Map.unionsWith
             merge

-            [ Map.fromListWith merge $
-              case mst of
-                Tree.Node MSTNode{mstNodeRangeCluster = (rootR, rootC)} ts ->
-                  (rootR, Map.singleton mstI (minSimil, Set.singleton rootC))
-                    : [ (range, Map.singleton mstI (minSimil, Set.singleton cluster))
-                      | MSTNode{mstNodeRangeCluster = (range, cluster)} <- ts & List.concatMap toList
-                      ]
-            | (mstI, mst) <- sortedMSF & List.zip [1 :: Int ..]
-            , let minSimil = mstMinimalSimilarity mst
-            ]
-  let showSimilarity (s :: Similarity) = showFFloat (Just 2) (s & runProbability & fromRational @Double) ""
-  dotComments [(BS.stringUtf8 $ show $ rangeToMSTToClusters & Map.map Map.keys)]
-  -- pTraceShow ("num of nodes", Map.size nodeToBranch, "num of branches", Map.size msf) $
-  dotLine "digraph g"
-  dotBlock do
-    dotLine "splines=\"ortho\""
-    indexFrom1M_ (rangeToMSTToClusters & Map.toList) \(srcR, mstToClusters) srcRI -> do
-      let srcRB = "r" <> BS.intDec srcRI
-      dotLine $ "subgraph cluster_" <> srcRB
-      dotBlock do
-        dotComments ["Create a node for the range " <> srcRB]
-        dotNode
-          srcRB
-          [ ("shape", "box")
-          , ("label", builderQuotedString (showHuman srcR))
-          , ("color", "gray")
-          , ("style", "filled")
-          , ("fillcolor", "gray")
-          ]
-        dotLine "color=gray"
-        dotBlock do
-          dotLine "rank=same"
-          dotComments ["Create the cluster nodes within the range " <> srcRB]
-          forM_ (mstToClusters & Map.toList) \(mstI, (minSimil, clusters)) -> do
-            indexFrom1M_ (clusters & toList) \srcC srcCI -> do
-              dotNodeCluster
-                srcRI
-                mstI
-                srcCI
-                [ ("label", builderQuotedString $ showHuman srcC <> "\nT" <> printf "%03d" mstI <> maybe "" (("\n" <>) . showSimilarity) minSimil)
-                , ("style", "filled")
-                , minSimil & maybe ("", "") (\s -> ("fillcolor", 1 + ((floor (runProbability s * 10)) `mod` 10) & BS.intDec))
-                , ("colorscheme", "ylorrd9")
-                , ("shape", "box")
-                ]
-          dotComments ["Horizontally align the cluster nodes within the same range"]
-          let row =
-                [ (mstI, clusterI)
-                | (mstI, (_minSimil, clusters)) <- mstToClusters & Map.toList
-                , clusterI <- [1 .. Set.size clusters]
-                ]
-          case row of
-            [] -> return ()
-            c@(firstTI, firstCI) : cs -> do
-              dotEdges
-                [srcRB, srcRB <> "t" <> BS.intDec firstTI <> "c" <> BS.intDec firstCI]
-                [ ("style", "invis")
-                ]
-              cs & (`foldM_` c) \(srcTI, srcCI) dst@(dstTI, dstCI) -> do
-                dotEdgesCluster
-                  [(srcRI, srcTI, srcCI), (srcRI, dstTI, dstCI)]
-                  [ ("weight", "10")
-                  , ("style", "invis")
+            [ Map.unionsWith
+              merge
+              [ Map.unionsWith
+                merge
+                [ Map.fromListWith merge $
+                  [ {-(if scaleI == 3
+                    then pTraceShow (["scaleToRangeToMstToGroupToClusters"], "scaleI", scaleI, "scaleSimil", scaleSimil, "range", range, "mstI", mstI, "clusterGroup", clusterGroup, "cluster", cluster)
+                    else id) $-}
+                  (scaleI,) $
+                    Map.singleton range $
+                      Map.singleton mstI $
+                        Map.singleton clusterGroup $
+                          Set.singleton cluster
+                  | MSTNode{mstNodeRangeCluster = (range, cluster)} <- scaleMST & toList

                   ]
                   ]

-                return dst
-    indexFrom1M_ sortedMSF \mst mstI -> do
-      dotComments ["Create the edges of the MST " <> BS.intDec mstI]
-      -- pTraceShowM (mstI, List.length (Tree.flatten mst))
-      let loop (Tree.Node MSTNode{mstNodeRangeCluster = src} dsts) = do
-            forM_ dsts \dstNode@(Tree.Node MSTNode{mstNodeRangeCluster = dst, mstNodeSimilarity = simil} _) -> do
-              -- let similB = BS.stringUtf8 $ showFFloat (Just 2) (simil & runProbability & fromRational @Double) ""
-              let indexRangeCluster (r, c) =
-                    ( 1 + Map.findIndex r rangeToMSTToClusters
-                    , mstI
-                    , 1 + Set.findIndex c (rangeToMSTToClusters Map.! r Map.! mstI & snd)
-                    )
-              dotEdgesCluster
-                [ indexRangeCluster src
-                , indexRangeCluster dst
-                ]
-                [ ("constraint", "false")
-                , ("color", (floor (runProbability simil * 10)) `mod` 10 & BS.intDec)
-                , ("colorscheme", "ylorrd9")
-                , -- , ("label", similB)
-                  ("fontcolor", "blue")
-                , ("dir", "both")
-                , ("arrowhead", "dot")
-                , ("arrowtail", "dot")
+                | (clusterGroup, scaleMST) <-
+                    -- (if mstI == 2 then pTraceShow ("scaleI", scaleI, "scaleMSF", scaleMSF) else id) $
+                    scaleMsf & List.zip [1 :: ClusterGroup ..]

                 ]
                 ]

-              loop dstNode
-      loop mst
-    dotRanges rangeToMSTToClusters
+              | (mstI, scaleMsf) <- mstToMsf & Map.toList
+              ]
+            | (scaleI, mstToMsf) <- mstScales sortedMSF & Map.toList
+            ]
+    showSimilarity (s :: Similarity) = showFFloat (Just 2) (s & runProbability & fromRational @Double) ""

 
 dotRanges :: range :-> a -> DOT
 dotRanges rangeTo = do
 
 dotRanges :: range :-> a -> DOT
 dotRanges rangeTo = do


@@ -201,7 +257,10 @@ dotLine s = do
   MT.lift $ MT.tell $ BS.shortByteString indent <> s <> "\n"
 
 dotComments :: [BS.Builder] -> DOT
   MT.lift $ MT.tell $ BS.shortByteString indent <> s <> "\n"
 
 dotComments :: [BS.Builder] -> DOT

-dotComments = mapM_ \c -> dotLine $ "// " <> c
+dotComments cs = do
+  dotLine "/*"
+  forM_ cs dotLine
+  dotLine "*/"

 
 dotEdges :: [BS.Builder] -> [(BS.Builder, BS.Builder)] -> DOT
 dotEdges names as = dotLine $ mconcat (List.intersperse " -> " names) <> builderAttrs as
 
 dotEdges :: [BS.Builder] -> [(BS.Builder, BS.Builder)] -> DOT
 dotEdges names as = dotLine $ mconcat (List.intersperse " -> " names) <> builderAttrs as

diff --git a/src/Phylomemy/TemporalMatching.hs b/src/Phylomemy/TemporalMatching.hs
index f26ebe8839e3a6c1ffafaf15b251b80a8b8f3949..ea8cb216d2f98017fe210a4f0536b68275fb7e03 100644 (file)
--- a/src/Phylomemy/TemporalMatching.hs
+++ b/src/Phylomemy/TemporalMatching.hs
@@ -1,7 +1,6 @@
 module Phylomemy.TemporalMatching where
 
 module Phylomemy.TemporalMatching where
 

--- import Data.Traversable (traverse)
--- import Debug.Pretty.Simple (pTraceShow, pTraceShowId)
+-- import Debug.Pretty.Simple (pTraceShow)

 import Control.Monad (Monad (..), foldM, forM_, unless)
 import Control.Monad.ST qualified as ST
 import Data.Bool (otherwise)
 import Control.Monad (Monad (..), foldM, forM_, unless)
 import Control.Monad.ST qualified as ST
 import Data.Bool (otherwise)


@@ -58,18 +57,18 @@ similarityJaccard x y =
 -- is the crux of understanding how it is computed:
 --
 -- - the `mstMinimalSimilarity` is the next `Similarity`
 -- is the crux of understanding how it is computed:
 --
 -- - the `mstMinimalSimilarity` is the next `Similarity`

--- that will split the `MaximalSpanningTree` into two or more `MaximalSpanningForest`.
+-- that will split the `MaximalSpanningTree` into two or more `MaximalSpanningTree`s.

 --
 -- - it explains what the "scale of a phylomemy" is:
 --
 -- - it explains what the "scale of a phylomemy" is:

--- merging clusters of the same range and same `MaximalSpanningTree`
+-- merging clusters of the same `range`

 -- when they still belong to the same `MaximalSpanningTree`.
 --
 -- ImplementationNote: using a `Tree.Tree` to represent a `MaximalSpanningTree`
 -- (instead of an adjacency edge map for instance)
 -- is motivated by the need to implement `mstSplit`,
 -- which needs to gather the `(range, cluster)` nodes
 -- when they still belong to the same `MaximalSpanningTree`.
 --
 -- ImplementationNote: using a `Tree.Tree` to represent a `MaximalSpanningTree`
 -- (instead of an adjacency edge map for instance)
 -- is motivated by the need to implement `mstSplit`,
 -- which needs to gather the `(range, cluster)` nodes

--- of the `MaximalSpanningForest` resulting from the cut,
--- which will then be filtered by `msfGlobalQuality`.
+-- of each `MaximalSpanningTree` resulting from the cut,
+-- because knowing that is required by `msfGlobalQuality`.

 --
 -- TODO: "Inadequacies of Minimum Spanning Trees in Molecular Epidemiology"
 -- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3187300/
 --
 -- TODO: "Inadequacies of Minimum Spanning Trees in Molecular Epidemiology"
 -- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3187300/


@@ -89,7 +88,6 @@ data MSTNode range cluster = MSTNode
   -- ImplementationNote: `maximalSpanningForest` puts a `Similarity` of `1` for the root node.
   -- and `mstSplit` leaves the `mstMinimalSimilarity` of the edge before splitting out the `MaximalSpanningTree`.
   , mstNodeRangeCluster :: (range, cluster)
   -- ImplementationNote: `maximalSpanningForest` puts a `Similarity` of `1` for the root node.
   -- and `mstSplit` leaves the `mstMinimalSimilarity` of the edge before splitting out the `MaximalSpanningTree`.
   , mstNodeRangeCluster :: (range, cluster)

-  -- , nodeMSTMinSimilarity :: Min Similarity

   }
   deriving (Show)
 
   }
   deriving (Show)
 


@@ -99,13 +97,15 @@ data MSTNode range cluster = MSTNode
 type MaximalSpanningForest range cluster =
   [MaximalSpanningTree range cluster]
 
 type MaximalSpanningForest range cluster =
   [MaximalSpanningTree range cluster]
 

--- | @(`maximalSpanningForest` allSimils)@
--- uses the Kruskal algorithm to find the maximal spanning trees
--- of the given `AllSimilarities`.
+-- | @(`maximalSpanningForest` similarity rangeToClusterToDocs)@
+-- uses the Kruskal algorithm to find the trees spanning all
+-- the given `(range, cluster)` nodes in `rangeToClusterToDocs`
+-- with the maximal total `similarity` between them.

 --
 -- ExplanationNote: https://en.wikipedia.org/wiki/Kruskal's_algorithm
 maximalSpanningForest ::
   forall range cluster doc.
 --
 -- ExplanationNote: https://en.wikipedia.org/wiki/Kruskal's_algorithm
 maximalSpanningForest ::
   forall range cluster doc.

+  HasCallStack =>

   Ord range =>
   Ord cluster =>
   {-similarityMeasure :::-} (cluster -> cluster -> Similarity) ->
   Ord range =>
   Ord cluster =>
   {-similarityMeasure :::-} (cluster -> cluster -> Similarity) ->


@@ -183,49 +183,60 @@ maximalSpanningForest similarity rangeToClusterToDocs = ST.runST do
 --
 -- See: in `Phylomemy.References.RefDrawMeScience`,
 -- « C.5 The sea-level rise algorithm and its implementation in Gargantext »
 --
 -- See: in `Phylomemy.References.RefDrawMeScience`,
 -- « C.5 The sea-level rise algorithm and its implementation in Gargantext »

-msfSplit ::
-  HasCallStack =>
+msfPrune ::

   forall range roots predictionMeasure.
   forall range roots predictionMeasure.

+  HasCallStack =>

   Show range =>
   Ord range =>
   predictionMeasure ::: (Set (range, Cluster) -> Set (range, Cluster) -> Decimal.Arith Similarity) ->
   roots ::: Set Root ->
   MaximalSpanningForest range Cluster ->
   MaximalSpanningForest range Cluster
   Show range =>
   Ord range =>
   predictionMeasure ::: (Set (range, Cluster) -> Set (range, Cluster) -> Decimal.Arith Similarity) ->
   roots ::: Set Root ->
   MaximalSpanningForest range Cluster ->
   MaximalSpanningForest range Cluster

-msfSplit predictionMeasure roots =
+msfPrune predictionMeasure roots =

   loop (return proba0) []
   where
   loop (return proba0) []
   where

+    loop ::
+      Decimal.Arith Probability ->
+      MaximalSpanningForest range Cluster ->
+      MaximalSpanningForest range Cluster ->
+      MaximalSpanningForest range Cluster

     loop previousQuality doneBranches currentBranches =
     loop previousQuality doneBranches currentBranches =

-      -- pTraceShow (["msfSplit", "loop"], ("previousQuality", previousQuality), ("doneBranches", List.length doneBranches), ("todoBranches", List.length currentBranches)) $
+      -- pTraceShow (["msfPrune", "loop"], ("previousQuality", previousQuality), ("doneBranches", List.length doneBranches), ("todoBranches", List.length currentBranches)) $

       case currentBranches of
         [] -> doneBranches
         currentBranch : todoBranches ->
           let splitBranches = mstSplit currentBranch
       case currentBranches of
         [] -> doneBranches
         currentBranch : todoBranches ->
           let splitBranches = mstSplit currentBranch

-          in -- pTraceShow (["msfSplit", "loop", "splitBranches"], ("size", Map.size splitBranches)) $
+          in -- pTraceShow (["msfPrune", "loop", "splitBranches"], ("size", Map.size splitBranches)) $

              if List.length splitBranches <= 1
               then loop previousQuality (doneBranches <> splitBranches) todoBranches
               else letName (fmap mstNodes $ (doneBranches <> splitBranches) <> todoBranches) \mstToNodes ->
                 let splitQuality = msfGlobalQuality predictionMeasure roots mstToNodes
              if List.length splitBranches <= 1
               then loop previousQuality (doneBranches <> splitBranches) todoBranches
               else letName (fmap mstNodes $ (doneBranches <> splitBranches) <> todoBranches) \mstToNodes ->
                 let splitQuality = msfGlobalQuality predictionMeasure roots mstToNodes

-                in if previousQuality < splitQuality
-                    then loop splitQuality doneBranches (splitBranches <> todoBranches)
+                in if Decimal.arithError previousQuality < Decimal.arithError splitQuality
+                    then -- CorrectnessFixMe: these `Decimal.arithError` may raise "arithmetic overflow",
+                    -- it has to be understood.
+                      loop splitQuality doneBranches (splitBranches <> todoBranches)

                     else loop previousQuality (doneBranches <> splitBranches) todoBranches
 
                     else loop previousQuality (doneBranches <> splitBranches) todoBranches
 

+-- | @(`mstSplit` mst)@ returns the `MaximalSpanningTree`s
+-- resulting from pruning out the given `MaximalSpanningTree`
+-- of all the edges having the minimal `Similarity` of that `MaximalSpanningTree`.

 mstSplit ::
   forall range cluster.
   HasCallStack =>
 mstSplit ::
   forall range cluster.
   HasCallStack =>

-  Show range =>
-  Show cluster =>

   Ord range =>
   Ord cluster =>
   MaximalSpanningTree range cluster ->
   MaximalSpanningForest range cluster
 mstSplit mst =
   Ord range =>
   Ord cluster =>
   MaximalSpanningTree range cluster ->
   MaximalSpanningForest range cluster
 mstSplit mst =

+  -- TODO: take minSimil as argument to avoid recomputing it when already known

   case mstMinimalSimilarity mst of
     Nothing -> [mst]
     Just minSimil -> cutMerge mst
       where
         cutMerge = uncurry (:) . cut
   case mstMinimalSimilarity mst of
     Nothing -> [mst]
     Just minSimil -> cutMerge mst
       where
         cutMerge = uncurry (:) . cut

-        cut :: MaximalSpanningTree range cluster -> (MaximalSpanningTree range cluster, [MaximalSpanningTree range cluster])
+        cut ::
+          MaximalSpanningTree range cluster ->
+          (MaximalSpanningTree range cluster, [MaximalSpanningTree range cluster])

         cut (Tree.Node node children) =
           let (keptChildren, cutChildren) =
                 children & List.partition \tree ->
         cut (Tree.Node node children) =
           let (keptChildren, cutChildren) =
                 children & List.partition \tree ->


@@ -245,7 +256,7 @@ mstMinimalSimilarity (Tree.Node _rootNode rootBranches)
   | List.null rootBranches = Nothing
   | otherwise =
       -- ExplanationNote: the root node of a `MaximalSpanningTree`,
   | List.null rootBranches = Nothing
   | otherwise =
       -- ExplanationNote: the root node of a `MaximalSpanningTree`,

-      -- being a root node, does not have parent,
+      -- being a root node, does not have a parent,

       -- hence its `mstNodeSimilarity` must be ignored.
       Just $
         List.minimum $
       -- hence its `mstNodeSimilarity` must be ignored.
       Just $
         List.minimum $


@@ -259,9 +270,55 @@ mstMinimalSimilarity (Tree.Node _rootNode rootBranches)
 mstSplittingSimilarities :: MaximalSpanningTree range cluster -> Set Similarity
 mstSplittingSimilarities (Tree.Node _rootNode rootBranches)
   | List.null rootBranches = Set.empty
 mstSplittingSimilarities :: MaximalSpanningTree range cluster -> Set Similarity
 mstSplittingSimilarities (Tree.Node _rootNode rootBranches)
   | List.null rootBranches = Set.empty

-  | otherwise = rootBranches & foldMap' (Tree.foldTree \node accs -> Set.unions (Set.singleton (mstNodeSimilarity node) : accs))
+  | otherwise =
+      rootBranches
+        & foldMap'
+          ( Tree.foldTree \node accs ->
+              Set.unions (Set.singleton (mstNodeSimilarity node) : accs)
+          )
+
+type Scale = Int -- > 0
+
+-- | @(`mstScales` msf)@
+-- returns the successive results of calling `mstSplit` on the given `MaximalSpanningTree`s in @(msf)@
+-- until each one of them is a single node.
+-- Even though the greatest `Scale`s may be different for each `MaximalSpanningTree` of @(msf)@,
+-- the result are grouped by `Scale` then by `MaximalSpanningTree`,
+-- which enabled to have a maximal `Scale` for the whole `msf`.
+mstScales ::
+  forall range cluster.
+  Ord range =>
+  Ord cluster =>
+  MaximalSpanningForest range cluster ->
+  Scale :-> {-mst-} Int :-> MaximalSpanningForest range cluster
+mstScales initMSF =
+  Map.unionsWith
+    (Map.unionWith (List.++))
+    [ Map.fromDistinctAscList
+      [ (scale, Map.singleton mstI msf)
+      | (scale, msf) <- scaleToMsf
+      ]
+    | (mstI, mst) <- initMSF & List.zip [1 :: Int ..]
+    , let scaleToMsf :: [(Scale, MaximalSpanningForest range cluster)] =
+            -- scanl :: (acc -> scale -> acc) -> acc -> [scale] -> [acc]
+            splitSimils
+              & Map.keys
+              & List.scanl'
+                (\(scale, msf) _minSimil -> (scale + 1, msf >>= mstSplit))
+                (1, [mst])
+    ]
+  where
+    splitSimils :: Similarity :-> () =
+      Map.unions
+        [ mst
+          & Tree.foldTree \node accs ->
+            Map.unionsWith
+              (\() () -> ())
+              (Map.singleton (mstNodeSimilarity node) () : accs)
+        | mst <- initMSF
+        ]

 
 

--- | @(`mstNodes` branch)@ returns the nodes of the given @(branch)@.
+-- | @(`mstNodes` mst)@ returns the nodes of the given @(mst)@.

 mstNodes ::
   HasCallStack =>
   Ord range =>
 mstNodes ::
   HasCallStack =>
   Ord range =>


@@ -334,7 +391,7 @@ predictionMeasureF lambda relevantNodes retrievedNodes
     recall = cardinal relevantRetrievedNodes % cardinal relevantNodes
     relevantRetrievedNodes = Set.intersection relevantNodes retrievedNodes
     lambdaDouble = lambda & Decimal.toScientificDecimal & toBoundedRealFloat @Double & fromLeft 1
     recall = cardinal relevantRetrievedNodes % cardinal relevantNodes
     relevantRetrievedNodes = Set.intersection relevantNodes retrievedNodes
     lambdaDouble = lambda & Decimal.toScientificDecimal & toBoundedRealFloat @Double & fromLeft 1

-    -- ExplanationNote: the `tan` is just to spread `lambda`
+    -- ExplanationNote: the `tan` is just to spread the `lambda ∈ [0,1]` from -∞ to +∞

     -- Two commonly used values for β are:
     -- - 2, which weighs recall higher than precision,
     -- - and 0.5, which weighs recall lower than precision.
     -- Two commonly used values for β are:
     -- - 2, which weighs recall higher than precision,
     -- - and 0.5, which weighs recall lower than precision.

diff --git a/tests/Phylomemy/TemporalMatchingSpec.hs b/tests/Phylomemy/TemporalMatchingSpec.hs
index eb9421e9c3bcb7a99fbef928282920ce12dc1547..d3f37219717d530b815adc2397384696cabc1935 100644 (file)
--- a/tests/Phylomemy/TemporalMatchingSpec.hs
+++ b/tests/Phylomemy/TemporalMatchingSpec.hs
@@ -5,7 +5,8 @@
 
 module Phylomemy.TemporalMatchingSpec where
 
 
 module Phylomemy.TemporalMatchingSpec where
 

-import Control.Monad (Monad (..), foldM, foldM_, forM_, void)
+import Control.Monad (Monad (..), foldM, foldM_, forM_, void, when)
+import Data.Eq (Eq (..))

 import Data.Function (($), (&), (.))
 import Data.Functor (Functor (..), (<$>), (<&>))
 import Data.GenValidity
 import Data.Function (($), (&), (.))
 import Data.Functor (Functor (..), (<$>), (<&>))
 import Data.GenValidity


@@ -30,6 +31,7 @@ import Data.Validity.Set ()
 import Data.Validity.Text ()
 import Debug.Pretty.Simple (pTraceShow, pTraceShowId)
 import GHC.IsList (toList)
 import Data.Validity.Text ()
 import Debug.Pretty.Simple (pTraceShow, pTraceShowId)
 import GHC.IsList (toList)

+import GHC.Stack (HasCallStack)

 import Logic
 import Numeric (showFFloat)
 import Numeric.Natural (Natural)
 import Logic
 import Numeric (showFFloat)
 import Numeric.Natural (Natural)


@@ -79,7 +81,7 @@ rangeToDocs0 =
     ]
 -}
 
     ]
 -}
 

-spec :: Spec
+spec :: HasCallStack => Spec

 spec = do
   {-
   describe "splitMaximalSpanningTree" do
 spec = do
   {-
   describe "splitMaximalSpanningTree" do


@@ -98,17 +100,17 @@ spec = do
               ]
             ]
     goldenBuilder ("mst=0" <.> "split=0") $
               ]
             ]
     goldenBuilder ("mst=0" <.> "split=0") $

-      dotMaximalSpanningTrees [mst0]
+      dotMaximalSpanningForest [mst0]

     goldenBuilder ("mst=0" <.> "split=1") $
     goldenBuilder ("mst=0" <.> "split=1") $

-      dotMaximalSpanningTrees $
+      dotMaximalSpanningForest $

         splitMaximalSpanningTree mst0
     goldenBuilder ("mst=0" <.> "split=2") $
         splitMaximalSpanningTree mst0
     goldenBuilder ("mst=0" <.> "split=2") $

-      dotMaximalSpanningTrees $
+      dotMaximalSpanningForest $

         mst0
           & splitMaximalSpanningTree
           >>= splitMaximalSpanningTree
     goldenBuilder ("mst=0" <.> "split=3") $
         mst0
           & splitMaximalSpanningTree
           >>= splitMaximalSpanningTree
     goldenBuilder ("mst=0" <.> "split=3") $

-      dotMaximalSpanningTrees $
+      dotMaximalSpanningForest $

         mst0
           & splitMaximalSpanningTree
           >>= splitMaximalSpanningTree
         mst0
           & splitMaximalSpanningTree
           >>= splitMaximalSpanningTree


@@ -121,14 +123,14 @@ spec = do
           let clusters = clusterize roots (assertStrictlyPositive minSupp) (assertStrictlyPositive minSize) rangeToDocs
           -- let allSimils = allSimilarities similarityJaccard (clusters <&> unName)
           let msf = maximalSpanningForest similarityJaccard (clusters <&> unName)
           let clusters = clusterize roots (assertStrictlyPositive minSupp) (assertStrictlyPositive minSize) rangeToDocs
           -- let allSimils = allSimilarities similarityJaccard (clusters <&> unName)
           let msf = maximalSpanningForest similarityJaccard (clusters <&> unName)

-          describe "dotMaximalSpanningTrees" do
-            forM_ ([0, 0.3, 1] :: [Rational]) \lambda -> do
+          describe "dotMaximalSpanningForest" do
+            forM_ ([0.3] :: [Rational]) \lambda -> do

               letName (predictionMeasureF (assertProbability lambda)) \predMeasure -> do
               letName (predictionMeasureF (assertProbability lambda)) \predMeasure -> do

-                goldenBuilder ("docs=docs0" <.> "minSupp=" <> show minSupp <.> "minSize=" <> show minSize <.> "lambda=" <> showFFloat (Just 2) (fromRational @Double lambda) "") $
-                  dotMaximalSpanningForest $
-                    msfSplit predMeasure roots msf
+                forM_ (msfPrune predMeasure roots msf & dotMaximalSpanningForest & Map.toList) \(scale, dot) ->
+                  -- when (scale == 3) do
+                  goldenBuilder ("docs=docs0" <.> "minSupp=" <> show minSupp <.> "minSize=" <> show minSize <.> "lambda=" <> showFFloat (Just 2) (fromRational @Double lambda) "" <.> "scale=" <> show scale) dot

 
 

--- describe "dotMaximalSpanningTrees" do
+-- describe "dotMaximalSpanningForest" do

 --  ([Map.keysSet similToMST | similToMST <- msf & Map.elems] & Set.unions & toList)
 --    & (`foldM_` msf) \acc simil -> do
 --      let similS = showFFloat Nothing (fromRational @Double (runProbability simil)) ""
 --  ([Map.keysSet similToMST | similToMST <- msf & Map.elems] & Set.unions & toList)
 --    & (`foldM_` msf) \acc simil -> do
 --      let similS = showFFloat Nothing (fromRational @Double (runProbability simil)) ""


@@ -136,13 +138,13 @@ spec = do
 --                          Map.unionWith (Map.unionWith (Map.unionWith (Seq.><))) $
 --                          splitMaximalSpanningTree mst
 --      goldenBuilder ("docs=docs0" <.> "minSupp=" <> show minSupp <.> "minSize=" <> show minSize <.> "simil=" <> similS) $
 --                          Map.unionWith (Map.unionWith (Map.unionWith (Seq.><))) $
 --                          splitMaximalSpanningTree mst
 --      goldenBuilder ("docs=docs0" <.> "minSupp=" <> show minSupp <.> "minSize=" <> show minSize <.> "simil=" <> similS) $

---        dotMaximalSpanningTrees acc
+--        dotMaximalSpanningForest acc

 --      return acc'
 -- describe "splitMaximalSpanningTrees" do
 --  forM_ ([0] :: [Rational]) \lambda -> do
 --    letName (predictionMeasureF (assertProbability lambda)) \predMeasure -> do
 --      goldenBuilder ("docs=docs0" <.> "minSupp=" <> show minSupp <.> "minSize=" <> show minSize <.> "lambda=" <> showFFloat (Just 2) (fromRational @Double lambda) "") $
 --      return acc'
 -- describe "splitMaximalSpanningTrees" do
 --  forM_ ([0] :: [Rational]) \lambda -> do
 --    letName (predictionMeasureF (assertProbability lambda)) \predMeasure -> do
 --      goldenBuilder ("docs=docs0" <.> "minSupp=" <> show minSupp <.> "minSize=" <> show minSize <.> "lambda=" <> showFFloat (Just 2) (fromRational @Double lambda) "") $

---        dotMaximalSpanningTrees $
+--        dotMaximalSpanningForest $

 --          splitMaximalSpanningTrees predMeasure roots msf
 -- describe "dotSimilarities" do
 -- forM_ ([0] :: [Rational]) \lambda -> do
 --          splitMaximalSpanningTrees predMeasure roots msf
 -- describe "dotSimilarities" do
 -- forM_ ([0] :: [Rational]) \lambda -> do

diff --git a/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.00.golden b/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.00.golden
deleted file mode 100644 (file)
index 076a302..0000000
--- a/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.00.golden
+++ /dev/null
@@ -1,161 +0,0 @@
-// fromList [(Pos 1,[1,2,3]),(Pos 2,[4,5,6]),(Pos 3,[7,8]),(Pos 4,[9,10,11,12]),(Pos 5,[13,14,15,16]),(Pos 6,[17,18,19,20,21,22])]
-digraph g
-{
-  splines="ortho"
-  subgraph cluster_r1
-  {
-    // Create a node for the range r1
-    r1[shape=box,label="1",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r1
-      r1t1c1[label="a & b & c
-T001",style=filled,colorscheme=ylorrd9,shape=box]
-      r1t2c1[label="a & d & e
-T002",style=filled,colorscheme=ylorrd9,shape=box]
-      r1t3c1[label="e & f & g
-T003",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r1 -> r1t1c1[style=invis]
-      r1t1c1 -> r1t2c1[weight=10,style=invis]
-      r1t2c1 -> r1t3c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r2
-  {
-    // Create a node for the range r2
-    r2[shape=box,label="2",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r2
-      r2t4c1[label="a & b
-T004",style=filled,colorscheme=ylorrd9,shape=box]
-      r2t5c1[label="a & d
-T005",style=filled,colorscheme=ylorrd9,shape=box]
-      r2t6c1[label="d & f
-T006",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r2 -> r2t4c1[style=invis]
-      r2t4c1 -> r2t5c1[weight=10,style=invis]
-      r2t5c1 -> r2t6c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r3
-  {
-    // Create a node for the range r3
-    r3[shape=box,label="3",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r3
-      r3t7c1[label="a & f & g
-T007",style=filled,colorscheme=ylorrd9,shape=box]
-      r3t8c1[label="d & f
-T008",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r3 -> r3t7c1[style=invis]
-      r3t7c1 -> r3t8c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r4
-  {
-    // Create a node for the range r4
-    r4[shape=box,label="4",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r4
-      r4t9c1[label="a & b & c
-T009",style=filled,colorscheme=ylorrd9,shape=box]
-      r4t10c1[label="a & d & e
-T010",style=filled,colorscheme=ylorrd9,shape=box]
-      r4t11c1[label="b & c
-T011",style=filled,colorscheme=ylorrd9,shape=box]
-      r4t12c1[label="b & c & e
-T012",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r4 -> r4t9c1[style=invis]
-      r4t9c1 -> r4t10c1[weight=10,style=invis]
-      r4t10c1 -> r4t11c1[weight=10,style=invis]
-      r4t11c1 -> r4t12c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r5
-  {
-    // Create a node for the range r5
-    r5[shape=box,label="5",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r5
-      r5t13c1[label="a & c & d
-T013",style=filled,colorscheme=ylorrd9,shape=box]
-      r5t14c1[label="a & f
-T014",style=filled,colorscheme=ylorrd9,shape=box]
-      r5t15c1[label="b & f
-T015",style=filled,colorscheme=ylorrd9,shape=box]
-      r5t16c1[label="d & f & g
-T016",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r5 -> r5t13c1[style=invis]
-      r5t13c1 -> r5t14c1[weight=10,style=invis]
-      r5t14c1 -> r5t15c1[weight=10,style=invis]
-      r5t15c1 -> r5t16c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r6
-  {
-    // Create a node for the range r6
-    r6[shape=box,label="6",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r6
-      r6t17c1[label="a & b & c
-T017",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t18c1[label="b & c
-T018",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t19c1[label="b & c & g
-T019",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t20c1[label="c & d & g
-T020",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t21c1[label="c & g
-T021",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t22c1[label="e & g
-T022",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r6 -> r6t17c1[style=invis]
-      r6t17c1 -> r6t18c1[weight=10,style=invis]
-      r6t18c1 -> r6t19c1[weight=10,style=invis]
-      r6t19c1 -> r6t20c1[weight=10,style=invis]
-      r6t20c1 -> r6t21c1[weight=10,style=invis]
-      r6t21c1 -> r6t22c1[weight=10,style=invis]
-    }
-  }
-  // Create the edges of the MST 1
-  // Create the edges of the MST 2
-  // Create the edges of the MST 3
-  // Create the edges of the MST 4
-  // Create the edges of the MST 5
-  // Create the edges of the MST 6
-  // Create the edges of the MST 7
-  // Create the edges of the MST 8
-  // Create the edges of the MST 9
-  // Create the edges of the MST 10
-  // Create the edges of the MST 11
-  // Create the edges of the MST 12
-  // Create the edges of the MST 13
-  // Create the edges of the MST 14
-  // Create the edges of the MST 15
-  // Create the edges of the MST 16
-  // Create the edges of the MST 17
-  // Create the edges of the MST 18
-  // Create the edges of the MST 19
-  // Create the edges of the MST 20
-  // Create the edges of the MST 21
-  // Create the edges of the MST 22
-  // Vertically align range nodes
-  r1 -> r2 -> r3 -> r4 -> r5 -> r6[weight=10,style=invis]
-}

diff --git a/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.30.golden b/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.30.golden
deleted file mode 100644 (file)
index 58fd974..0000000
--- a/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=0.30.golden
+++ /dev/null
@@ -1,180 +0,0 @@
-// fromList [(Pos 1,[1,2,5]),(Pos 2,[1,3,5]),(Pos 3,[3,4]),(Pos 4,[1,5]),(Pos 5,[1,3,4,6]),(Pos 6,[2,5,7,8])]
-digraph g
-{
-  splines="ortho"
-  subgraph cluster_r1
-  {
-    // Create a node for the range r1
-    r1[shape=box,label="1",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r1
-      r1t1c1[label="a & d & e
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r1t2c1[label="e & f & g
-T002
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r1t5c1[label="a & b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r1 -> r1t1c1[style=invis]
-      r1t1c1 -> r1t2c1[weight=10,style=invis]
-      r1t2c1 -> r1t5c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r2
-  {
-    // Create a node for the range r2
-    r2[shape=box,label="2",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r2
-      r2t1c1[label="a & d
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r2t3c1[label="d & f
-T003
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r2t5c1[label="a & b
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r2 -> r2t1c1[style=invis]
-      r2t1c1 -> r2t3c1[weight=10,style=invis]
-      r2t3c1 -> r2t5c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r3
-  {
-    // Create a node for the range r3
-    r3[shape=box,label="3",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r3
-      r3t3c1[label="d & f
-T003
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r3t4c1[label="a & f & g
-T004
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r3 -> r3t3c1[style=invis]
-      r3t3c1 -> r3t4c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r4
-  {
-    // Create a node for the range r4
-    r4[shape=box,label="4",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r4
-      r4t1c1[label="a & d & e
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r4t5c1[label="a & b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r4t5c2[label="b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r4t5c3[label="b & c & e
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r4 -> r4t1c1[style=invis]
-      r4t1c1 -> r4t5c1[weight=10,style=invis]
-      r4t5c1 -> r4t5c2[weight=10,style=invis]
-      r4t5c2 -> r4t5c3[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r5
-  {
-    // Create a node for the range r5
-    r5[shape=box,label="5",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r5
-      r5t1c1[label="a & c & d
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r5t3c1[label="d & f & g
-T003
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r5t4c1[label="a & f
-T004
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r5t6c1[label="b & f
-T006",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r5 -> r5t1c1[style=invis]
-      r5t1c1 -> r5t3c1[weight=10,style=invis]
-      r5t3c1 -> r5t4c1[weight=10,style=invis]
-      r5t4c1 -> r5t6c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r6
-  {
-    // Create a node for the range r6
-    r6[shape=box,label="6",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r6
-      r6t2c1[label="e & g
-T002
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t5c1[label="a & b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t5c2[label="b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t5c3[label="b & c & g
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t7c1[label="c & d & g
-T007",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t8c1[label="c & g
-T008",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r6 -> r6t2c1[style=invis]
-      r6t2c1 -> r6t5c1[weight=10,style=invis]
-      r6t5c1 -> r6t5c2[weight=10,style=invis]
-      r6t5c2 -> r6t5c3[weight=10,style=invis]
-      r6t5c3 -> r6t7c1[weight=10,style=invis]
-      r6t7c1 -> r6t8c1[weight=10,style=invis]
-    }
-  }
-  // Create the edges of the MST 1
-  r1t1c1 -> r5t1c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t1c1 -> r2t1c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t1c1 -> r4t1c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 2
-  r1t2c1 -> r6t2c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 3
-  r2t3c1 -> r5t3c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r2t3c1 -> r3t3c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 4
-  r3t4c1 -> r5t4c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 5
-  r4t5c3 -> r1t5c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r6t5c3[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r4t5c2[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r4t5c2 -> r6t5c2[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r2t5c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r6t5c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r4t5c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 6
-  // Create the edges of the MST 7
-  // Create the edges of the MST 8
-  // Vertically align range nodes
-  r1 -> r2 -> r3 -> r4 -> r5 -> r6[weight=10,style=invis]
-}

diff --git a/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=1.00.golden b/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=1.00.golden
deleted file mode 100644 (file)
index 58fd974..0000000
--- a/tests/Phylomemy/TemporalMatchingSpec/dotMaximalSpanningTrees/docs=docs0.minSupp=1.minSize=2.lambda=1.00.golden
+++ /dev/null
@@ -1,180 +0,0 @@
-// fromList [(Pos 1,[1,2,5]),(Pos 2,[1,3,5]),(Pos 3,[3,4]),(Pos 4,[1,5]),(Pos 5,[1,3,4,6]),(Pos 6,[2,5,7,8])]
-digraph g
-{
-  splines="ortho"
-  subgraph cluster_r1
-  {
-    // Create a node for the range r1
-    r1[shape=box,label="1",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r1
-      r1t1c1[label="a & d & e
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r1t2c1[label="e & f & g
-T002
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r1t5c1[label="a & b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r1 -> r1t1c1[style=invis]
-      r1t1c1 -> r1t2c1[weight=10,style=invis]
-      r1t2c1 -> r1t5c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r2
-  {
-    // Create a node for the range r2
-    r2[shape=box,label="2",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r2
-      r2t1c1[label="a & d
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r2t3c1[label="d & f
-T003
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r2t5c1[label="a & b
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r2 -> r2t1c1[style=invis]
-      r2t1c1 -> r2t3c1[weight=10,style=invis]
-      r2t3c1 -> r2t5c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r3
-  {
-    // Create a node for the range r3
-    r3[shape=box,label="3",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r3
-      r3t3c1[label="d & f
-T003
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r3t4c1[label="a & f & g
-T004
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r3 -> r3t3c1[style=invis]
-      r3t3c1 -> r3t4c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r4
-  {
-    // Create a node for the range r4
-    r4[shape=box,label="4",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r4
-      r4t1c1[label="a & d & e
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r4t5c1[label="a & b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r4t5c2[label="b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r4t5c3[label="b & c & e
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r4 -> r4t1c1[style=invis]
-      r4t1c1 -> r4t5c1[weight=10,style=invis]
-      r4t5c1 -> r4t5c2[weight=10,style=invis]
-      r4t5c2 -> r4t5c3[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r5
-  {
-    // Create a node for the range r5
-    r5[shape=box,label="5",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r5
-      r5t1c1[label="a & c & d
-T001
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r5t3c1[label="d & f & g
-T003
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r5t4c1[label="a & f
-T004
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r5t6c1[label="b & f
-T006",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r5 -> r5t1c1[style=invis]
-      r5t1c1 -> r5t3c1[weight=10,style=invis]
-      r5t3c1 -> r5t4c1[weight=10,style=invis]
-      r5t4c1 -> r5t6c1[weight=10,style=invis]
-    }
-  }
-  subgraph cluster_r6
-  {
-    // Create a node for the range r6
-    r6[shape=box,label="6",color=gray,style=filled,fillcolor=gray]
-    color=gray
-    {
-      rank=same
-      // Create the cluster nodes within the range r6
-      r6t2c1[label="e & g
-T002
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t5c1[label="a & b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t5c2[label="b & c
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t5c3[label="b & c & g
-T005
-0.67",style=filled,fillcolor=7,colorscheme=ylorrd9,shape=box]
-      r6t7c1[label="c & d & g
-T007",style=filled,colorscheme=ylorrd9,shape=box]
-      r6t8c1[label="c & g
-T008",style=filled,colorscheme=ylorrd9,shape=box]
-      // Horizontally align the cluster nodes within the same range
-      r6 -> r6t2c1[style=invis]
-      r6t2c1 -> r6t5c1[weight=10,style=invis]
-      r6t5c1 -> r6t5c2[weight=10,style=invis]
-      r6t5c2 -> r6t5c3[weight=10,style=invis]
-      r6t5c3 -> r6t7c1[weight=10,style=invis]
-      r6t7c1 -> r6t8c1[weight=10,style=invis]
-    }
-  }
-  // Create the edges of the MST 1
-  r1t1c1 -> r5t1c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t1c1 -> r2t1c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t1c1 -> r4t1c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 2
-  r1t2c1 -> r6t2c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 3
-  r2t3c1 -> r5t3c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r2t3c1 -> r3t3c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 4
-  r3t4c1 -> r5t4c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 5
-  r4t5c3 -> r1t5c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r6t5c3[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r4t5c2[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r4t5c2 -> r6t5c2[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r2t5c1[constraint=false,color=6,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r6t5c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  r1t5c1 -> r4t5c1[constraint=false,color=0,colorscheme=ylorrd9,fontcolor=blue,dir=both,arrowhead=dot,arrowtail=dot]
-  // Create the edges of the MST 6
-  // Create the edges of the MST 7
-  // Create the edges of the MST 8
-  // Vertically align range nodes
-  r1 -> r2 -> r3 -> r4 -> r5 -> r6[weight=10,style=invis]
-}