Merge branch 'dev' into 70-dev-searx-parser

CHANGELOG.md

+## Version 0.0.4.9.5
+* [FEAT] Order 2 fixed with filtered edges
+
+## Version 0.0.4.9.4
+* [FEAT] Order 1 similarity validated and optimized
+
+## Version 0.0.4.9.3
+* [FIX] Node Calc import + more flexible delimiter for CSV parser
+
+## Version 0.0.4.9.2
+* [FEAT] Node Calc Parsing added (in tests)
+
 ## Version 0.0.4.9.1
 * [FIX] Graph Screenshot
 

package.yaml

 name: gargantext
-version: '0.0.4.9.1'
+version: '0.0.4.9.5'
 synopsis: Search, map, share
 description: Please see README.md
 category: Data

src/Gargantext/API/Ngrams/Types.hs

@@ -11,6 +11,7 @@ module Gargantext.API.Ngrams.Types where
 
 import Codec.Serialise (Serialise())
 import Control.Category ((>>>))
+import Control.DeepSeq (NFData)
 import Control.Lens (makeLenses, makePrisms, Iso', iso, from, (.~), (?=), (#), to, folded, {-withIndex, ifolded,-} view, use, (^.), (^?), (%~), (.~), (%=), at, _Just, Each(..), itraverse_, both, forOf_, (?~))
 import Control.Monad.State
 import Data.Aeson hiding ((.=))
@@ -121,7 +122,7 @@ instance (ToJSONKey a, ToSchema a) => ToSchema (MSet a) where
 
 ------------------------------------------------------------------------
 newtype NgramsTerm = NgramsTerm { unNgramsTerm :: Text }
-  deriving (Ord, Eq, Show, Generic, ToJSONKey, ToJSON, FromJSON, Semigroup, Arbitrary, Serialise, ToSchema, Hashable)
+  deriving (Ord, Eq, Show, Generic, ToJSONKey, ToJSON, FromJSON, Semigroup, Arbitrary, Serialise, ToSchema, Hashable, NFData)
 
 instance IsHashable NgramsTerm where
   hash (NgramsTerm t) = hash t

src/Gargantext/API/Node/FrameCalcUpload.hs

@@ -80,6 +80,7 @@ frameCalcUploadAsync uId nId _f logStatus jobLog = do
     httpLbs req manager
   let body = T.pack $ BSU8.toString $ BSL.toStrict $ responseBody res
 
+  -- printDebug "body" body
   mCId <- getClosestParentIdByType nId NodeCorpus
   -- printDebug "[frameCalcUploadAsync] mCId" mCId
 

src/Gargantext/Core/Ext/IMTUser.hs

@@ -123,7 +123,7 @@ readCSVFile_Annuaire' :: FilePath -> IO (Header, Vector IMTUser)
 readCSVFile_Annuaire' = fmap readCsvHalLazyBS' . BL.readFile
   where
     readCsvHalLazyBS' :: BL.ByteString -> (Header, Vector IMTUser)
-    readCsvHalLazyBS' bs = case decodeByNameWith csvDecodeOptions bs of
+    readCsvHalLazyBS' bs = case decodeByNameWith (csvDecodeOptions Tab) bs of
           Left  e    -> panic (cs e)
           Right rows -> rows
 

src/Gargantext/Core/Methods/Distances/Conditional.hs

@@ -15,108 +15,44 @@ Motivation and definition of the @Conditional@ distance.
 module Gargantext.Core.Methods.Distances.Conditional
   where
 
-import Data.List (sortOn)
-import Data.Map (Map)
-import Data.Matrix hiding (identity)
-import Gargantext.Core.Viz.Graph.Utils
+import Control.DeepSeq (NFData)
+import Control.Parallel.Strategies (parList, rdeepseq, using)
+import Data.Hashable (Hashable)
+import Data.List (unzip)
+import Data.Maybe (catMaybes)
 import Gargantext.Prelude
-import qualified Data.Map as M
-import qualified Data.Set as S
-import qualified Data.Vector as V
+import Gargantext.Core.Viz.Graph.Utils (getMax)
+import qualified Data.HashMap.Strict as Map
+import qualified Data.Set            as Set
 
-------------------------------------------------------------------------
--- | Optimisation issue
-toBeOptimized :: (Num a, Fractional a, Ord a) => Matrix a -> Matrix a
-toBeOptimized m = proba Col m
 
+type HashMap = Map.HashMap
 ------------------------------------------------------------------------
--- | Main Functions
--- Compute the probability from axis
--- x' = x / (sum Col x)
-proba :: (Num a, Fractional a) => Axis -> Matrix a -> Matrix a
-proba a m = mapOn a (\c x -> x / V.sum (axis a c m)) m
-
-
-mapOn :: Axis -> (AxisId -> a -> a) -> Matrix a -> Matrix a
-mapOn a f m = V.foldl' f'  m (V.enumFromTo 1 (nOf a m))
+-- First version as first implementation
+-- - qualitatively verified
+-- - parallized as main optimization
+conditional :: (Ord a, Hashable a, NFData a)
+            => HashMap (a,a) Int
+            -> HashMap (a,a) Double
+conditional m' = Map.fromList $ ((catMaybes results') `using` parList rdeepseq)
   where
-    f' m' c = mapOnly a f c m'
+    results' = [ let
+                  ij = (/) <$> Map.lookup (i,j) m <*> Map.lookup (i,i) m
+                  ji = (/) <$> Map.lookup (j,i) m <*> Map.lookup (j,j) m
+                  in getMax (i,j) ij ji
 
-mapOnly :: Axis -> (AxisId -> a -> a) -> AxisId -> Matrix a -> Matrix a
-mapOnly Col = mapCol
-mapOnly Row = mapRow
+               | i <- keys
+               , j <- keys
+               , i < j
+               ]
+    -- Converting from Int to Double
+    m       = Map.map fromIntegral m'
 
-mapAll :: (a -> a) -> Matrix a -> Matrix a
-mapAll f m = mapOn Col (\_ -> f) m
+    -- Get the matrix coordinates, removing duplicates
+    keys    = Set.toList $ Set.fromList (x <> y)
+    (x,y)   = unzip $ Map.keys m
 
----------------------------------------------------------------
--- | Compute a distance from axis
--- xs = (sum Col x') - x'
-distFromSum :: (Num a, Fractional a)
-         => Axis -> Matrix a -> Matrix a
-distFromSum  a m = mapOn a (\c x -> V.sum (axis a c m) - x) m
----------------------------------------------------------------
----------------------------------------------------------------
--- | To compute included/excluded or specific/generic scores
-opWith  :: (Fractional a1, Num a1)
-         => (Matrix a2 -> t -> Matrix a1) -> Matrix a2 -> t -> Matrix a1
-opWith op xs ys = mapAll (\x -> x / (2*n -1)) (xs `op` ys)
-  where
-    n = fromIntegral $ nOf Col xs
----------------------------------------------------------------
 
 
--------------------------------------------------------
-conditional :: (Num a, Fractional a, Ord a) => Matrix a -> Matrix a
-conditional m = filterMat (threshold m') m'
-  where
-------------------------------------------------------------------------
-    -- | Main Operations
-    -- x' = x / (sum Col x)
-    x' = proba Col m
-
-------------------------------------------------------------------------
-    -- xs = (sum Col x') - x'
-    xs = distFromSum Col x'
-    -- ys = (sum Row x') - x'
-    ys = distFromSum Row x'
 
-------------------------------------------------------------------------
---  | Top included or excluded
-    ie = opWith (+) xs ys
---  ie = ( xs + ys) / (2 * (x.shape[0] - 1))
 
---  | Top specific or generic
-    sg = opWith (-) xs ys
---  sg = ( xs - ys) / (2 * (x.shape[0] - 1))
-
-    nodes_kept :: [Int]
-    nodes_kept = take k' $ S.toList
-                         $ foldl' (\s (n1,n2) -> insert [n1,n2] s) S.empty
-                         $ map fst
-                         $ nodes_included k <> nodes_specific k
-
-    nodes_included n = take n $ sortOn snd $ toListsWithIndex ie
-    nodes_specific n = take n $ sortOn snd $ toListsWithIndex sg
-    insert as s = foldl' (\s' a -> S.insert a s') s as
-    k' = 2*k
-    k = 10
-
-    dico_nodes :: Map Int Int
-    dico_nodes     = M.fromList $ zip ([1..] :: [Int]) nodes_kept
-    --dico_nodes_rev = M.fromList $ zip nodes_kept [1..]
-
-    m' = matrix (length nodes_kept) 
-                (length nodes_kept) 
-                (\(i,j) -> getElem ((M.!) dico_nodes i) ((M.!) dico_nodes j) x')
-
-    threshold m'' = V.minimum
-                  $ V.map (\cId -> V.maximum $ getCol cId m'')
-                          (V.enumFromTo 1 (nOf Col m'')      )
-
-    filterMat t m''  = mapAll (\x -> filter' t x) m''
-      where
-        filter' t' x = case (x >= t') of
-                        True  -> x
-                        False -> 0
-------------------------------------------------------------------------

src/Gargantext/Core/Text/Corpus/Parsers/CSV.hs

@@ -218,14 +218,17 @@ hyperdataDocument2csvDoc h = CsvDoc { csv_title = m $ _hd_title h
     mI = maybe 0 identity
 
 
-csvDecodeOptions :: DecodeOptions
-csvDecodeOptions = defaultDecodeOptions {decDelimiter = delimiter}
+data Delimiter = Tab | Comma
 
-csvEncodeOptions :: EncodeOptions
-csvEncodeOptions = defaultEncodeOptions {encDelimiter = delimiter}
+csvDecodeOptions :: Delimiter -> DecodeOptions
+csvDecodeOptions d = defaultDecodeOptions {decDelimiter = delimiter d}
 
-delimiter :: Word8
-delimiter = fromIntegral $ ord '\t'
+csvEncodeOptions :: Delimiter -> EncodeOptions
+csvEncodeOptions d = defaultEncodeOptions {encDelimiter = delimiter d}
+
+delimiter :: Delimiter -> Word8
+delimiter Tab   = fromIntegral $ ord '\t'
+delimiter Comma = fromIntegral $ ord ','
 ------------------------------------------------------------------------
 ------------------------------------------------------------------------
 readCsvOn' :: [CsvDoc -> Text] -> FilePath -> IO (Either Prelude.String [Text])
@@ -237,27 +240,44 @@ readCsvOn' fields fp = do
 
 ------------------------------------------------------------------------
 
-readFileLazy :: (FromNamedRecord a) => proxy a -> FilePath -> IO (Either Prelude.String (Header, Vector a))
-readFileLazy f = fmap (readByteStringLazy f) . BL.readFile
-
-readFileStrict :: (FromNamedRecord a) => proxy a -> FilePath -> IO (Either Prelude.String (Header, Vector a))
-readFileStrict f = fmap (readByteStringStrict f) . BS.readFile
-
-readByteStringLazy :: (FromNamedRecord a) => proxy a -> BL.ByteString -> Either Prelude.String (Header, Vector a)
-readByteStringLazy _f bs = decodeByNameWith csvDecodeOptions bs
-
-readByteStringStrict :: (FromNamedRecord a) => proxy a -> BS.ByteString -> Either Prelude.String (Header, Vector a)
-readByteStringStrict ff = (readByteStringLazy ff) . BL.fromStrict
+readFileLazy :: (FromNamedRecord a) => proxy a -> Delimiter -> FilePath -> IO (Either Prelude.String (Header, Vector a))
+readFileLazy d f = fmap (readByteStringLazy d f) . BL.readFile
+
+readFileStrict :: (FromNamedRecord a)
+               => proxy a
+               -> Delimiter
+               -> FilePath
+               -> IO (Either Prelude.String (Header, Vector a))
+readFileStrict d f = fmap (readByteStringStrict d f) . BS.readFile
+
+readByteStringLazy :: (FromNamedRecord a)
+                   => proxy a
+                   -> Delimiter
+                   -> BL.ByteString
+                   -> Either Prelude.String (Header, Vector a)
+readByteStringLazy _f d bs = decodeByNameWith (csvDecodeOptions d) bs
+
+readByteStringStrict :: (FromNamedRecord a)
+                     => proxy a
+                     -> Delimiter
+                     -> BS.ByteString
+                     -> Either Prelude.String (Header, Vector a)
+readByteStringStrict d ff = (readByteStringLazy d ff) . BL.fromStrict
 
 ------------------------------------------------------------------------
 -- | TODO use readFileLazy
 readFile :: FilePath -> IO (Either Prelude.String (Header, Vector CsvDoc))
-readFile = fmap readCsvLazyBS . BL.readFile
+readFile fp = do
+  result <- fmap (readCsvLazyBS Comma) $ BL.readFile fp
+  case result of
+    Left _err -> fmap (readCsvLazyBS Tab) $ BL.readFile fp
+    Right res -> pure $ Right res
+
 
 
 -- | TODO use readByteStringLazy
-readCsvLazyBS :: BL.ByteString -> Either Prelude.String (Header, Vector CsvDoc)
-readCsvLazyBS bs = decodeByNameWith csvDecodeOptions bs
+readCsvLazyBS :: Delimiter -> BL.ByteString -> Either Prelude.String (Header, Vector CsvDoc)
+readCsvLazyBS d bs = decodeByNameWith (csvDecodeOptions d) bs
 
 ------------------------------------------------------------------------
 -- | TODO use readFileLazy
@@ -266,7 +286,7 @@ readCsvHal = fmap readCsvHalLazyBS . BL.readFile
 
 -- | TODO use readByteStringLazy
 readCsvHalLazyBS :: BL.ByteString -> Either Prelude.String (Header, Vector CsvHal)
-readCsvHalLazyBS bs = decodeByNameWith csvDecodeOptions bs
+readCsvHalLazyBS bs = decodeByNameWith (csvDecodeOptions Tab) bs
 
 readCsvHalBSStrict :: BS.ByteString -> Either Prelude.String (Header, Vector CsvHal)
 readCsvHalBSStrict = readCsvHalLazyBS . BL.fromStrict
@@ -274,13 +294,13 @@ readCsvHalBSStrict = readCsvHalLazyBS . BL.fromStrict
 ------------------------------------------------------------------------
 writeFile :: FilePath -> (Header, Vector CsvDoc) -> IO ()
 writeFile fp (h, vs) = BL.writeFile fp $
-                      encodeByNameWith csvEncodeOptions h (V.toList vs)
+                      encodeByNameWith (csvEncodeOptions Tab) h (V.toList vs)
 
 writeDocs2Csv :: FilePath -> [HyperdataDocument] -> IO ()
 writeDocs2Csv fp hs = BL.writeFile fp $ hyperdataDocument2csv hs
 
 hyperdataDocument2csv :: [HyperdataDocument] -> BL.ByteString
-hyperdataDocument2csv hs = encodeByNameWith csvEncodeOptions headerCsvGargV3 (map hyperdataDocument2csvDoc hs)
+hyperdataDocument2csv hs = encodeByNameWith (csvEncodeOptions Tab) headerCsvGargV3 (map hyperdataDocument2csvDoc hs)
 
 ------------------------------------------------------------------------
 -- Hal Format
@@ -425,13 +445,22 @@ parseHal' :: BL.ByteString -> Either Prelude.String [HyperdataDocument]
 parseHal' bs = (V.toList . V.map csvHal2doc . snd) <$> readCsvHalLazyBS bs
 
 ------------------------------------------------------------------------
+
 parseCsv :: FilePath -> IO (Either Prelude.String [HyperdataDocument])
-parseCsv fp = do
-  r <- readFile fp
-  pure $ (V.toList . V.map csv2doc . snd) <$> r
+parseCsv fp = fmap (V.toList . V.map csv2doc . snd) <$> readFile fp
+
+{-
+parseCsv' ::  BL.ByteString -> Either Prelude.String [HyperdataDocument]
+parseCsv' bs = (V.toList . V.map csv2doc . snd) <$> readCsvLazyBS Comma bs
+-}
 
 parseCsv' :: BL.ByteString -> Either Prelude.String [HyperdataDocument]
-parseCsv' bs = (V.toList . V.map csv2doc . snd) <$> readCsvLazyBS bs
+parseCsv' bs = do
+  let
+    result = case readCsvLazyBS Comma bs of
+      Left  _err -> readCsvLazyBS Tab bs
+      Right res -> Right res
+  (V.toList . V.map csv2doc . snd) <$> result
 
 ------------------------------------------------------------------------
 -- Csv v3 weighted for phylo
@@ -462,7 +491,7 @@ instance FromNamedRecord Csv' where
 readWeightedCsv :: FilePath -> IO (Header, Vector Csv')
 readWeightedCsv fp =
   fmap (\bs ->
-    case decodeByNameWith csvDecodeOptions bs of
+    case decodeByNameWith (csvDecodeOptions Tab) bs of
       Left e       -> panic (pack e)
       Right corpus -> corpus
     ) $ BL.readFile fp

src/Gargantext/Core/Viz/Graph/Tools.hs

@@ -18,13 +18,15 @@ module Gargantext.Core.Viz.Graph.Tools
 import Data.HashMap.Strict (HashMap)
 import Data.Map (Map)
 import Data.Text (Text)
-import Debug.Trace (trace)
+-- import Debug.Trace (trace)
 import GHC.Float (sin, cos)
 import Gargantext.API.Ngrams.Types (NgramsTerm(..))
+import Gargantext.Core.Methods.Distances.Conditional (conditional)
 import Gargantext.Core.Methods.Distances (Distance(..), measure)
 import Gargantext.Core.Methods.Graph.BAC.Proxemy (confluence)
 import Gargantext.Core.Statistics
 import Gargantext.Core.Viz.Graph
+import Gargantext.Core.Viz.Graph.Utils (edgesFilter)
 import Gargantext.Core.Viz.Graph.Bridgeness (bridgeness, Partitions, ToComId(..))
 import Gargantext.Core.Viz.Graph.Index (createIndices, toIndex, map2mat, mat2map, Index, MatrixShape(..))
 import Gargantext.Core.Viz.Graph.Tools.IGraph (mkGraphUfromEdges, spinglass)
@@ -49,6 +51,7 @@ defaultClustering x = spinglass 1 x
 -------------------------------------------------------------
 type Threshold = Double
 
+
 cooc2graph' :: Ord t => Distance
                      -> Double
                      -> Map (t, t) Int
@@ -96,7 +99,6 @@ cooc2graphWith' doPartitions distance threshold myCooc = do
       where
         (as, bs) = List.unzip $ Map.keys distanceMap
         n' = Set.size $ Set.fromList $ as <> bs
-    ClustersParams rivers _level = clustersParams nodesApprox
 
 {- -- Debug
   saveAsFileDebug "debug/distanceMap" distanceMap
@@ -108,9 +110,7 @@ cooc2graphWith' doPartitions distance threshold myCooc = do
       else panic "Text.Flow: DistanceMap is empty"
 
   let
-    -- bridgeness' = distanceMap
-    bridgeness' = trace ("Rivers: " <> show rivers)
-                $ bridgeness rivers partitions distanceMap
+    bridgeness' = bridgeness (fromIntegral nodesApprox) partitions distanceMap
 
     confluence' = confluence (Map.keys bridgeness') 3 True False
 
@@ -118,7 +118,6 @@ cooc2graphWith' doPartitions distance threshold myCooc = do
                     diag bridgeness' confluence' partitions
 
 
-
 doDistanceMap :: Distance
               -> Threshold
               -> HashMap (NgramsTerm, NgramsTerm) Int
@@ -126,7 +125,7 @@ doDistanceMap :: Distance
                  , Map (Index, Index) Int
                  , Map NgramsTerm Index
                  )
-doDistanceMap distance threshold myCooc = (distanceMap, toIndex ti diag, ti)
+doDistanceMap Distributional threshold myCooc = (distanceMap, toIndex ti diag, ti)
   where
     -- TODO remove below
     (diag, theMatrix) = Map.partitionWithKey (\(x,y) _ -> x == y)
@@ -136,43 +135,45 @@ doDistanceMap distance threshold myCooc = (distanceMap, toIndex ti diag, ti)
     (ti, _it) = createIndices theMatrix
     tiSize  = Map.size ti
 
+{-
     matCooc = case distance of  -- Shape of the Matrix
                 Conditional    -> map2mat Triangle 0 tiSize
                 Distributional -> map2mat Square   0 tiSize
-            {-$ case distance of   -- Removing the Diagonal ?
-                Conditional     -> Map.filterWithKey (\(a,b) _ -> a /= b)
-                Distributional  -> Map.filterWithKey (\(a,b) _ -> a /= b)
-                -}
             $ toIndex ti theMatrix
-
     similarities = measure distance matCooc
+-}
+
+    similarities = measure Distributional
+                 $ map2mat Square 0 tiSize
+                 $ toIndex ti theMatrix
+
     links = round (let n :: Double = fromIntegral tiSize in n * log n)
 
     distanceMap = Map.fromList
                 $ List.take links
                 $ List.sortOn snd
                 $ Map.toList
+                $ edgesFilter
                 $ Map.filter (> threshold)
                 $ mat2map similarities
 
+doDistanceMap Conditional _threshold myCooc = (distanceMap, toIndex ti myCooc', ti)
+  where
+    myCooc' = Map.fromList $ HashMap.toList myCooc
+    (ti, _it) = createIndices myCooc'
+    -- tiSize  = Map.size ti
 
+    -- links = round (let n :: Double = fromIntegral tiSize in n * log n)
+
+    distanceMap = toIndex ti
+                $ Map.fromList
+                -- $ List.take links
+                -- $ List.sortOn snd
+                $ HashMap.toList
+                -- $ HashMap.filter (> threshold)
+                $ conditional myCooc
 
 
-------------------------------------------------------------------------
-------------------------------------------------------------------------
-data ClustersParams = ClustersParams { bridgness :: Double
-                                     , louvain   :: Text
-                                     } deriving (Show)
-
-clustersParams :: Int -> ClustersParams
-clustersParams x = ClustersParams (fromIntegral x) "0.00000001" -- y
-  {- where
-    y | x < 100  = "0.000001"
-      | x < 350  = "0.000001"
-      | x < 500  = "0.000001"
-      | x < 1000 = "0.000001"
-      | otherwise = "1"
- -}
 
 ----------------------------------------------------------
 -- | From data to Graph
@@ -188,7 +189,8 @@ data2graph :: ToComId a
            -> Graph
 data2graph labels occurences bridge conf partitions = Graph { _graph_nodes = nodes
                                                             , _graph_edges = edges
-                                                       , _graph_metadata = Nothing }
+                                                            , _graph_metadata = Nothing
+                                                            }
   where
 
     community_id_by_node_id = Map.fromList
@@ -215,14 +217,15 @@ data2graph labels occurences bridge conf partitions = Graph { _graph_nodes = nod
 
     edges = [ Edge { edge_source = cs (show s)
                        , edge_target = cs (show t)
-                       , edge_weight =  d
+                       , edge_weight = weight
                        , edge_confluence = maybe 0 identity $ Map.lookup (s,t) conf
                    -- , edge_confluence = maybe (panic "E: data2graph edges") identity $ Map.lookup (s,t) conf
                        , edge_id     = cs (show i)
                    }
-                   | (i, ((s,t), d)) <- zip ([0..]::[Integer] )
+            | (i, ((s,t), weight)) <- zip ([0..]::[Integer] )
                                      (Map.toList bridge)
-                   , s /= t, d > 0
+            , s /= t
+            , weight > 0
             ]
 
 

src/Gargantext/Core/Viz/Graph/Utils.hs

@@ -17,14 +17,16 @@ These functions are used for Vector.Matrix only.
 module Gargantext.Core.Viz.Graph.Utils
   where
 
+import Data.Map (Map)
 import Data.Matrix hiding (identity)
-
 import Data.Vector (Vector)
-import qualified Data.Vector as V
-
 import qualified Data.List   as L
+import qualified Data.Map    as Map
 import Gargantext.Prelude
-
+import Data.List (unzip)
+import qualified Data.Vector as V
+import Data.Maybe (catMaybes)
+import qualified Data.Set    as Set
 ------------------------------------------------------------------------
 -- | Some utils to build the matrix from cooccurrence results
 
@@ -63,8 +65,35 @@ toListsWithIndex m = concat' $ zip [1..] $ map (\c -> zip [1..] c) $ toLists m
     concat' :: [(Int, [(Int, a)])] -> [((Int, Int), a)]
     concat' xs = L.concat $ map (\(x, ys) -> map (\(y, a) -> ((x,y), a)) ys ) xs
 
+------------------------------------------------------------------------
+-- Utils to manage Graphs
 
-
-
+edgesFilter :: (Ord a, Ord b) => Map (a,a) b -> Map (a,a) b
+edgesFilter m = Map.fromList $ catMaybes results
+  where
+    results = [ let
+                  ij = Map.lookup (i,j) m
+                  ji = Map.lookup (j,i) m
+                  in getMax (i,j) ij ji
+              | i <- keys
+              , j <- keys
+              , i < j
+              ]
+    keys    = Set.toList $ Set.fromList (x <> y)
+    (x,y)   = unzip $ Map.keys m
+
+
+
+
+getMax :: Ord b
+       => (a,a)
+       -> Maybe b
+       -> Maybe b
+       -> Maybe ((a,a), b)
+getMax (i,j) (Just d) Nothing   = Just ((i,j), d)
+getMax (i,j) Nothing (Just d)   = Just ((j,i), d)
+getMax ij   (Just di) (Just dj) = if di >= dj then getMax ij (Just di) Nothing
+                                              else getMax ij Nothing   (Just dj)
+getMax _ _ _ = Nothing