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New similarity measure for inter-temporal matching added named WeightedLogSim Adapted...
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1 {-|
2 Module : Gargantext.Core.Viz.Phylo.PhyloTools
3 Description : Module dedicated to all the tools needed for making a Phylo
4 Copyright : (c) CNRS, 2017-Present
5 License : AGPL + CECILL v3
6 Maintainer : team@gargantext.org
7 Stability : experimental
8 Portability : POSIX
9 -}
10
11 {-# LANGUAGE ViewPatterns #-}
12
13 module Gargantext.Core.Viz.Phylo.PhyloTools where
14
15 import Data.Vector (Vector, elemIndex)
16 import Data.List (sort, concat, null, union, (++), tails, sortOn, nub, init, tail, partition, tails, nubBy, group)
17 import Data.Set (Set, disjoint)
18 import Data.Map (Map, elems, fromList, unionWith, keys, member, (!), filterWithKey, fromListWith, empty, restrictKeys)
19 import Data.String (String)
20 import Data.Text (Text)
21
22 import Prelude (floor)
23
24 import Gargantext.Prelude
25 import Gargantext.Core.Viz.AdaptativePhylo
26 import Text.Printf
27
28
29 import Debug.Trace (trace)
30 import Control.Lens hiding (Level)
31
32 import qualified Data.Vector as Vector
33 import qualified Data.List as List
34 import qualified Data.Set as Set
35 import qualified Data.Map as Map
36 import qualified Data.Text as Text
37
38 ------------
39 -- | Io | --
40 ------------
41
42 -- | To print an important message as an IO()
43 printIOMsg :: String -> IO ()
44 printIOMsg msg =
45 putStrLn ( "\n"
46 <> "------------"
47 <> "\n"
48 <> "-- | " <> msg <> "\n" )
49
50
51 -- | To print a comment as an IO()
52 printIOComment :: String -> IO ()
53 printIOComment cmt =
54 putStrLn ( "\n" <> cmt <> "\n" )
55
56
57 --------------
58 -- | Misc | --
59 --------------
60
61 -- truncate' :: Double -> Int -> Double
62 -- truncate' x n = (fromIntegral (floor (x * t))) / t
63 -- where t = 10^n
64
65 truncate' :: Double -> Int -> Double
66 truncate' x n = (fromIntegral $ (floor (x * t) :: Int)) / t
67 where
68 --------------
69 t :: Double
70 t = 10 ^n
71
72 getInMap :: Int -> Map Int Double -> Double
73 getInMap k m =
74 if (member k m)
75 then m ! k
76 else 0
77
78 roundToStr :: (PrintfArg a, Floating a) => Int -> a -> String
79 roundToStr = printf "%0.*f"
80
81
82 countSup :: Double -> [Double] -> Int
83 countSup s l = length $ filter (>s) l
84
85
86 dropByIdx :: Int -> [a] -> [a]
87 dropByIdx k l = take k l ++ drop (k+1) l
88
89
90 elemIndex' :: Eq a => a -> [a] -> Int
91 elemIndex' e l = case (List.elemIndex e l) of
92 Nothing -> panic ("[ERR][Viz.Phylo.PhyloTools] element not in list")
93 Just i -> i
94
95
96 commonPrefix :: Eq a => [a] -> [a] -> [a] -> [a]
97 commonPrefix lst lst' acc =
98 if (null lst || null lst')
99 then acc
100 else if (head' "commonPrefix" lst == head' "commonPrefix" lst')
101 then commonPrefix (tail lst) (tail lst') (acc ++ [head' "commonPrefix" lst])
102 else acc
103
104
105 ---------------------
106 -- | Foundations | --
107 ---------------------
108
109
110 -- | Is this Ngrams a Foundations Root ?
111 isRoots :: Ngrams -> Vector Ngrams -> Bool
112 isRoots n ns = Vector.elem n ns
113
114 -- | To transform a list of nrams into a list of foundation's index
115 ngramsToIdx :: [Ngrams] -> Vector Ngrams -> [Int]
116 ngramsToIdx ns fdt = map (\n -> fromJust $ elemIndex n fdt) ns
117
118 -- | To transform a list of Ngrams Indexes into a Label
119 ngramsToLabel :: Vector Ngrams -> [Int] -> Text
120 ngramsToLabel ngrams l = Text.unwords $ tail' "ngramsToLabel" $ concat $ map (\n -> ["|",n]) $ ngramsToText ngrams l
121
122 idxToLabel :: [Int] -> String
123 idxToLabel l = List.unwords $ tail' "idxToLabel" $ concat $ map (\n -> ["|",show n]) l
124
125 idxToLabel' :: [Double] -> String
126 idxToLabel' l = List.unwords $ tail' "idxToLabel" $ concat $ map (\n -> ["|",show n]) l
127
128 -- | To transform a list of Ngrams Indexes into a list of Text
129 ngramsToText :: Vector Ngrams -> [Int] -> [Text]
130 ngramsToText ngrams l = map (\idx -> ngrams Vector.! idx) l
131
132
133 --------------
134 -- | Time | --
135 --------------
136
137 -- | To transform a list of periods into a set of Dates
138 periodsToYears :: [(Date,Date)] -> Set Date
139 periodsToYears periods = (Set.fromList . sort . concat)
140 $ map (\(d,d') -> [d..d']) periods
141
142
143 findBounds :: [Date] -> (Date,Date)
144 findBounds dates =
145 let dates' = sort dates
146 in (head' "findBounds" dates', last' "findBounds" dates')
147
148
149 toPeriods :: [Date] -> Int -> Int -> [(Date,Date)]
150 toPeriods dates p s =
151 let (start,end) = findBounds dates
152 in map (\dates' -> (head' "toPeriods" dates', last' "toPeriods" dates'))
153 $ chunkAlong p s [start .. end]
154
155
156 -- | Get a regular & ascendante timeScale from a given list of dates
157 toTimeScale :: [Date] -> Int -> [Date]
158 toTimeScale dates step =
159 let (start,end) = findBounds dates
160 in [start, (start + step) .. end]
161
162
163 getTimeStep :: TimeUnit -> Int
164 getTimeStep time = case time of
165 Year _ s _ -> s
166
167 getTimePeriod :: TimeUnit -> Int
168 getTimePeriod time = case time of
169 Year p _ _ -> p
170
171 getTimeFrame :: TimeUnit -> Int
172 getTimeFrame time = case time of
173 Year _ _ f -> f
174
175 -------------
176 -- | Fis | --
177 -------------
178
179
180 -- | To find if l' is nested in l
181 isNested :: Eq a => [a] -> [a] -> Bool
182 isNested l l'
183 | null l' = True
184 | length l' > length l = False
185 | (union l l') == l = True
186 | otherwise = False
187
188
189 -- | To filter Fis with small Support but by keeping non empty Periods
190 keepFilled :: (Int -> [a] -> [a]) -> Int -> [a] -> [a]
191 keepFilled f thr l = if (null $ f thr l) && (not $ null l)
192 then keepFilled f (thr - 1) l
193 else f thr l
194
195
196 traceClique :: Map (Date, Date) [PhyloClique] -> String
197 traceClique mFis = foldl (\msg cpt -> msg <> show (countSup cpt cliques) <> " (>" <> show (cpt) <> ") " ) "" [1..6]
198 where
199 --------------------------------------
200 cliques :: [Double]
201 cliques = sort $ map (fromIntegral . length . _phyloClique_nodes) $ concat $ elems mFis
202 --------------------------------------
203
204
205 traceSupport :: Map (Date, Date) [PhyloClique] -> String
206 traceSupport mFis = foldl (\msg cpt -> msg <> show (countSup cpt supports) <> " (>" <> show (cpt) <> ") " ) "" [1..6]
207 where
208 --------------------------------------
209 supports :: [Double]
210 supports = sort $ map (fromIntegral . _phyloClique_support) $ concat $ elems mFis
211 --------------------------------------
212
213
214 traceFis :: [Char] -> Map (Date, Date) [PhyloClique] -> Map (Date, Date) [PhyloClique]
215 traceFis msg mFis = trace ( "\n" <> "-- | " <> msg <> " : " <> show (sum $ map length $ elems mFis) <> "\n"
216 <> "Support : " <> (traceSupport mFis) <> "\n"
217 <> "Nb Ngrams : " <> (traceClique mFis) <> "\n" ) mFis
218
219
220 ---------------
221 -- | Clique| --
222 ---------------
223
224
225 getCliqueSupport :: Clique -> Int
226 getCliqueSupport unit = case unit of
227 Fis s _ -> s
228 MaxClique _ -> 0
229
230 getCliqueSize :: Clique -> Int
231 getCliqueSize unit = case unit of
232 Fis _ s -> s
233 MaxClique s -> s
234
235
236 --------------
237 -- | Cooc | --
238 --------------
239
240 listToCombi' :: [a] -> [(a,a)]
241 listToCombi' l = [(x,y) | (x:rest) <- tails l, y <- rest]
242
243 listToEqual' :: Eq a => [a] -> [(a,a)]
244 listToEqual' l = [(x,y) | x <- l, y <- l, x == y]
245
246 listToKeys :: Eq a => [a] -> [(a,a)]
247 listToKeys lst = (listToCombi' lst) ++ (listToEqual' lst)
248
249 listToMatrix :: [Int] -> Map (Int,Int) Double
250 listToMatrix lst = fromList $ map (\k -> (k,1)) $ listToKeys $ sort lst
251
252 listToMatrix' :: [Ngrams] -> Map (Ngrams,Ngrams) Int
253 listToMatrix' lst = fromList $ map (\k -> (k,1)) $ listToKeys $ sort lst
254
255 listToSeq :: Eq a => [a] -> [(a,a)]
256 listToSeq l = nubBy (\x y -> fst x == fst y) $ [ (x,y) | (x:rest) <- tails l, y <- rest ]
257
258 sumCooc :: Cooc -> Cooc -> Cooc
259 sumCooc cooc cooc' = unionWith (+) cooc cooc'
260
261 getTrace :: Cooc -> Double
262 getTrace cooc = sum $ elems $ filterWithKey (\(k,k') _ -> k == k') cooc
263
264 coocToDiago :: Cooc -> Cooc
265 coocToDiago cooc = filterWithKey (\(k,k') _ -> k == k') cooc
266
267 -- | To build the local cooc matrix of each phylogroup
268 ngramsToCooc :: [Int] -> [Cooc] -> Cooc
269 ngramsToCooc ngrams coocs =
270 let cooc = foldl (\acc cooc' -> sumCooc acc cooc') empty coocs
271 pairs = listToKeys ngrams
272 in filterWithKey (\k _ -> elem k pairs) cooc
273
274
275 --------------------
276 -- | PhyloGroup | --
277 --------------------
278
279 getGroupId :: PhyloGroup -> PhyloGroupId
280 getGroupId g = ((g ^. phylo_groupPeriod, g ^. phylo_groupLevel), g ^. phylo_groupIndex)
281
282 idToPrd :: PhyloGroupId -> PhyloPeriodId
283 idToPrd id = (fst . fst) id
284
285 groupByField :: Ord a => (PhyloGroup -> a) -> [PhyloGroup] -> Map a [PhyloGroup]
286 groupByField toField groups = fromListWith (++) $ map (\g -> (toField g, [g])) groups
287
288 getPeriodPointers :: Filiation -> PhyloGroup -> [Pointer]
289 getPeriodPointers fil g =
290 case fil of
291 ToChilds -> g ^. phylo_groupPeriodChilds
292 ToParents -> g ^. phylo_groupPeriodParents
293
294 filterProximity :: Proximity -> Double -> Double -> Bool
295 filterProximity proximity thr local =
296 case proximity of
297 WeightedLogJaccard _ -> local >= thr
298 WeightedLogSim _ -> local >= thr
299 Hamming -> undefined
300
301 getProximityName :: Proximity -> String
302 getProximityName proximity =
303 case proximity of
304 WeightedLogJaccard _ -> "WLJaccard"
305 WeightedLogSim _ -> "WeightedLogSim"
306 Hamming -> "Hamming"
307
308 ---------------
309 -- | Phylo | --
310 ---------------
311
312 addPointers :: Filiation -> PointerType -> [Pointer] -> PhyloGroup -> PhyloGroup
313 addPointers fil pty pointers g =
314 case pty of
315 TemporalPointer -> case fil of
316 ToChilds -> g & phylo_groupPeriodChilds .~ pointers
317 ToParents -> g & phylo_groupPeriodParents .~ pointers
318 LevelPointer -> case fil of
319 ToChilds -> g & phylo_groupLevelChilds .~ pointers
320 ToParents -> g & phylo_groupLevelParents .~ pointers
321
322
323 getPeriodIds :: Phylo -> [(Date,Date)]
324 getPeriodIds phylo = sortOn fst
325 $ keys
326 $ phylo ^. phylo_periods
327
328 getLevelParentId :: PhyloGroup -> PhyloGroupId
329 getLevelParentId g = fst $ head' "getLevelParentId" $ g ^. phylo_groupLevelParents
330
331 getLastLevel :: Phylo -> Level
332 getLastLevel phylo = last' "lastLevel" $ getLevels phylo
333
334 getLevels :: Phylo -> [Level]
335 getLevels phylo = nub
336 $ map snd
337 $ keys $ view ( phylo_periods
338 . traverse
339 . phylo_periodLevels ) phylo
340
341 getSeaElevation :: Phylo -> SeaElevation
342 getSeaElevation phylo = seaElevation (getConfig phylo)
343
344
345 getConfig :: Phylo -> Config
346 getConfig phylo = (phylo ^. phylo_param) ^. phyloParam_config
347
348
349 getRoots :: Phylo -> Vector Ngrams
350 getRoots phylo = (phylo ^. phylo_foundations) ^. foundations_roots
351
352 phyloToLastBranches :: Phylo -> [[PhyloGroup]]
353 phyloToLastBranches phylo = elems
354 $ fromListWith (++)
355 $ map (\g -> (g ^. phylo_groupBranchId, [g]))
356 $ getGroupsFromLevel (last' "byBranches" $ getLevels phylo) phylo
357
358 getGroupsFromLevel :: Level -> Phylo -> [PhyloGroup]
359 getGroupsFromLevel lvl phylo =
360 elems $ view ( phylo_periods
361 . traverse
362 . phylo_periodLevels
363 . traverse
364 . filtered (\phyloLvl -> phyloLvl ^. phylo_levelLevel == lvl)
365 . phylo_levelGroups ) phylo
366
367
368 getGroupsFromLevelPeriods :: Level -> [PhyloPeriodId] -> Phylo -> [PhyloGroup]
369 getGroupsFromLevelPeriods lvl periods phylo =
370 elems $ view ( phylo_periods
371 . traverse
372 . filtered (\phyloPrd -> elem (phyloPrd ^. phylo_periodPeriod) periods)
373 . phylo_periodLevels
374 . traverse
375 . filtered (\phyloLvl -> phyloLvl ^. phylo_levelLevel == lvl)
376 . phylo_levelGroups ) phylo
377
378
379 getGroupsFromPeriods :: Level -> Map PhyloPeriodId PhyloPeriod -> [PhyloGroup]
380 getGroupsFromPeriods lvl periods =
381 elems $ view ( traverse
382 . phylo_periodLevels
383 . traverse
384 . filtered (\phyloLvl -> phyloLvl ^. phylo_levelLevel == lvl)
385 . phylo_levelGroups ) periods
386
387
388 updatePhyloGroups :: Level -> Map PhyloGroupId PhyloGroup -> Phylo -> Phylo
389 updatePhyloGroups lvl m phylo =
390 over ( phylo_periods
391 . traverse
392 . phylo_periodLevels
393 . traverse
394 . filtered (\phyloLvl -> phyloLvl ^. phylo_levelLevel == lvl)
395 . phylo_levelGroups
396 . traverse
397 ) (\g ->
398 let id = getGroupId g
399 in
400 if member id m
401 then m ! id
402 else g ) phylo
403
404
405 traceToPhylo :: Level -> Phylo -> Phylo
406 traceToPhylo lvl phylo =
407 trace ("\n" <> "-- | End of phylo making at level " <> show (lvl) <> " with "
408 <> show (length $ getGroupsFromLevel lvl phylo) <> " groups and "
409 <> show (length $ nub $ map _phylo_groupBranchId $ getGroupsFromLevel lvl phylo) <> " branches" <> "\n") phylo
410
411 --------------------
412 -- | Clustering | --
413 --------------------
414
415 mergeBranchIds :: [[Int]] -> [Int]
416 mergeBranchIds ids = (head' "mergeBranchIds" . sort . mostFreq') ids
417 where
418 -- | 2) find the most Up Left ids in the hierarchy of similarity
419 -- mostUpLeft :: [[Int]] -> [[Int]]
420 -- mostUpLeft ids' =
421 -- let groupIds = (map (\gIds -> (length $ head' "gIds" gIds, head' "gIds" gIds)) . groupBy (\id id' -> length id == length id') . sortOn length) ids'
422 -- inf = (fst . minimum) groupIds
423 -- in map snd $ filter (\gIds -> fst gIds == inf) groupIds
424 -- | 1) find the most frequent ids
425 mostFreq' :: [[Int]] -> [[Int]]
426 mostFreq' ids' =
427 let groupIds = (map (\gIds -> (length gIds, head' "gIds" gIds)) . group . sort) ids'
428 sup = (fst . maximum) groupIds
429 in map snd $ filter (\gIds -> fst gIds == sup) groupIds
430
431
432 mergeMeta :: [Int] -> [PhyloGroup] -> Map Text [Double]
433 mergeMeta bId groups =
434 let ego = head' "mergeMeta" $ filter (\g -> (snd (g ^. phylo_groupBranchId)) == bId) groups
435 in fromList [("breaks",(ego ^. phylo_groupMeta) ! "breaks"),("seaLevels",(ego ^. phylo_groupMeta) ! "seaLevels")]
436
437
438 groupsToBranches :: Map PhyloGroupId PhyloGroup -> [[PhyloGroup]]
439 groupsToBranches groups =
440 {- run the related component algorithm -}
441 let egos = map (\g -> [getGroupId g]
442 ++ (map fst $ g ^. phylo_groupPeriodParents)
443 ++ (map fst $ g ^. phylo_groupPeriodChilds)
444 ++ (map fst $ g ^. phylo_groupAncestors)) $ elems groups
445 graph = relatedComponents egos
446 {- update each group's branch id -}
447 in map (\ids ->
448 let groups' = elems $ restrictKeys groups (Set.fromList ids)
449 bId = mergeBranchIds $ map (\g -> snd $ g ^. phylo_groupBranchId) groups'
450 in map (\g -> g & phylo_groupBranchId %~ (\(lvl,_) -> (lvl,bId))) groups') graph
451
452 relatedComponents :: Ord a => [[a]] -> [[a]]
453 relatedComponents graph = foldl' (\acc groups ->
454 if (null acc)
455 then acc ++ [groups]
456 else
457 let acc' = partition (\groups' -> disjoint (Set.fromList groups') (Set.fromList groups)) acc
458 in (fst acc') ++ [nub $ concat $ (snd acc') ++ [groups]]) [] graph
459
460 toRelatedComponents :: [PhyloGroup] -> [((PhyloGroup,PhyloGroup),Double)] -> [[PhyloGroup]]
461 toRelatedComponents nodes edges =
462 let ref = fromList $ map (\g -> (getGroupId g, g)) nodes
463 clusters = relatedComponents $ ((map (\((g,g'),_) -> [getGroupId g, getGroupId g']) edges) ++ (map (\g -> [getGroupId g]) nodes))
464 in map (\cluster -> map (\gId -> ref ! gId) cluster) clusters
465
466
467 traceSynchronyEnd :: Phylo -> Phylo
468 traceSynchronyEnd phylo =
469 trace ( "-- | End synchronic clustering at level " <> show (getLastLevel phylo)
470 <> " with " <> show (length $ getGroupsFromLevel (getLastLevel phylo) phylo) <> " groups"
471 <> " and " <> show (length $ nub $ map _phylo_groupBranchId $ getGroupsFromLevel (getLastLevel phylo) phylo) <> " branches"
472 <> "\n" ) phylo
473
474 traceSynchronyStart :: Phylo -> Phylo
475 traceSynchronyStart phylo =
476 trace ( "\n" <> "-- | Start synchronic clustering at level " <> show (getLastLevel phylo)
477 <> " with " <> show (length $ getGroupsFromLevel (getLastLevel phylo) phylo) <> " groups"
478 <> " and " <> show (length $ nub $ map _phylo_groupBranchId $ getGroupsFromLevel (getLastLevel phylo) phylo) <> " branches"
479 <> "\n" ) phylo
480
481
482 -------------------
483 -- | Proximity | --
484 -------------------
485
486 getSensibility :: Proximity -> Double
487 getSensibility proxi = case proxi of
488 WeightedLogJaccard s -> s
489 WeightedLogSim s -> s
490 Hamming -> undefined
491
492 ----------------
493 -- | Branch | --
494 ----------------
495
496 intersectInit :: Eq a => [a] -> [a] -> [a] -> [a]
497 intersectInit acc lst lst' =
498 if (null lst) || (null lst')
499 then acc
500 else if (head' "intersectInit" lst) == (head' "intersectInit" lst')
501 then intersectInit (acc ++ [head' "intersectInit" lst]) (tail lst) (tail lst')
502 else acc
503
504 branchIdsToProximity :: PhyloBranchId -> PhyloBranchId -> Double -> Double -> Double
505 branchIdsToProximity id id' thrInit thrStep = thrInit + thrStep * (fromIntegral $ length $ intersectInit [] (snd id) (snd id'))
506
507 ngramsInBranches :: [[PhyloGroup]] -> [Int]
508 ngramsInBranches branches = nub $ foldl (\acc g -> acc ++ (g ^. phylo_groupNgrams)) [] $ concat branches
509
510
511 traceMatchSuccess :: Double -> Double -> Double -> [[[PhyloGroup]]] -> [[[PhyloGroup]]]
512 traceMatchSuccess thr qua qua' nextBranches =
513 trace ( "\n" <> "-- local branches : " <> (init $ show ((init . init . snd)
514 $ (head' "trace" $ head' "trace" $ head' "trace" nextBranches) ^. phylo_groupBranchId))
515 <> ",(1.." <> show (length nextBranches) <> ")]"
516 <> " | " <> show ((length . concat . concat) nextBranches) <> " groups" <> "\n"
517 <> " - splited with success in " <> show (map length nextBranches) <> " sub-branches" <> "\n"
518 <> " - for the local threshold " <> show (thr) <> " ( quality : " <> show (qua) <> " < " <> show(qua') <> ")\n" ) nextBranches
519
520
521 traceMatchFailure :: Double -> Double -> Double -> [[PhyloGroup]] -> [[PhyloGroup]]
522 traceMatchFailure thr qua qua' branches =
523 trace ( "\n" <> "-- local branches : " <> (init $ show ((init . snd) $ (head' "trace" $ head' "trace" branches) ^. phylo_groupBranchId))
524 <> ",(1.." <> show (length branches) <> ")]"
525 <> " | " <> show (length $ concat branches) <> " groups" <> "\n"
526 <> " - split with failure for the local threshold " <> show (thr) <> " ( quality : " <> show (qua) <> " > " <> show(qua') <> ")\n"
527 ) branches
528
529
530 traceMatchNoSplit :: [[PhyloGroup]] -> [[PhyloGroup]]
531 traceMatchNoSplit branches =
532 trace ( "\n" <> "-- local branches : " <> (init $ show ((init . snd) $ (head' "trace" $ head' "trace" branches) ^. phylo_groupBranchId))
533 <> ",(1.." <> show (length branches) <> ")]"
534 <> " | " <> show (length $ concat branches) <> " groups" <> "\n"
535 <> " - unable to split in smaller branches" <> "\n"
536 ) branches
537
538
539 traceMatchLimit :: [[PhyloGroup]] -> [[PhyloGroup]]
540 traceMatchLimit branches =
541 trace ( "\n" <> "-- local branches : " <> (init $ show ((init . snd) $ (head' "trace" $ head' "trace" branches) ^. phylo_groupBranchId))
542 <> ",(1.." <> show (length branches) <> ")]"
543 <> " | " <> show (length $ concat branches) <> " groups" <> "\n"
544 <> " - unable to increase the threshold above 1" <> "\n"
545 ) branches
546
547
548 traceMatchEnd :: [PhyloGroup] -> [PhyloGroup]
549 traceMatchEnd groups =
550 trace ("\n" <> "-- | End temporal matching with " <> show (length $ nub $ map (\g -> g ^. phylo_groupBranchId) groups)
551 <> " branches and " <> show (length groups) <> " groups" <> "\n") groups
552
553
554 traceTemporalMatching :: [PhyloGroup] -> [PhyloGroup]
555 traceTemporalMatching groups =
556 trace ( "\n" <> "-- | Start temporal matching for " <> show(length groups) <> " groups" <> "\n") groups
557
558
559 traceGroupsProxi :: Map (PhyloGroupId,PhyloGroupId) Double -> Map (PhyloGroupId,PhyloGroupId) Double
560 traceGroupsProxi m =
561 trace ( "\n" <> "-- | " <> show(Map.size m) <> " computed pairs of groups proximity" <> "\n") m