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{-# LANGUAGE NoMonomorphismRestriction #-}
import System.Random
import Control.Monad.State
import Data.Maybe
import Data.List
import Data.Tuple
import Graphics.Rendering.Chart.Easy
import Graphics.Rendering.Chart.Backend.Cairo
import Data.Colour.Names
import Diagrams.Prelude
import Diagrams.Backend.SVG.CmdLine
-----------------------------------------
-- Network construction and properties --
-----------------------------------------
type Node = Int
type Edge = (Node, Node)
type Adjacency = [Node]
type Network = [Adjacency]
hasNode :: Node -> Network -> Bool
hasNode v n = v < (length n)
addNode :: Network -> Network
addNode n = n <> [[]]
addHalfedge :: Node -> Node -> Network -> Network
addHalfedge v1 v2 n = (take v1 n) <> [(n !! v1) ++ [v2]] ++ (drop (v1 + 1) n)
addEdge :: Edge -> Network -> Network
addEdge (v1, v2) n = addHalfedge v1 v2 (addHalfedge v2 v1 n)
getNodes :: Network -> [Node]
getNodes n = [0..(length n - 1)]
getEdges :: Network -> [Edge]
getEdges n = foldr (<>) [] $ map (\i -> map (\j -> (fst i, j)) (snd i)) (zip (getNodes n) n)
getNeighbors :: Network -> Node -> Adjacency
getNeighbors n v = n !! v
emptyNetwork :: Int -> Network
emptyNetwork 0 = []
emptyNetwork l = addNode (emptyNetwork (l - 1))
-- | Take a network and add z short edges to each bond.
addShortEdges :: Int -> Network -> Network
addShortEdges 0 n = n
addShortEdges 1 n = n
addShortEdges z n = let
l = length n
addZEdge v = addEdge (v, mod (v + quot z 2) l)
in addShortEdges (z - 2) (foldr addZEdge n [0..(l - 1)])
-- | Lists all possible long edges.
possibleLongEdges l z = let
d = quot z 2 + 1
e v = (\u -> (v, mod (v + u) l)) <$> [d..(l - d)]
in foldr (<>) [] $ e <$> [0..(l - 1)]
-- | Take a random element from a list, removing it from the list.
randomChoice :: RandomGen g => State ([a], g) (Maybe a)
randomChoice = get >>= (\(xs, g) -> if (length xs == 0) then (return Nothing) else (let (r, g2) = randomR (0, length xs - 1) g in (put ((take r xs) ++ (drop (r+1) xs), g2)) >> return (Just (xs !! r))))
-- | Returns a list of randomly chosen values with no repeats.
randomChoices :: RandomGen g => Int -> State ([a], g) [a]
randomChoices n = state (\si ->
let (maybeVals, sf) = runState (sequence $ replicate n randomChoice) si
in (catMaybes maybeVals, sf)
)
-- | Adds the appropriate number of long edges to a network.
addLongEdges :: (RealFrac a, RandomGen g) => Int -> Int -> a -> Network -> State g Network
addLongEdges l z p n = state (\g ->
let
nle = floor (p * fromIntegral (l * quot z 2))
(es, (_, g2)) = runState (randomChoices nle) (possibleLongEdges l z, g)
in (foldr addEdge n $ es, g2)
)
constructNetwork :: (RealFrac a, RandomGen g) => Int -> Int -> a -> State g Network
constructNetwork l z p = addLongEdges l z p $ addShortEdges z $ emptyNetwork l
----------------------------
-- Finding shortest paths --
----------------------------
pathLengths :: Network -> (Int, [Node], [Maybe Int]) -> (Int, [Node], [Maybe Int])
pathLengths n (level, curNodes, knownDists) =
let
setVertexFound node dists =
if isNothing (head after)
then (before ++ [Just level] ++ (drop 1 after))
else dists
where (before, after) = splitAt node dists
newDists = foldr setVertexFound knownDists curNodes
in (level + 1, nub $ filter (\x -> isNothing (newDists !! x)) $ foldr (<>) [] $ getNeighbors n <$> curNodes, newDists)
findPathLengthsFromNode :: Network -> Node -> [Int]
findPathLengthsFromNode n v = catMaybes $ (\(_,_,d) -> d) $ head $ dropWhile (\(_,nodes,_) -> length nodes > 0) $ iterate (pathLengths n) (0, [v], replicate (length n) Nothing)
findAllPathLengths :: Network -> [Int]
findAllPathLengths n = foldr (<>) [] $ (findPathLengthsFromNode n) <$> getNodes n
findAveragePathLength :: RealFrac a => Network -> a
findAveragePathLength n = let xs = findAllPathLengths n in fromIntegral (sum xs) / fromIntegral (length xs)
shortestPath f n i j 0 | i == j = 0
| elem (i, j) $ getEdges n = 1
| elem (j, i) $ getEdges n = 1
| otherwise = length n
shortestPath f n i j k = min (f n i j (k - 1)) (f n i k (k - 1) + f n k j (k - 1))
data NaturalTree a = NNode a (NaturalTree a) (NaturalTree a)
NNode a tl tr !!! 0 = a
NNode a tl tr !!! n =
if odd n
then tl !!! top
else tr !!! (top-1)
where top = n `div` 2
instance Functor NaturalTree where
fmap f (NNode a tl tr) = NNode (f a) (fmap f tl) (fmap f tr)
naturals r n =
NNode n
((naturals $! r2) $! (n+r))
((naturals $! r2) $! (n+r2))
where r2 = 2*r
shortestPaths n =
let
nodes = getNodes n
memo = fmap (\y -> fmap (\z -> fmap z (naturals 1 0)) y) (fmap (\x -> fmap x (naturals 1 0)) (fmap (shortestPath shortestPath' n) (naturals 1 0)))
shortestPath' n a b c = memo !!! a !!! b !!! c
in
(\i j -> shortestPath' n i j (length n - 1)) <$> nodes <*> nodes
----------------------------
-- Betweenness centrality --
----------------------------
----------------------
-- Drawing routines --
----------------------
drawNode :: Node -> Diagram B
drawNode n = named n $ fc black $ circle 0.1
drawEdge :: Edge -> (Diagram B -> Diagram B)
drawEdge (n1, n2) = withName n1 $ \b1 -> withName n2 $ \b2 -> Diagrams.Prelude.atop ((location b1 ~~ location b2))
drawNetwork :: Network -> Diagram B
drawNetwork n = atPoints (trailVertices $ regPoly (length n) 1) (map drawNode $ getNodes n) Diagrams.Prelude.# applyAll (map drawEdge $ getEdges n)
-----------------------
-- Plotting routines --
-----------------------
lengthHistogram :: Colour Double -> [Int] -> EC (Layout Double Int) ()
lengthHistogram color lengths = plot $ fmap histToPlot $ liftEC $ do
plot_hist_fill_style .= def {_fill_color = (withOpacity color 0.5)}
plot_hist_line_style .= def {_line_color = (withOpacity color 1.0)}
plot_hist_bins .= 20
plot_hist_values .= ((fromIntegral <$> lengths) :: [Double])
plot_hist_norm_func .= const id
main = do
g1 <- newStdGen
g2 <- newStdGen
void $ renderableToFile (def { _fo_format = SVG}) "01.07.hist.svg" $ fillBackground def $ toRenderable $ do
lengthHistogram blue $ shortestPaths $ evalState (constructNetwork 200 2 0.02) g1
lengthHistogram red $ shortestPaths $ evalState (constructNetwork 200 2 0.20) g2
-- mainWith (drawNetwork n)
|
