teams (empty) → 0.0.1
raw patch · 7 files changed
+1448/−0 lines, 7 filesdep +basedep +containersdep +fglsetup-changed
Dependencies added: base, containers, fgl, graphviz
Files
- Data/Teams/Examples/DecMdp.hs +25/−0
- Data/Teams/Examples/Wit79.hs +38/−0
- Data/Teams/Graph.hs +366/−0
- Data/Teams/Structure.hs +324/−0
- LICENSE +674/−0
- Setup.hs +2/−0
- teams.cabal +19/−0
+ Data/Teams/Examples/DecMdp.hs view
@@ -0,0 +1,25 @@+-- | Decentralized MDP+-- Based on an email exchange with Ashutosh Nayyar++module Data.Teams.Examples.DecMdp where+import Data.Teams.Structure ++x = mkNonReward "x"+u1 = mkNonReward "u1"+u2 = mkNonReward "u2"+r = mkReward "r"++f = mkDynamics "f"+g1 = mkControl "g1"+g2 = mkControl "g2"+d = mkDynamics "d"++dynamics t = f(t).$.(x(t) .|. if t == 1 then [] else [x(t-1), u1(t-1), u2(t-1)])+ ++ g1(t).$.(u1(t) .|. map x[1..t] ++ map u1[1..t-1])+ ++ g2(t).$.(u2(t) .|. map x[1..t] ++ map u2[1..t-1])+ ++ d(t) .$.(r(t) .|. [x(t), u1(t), u2(t)])++decMdp = mkTeamTime dynamics 4++decMdp' = simplify decMdp+
+ Data/Teams/Examples/Wit79.hs view
@@ -0,0 +1,38 @@+-- | Real time source coding +-- Based on+-- Hans S. Witsenhausen +-- "On the structure of real-time source coders,"+-- Bell Systems Technical Journal, +-- vol 58, no 6, pp 1437-1451, July-August 1979++module Data.Teams.Examples.Wit79 where++import Data.Teams.Structure ++x = mkNonReward "x"+x' = mkNonReward "x'"+y = mkNonReward "y"+m = mkNonReward "m"+r = mkReward "r"++f = mkDynamics "f"+c = mkControl "c"+g = mkControl "g"+l = mkControl "l"+d = mkDynamics "d"++dynamics t | t == 1 = f(1).$.(x(1) .|. [])+ ++ c(1).$.(y(1) .|. [x(1)])+ ++ g(1).$.(x'(1).|. [y(1)])+ ++ l(1).$.(m(1) .|. [y(1)])+ ++ d(1).$.(r(1) .|. [x(1), x'(1)])+ | otherwise = f(t).$.(x(t) .|. [x(t-1)])+ ++ c(t).$.(y(t) .|. map x[1..t] ++ map y[1..t-1])+ ++ g(t).$.(x'(t).|. [y(t), m(t-1)])+ ++ l(t).$.(m(t) .|. [y(t), m(t-1)])+ ++ d(t).$.(r(t) .|. [x(t), x'(t)])++rt = mkTeamTime dynamics 4++rt' = simplify rt+
+ Data/Teams/Graph.hs view
@@ -0,0 +1,366 @@+-- (c) Aditya Mahajan <aditya.mahajan@yale.edu>+-- | This Haskell library implements the algorithm for simplifying sequential+-- teams presented +--+-- Aditya Mahajan and Sekhar Tatikonda, A graphical modeling approach to+-- simplifying sequential teams, proceedings of 7th International Symposium on+-- Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt),+-- Control over Communication Channels (ConCom) Workshop, Seoul, South Korea,+-- June 27, 2009.+--+-- The paper can be obtained from+-- <http://pantheon.yale.edu/~am894/publications.html#concom-2009>. See+-- <http://pantheon.yale.edu/~am894/code/teams/> for a usage example.+--+-- A team is a multi-agent stochastic control problem in which all agents have a+-- common objective. A team is sequential if and only if there is a partial+-- order between all the system variables. These partial order relationship can+-- be represented using a directed graph, in particular, using a directed factor+-- graph. The variable nodes of the factor graph represent the system variables+-- and the factor nodes represent the system dynamics and control functions. The+-- structural results for these system are equivalent to simplification of the+-- factor graph. An automated algorithm for graph simplification is presented in+-- the "Data.Teams.Structure" module.+++module Data.Teams.Graph + ( -- * Classes+ Vertex (..)+ -- * Types+ , Time , Variable (..) , Factor (..) , Node + , Edge , EdgeType (..)+ , Team+ -- * Constructors for nodes+ , mkVertex , mkReward , mkNonReward , mkDynamics , mkControl+ -- * Constructor for edges+ , (.$.) , (.|.)+ -- * Constructors for teams+ , mkTeam , mkTeamTime , mkTeamTimeBy+ -- * Select specific nodes+ , selNodes , variables, rewards, factors, controls+ -- * Graph elements+ , parents , children , ancestors , ancestoral , descendants + , futureNodes , pastNodes+ -- * Display functions+ , printTeam , showTeam , graphToDot , printGraph+ -- * Utility functions for "Data.Graph.Inductive"+ , label, labels+ ) where++import qualified Data.Graph.Inductive as G+import qualified Data.GraphViz as G+import Data.Maybe (fromJust)+import Data.List (nub, intercalate, delete)+import Text.Printf (printf)++-- | Time+type Time = Int++-- | Variable nodes+data Variable = Reward String -- ^ Reward variable node+ | NonReward String -- ^ Non reard variable node+ deriving (Eq, Ord, Show)++-- | Factor Vertexs+data Factor = Dynamics String -- ^ Factor node representing system dynamics+ | Control String -- ^ Factor node representing control function+ deriving (Eq, Ord, Show)++-- | Create a sequence of nodes of a specific type+mkVertex :: (String -> a) -> String -> Time -> a+mkVertex t s = t . (s ++ ) . show++-- | Create a sequence of reward nodes+mkReward :: String -> Time -> Variable+mkReward = mkVertex Reward ++-- | Create a sequence of non reward nodes+mkNonReward :: String -> Time -> Variable+mkNonReward = mkVertex NonReward++-- | Create a sequence of system dynamics nodes+mkDynamics :: String -> Time -> Factor+mkDynamics = mkVertex Dynamics++-- | Create a sequence of control nodes+mkControl :: String -> Time -> Factor+mkControl = mkVertex Control++-- | A generic node of a graph+type Node = Either Factor Variable++-- | A type class for defining operations on all nodes+class Vertex a where+ -- | Name of node @a@+ name :: a -> String+ -- | Name of a list of nodes+ names :: [a] -> String+ -- | Check if node @a@ is a reward node+ isReward :: a -> Bool+ -- | Check if node @a@ is a non reward node+ isNonReward :: a -> Bool+ -- | Check if node @a@ is a variable node+ isVariable :: a -> Bool+ -- | Check if node @a@ is a system dynamics+ isDynamics :: a -> Bool+ -- | Check if node @a@ is a control node+ isControl :: a -> Bool+ -- | Check if node @a@ is a factor node+ isFactor :: a -> Bool+ -- | The attributes of the node. Used to contruct the dot file.+ attribute :: a -> [G.Attribute]+ -- Default implmentation+ names xs = "[" ++ intercalate ", " (map name xs) ++ "]"+ isVariable = or . sequence [isReward, isNonReward]+ isFactor = or . sequence [isControl, isDynamics]+++instance Vertex Variable where+ name (Reward a) = a+ name (NonReward a) = a+ + isReward (Reward _) = True+ isReward (NonReward _) = False++ isNonReward (Reward _) = False+ isNonReward (NonReward _) = True++ isDynamics _ = False+ isControl _ = False++ attribute (Reward a) = [G.Style G.Filled, G.FillColor (G.RGB 0 255 0)+ , G.Shape G.Circle+ , G.Label a]+ attribute (NonReward a) = [G.Shape G.Circle+ , G.Label a]++instance Vertex Factor where+ name (Dynamics a) = a+ name (Control a) = a++ isDynamics (Dynamics _) = True+ isDynamics (Control _) = False++ isControl (Dynamics _) = False+ isControl (Control _) = True++ isReward _ = False+ isNonReward _ = False++ attribute (Dynamics a) = [G.Shape G.Rectangle+ , G.Label a]+ attribute (Control a) = [G.Style G.Filled, G.FillColor (G.RGB 255 0 0)+ , G.Shape G.Rectangle+ , G.Label a]++instance (Vertex a, Vertex b) => Vertex (Either a b) where+ name = either name name+ isReward = either isReward isReward+ isNonReward = either isNonReward isNonReward+ isDynamics = either isDynamics isDynamics + isControl = either isControl isControl+ attribute = either attribute attribute++-- | An edge in a graph+type Edge = (Node, Node, EdgeType)++-- | Currently all edges are Influence edges. Future versions will have+-- belief edges.+data EdgeType = Influence | Belief deriving (Eq, Ord, Show)++-- | Since all edges are Influence edges, we do not differential between the+-- edges+edgeAttribute :: EdgeType -> [G.Attribute]+edgeAttribute _ = []++-- | Used with @(.|.)@ to specify relation between the nodes. For example, if+-- @x@ is a function of @y@ and @z@, we can write+-- +-- @f.$.(x.|.[y,z])@.++(.$.) :: Factor -> (Variable, [Variable]) -> [Edge]+(.$.) f (x,ys) = (Left f, Right x, Influence) + : map (\y -> (Right y, Left f, Influence)) ys++-- | Used with @(.$.)@ to specify relation between the nodes. For example, if+-- @x@ is a function of @y@ and @z@, we can write+--+-- @f.$.(x.|.[y,z])@.+(.|.) :: Variable -> [Variable] -> (Variable, [Variable])+(.|.) x ys = (x,ys)++infixr 4 .|.+infixr 6 .$.++-- | A sequential team as a directed acyclic factor graph (DAFG)+type Team = G.Gr Node EdgeType++-- | Construct a DAFG from a set of edges. For example, +--+-- @+-- f = 'Control' \"f\"+-- x = 'Reward' \"x\"+-- y = 'NonReward' \"y\"+-- z = 'NonReward' \"z\"+-- g = mkTeam $ f.$.(x.|.[y,z])+-- @+--+mkTeam :: [Edge] -> Team+mkTeam es = G.mkGraph nodes edges where+ (nodes,nodeMap) = G.mkNodes G.new . nub . concatMap (\(a,b,_) -> [a,b]) $ es+ edges = fromJust . G.mkEdges nodeMap $ es ++{- |To make a time homogeneous system. As an example, an MDP can be created as+follows++@+x = 'mkNonReward' \"x\"+u = 'mkNonReward' \"u\"+r = 'mkReward' \"r\"++f = 'mkDynamics' \"f\"+g = 'mkControl' \"g\"+d = 'mkDynamics' \"d\"++dynamics t = f(t-1).$.( x(t) .|. if t == 1 then [] else [x(t-1), u(t-1)] )+ ++ g(t) .$.( u(t) .|. map x[1..t] ++ map u[1..t-1] )+ ++ d(t) .$.( r(t) .|. [ x(t), u(t) ] )++mdp = 'mkTeamTime' dynamics 3+@+-}+mkTeamTime :: (Time -> [Edge]) -> Time -> Team+mkTeamTime dyn = mkTeamTimeBy [] dyn (const [])+ +{- To make a time homogeneous system with specific start and stop dynamics+As an example, a communication system with feedback can be created as+follows.++@+m = 'NonReward' \"m\"+mhat = 'NonReward' \"mhat\"+r = 'Reward' \"r\"+h = 'Dynamics' \"h\"+g = 'Control' \"g\"+d = 'Dynamics' \"d\"++x = 'mkNonReward' \"x\"+y = 'mkNonReward' \"y\"++f = 'mkControl' \"f\"+c = 'mkDynamics' \"c\"++start = h .$.( m .|. [] )+dynamics t = f(t) .$. ( x(t) .|. m : map x [1..t-1] ++ map y [1..t-1] )+ ++ c(t) .$. ( y(t) .|. [ x(t) ] )+stop t = g .$. ( mhat .|. map y [1..t] )+ ++ d .$. (r .|. [m, mhat] )++commfb = 'mkTeamTimeBy' start dynamics stop 3+-}++mkTeamTimeBy :: [Edge] -> (Time -> [Edge]) -> (Time -> [Edge]) -> Time -> Team+mkTeamTimeBy start dyn stop horizon = mkTeam nodes where+ nodes = start ++ concatMap dyn [1..horizon] ++ stop horizon+++-- * Utility functions++-- filterNodes :: (Node -> Bool) -> Team -> [G.Node] -> [G.Node]+-- filterNodes p team = filter (p . label team) ++-- | Select nodes whose label satisfy a particular predicate+selNodes :: G.Graph gr => (a -> Bool) -> gr a b -> [G.Node]+selNodes p = map G.node' . G.gsel (p.G.lab') ++-- | All variable nods+variables :: Team -> [G.Node]+variables = selNodes isVariable++-- | All reward nodes+rewards :: Team -> [G.Node]+rewards = selNodes isReward++-- | All control factors+controls :: Team -> [G.Node] +controls = selNodes isControl++-- | All factors+factors :: Team -> [G.Node]+factors = selNodes isFactor++-- * Graph relations++-- | find indices of parents from the index of a node+parents :: Team -> G.Node -> [G.Node]+parents = G.pre ++-- | find indices of children from the index of a node+children :: Team -> G.Node -> [G.Node]+children = G.suc ++-- | find indices of descendants from the index of a node+descendants :: Team -> G.Node -> [G.Node]+descendants team idx = idx `delete` G.reachable idx team++-- | find indices of ancestors from the index of a node+ancestors :: Team -> G.Node -> [G.Node]+ancestors team idx = idx `delete` G.reachable idx (G.grev team)++-- | find the indices of the ancestoral set from the indices of a given set.+ancestoral :: Team -> [G.Node] -> [G.Node]+ancestoral team = nub . concatMap (flip G.reachable (G.grev team))++-- | find the indices of future nodes that satisfy a particular predicate+futureNodes :: Team -> (Node -> Bool) -> G.Node -> [G.Node]+futureNodes team p = filter (p . label team) . descendants team++-- | find the indices of past nodes that satisfy a particular predicate+pastNodes :: Team -> (Node -> Bool) -> G.Node -> [G.Node]+pastNodes team p = filter (p . label team) . ancestors team+++-- * Display functions++-- | Pretty print the team specification+printTeam :: Team -> IO ()+printTeam = putStr . showTeam++-- | Pretty print the team specification+showTeam :: Team -> String+showTeam team = showTeamBy team isDynamics "Dynamics:" ++ "\n"+ ++ showTeamBy team isControl "Control :" ++ "\n"++showTeamBy :: Team -> (Node -> Bool) -> String -> String+showTeamBy team p str = if null equations + then "" + else unlines (header ++ equations)+ where header = [str, map (const '=') str]+ equations = map showFactor . filter (p.snd) . G.labNodes $ team+ showFactor (idx,lab) = printf "%s.$.(%s.|.%s)" (name lab)+ (names.labels team $ suc)+ (names.labels team $ pre)+ where suc = G.suc team idx+ pre = G.pre team idx+++-- * Convert to Graphviz graphs++-- | Convert the graph to a dot file+graphToDot :: Team -> G.DotGraph+graphToDot team = G.graphToDot team [] (attribute.snd) + (edgeAttribute. \(_,_,b) -> b)++-- | Convert the dot file to a pdf+printGraph :: Team -> FilePath -> IO Bool+printGraph team = G.runGraphviz (graphToDot team) G.Pdf ++-- | Extensions of Data.Graph.Inductive++-- | Label of a particular node+label :: G.Graph gr => gr a b -> G.Node -> a+label gr = fromJust . G.lab gr++-- | Labels of a list of nodes+labels :: G.Graph gr => gr a b -> [G.Node] -> [a]+labels = map . label
+ Data/Teams/Structure.hs view
@@ -0,0 +1,324 @@+-- (c) Aditya Mahajan <aditya.mahajan@yale.edu>+{- |++This module implments an automated algortihm to simplify sequential teams. The+simplification is based on conditional independences. Conditional independence+is checked using the Bayes Ball algorithm+<http://citeseer.ist.psu.edu/old/399661.html>++-}++module Data.Teams.Structure + ( module Data.Teams.Graph+ -- * Determine conditional independence+ , observations , irrelevant , determined , effective + -- * Structural results for teams+ , simplifyAt , simplifyOnce , simplify+ ) where++import Data.Teams.Graph+import qualified Data.Graph.Inductive as G+import Data.List (intersect, (\\) )+import Debug.Trace+++{-+The Bayes Ball algortihm keeps track of a state for each node. The state+consists of a mark (indicating if it has been visited from top or bottom+before), a schedule (indicating if it was scheduled to be visited from top or+bottom), and a flag (indicating if it has been visited or not). +-}++-- | Mark+data Mark = NotMarked | TopMarked | BottomMarked | BothMarked+ deriving (Eq, Ord, Show)++-- | Change mark+chMark :: Mark -> Mark -> Mark+chMark NotMarked a = a+chMark _ NotMarked = NotMarked+chMark BothMarked _ = BothMarked+chMark _ BothMarked = BothMarked+chMark BottomMarked TopMarked = BothMarked +chMark TopMarked BottomMarked = BothMarked +chMark BottomMarked BottomMarked = BottomMarked +chMark TopMarked TopMarked = TopMarked ++-- | Schedule+data Schedule = NotScheduled | TopScheduled | BottomScheduled | BothScheduled+ deriving (Eq, Ord, Show)++-- | Change schedule+chSchedule :: Schedule -> Schedule -> Schedule+chSchedule NotScheduled a = a+chSchedule _ NotScheduled = NotScheduled+chSchedule BothScheduled _ = BothScheduled+chSchedule _ BothScheduled = BothScheduled+chSchedule BottomScheduled TopScheduled = BothScheduled +chSchedule TopScheduled BottomScheduled = BothScheduled +chSchedule BottomScheduled BottomScheduled = BottomScheduled +chSchedule TopScheduled TopScheduled = TopScheduled ++-- | Visit+data Visit = Visited | NotVisited+ deriving (Eq, Ord, Show)++-- | A marked node of a graph+data Marked = VMarked Variable Mark Schedule Visit+ | FMarked Factor Mark Schedule Visit+ deriving (Eq, Ord, Show)++-- | The mark of a marked node+mark :: Marked -> Mark+mark (VMarked _ m _ _) = m+mark (FMarked _ m _ _) = m++-- | The node label of the marked node+node :: Marked -> Node+node (VMarked a _ _ _) = Right a+node (FMarked a _ _ _) = Left a++-- | The scedule of a marked node+schedule :: Marked -> Schedule+schedule (VMarked _ _ s _) = s+schedule (FMarked _ _ s _) = s++-- | The visit status of a marked node+visit :: Marked -> Visit+visit (VMarked _ _ _ v) = v+visit (FMarked _ _ _ v) = v++-- | Add a mark to a marked node+addMark :: Mark -> Marked -> Marked+addMark n (VMarked a m s v) = VMarked a (chMark m n) s v +addMark n (FMarked a m s v) = FMarked a (chMark m n) s v++-- | Add a schedule to a marked node+addSchedule :: Schedule -> Marked -> Marked+addSchedule n (VMarked a m s v) = VMarked a m (chSchedule s n) v+addSchedule n (FMarked a m s v) = FMarked a m (chSchedule s n) v++-- | Add a visit to a marked node+addVisit :: Marked -> Marked+addVisit (VMarked a m s _) = VMarked a m s Visited+addVisit (FMarked a m s _) = FMarked a m s Visited++-- | Remove all flags from the marked node+clean :: Marked -> Marked+clean (VMarked a _ _ _) = VMarked a NotMarked NotScheduled NotVisited+clean (FMarked a _ _ _) = FMarked a NotMarked NotScheduled NotVisited++-- | Check if a marked node is marked on top+isTopMarked :: Marked -> Bool+isTopMarked n = let m = mark n in (m==TopMarked || m == BothMarked)++-- | Check if a marked node is marked on bottom+isBottomMarked :: Marked -> Bool+isBottomMarked n = let m = mark n in (m==BottomMarked || m == BothMarked)++-- | Check if a marked node is scheduled+isScheduled :: Marked -> Bool+isScheduled n = NotScheduled /= schedule n++-- | Check if a marked node is visited+isVisited :: Marked -> Bool+isVisited n = Visited == visit n++-- | A class to convert a normal graph to a marked graph+class Initializable a where+ mkClean :: a -> Marked++instance Initializable Variable where+ mkClean v@(Reward _) = VMarked v NotMarked NotScheduled NotVisited+ mkClean v@(NonReward _) = VMarked v NotMarked NotScheduled NotVisited++instance Initializable Factor where+ mkClean f@(Dynamics _) = FMarked f NotMarked NotScheduled NotVisited+ mkClean f@(Control _) = FMarked f NotMarked NotScheduled NotVisited++instance (Initializable a, Initializable b) => Initializable (Either a b) where+ mkClean (Left a) = mkClean a+ mkClean (Right a) = mkClean a++-- | A marked gream+type MTeam = G.Gr Marked EdgeType++-- | All scheduled nodes+scheduledNodes :: MTeam -> [G.Node]+scheduledNodes = selNodes isScheduled++-- | The Bayes Ball algorithm+bayesBall :: Team -> [G.Node] -> [G.Node] -> MTeam+bayesBall team condition reward = doBayesBall condition mteam where+ -- Initialize all nodes as neither marked, nor scheduled, nor visited+ -- Then schedule all reward nodes to be visited from bottom.+ mteam = G.gmap initialize . G.nmap mkClean $ team+ initialize (pre,idx,lab,suc) = (pre, idx, lab', suc) + where lab' = if idx `elem` reward + then addSchedule BottomScheduled lab + else lab++-- | The main loop of the Bayes Ball algorithm+doBayesBall :: [G.Node] -> MTeam -> MTeam+doBayesBall condition gr = case scheduledNodes gr of+ -- If there are no more scheduled nodes, then we are done.+ [] -> gr+ -- Otherwise we modify the graph and loop again+ (x:_) -> doBayesBall condition (modify gr) where+ modify | isFactor . node $ mLabel = modifyFactor+ | otherwise = modifyVariable+ where mLabel = label gr x+ mSchedule = schedule mLabel++ -- If we are a factor node, let the ball pass through+ -- Do not mark the node+ modifyFactor = case mSchedule of+ BottomScheduled -> markClean . bottomThrough+ TopScheduled -> markClean . topThrough+ BothScheduled -> markClean . bothThrough+ NotScheduled -> error ("Node " ++ show x ++ " not scheduled") ++ -- If we are at a variable node, bounce the ball intelligently+ -- Then mark the nodes as visited and not scheduled.+ modifyVariable = case mSchedule of+ BottomScheduled -> markVisited . bottomVisit+ TopScheduled -> markVisited . topVisit + BothScheduled -> markVisited . bothVisit + NotScheduled -> error ("Node " ++ show x ++ " not scheduled")++ -- When the visit is from bottom, if the node is in the+ -- conditioning nodes, do nothing. Otherwise, if the bottom of the+ -- node is not marked, mark the bottom and schedule all of its+ -- parents (pass the ball). Further, if the node is not a+ -- deterministic node, mark its top and visit all its children+ -- (bounce the ball)+ bottomVisit | x `elem` condition = id+ | otherwise = checkAction . markBottom+ -- Check if a node is a deterministic node or not. + checkAction | isDeterministic gr x = id+ | otherwise = markTop+ -- When the visit is from the top, is the node is in the+ -- conditioning node and its bottom is not marked, mark its bottom+ -- and schedule all of its parents to be visisted (bounce the+ -- ball). Otherwise, if the node is not in the conditioning nodes+ -- and its top is not marked, mark its top and schedule all of its+ -- children (pass the ball)+ topVisit | x `elem` condition = markBottom+ | otherwise = markTop+ -- When the visit is both from the top and bottom, combine the+ -- actions.+ bothVisit | x `elem` condition = markBottom+ | otherwise = markTop . markBottom+ + -- To mark the top. If the top is not marked, mark the top and pass+ -- the ball throgh. Otherwise, swallow the ball.+ markTop g | not . isTopMarked . label g $ x = + topThrough (markNode TopMarked x g)+ | otherwise = g++ -- To mark the bottom. If the bottom is not marked, mark the bottom+ -- and pass the ball throgh. Otherwise, swallow the ball.+ markBottom g | not . isBottomMarked . label g $ x = + bottomThrough (markNode BottomMarked x g)+ | otherwise = g++ -- Passing the ball through+ topThrough g = scheduleNodes TopScheduled g (G.suc g x)+ bottomThrough g = scheduleNodes BottomScheduled g (G.pre g x)+ bothThrough = topThrough . bottomThrough++ -- Marking the node visited or clean+ markVisited{- g -} = visitNode x -- g + markClean {- g -} = cleanNode x -- g ++-- | Check if a node is deterministic. Currently we simply check if its parent+-- is a control node.+isDeterministic :: MTeam -> G.Node -> Bool+isDeterministic mteam x = case G.pre mteam x of + [] -> True+ [y] -> isControl. node . label mteam $ y+ _ -> False++-- | Modify a marked node+modifyNode :: (a -> Marked -> Marked) -> a -> G.Node -> MTeam -> MTeam+modifyNode f m x mteam = case G.match x mteam of+ (Nothing, _ ) -> error ("Cannot modify node " ++ show x ++ " : Not in graph")+ (Just (pre,idx,lab,suc), gr') -> (pre, idx, f m lab, suc) G.& gr'++-- | Mark a node+markNode :: Mark -> G.Node -> MTeam -> MTeam+markNode = modifyNode addMark++-- | Schedule a node+scheduleNode :: Schedule -> G.Node -> MTeam -> MTeam+scheduleNode = modifyNode addSchedule++-- | Schedule a list of nodes+scheduleNodes :: Schedule -> MTeam -> [G.Node] -> MTeam+scheduleNodes = foldr . scheduleNode ++-- | Visit a node+visitNode :: G.Node -> MTeam -> MTeam+visitNode = modifyNode (\s -> addSchedule s . addVisit) NotScheduled++-- | Clean a node of all marked+cleanNode :: G.Node -> MTeam -> MTeam+cleanNode = modifyNode (const clean) id++-- | Filter out the result from the bayes ball algortihm+result :: (Marked -> Bool) -> Team -> [G.Node] -> [G.Node] -> [G.Node]+result p team condition = map fst . filter (p.snd) . G.labNodes + . bayesBall team condition ++-- | Irrelevant nodes+-- The nodes that have not been visited from their parents are irrelevant+irrelevant :: Team -> [G.Node] -> [G.Node] -> [G.Node]+irrelevant = result (and . sequence [not.isTopMarked, isVariable.node] )++-- | Requisite observations+-- The observation nodes are thouse nodes in the condition that are marked as+-- visited+observations :: Team -> [G.Node] -> [G.Node] -> [G.Node]+observations team condition reward = condition `intersect` + result isVisited team condition reward++-- | Functionally determined nodes+-- Nodes that are irrelevant when we want to know about all variable nodes+determined :: Team -> [G.Node] -> [G.Node]+determined team var = irrelevant team var (variables team) ++-- | Effectively observed nodes+-- All the ancestors of the reward nodes that are functionally determined by+-- conditioned nodes.+effective :: Team -> [G.Node] -> [G.Node] -> [G.Node]+effective team conditioned reward = (determined team conditioned `intersect`+ ancestoral team reward) \\ conditioned++-- | The graph restructuring algorithm of the paper.+simplifyAt :: Team -> G.Node -> Team+simplifyAt team control = G.insEdges insEdges . G.delEdges delEdges $ team where+ pa = parents team control+ ch = children team control+ ne = ch ++ pa+ de = descendants team control+ rd = futureNodes team isReward control+ ob = observations team ne rd \\ ch+ ef = effective team pa rd \\ de+ delEdges = map (\ a -> (a, control)) (pa \\ ob)+ insEdges = map (\ a -> (a, control, Influence)) (ef \\ de)++-- | Simplify all nodes of the graph once+simplifyOnce :: Team -> Team +simplifyOnce team = foldr (flip simplifyAt) team (controls team) where++-- | The graph simplification aglorithm of the paper+-- I believe that this algorithm will always converge. So, I do not stop the+-- loop after a finite number of iterations. If you find an example that does+-- not converge, please let me know.+simplify :: Team -> Team+simplify team = untilEqual . zip stream $ [(1::Int)..] where+ stream = iterate simplifyOnce team+ untilEqual ((a,n):as@((b,_):_)) = trace ("Simplify : Iteration " ++ show n) $+ if G.equal a b then a+ else untilEqual as+ untilEqual _ = error "Infinite stream ended. This should not happen"
+ LICENSE view
@@ -0,0 +1,674 @@+ GNU GENERAL PUBLIC LICENSE+ Version 3, 29 June 2007++ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>+ Everyone is permitted to copy and distribute verbatim copies+ of this license document, but changing it is not allowed.++ Preamble++ The GNU General Public License is a free, copyleft license for+software and other kinds of works.++ The licenses for most software and other practical works are designed+to take away your freedom to share and change the works. By contrast,+the GNU General Public License is intended to guarantee your freedom to+share and change all versions of a program--to make sure it remains free+software for all its users. We, the Free Software Foundation, use the+GNU General Public License for most of our software; it applies also to+any other work released this way by its authors. You can apply it to+your programs, too.++ When we speak of free software, we are referring to freedom, not+price. 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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ teams.cabal view
@@ -0,0 +1,19 @@+Name: teams+Version: 0.0.1+Description: Graphical modeling tools for sequential teams+License: GPL+License-file: LICENSE+Author: Aditya Mahajan+Maintainer: aditya DOT mahajan AT yale DOT edu+Build-Type: Simple+Cabal-Version: >=1.2+Category: Algorithms, Stochastic Control+Stability: experimental+Synopsis: Graphical modeling tools for sequential teams+Library+ Build-Depends: base, fgl>=5.4, containers, graphviz>=2009.5.1+ Exposed-modules: Data.Teams.Graph+ Data.Teams.Structure+ Data.Teams.Examples.Wit79+ Data.Teams.Examples.DecMdp+ ghc-options: -Wall