diff --git a/.travis.yml b/.travis.yml new file mode 100644 --- /dev/null +++ b/.travis.yml @@ -0,0 +1,1 @@ +language: haskell diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -18,19 +18,21 @@ Arithmetic solver for the following problems: * Mixed Integer Liner Programming (MILP or MIP) +* Real Closed Field * LA(Q), LA(Z) (NOT IMPLEMENTED YET) Usage: toysolver [OPTION...] file.lp -h --help show help -v --version show version number - --solver=SOLVER mip (default), omega-test, cooper, old-mip + --solver=SOLVER mip (default), omega-test, cooper, cad, old-mip, ct ### toysat SAT-based solver for the following problems: * SAT + * Minimally Unsatisfiable Subset (MUS) * PB * Pseudo Boolean Satisfaction (PBS) * Pseudo Boolean Optimization (PBO) @@ -41,43 +43,41 @@ Usage: toysat [file.cnf||-] + toysat --mus [file.gcnf|file.cnf|-] toysat --pb [file.opb|-] toysat --wbo [file.wbo|-] toysat --maxsat [file.cnf|file.wcnf|-] - toysat --lp [file.lp|-] - -### lp2yices + toysat --lp [file.lp|file.mps|-] -Converter from LP file to Yices input file. +PB'12 competition result: -Usage: lp2yice [file.lp|-] +* toysat placed 2nd in PARTIAL-BIGINT-LIN and SOFT-BIGINT-LIN categories +* toysat placed 4th in PARTIAL-SMALLINT-LIN and SOFT-SMALLINT-LIN categories +* toysat placed 8th in OPT-BIGINT-LIN category - -h --help show help - --optimize output optimiality condition which uses quantifiers - --no-check do not output "(check)" +### toyfmf -### cnf2lp +SAT-based finite model finder for first order logic (FOL). -Converter from DIMACS .cnf file to .lp file. +Usage: -Usage: cnf2lp [file.cnf|-] + toyfmf file.tptp size -### maxsat2lp +### lpconvert -Converter from .cnf/.wcnf file to .lp file. +Converter between LP/MIP/SAT-related formats -Usage: maxsat2lp [file.cnf|file.wcnf|-] +Usage: -### pb2lp + lpconvert -o -Converter from .opb/.wbo file to .lp file. +Supported formats: -Usage: pb2lp [--wbo] [file.opb|file.wbo|-] +* Input formats: lp, mps, cnf, wcnf, opb, wbo +* Output formats: lp, smt2, ys TODO ---- -* Gröbner basis -* Cylindrical algebraic decomposition * Local search * Suvery propagation diff --git a/benchmarks/BenchmarkSATLIB.hs b/benchmarks/BenchmarkSATLIB.hs new file mode 100644 --- /dev/null +++ b/benchmarks/BenchmarkSATLIB.hs @@ -0,0 +1,39 @@ +module Main where + +import Control.Monad +import Data.Array.IArray +import Text.Printf +import Criterion.Main +import qualified Language.CNF.Parse.ParseDIMACS as DIMACS +import qualified SAT + +solve :: FilePath -> IO () +solve fname = do + ret <- DIMACS.parseFile fname + case ret of + Left err -> error $ show err + Right cnf -> do + solver <- SAT.newSolver + SAT.setRandomFreq solver 0 + _ <- replicateM (DIMACS.numVars cnf) (SAT.newVar solver) + forM_ (DIMACS.clauses cnf) $ \clause -> + SAT.addClause solver (elems clause) + SAT.solve solver + return () + +main :: IO () +main = do + Criterion.Main.defaultMain + [ bgroup "uf250-1065" + [ bench fname (solve path) + | i <- [(1::Int)..100] + , let fname = printf "uf250-0%d.cnf" i + , let path = "benchmarks/UF250.1065.100/" ++ fname + ] + , bgroup "uuf250-1065" + [ bench fname (solve path) + | i <- [(1::Int)..100] + , let fname = printf "uuf250-0%d.cnf" i + , let path = "benchmarks/UUF250.1065.100/" ++ fname + ] + ] diff --git a/benchmarks/UF250.1065.100/uf250-01.cnf b/benchmarks/UF250.1065.100/uf250-01.cnf new file mode 100644 --- /dev/null +++ b/benchmarks/UF250.1065.100/uf250-01.cnf @@ -0,0 +1,1076 @@ +c This Formular is generated by mcnf +c +c horn? no +c forced? no +c mixed sat? no +c clause length = 3 +c +p cnf 250 1065 + -248 -113 -236 0 +-133 -242 72 0 +-54 -239 -238 0 +166 239 -39 0 +46 -244 -249 0 +-220 187 22 0 +-176 196 -2 0 +66 125 201 0 +214 -170 -113 0 +-179 4 185 0 +87 61 109 0 +-217 -70 121 0 +28 15 -34 0 +45 -189 -21 0 +-226 150 146 0 +239 -103 -80 0 +217 111 -23 0 +-170 -102 -178 0 +-111 227 136 0 +-94 -249 -181 0 +9 -140 -51 0 +43 203 -55 0 +-229 -208 157 0 +-22 -137 238 0 +-247 159 -201 0 +-245 -198 -84 0 +-136 197 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+----------------------------------------------------------------------------- + +module Main where + +import Data.Char +import qualified Data.Version as V +import System.Environment +import System.IO +import System.Exit +import System.FilePath +import System.Console.GetOpt +import qualified Language.CNF.Parse.ParseDIMACS as DIMACS + +import qualified Text.LPFile as LPFile +import qualified Text.MaxSAT as MaxSAT +import qualified Text.MPSFile as MPSFile +import qualified Text.PBFile as PBFile +import Converter.ObjType +import qualified Converter.CNF2LP as CNF2LP +import qualified Converter.LP2SMT as LP2SMT +import qualified Converter.MaxSAT2LP as MaxSAT2LP +import qualified Converter.PB2LP as PB2LP +import Version + +data Flag + = Help + | Version + | Output String + | AsMaxSAT + | ObjType ObjType + | IndicatorConstraint + | Optimize + | NoCheck + | NoProduceModel + deriving Eq + +options :: [OptDescr Flag] +options = + [ Option ['h'] ["help"] (NoArg Help) "show help" + , Option ['v'] ["version"] (NoArg Version) "show version number" + , Option ['o'] [] (ReqArg Output "FILE") "output filename" + , Option [] ["max-sat"] (NoArg AsMaxSAT) "treat *.cnf file as MAX-SAT problem" + , Option [] ["obj"] (ReqArg (ObjType . parseObjType) "STRING") "objective function for SAT/PBS: none (default), max-one, max-zero" + , Option [] ["indicator"] (NoArg IndicatorConstraint) "use indicator constraints in output LP file" + , Option [] ["smt-optimize"] (NoArg Optimize) "output optimiality condition which uses quantifiers" + , Option [] ["smt-no-check"] (NoArg NoCheck) "do not output \"(check)\"" + , Option [] ["smt-no-produce-model"] (NoArg NoProduceModel) "do not output \"(set-option :produce-models true)\"" + ] + where + parseObjType s = + case map toLower s of + "none" -> ObjNone + "max-one" -> ObjMaxOne + "max-zero" -> ObjMaxZero + _ -> error ("unknown obj: " ++ s) + +header :: String +header = unlines + [ "Usage:" + , " lpconvert -o " + , "" + , "Supported formats:" + , " input: .lp .mps .cnf .wcnf .opb .wbo" + , " output: .lp .smt2 .ys" + , "" + , "Options:" + ] + +readLP :: [Flag] -> String -> IO LPFile.LP +readLP o fname = do + let objType = last (ObjNone : [t | ObjType t <- o]) + case map toLower (takeExtension fname) of + ".cnf" + | AsMaxSAT `elem` o -> readWCNF + | otherwise -> do + ret <- DIMACS.parseFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right cnf -> do + let (lp, _) = CNF2LP.convert objType cnf + return lp + ".wcnf" -> readWCNF + ".opb" -> do + ret <- PBFile.parseOPBFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right formula -> do + let (lp, _) = PB2LP.convert objType formula + return lp + ".wbo" -> do + ret <- PBFile.parseWBOFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right formula -> do + let (lp, _) = PB2LP.convertWBO (IndicatorConstraint `elem` o) formula + return lp + ".lp" -> do + ret <- LPFile.parseFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right lp -> return lp + ".mps" -> do + ret <- MPSFile.parseFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right lp -> return lp + ext -> + error $ "unknown file extension: " ++ show ext + where + readWCNF = do + ret <- MaxSAT.parseWCNFFile fname + case ret of + Left err -> hPutStrLn stderr err >> exitFailure + Right wcnf -> do + let (lp, _) = MaxSAT2LP.convert wcnf + return lp + +writeLP :: [Flag] -> LPFile.LP -> IO () +writeLP o lp = do + let lp2smtOpt = + LP2SMT.defaultOptions + { LP2SMT.optCheckSAT = not (NoCheck `elem` o) + , LP2SMT.optProduceModel = not (NoProduceModel `elem` o) + , LP2SMT.optOptimize = Optimize `elem` o + } + + case head ([Just fname | Output fname <- o] ++ [Nothing]) of + Nothing -> do + case LPFile.render lp of + Nothing -> hPutStrLn stderr "conversion failure" >> exitFailure + Just s -> putStr s + Just fname -> do + case map toLower (takeExtension fname) of + ".lp" -> do + case LPFile.render lp of + Nothing -> hPutStrLn stderr "conversion failure" >> exitFailure + Just s -> writeFile fname s + ".smt2" -> do + writeFile fname (LP2SMT.convert lp2smtOpt lp "") + ".ys" -> do + writeFile fname (LP2SMT.convert lp2smtOpt{ LP2SMT.optLanguage = LP2SMT.YICES } lp "") + ext -> do + error $ "unknown file extension: " ++ show ext + +main :: IO () +main = do + args <- getArgs + case getOpt Permute options args of + (o,_,[]) + | Help `elem` o -> putStrLn (usageInfo header options) + | Version `elem` o -> putStrLn (V.showVersion version) + (o,[fname],[]) -> do + lp <- readLP o fname + writeLP o lp + (_,_,errs) -> do + hPutStrLn stderr $ concat errs ++ usageInfo header options + exitFailure diff --git a/samples/gcnf/test250.gcnf b/samples/gcnf/test250.gcnf new file mode 100644 --- /dev/null +++ b/samples/gcnf/test250.gcnf @@ -0,0 +1,1066 @@ +p gcnf 250 1065 10 +{1} -128 -209 148 0 +{1} 2 196 -115 0 +{1} -66 -189 -241 0 +{1} -84 -132 -93 0 +{1} 214 179 66 0 +{1} 203 132 -237 0 +{1} 164 -13 -172 0 +{1} -157 198 160 0 +{1} -91 -164 235 0 +{1} -70 -116 54 0 +{1} -164 171 -189 0 +{1} 126 -184 211 0 +{1} -19 118 41 0 +{1} 32 105 -33 0 +{1} -141 -108 50 0 +{1} -1 156 -188 0 +{1} 138 -181 142 0 +{1} -191 -247 -220 0 +{1} -101 -207 -88 0 +{1} 68 114 -234 0 +{1} 134 -57 -131 0 +{1} -30 -133 116 0 +{1} -24 -173 92 0 +{1} 226 -4 -224 0 +{1} -190 204 61 0 +{1} 148 205 -174 0 +{1} 213 -56 53 0 +{1} 174 -250 206 0 +{1} 32 219 -112 0 +{1} 203 -222 202 0 +{1} 130 42 226 0 +{1} 222 33 58 0 +{1} 58 35 34 0 +{1} -121 80 245 0 +{1} -231 38 -248 0 +{1} -205 -179 184 0 +{1} -182 -204 -36 0 +{1} 23 35 -181 0 +{1} 82 -168 -59 0 +{1} 103 132 -182 0 +{1} -243 -18 -160 0 +{1} -180 130 95 0 +{1} 111 -140 -107 0 +{1} 19 28 -72 0 +{1} -222 207 -103 0 +{1} 134 -50 -184 0 +{1} 185 155 -11 0 +{1} -102 230 -18 0 +{1} -112 39 242 0 +{1} 154 -87 53 0 +{1} 173 -123 -159 0 +{1} -238 -101 -40 0 +{1} -126 -232 -139 0 +{1} 107 -51 197 0 +{1} -194 -138 -150 0 +{1} 106 -66 -11 0 +{1} -150 -159 -27 0 +{1} -98 -32 138 0 +{1} 144 -32 128 0 +{1} 153 74 -249 0 +{1} -190 -175 -208 0 +{1} -127 88 -38 0 +{1} -59 125 -225 0 +{1} -23 4 181 0 +{1} 12 247 -133 0 +{1} 151 -238 127 0 +{1} 237 -65 -154 0 +{1} -218 -26 -55 0 +{1} 91 -245 169 0 +{1} -81 -156 10 0 +{1} 166 -66 -45 0 +{1} 109 -162 47 0 +{1} -193 153 40 0 +{1} 162 -186 -7 0 +{1} 93 38 -58 0 +{1} -159 -167 -39 0 +{1} -187 68 124 0 +{1} 247 23 212 0 +{1} 49 182 -243 0 +{1} 206 -105 -237 0 +{1} 236 116 154 0 +{1} 236 -6 182 0 +{1} -168 236 35 0 +{1} -186 70 -236 0 +{1} 127 80 103 0 +{1} 100 79 -176 0 +{1} 117 -88 -1 0 +{1} 60 -115 -224 0 +{1} -148 181 -65 0 +{1} -132 235 19 0 +{1} -44 -197 190 0 +{1} -214 67 129 0 +{1} -203 175 -191 0 +{1} -172 166 -115 0 +{1} -176 -180 207 0 +{1} -56 -208 -1 0 +{1} -37 140 -19 0 +{1} -242 -55 58 0 +{1} -116 -153 241 0 +{1} -203 64 -219 0 +{1} -214 64 90 0 +{1} -166 96 155 0 +{1} 68 -2 63 0 +{1} -200 49 196 0 +{1} -230 -232 -148 0 +{1} -81 105 219 0 +{1} 187 -236 -123 0 +{1} -99 237 136 0 +{1} -205 61 -118 0 +{1} -235 -230 128 0 +{1} 38 -9 -124 0 +{1} -34 -116 179 0 +{1} -40 -55 -85 0 +{1} 244 170 6 0 +{1} -7 -54 -236 0 +{1} 153 -223 173 0 +{1} -219 -13 -217 0 +{1} 244 -210 -228 0 +{1} 23 -128 -113 0 +{1} 35 -245 -235 0 +{1} 184 31 143 0 +{2} -207 -24 135 0 +{2} 97 -165 -14 0 +{2} -17 15 26 0 +{2} 61 78 -8 0 +{2} 215 -30 -166 0 +{2} 229 93 -246 0 +{2} -167 -113 80 0 +{2} 78 205 -87 0 +{2} 117 -144 207 0 +{2} -10 153 -84 0 +{2} -147 238 61 0 +{2} -58 -17 -190 0 +{2} 209 -25 -81 0 +{2} -175 244 -57 0 +{2} 185 127 -147 0 +{2} 237 199 -144 0 +{2} 124 148 -10 0 +{2} 190 244 231 0 +{2} -185 214 -101 0 +{2} -237 31 -94 0 +{2} -39 36 -94 0 +{2} -175 206 81 0 +{2} 141 -209 -109 0 +{2} 228 -165 -112 0 +{2} -45 142 238 0 +{2} -34 -64 -71 0 +{2} -60 170 -109 0 +{2} 6 245 87 0 +{2} 12 -93 -231 0 +{2} 80 216 28 0 +{2} -103 137 116 0 +{2} -77 -73 -30 0 +{2} -63 219 -129 0 +{2} -215 -94 86 0 +{2} 81 46 221 0 +{2} 161 -215 -212 0 +{2} -137 -215 48 0 +{2} -50 211 229 0 +{2} 172 74 154 0 +{2} -14 -100 166 0 +{2} 59 -119 -243 0 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-135 -86 -5 0 +{6} -190 -44 -223 0 +{9} -17 -141 6 0 +{2} 165 39 237 0 +{6} 221 -62 -104 0 +{5} -206 107 -223 0 +{9} -159 -243 -13 0 +{8} 118 -9 57 0 diff --git a/samples/gcnf/uuf50-01.gcnf b/samples/gcnf/uuf50-01.gcnf new file mode 100644 --- /dev/null +++ b/samples/gcnf/uuf50-01.gcnf @@ -0,0 +1,226 @@ +c This Formular is generated by mcnf +c +c horn? no +c forced? no +c mixed sat? no +c clause length = 3 +c +p gcnf 50 218 10 +{1} 18 -8 29 0 +{1} -16 3 18 0 +{1} -36 -11 -30 0 +{1} -50 20 32 0 +{1} -6 9 35 0 +{1} 42 -38 29 0 +{1} 43 -15 10 0 +{1} -48 -47 1 0 +{1} -45 -16 33 0 +{1} 38 42 22 0 +{1} -49 41 -34 0 +{1} 12 17 35 0 +{2} 22 -49 7 0 +{2} -10 -11 -39 0 +{2} -28 -36 -37 0 +{2} -13 -46 -41 0 +{2} 21 -4 9 0 +{2} 12 48 10 0 +{2} 24 23 15 0 +{2} -8 -41 -43 0 +{2} -44 -2 -35 0 +{2} -27 18 31 0 +{2} 47 35 6 0 +{3} -11 -27 41 0 +{3} -33 -47 -45 0 +{3} -16 36 -37 0 +{3} 27 -46 2 0 +{3} 15 -28 10 0 +{3} -38 46 -39 0 +{3} -33 -4 24 0 +{3} -12 -45 50 0 +{3} -32 -21 -15 0 +{3} 8 42 24 0 +{4} 30 -49 4 0 +{4} 45 -9 28 0 +{4} -33 -47 -1 0 +{4} 1 27 -16 0 +{4} -11 -17 -35 0 +{4} -42 -15 45 0 +{4} -19 -27 30 0 +{4} 3 28 12 0 +{4} 48 -11 -33 0 +{4} -6 37 -9 0 +{5} -37 13 -7 0 +{5} -2 26 16 0 +{5} 46 -24 -38 0 +{5} -13 -24 -8 0 +{5} -36 -42 -21 0 +{5} -37 -19 3 0 +{5} -31 -50 35 0 +{5} -7 -26 29 0 +{5} -42 -45 29 0 +{5} 33 25 -6 0 +{6} -45 -5 7 0 +{6} -7 28 -6 0 +{6} -48 31 -11 0 +{6} 32 16 -37 0 +{6} -24 48 1 0 +{6} 18 -46 23 0 +{6} -30 -50 48 0 +{6} -21 39 -2 0 +{6} 24 47 42 0 +{6} -36 30 4 0 +{7} -5 28 -1 0 +{7} -47 32 -42 0 +{7} 16 37 -22 0 +{7} -43 42 -34 0 +{7} -40 39 -20 0 +{7} -49 29 6 0 +{7} -41 -3 39 0 +{7} -16 -12 43 0 +{7} 24 22 3 0 +{7} 47 -45 43 0 +{8} 45 -37 46 0 +{8} -9 26 5 0 +{8} -3 23 -13 0 +{8} 5 -34 13 0 +{8} 12 39 13 0 +{8} 22 50 37 0 +{8} 19 9 46 0 +{8} -24 8 -27 0 +{8} -28 7 21 0 +{8} 8 -25 50 0 +{9} 20 50 4 0 +{9} 27 36 13 0 +{9} 26 31 -25 0 +{9} 39 -44 -32 0 +{9} -20 41 -10 0 +{9} 49 -28 35 0 +{9} 1 44 34 0 +{9} 39 35 -11 0 +{9} -50 -42 -7 0 +{9} -24 7 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34 0 +{10} -12 43 -29 0 +{10} 24 2 -49 0 +{10} 10 -4 40 0 +{10} 11 5 12 0 +{10} -3 47 -31 0 +{10} 43 -23 21 0 +{10} -41 -36 -50 0 +{10} -8 -42 -24 0 +{10} 39 45 7 0 +{10} 7 37 -45 0 +{10} 41 40 8 0 +{10} -50 -10 -8 0 +{10} -5 -39 -14 0 +{10} -22 -24 -43 0 +{10} -36 40 35 0 +{10} 17 49 41 0 +{10} -32 7 24 0 +{10} -30 -8 -9 0 +{10} -41 -13 -10 0 +{10} 31 26 -33 0 +{10} 17 -22 -39 0 +{10} -21 28 3 0 +{10} -14 46 23 0 +{10} 29 16 19 0 +{10} 42 -32 -44 0 +{10} -24 10 23 0 +{10} -1 -32 -21 0 +{10} -8 -44 -39 0 +{10} 39 11 9 0 +{10} 19 14 -46 0 +{10} 46 44 -42 0 +{10} 37 23 -29 0 +{10} 32 25 20 0 +{10} 14 -43 -12 0 +{10} -36 -18 46 0 +{10} 14 -26 -10 0 +{10} -2 -30 5 0 +{10} 6 -18 46 0 +{10} -26 2 -44 0 +{10} 20 -8 -11 0 +{10} -31 3 16 0 +{10} -22 -9 39 0 +{10} -49 44 -42 0 +{10} -45 -44 31 0 +{10} -31 50 -11 0 +{10} -32 -46 2 0 +{10} -6 -7 17 0 +{10} 19 -32 48 0 +{10} 39 20 -10 0 +{10} -22 -37 38 0 +{10} -31 9 -48 0 +{10} 40 12 7 0 +{10} -24 -4 9 0 +{10} -22 49 33 0 +{10} -12 43 10 0 +{10} 25 -30 -10 0 +{10} 46 47 31 0 +{10} 13 27 -7 0 +{10} -45 32 -35 0 +{10} -50 34 9 0 +{10} 2 34 30 0 +{10} 3 16 2 0 +{10} -18 45 -12 0 +{10} 33 37 10 0 +{10} 43 7 -18 0 +{10} -22 44 -19 0 +{10} -31 -27 -42 0 +{10} -3 -40 8 0 +{10} -23 -31 38 0 diff --git a/samples/gcnf/uuf50-01b.gcnf b/samples/gcnf/uuf50-01b.gcnf new file mode 100644 --- /dev/null +++ b/samples/gcnf/uuf50-01b.gcnf @@ -0,0 +1,226 @@ +c This Formular is generated by mcnf +c +c horn? no +c forced? no +c mixed sat? no +c clause length = 3 +c +p gcnf 50 218 9 +{5} 18 -8 29 0 +{2} -16 3 18 0 +{3} -36 -11 -30 0 +{7} -50 20 32 0 +{5} -6 9 35 0 +{8} 42 -38 29 0 +{2} 43 -15 10 0 +{0} -48 -47 1 0 +{4} -45 -16 33 0 +{0} 38 42 22 0 +{3} -49 41 -34 0 +{9} 12 17 35 0 +{1} 22 -49 7 0 +{9} -10 -11 -39 0 +{6} -28 -36 -37 0 +{3} -13 -46 -41 0 +{4} 21 -4 9 0 +{5} 12 48 10 0 +{3} 24 23 15 0 +{0} -8 -41 -43 0 +{3} -44 -2 -35 0 +{4} -27 18 31 0 +{5} 47 35 6 0 +{3} -11 -27 41 0 +{8} -33 -47 -45 0 +{3} -16 36 -37 0 +{3} 27 -46 2 0 +{2} 15 -28 10 0 +{4} -38 46 -39 0 +{1} -33 -4 24 0 +{8} -12 -45 50 0 +{7} -32 -21 -15 0 +{2} 8 42 24 0 +{4} 30 -49 4 0 +{0} 45 -9 28 0 +{7} -33 -47 -1 0 +{0} 1 27 -16 0 +{3} -11 -17 -35 0 +{3} -42 -15 45 0 +{8} -19 -27 30 0 +{4} 3 28 12 0 +{0} 48 -11 -33 0 +{9} -6 37 -9 0 +{7} -37 13 -7 0 +{8} -2 26 16 0 +{0} 46 -24 -38 0 +{8} -13 -24 -8 0 +{1} -36 -42 -21 0 +{1} -37 -19 3 0 +{9} -31 -50 35 0 +{5} -7 -26 29 0 +{9} -42 -45 29 0 +{7} 33 25 -6 0 +{1} -45 -5 7 0 +{2} -7 28 -6 0 +{5} -48 31 -11 0 +{3} 32 16 -37 0 +{8} -24 48 1 0 +{9} 18 -46 23 0 +{4} -30 -50 48 0 +{4} -21 39 -2 0 +{3} 24 47 42 0 +{6} -36 30 4 0 +{6} -5 28 -1 0 +{2} -47 32 -42 0 +{1} 16 37 -22 0 +{9} -43 42 -34 0 +{6} -40 39 -20 0 +{1} -49 29 6 0 +{8} -41 -3 39 0 +{3} -16 -12 43 0 +{9} 24 22 3 0 +{0} 47 -45 43 0 +{1} 45 -37 46 0 +{1} -9 26 5 0 +{5} -3 23 -13 0 +{4} 5 -34 13 0 +{6} 12 39 13 0 +{8} 22 50 37 0 +{2} 19 9 46 0 +{3} -24 8 -27 0 +{5} -28 7 21 0 +{8} 8 -25 50 0 +{0} 20 50 4 0 +{0} 27 36 13 0 +{4} 26 31 -25 0 +{1} 39 -44 -32 0 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-1 6 -12 0 +{1} 6 -2 -7 0 +{7} 32 -20 34 0 +{5} -12 43 -29 0 +{8} 24 2 -49 0 +{5} 10 -4 40 0 +{3} 11 5 12 0 +{7} -3 47 -31 0 +{4} 43 -23 21 0 +{3} -41 -36 -50 0 +{1} -8 -42 -24 0 +{3} 39 45 7 0 +{4} 7 37 -45 0 +{8} 41 40 8 0 +{0} -50 -10 -8 0 +{2} -5 -39 -14 0 +{0} -22 -24 -43 0 +{2} -36 40 35 0 +{9} 17 49 41 0 +{6} -32 7 24 0 +{3} -30 -8 -9 0 +{6} -41 -13 -10 0 +{6} 31 26 -33 0 +{1} 17 -22 -39 0 +{2} -21 28 3 0 +{7} -14 46 23 0 +{6} 29 16 19 0 +{0} 42 -32 -44 0 +{4} -24 10 23 0 +{3} -1 -32 -21 0 +{1} -8 -44 -39 0 +{6} 39 11 9 0 +{1} 19 14 -46 0 +{8} 46 44 -42 0 +{9} 37 23 -29 0 +{8} 32 25 20 0 +{9} 14 -43 -12 0 +{5} -36 -18 46 0 +{1} 14 -26 -10 0 +{3} -2 -30 5 0 +{4} 6 -18 46 0 +{8} -26 2 -44 0 +{9} 20 -8 -11 0 +{0} -31 3 16 0 +{3} -22 -9 39 0 +{3} -49 44 -42 0 +{5} -45 -44 31 0 +{7} -31 50 -11 0 +{8} -32 -46 2 0 +{9} -6 -7 17 0 +{4} 19 -32 48 0 +{3} 39 20 -10 0 +{7} -22 -37 38 0 +{1} -31 9 -48 0 +{7} 40 12 7 0 +{5} -24 -4 9 0 +{4} -22 49 33 0 +{9} -12 43 10 0 +{1} 25 -30 -10 0 +{4} 46 47 31 0 +{3} 13 27 -7 0 +{1} -45 32 -35 0 +{1} -50 34 9 0 +{3} 2 34 30 0 +{2} 3 16 2 0 +{5} -18 45 -12 0 +{4} 33 37 10 0 +{0} 43 7 -18 0 +{6} -22 44 -19 0 +{0} -31 -27 -42 0 +{5} -3 -40 8 0 +{0} -23 -31 38 0 diff --git a/samples/gcnf/uuf50-01c.gcnf b/samples/gcnf/uuf50-01c.gcnf new file mode 100644 --- /dev/null +++ b/samples/gcnf/uuf50-01c.gcnf @@ -0,0 +1,226 @@ +c This Formular is generated by mcnf +c +c horn? no +c forced? no +c mixed sat? no +c clause length = 3 +c +p gcnf 50 218 20 +{1} 18 -8 29 0 +{12} -16 3 18 0 +{13} -36 -11 -30 0 +{13} -50 20 32 0 +{1} -6 9 35 0 +{10} 42 -38 29 0 +{7} 43 -15 10 0 +{6} -48 -47 1 0 +{15} -45 -16 33 0 +{6} 38 42 22 0 +{9} -49 41 -34 0 +{18} 12 17 35 0 +{15} 22 -49 7 0 +{5} -10 -11 -39 0 +{20} -28 -36 -37 0 +{0} -13 -46 -41 0 +{20} 21 -4 9 0 +{12} 12 48 10 0 +{8} 24 23 15 0 +{18} -8 -41 -43 0 +{3} -44 -2 -35 0 +{9} -27 18 31 0 +{20} 47 35 6 0 +{8} -11 -27 41 0 +{16} -33 -47 -45 0 +{4} -16 36 -37 0 +{13} 27 -46 2 0 +{4} 15 -28 10 0 +{7} -38 46 -39 0 +{2} -33 -4 24 0 +{16} -12 -45 50 0 +{14} -32 -21 -15 0 +{7} 8 42 24 0 +{17} 30 -49 4 0 +{5} 45 -9 28 0 +{6} -33 -47 -1 0 +{14} 1 27 -16 0 +{13} -11 -17 -35 0 +{3} -42 -15 45 0 +{6} -19 -27 30 0 +{11} 3 28 12 0 +{13} 48 -11 -33 0 +{15} -6 37 -9 0 +{8} -37 13 -7 0 +{17} -2 26 16 0 +{5} 46 -24 -38 0 +{8} -13 -24 -8 0 +{8} -36 -42 -21 0 +{11} -37 -19 3 0 +{5} -31 -50 35 0 +{13} -7 -26 29 0 +{15} -42 -45 29 0 +{20} 33 25 -6 0 +{6} -45 -5 7 0 +{3} -7 28 -6 0 +{8} -48 31 -11 0 +{6} 32 16 -37 0 +{4} -24 48 1 0 +{9} 18 -46 23 0 +{0} -30 -50 48 0 +{3} -21 39 -2 0 +{9} 24 47 42 0 +{15} -36 30 4 0 +{20} -5 28 -1 0 +{20} -47 32 -42 0 +{4} 16 37 -22 0 +{5} -43 42 -34 0 +{20} -40 39 -20 0 +{14} -49 29 6 0 +{16} -41 -3 39 0 +{12} -16 -12 43 0 +{13} 24 22 3 0 +{12} 47 -45 43 0 +{10} 45 -37 46 0 +{5} -9 26 5 0 +{0} -3 23 -13 0 +{10} 5 -34 13 0 +{4} 12 39 13 0 +{9} 22 50 37 0 +{0} 19 9 46 0 +{17} -24 8 -27 0 +{4} -28 7 21 0 +{18} 8 -25 50 0 +{17} 20 50 4 0 +{5} 27 36 13 0 +{10} 26 31 -25 0 +{2} 39 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+{15} -24 -4 9 0 +{1} -22 49 33 0 +{12} -12 43 10 0 +{12} 25 -30 -10 0 +{2} 46 47 31 0 +{0} 13 27 -7 0 +{19} -45 32 -35 0 +{20} -50 34 9 0 +{0} 2 34 30 0 +{19} 3 16 2 0 +{16} -18 45 -12 0 +{16} 33 37 10 0 +{13} 43 7 -18 0 +{2} -22 44 -19 0 +{19} -31 -27 -42 0 +{18} -3 -40 8 0 +{11} -23 -31 38 0 diff --git a/samples/lp/factor137874311.lp b/samples/lp/factor137874311.lp new file mode 100644 --- /dev/null +++ b/samples/lp/factor137874311.lp @@ -0,0 +1,13 @@ +\ toysolver: NG +\ toysat: OK (90.117s) +\ scip-2.1.1.darwin.x86_64.gnu.opt.spx.nozimpl: wrong answer +Minimize + obj: P +Subject To + [ P * Q ] = 137874311 \ = 7927*17393 +Bounds + 2 <= P <= 11741 \ = sqrt 137874311 + 2 <= Q <= 68937155 \ = 137874311/2 +General + P Q +End diff --git a/samples/lp/factor35.lp b/samples/lp/factor35.lp new file mode 100644 --- /dev/null +++ b/samples/lp/factor35.lp @@ -0,0 +1,13 @@ +\ toysolver: NG +\ toysat: OK +\ scip-2.1.1.darwin.x86_64.gnu.opt.spx.nozimpl: OK +Minimize + obj: P +Subject To + [ P * Q ] = 35 +Bounds + 2 <= P <= 7 + 2 <= Q <= 7 +General + P Q +End diff --git a/samples/lp/factor672263.lp b/samples/lp/factor672263.lp new file mode 100644 --- /dev/null +++ b/samples/lp/factor672263.lp @@ -0,0 +1,13 @@ +\ toysolver: NG +\ toysat: OK +\ scip-2.1.1.darwin.x86_64.gnu.opt.spx.nozimpl: OK +Minimize + obj: P +Subject To + [ P * Q ] = 672263 \ = 547*1229 +Bounds + 2 <= P <= 819 \ = sqrt 672263 + 2 <= Q <= 336131 \ = 672263/2 +General + P Q +End diff --git a/samples/sat/empty-clause.cnf b/samples/sat/empty-clause.cnf new file mode 100644 --- /dev/null +++ b/samples/sat/empty-clause.cnf @@ -0,0 +1,3 @@ +p cnf 0 1 +0 + diff --git a/src/Algorithm/BoundsInference.hs b/src/Algorithm/BoundsInference.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/BoundsInference.hs @@ -0,0 +1,85 @@ +{-# LANGUAGE ScopedTypeVariables, BangPatterns #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.BoundsInference +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (ScopedTypeVariables, BangPatterns) +-- +-- Tightening variable bounds by constraint propagation. +-- +----------------------------------------------------------------------------- +module Algorithm.BoundsInference + ( BoundsEnv + , inferBounds + , LA.computeInterval + ) where + +import Control.Monad +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS + +import Data.Expr +import Data.ArithRel +import Data.Linear +import Data.Interval +import Data.LA (BoundsEnv) +import qualified Data.LA as LA +import Util (isInteger) + +type C r = (RelOp, LA.Expr r) + +-- | tightening variable bounds by constraint propagation. +inferBounds :: forall r. (RealFrac r) + => LA.BoundsEnv r -- ^ initial bounds + -> [LA.Atom r] -- ^ constraints + -> VarSet -- ^ integral variables + -> Int -- ^ limit of iterations + -> LA.BoundsEnv r +inferBounds bounds constraints ivs limit = loop 0 bounds + where + cs :: VarMap [C r] + cs = IM.fromListWith (++) $ do + Rel lhs op rhs <- constraints + let m = LA.coeffMap (lhs .-. rhs) + (v,c) <- IM.toList m + guard $ v /= LA.unitVar + let op' = if c < 0 then flipOp op else op + rhs' = (-1/c) .*. LA.fromCoeffMap (IM.delete v m) + return (v, [(op', rhs')]) + + loop :: Int -> LA.BoundsEnv r -> LA.BoundsEnv r + loop !i b = if (limit>=0 && i>=limit) || b==b' then b else loop (i+1) b' + where + b' = refine b + + refine :: LA.BoundsEnv r -> LA.BoundsEnv r + refine b = IM.mapWithKey (\v i -> tighten v $ f b (IM.findWithDefault [] v cs) i) b + + -- tighten bounds of integer variables + tighten :: Var -> Interval r -> Interval r + tighten v x = + if v `IS.notMember` ivs + then x + else tightenToInteger x + +f :: (Real r, Fractional r) => LA.BoundsEnv r -> [C r] -> Interval r -> Interval r +f b cs i = foldr intersection i $ do + (op, rhs) <- cs + let i' = LA.computeInterval b rhs + lb = lowerBound i' + ub = upperBound i' + case op of + Eql -> return i' + Le -> return $ interval Nothing ub + Ge -> return $ interval lb Nothing + Lt -> return $ interval Nothing (strict ub) + Gt -> return $ interval (strict lb) Nothing + NEq -> [] + +strict :: EndPoint r -> EndPoint r +strict Nothing = Nothing +strict (Just (_,val)) = Just (False,val) diff --git a/src/Algorithm/CAD.hs b/src/Algorithm/CAD.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/CAD.hs @@ -0,0 +1,630 @@ +{-# LANGUAGE ScopedTypeVariables, BangPatterns #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.CAD +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (ScopedTypeVariables, BangPatterns) +-- +-- References: +-- +-- * Christian Michaux and Adem Ozturk. +-- Quantifier Elimination following Muchnik +-- +-- +-- * Arnab Bhattacharyya. +-- Something you should know about: Quantifier Elimination (Part I) +-- +-- +-- * Arnab Bhattacharyya. +-- Something you should know about: Quantifier Elimination (Part II) +-- +-- +----------------------------------------------------------------------------- +module Algorithm.CAD + ( + -- * Basic data structures + Point (..) + , Cell (..) + + -- * Algebra os Sign + , Sign (..) + , signNegate + , signMul + , signDiv + , signExp + , signOfConst + + -- * Projection + , project + + -- * Solving + , solve + , solve' + + -- * Model + , Model + , findSample + , evalCell + , evalPoint + ) where + +import Control.Exception +import Control.Monad.State +import Data.List +import Data.Maybe +import Data.Ord +import qualified Data.Map as Map +import qualified Data.Set as Set +import Text.Printf + +import Data.ArithRel +import qualified Data.AlgebraicNumber as AReal +import Data.Formula (DNF (..)) +import Data.Polynomial + +import Debug.Trace + +-- --------------------------------------------------------------------------- + +data Point c = NegInf | RootOf (UPolynomial c) Int | PosInf + deriving (Eq, Ord, Show) + +data Cell c + = Point (Point c) + | Interval (Point c) (Point c) + deriving (Eq, Ord, Show) + +showCell :: (Num c, Ord c, RenderCoeff c) => Cell c -> String +showCell (Point pt) = showPoint pt +showCell (Interval lb ub) = printf "(%s, %s)" (showPoint lb) (showPoint ub) + +showPoint :: (Num c, Ord c, RenderCoeff c) => Point c -> String +showPoint NegInf = "-inf" +showPoint PosInf = "+inf" +showPoint (RootOf p n) = "rootOf(" ++ render p ++ ", " ++ show n ++ ")" + +-- --------------------------------------------------------------------------- + +data Sign = Neg | Zero | Pos + deriving (Eq, Ord, Show) + +signNegate :: Sign -> Sign +signNegate Neg = Pos +signNegate Zero = Zero +signNegate Pos = Neg + +signMul :: Sign -> Sign -> Sign +signMul Pos s = s +signMul s Pos = s +signMul Neg s = signNegate s +signMul s Neg = signNegate s +signMul _ _ = Zero + +signDiv :: Sign -> Sign -> Sign +signDiv s Pos = s +signDiv _ Zero = error "signDiv: division by zero" +signDiv s Neg = signNegate s + +signExp :: Sign -> Integer -> Sign +signExp _ 0 = Pos +signExp Pos _ = Pos +signExp Zero _ = Zero +signExp Neg n = if even n then Pos else Neg + +signOfConst :: (Num a, Ord a) => a -> Sign +signOfConst r = + case r `compare` 0 of + LT -> Neg + EQ -> Zero + GT -> Pos + +-- --------------------------------------------------------------------------- + +type SignConf c = [(Cell c, Map.Map (UPolynomial c) Sign)] + +emptySignConf :: SignConf c +emptySignConf = + [ (Point NegInf, Map.empty) + , (Interval NegInf PosInf, Map.empty) + , (Point PosInf, Map.empty) + ] + +showSignConf :: forall c. (Num c, Ord c, RenderCoeff c) => SignConf c -> [String] +showSignConf = f + where + f :: SignConf c -> [String] + f = concatMap $ \(cell, m) -> showCell cell : g m + + g :: Map.Map (UPolynomial c) Sign -> [String] + g m = + [printf " %s: %s" (render p) (showSign s) | (p, s) <- Map.toList m] + + showSign :: Sign -> String + showSign Pos = "+" + showSign Neg = "-" + showSign Zero = "0" + +-- --------------------------------------------------------------------------- + +-- modified reminder +mr + :: forall k. (Ord k, Show k, Num k, RenderCoeff k) + => UPolynomial k + -> UPolynomial k + -> (k, Integer, UPolynomial k) +mr p q + | n >= m = assert (constant (bm^(n-m+1)) * p == q * l + r && m > deg r) $ (bm, n-m+1, r) + | otherwise = error "mr p q: not (deg p >= deg q)" + where + x = var () + n = deg p + m = deg q + (bm, _) = leadingTerm grlex q + (l,r) = f p n + + f :: UPolynomial k -> Integer -> (UPolynomial k, UPolynomial k) + f p n + | n==m = + let l = constant an + r = constant bm * p - constant an * q + in assert (constant (bm^(n-m+1)) * p == q*l + r && m > deg r) $ (l, r) + | otherwise = + let p' = (constant bm * p - constant an * x^(n-m) * q) + (l',r) = f p' (n-1) + l = l' + constant (an*bm^(n-m)) * x^(n-m) + in assert (n > deg p') $ + assert (constant (bm^(n-m+1)) * p == q*l + r && m > deg r) $ (l, r) + where + an = coeff (mmFromList [((), n)]) p + +test_mr_1 :: (Coeff Int, Integer, UPolynomial (Coeff Int)) +test_mr_1 = mr (toUPolynomialOf p 3) (toUPolynomialOf q 3) + where + a = var 0 + b = var 1 + c = var 2 + x = var 3 + p = a*x^(2::Int) + b*x + c + q = 2*a*x + b + +test_mr_2 :: (Coeff Int, Integer, UPolynomial (Coeff Int)) +test_mr_2 = mr (toUPolynomialOf p 3) (toUPolynomialOf p 3) + where + a = var 0 + b = var 1 + c = var 2 + x = var 3 + p = a*x^(2::Int) + b*x + c + +-- --------------------------------------------------------------------------- + +type Coeff v = Polynomial Rational v + +type M v = StateT (Map.Map (Polynomial Rational v) (Set.Set Sign)) [] + +runM :: M v a -> [(a, Map.Map (Polynomial Rational v) (Set.Set Sign))] +runM m = runStateT m Map.empty + +assume :: (Ord v, Show v, RenderVar v) => Polynomial Rational v -> [Sign] -> M v () +assume p ss = + if deg p == 0 + then do + let c = coeff mmOne p + guard $ signOfConst c `elem` ss + else do + let (c,_) = leadingTerm grlex p + p' = mapCoeff (/c) p + m <- get + let ss1 = Map.findWithDefault (Set.fromList [Neg, Zero, Pos]) p' m + ss2 = Set.intersection ss1 $ Set.fromList $ [s `signDiv` signOfConst c | s <- ss] + guard $ not $ Set.null ss2 + put $ Map.insert p' ss2 m + +project + :: forall v. (Ord v, Show v, RenderVar v) + => [(UPolynomial (Polynomial Rational v), [Sign])] + -> [([(Polynomial Rational v, [Sign])], [Cell (Polynomial Rational v)])] +project cs = [ (guess2cond gs, cells) | (cells, gs) <- result ] + where + result :: [([Cell (Polynomial Rational v)], Map.Map (Polynomial Rational v) (Set.Set Sign))] + result = runM $ do + forM_ cs $ \(p,ss) -> do + when (1 > deg p) $ assume (coeff mmOne p) ss + conf <- buildSignConf (map fst cs) + let satCells = [cell | (cell, m) <- conf, cell /= Point NegInf, cell /= Point PosInf, ok m] + guard $ not $ null satCells + return satCells + + ok :: Map.Map (UPolynomial (Polynomial Rational v)) Sign -> Bool + ok m = and [checkSign m p ss | (p,ss) <- cs] + where + checkSign m p ss = + if 1 > deg p + then True -- already assumed + else (m Map.! p) `elem` ss + + guess2cond :: Map.Map (Polynomial Rational v) (Set.Set Sign) -> [(Polynomial Rational v, [Sign])] + guess2cond gs = [(p, Set.toList ss) | (p, ss) <- Map.toList gs] + +buildSignConf + :: (Ord v, Show v, RenderVar v) + => [UPolynomial (Polynomial Rational v)] + -> M v (SignConf (Polynomial Rational v)) +buildSignConf ps = do + ps2 <- collectPolynomials (Set.fromList ps) + let ts = sortBy (comparing deg) (Set.toList ps2) + foldM (flip refineSignConf) emptySignConf ts + +collectPolynomials + :: (Ord v, Show v, RenderVar v) + => Set.Set (UPolynomial (Polynomial Rational v)) + -> M v (Set.Set (UPolynomial (Polynomial Rational v))) +collectPolynomials ps = go Set.empty (f ps) + where + f = Set.filter (\p -> deg p > 0) + go result ps | Set.null ps = return result + go result ps = do + let rs1 = filter (\p -> deg p > 0) [deriv p () | p <- Set.toList ps] + rs2 <- liftM (filter (\p -> deg p > 0) . map (\(_,_,r) -> r) . concat) $ + forM [(p1,p2) | p1 <- Set.toList ps, p2 <- Set.toList ps ++ Set.toList result, p1 /= p2] $ \(p1,p2) -> do + ret1 <- zmod p1 p2 + ret2 <- zmod p2 p1 + return $ catMaybes [ret1,ret2] + let ps' = Set.unions [Set.fromList rs | rs <- [rs1,rs2]] `Set.difference` result + go (result `Set.union` ps) ps' + +getHighestNonzeroTerm + :: forall v. (Ord v, Show v, RenderVar v) + => UPolynomial (Polynomial Rational v) + -> M v (Polynomial Rational v, Integer) +getHighestNonzeroTerm p = go $ sortBy (flip (comparing snd)) cs + where + cs = [(c, mmDegree mm) | (c,mm) <- terms p] + + go :: [(Polynomial Rational v, Integer)] -> M v (Polynomial Rational v, Integer) + go [] = return (0, -1) + go ((c,d):xs) = + mplus + (assume c [Pos, Neg] >> return (c,d)) + (assume c [Zero] >> go xs) + +zmod + :: forall v. (Ord v, Show v, RenderVar v) + => UPolynomial (Polynomial Rational v) + -> UPolynomial (Polynomial Rational v) + -> M v (Maybe (Polynomial Rational v, Integer, UPolynomial (Polynomial Rational v))) +zmod p q = do + (_, d) <- getHighestNonzeroTerm p + (_, e) <- getHighestNonzeroTerm q + if not (d >= e) || 0 >= e + then return Nothing + else do + let p' = fromTerms [(pi, mm) | (pi, mm) <- terms p, mmDegree mm <= d] + q' = fromTerms [(qi, mm) | (qi, mm) <- terms q, mmDegree mm <= e] + return $ Just $ mr p' q' + +refineSignConf + :: forall v. (Show v, Ord v, RenderVar v) + => UPolynomial (Polynomial Rational v) + -> SignConf (Polynomial Rational v) + -> M v (SignConf (Polynomial Rational v)) +refineSignConf p conf = liftM (extendIntervals 0) $ mapM extendPoint conf + where + extendPoint + :: (Cell (Polynomial Rational v), Map.Map (UPolynomial (Polynomial Rational v)) Sign) + -> M v (Cell (Polynomial Rational v), Map.Map (UPolynomial (Polynomial Rational v)) Sign) + extendPoint (Point pt, m) = do + s <- signAt pt m + return (Point pt, Map.insert p s m) + extendPoint x = return x + + extendIntervals + :: Int + -> [(Cell (Polynomial Rational v), Map.Map (UPolynomial (Polynomial Rational v)) Sign)] + -> [(Cell (Polynomial Rational v), Map.Map (UPolynomial (Polynomial Rational v)) Sign)] + extendIntervals !n (pt1@(Point _, m1) : (Interval lb ub, m) : pt2@(Point _, m2) : xs) = + pt1 : ys ++ extendIntervals n2 (pt2 : xs) + where + s1 = m1 Map.! p + s2 = m2 Map.! p + n1 = if s1 == Zero then n+1 else n + root = RootOf p n1 + (ys, n2) + | s1 == s2 = ( [ (Interval lb ub, Map.insert p s1 m) ], n1 ) + | s1 == Zero = ( [ (Interval lb ub, Map.insert p s2 m) ], n1 ) + | s2 == Zero = ( [ (Interval lb ub, Map.insert p s1 m) ], n1 ) + | otherwise = ( [ (Interval lb root, Map.insert p s1 m) + , (Point root, Map.insert p Zero m) + , (Interval root ub, Map.insert p s2 m) + ] + , n1 + 1 + ) + extendIntervals _ xs = xs + + signAt :: Point (Polynomial Rational v) -> Map.Map (UPolynomial (Polynomial Rational v)) Sign -> M v Sign + signAt PosInf _ = do + (c,_) <- getHighestNonzeroTerm p + signCoeff c + signAt NegInf _ = do + (c,d) <- getHighestNonzeroTerm p + if even d + then signCoeff c + else liftM signNegate $ signCoeff c + signAt (RootOf q _) m = do + Just (bm,k,r) <- zmod p q + s1 <- if deg r > 0 + then return $ m Map.! r + else signCoeff $ coeff mmOne r + -- 場合分けを出来るだけ避ける + if even k + then return s1 + else do + s2 <- signCoeff bm + return $ signDiv s1 (signExp s2 k) + + signCoeff :: Polynomial Rational v -> M v Sign + signCoeff c = + msum [ assume c [s] >> return s + | s <- [Neg, Zero, Pos] + ] + +-- --------------------------------------------------------------------------- + +type Model v = Map.Map v AReal.AReal + +findSample :: Ord v => Model v -> Cell (Polynomial Rational v) -> Maybe AReal.AReal +findSample m cell = + case evalCell m cell of + Point (RootOf p n) -> + Just $ AReal.realRoots p !! n + Interval NegInf PosInf -> + Just $ 0 + Interval NegInf (RootOf p n) -> + Just $ fromInteger $ floor ((AReal.realRoots p !! n) - 1) + Interval (RootOf p n) PosInf -> + Just $ fromInteger $ ceiling ((AReal.realRoots p !! n) + 1) + Interval (RootOf p1 n1) (RootOf p2 n2) + | (pt1 < pt2) -> Just $ (pt1 + pt2) / 2 + | otherwise -> Nothing + where + pt1 = AReal.realRoots p1 !! n1 + pt2 = AReal.realRoots p2 !! n2 + _ -> error $ "findSample: should not happen" + +evalCell :: Ord v => Model v -> Cell (Polynomial Rational v) -> Cell Rational +evalCell m (Point pt) = Point $ evalPoint m pt +evalCell m (Interval pt1 pt2) = Interval (evalPoint m pt1) (evalPoint m pt2) + +evalPoint :: Ord v => Model v -> Point (Polynomial Rational v) -> Point Rational +evalPoint _ NegInf = NegInf +evalPoint _ PosInf = PosInf +evalPoint m (RootOf p n) = + RootOf (AReal.simpARealPoly $ mapCoeff (eval (m Map.!) . mapCoeff fromRational) p) n + +-- --------------------------------------------------------------------------- + +solve + :: forall v. (Ord v, Show v, RenderVar v) + => [(Rel (Polynomial Rational v))] + -> Maybe (Model v) +solve cs0 = solve' (map f cs0) + where + f (Rel lhs op rhs) = (lhs - rhs, g op) + g Le = [Zero, Neg] + g Ge = [Zero, Pos] + g Lt = [Neg] + g Gt = [Pos] + g Eql = [Zero] + g NEq = [Pos,Neg] + +solve' + :: forall v. (Ord v, Show v, RenderVar v) + => [(Polynomial Rational v, [Sign])] + -> Maybe (Model v) +solve' cs0 = go vs0 cs0 + where + vs0 = Set.toList $ Set.unions [variables p | (p,_) <- cs0] + + go :: [v] -> [(Polynomial Rational v, [Sign])] -> Maybe (Model v) + go [] cs = + if and [signOfConst v `elem` ss | (p,ss) <- cs, let v = eval (\_ -> undefined) p] + then Just Map.empty + else Nothing + go (v:vs) cs = listToMaybe $ do + (cs2, cell:_) <- project [(toUPolynomialOf p v, ss) | (p,ss) <- cs] + case go vs cs2 of + Nothing -> mzero + Just m -> do + let Just val = findSample m cell + seq val $ return $ Map.insert v val m + +-- --------------------------------------------------------------------------- + +showDNF :: (Ord v, Show v, RenderVar v) => DNF (Polynomial Rational v, [Sign]) -> String +showDNF (DNF xss) = intercalate " | " [showConj xs | xs <- xss] + where + showConj xs = "(" ++ intercalate " & " [f p ss | (p,ss) <- xs] ++ ")" + f p ss = render p ++ g ss + g [Zero] = " = 0" + g [Pos] = " > 0" + g [Neg] = " < 0" + g xs + | Set.fromList xs == Set.fromList [Pos,Neg] = "/= 0" + | Set.fromList xs == Set.fromList [Zero,Pos] = ">= 0" + | Set.fromList xs == Set.fromList [Zero,Neg] = "<= 0" + | otherwise = error "showDNF: should not happen" + +dumpProjection + :: (Ord v, Show v, RenderVar v) + => [([(Polynomial Rational v, [Sign])], [Cell (Polynomial Rational v)])] + -> IO () +dumpProjection xs = + forM_ xs $ \(gs, cells) -> do + putStrLn "============" + forM_ gs $ \(p, ss) -> do + putStrLn $ f p ss + putStrLn " =>" + forM_ cells $ \cell -> do + putStrLn $ showCell cell + where + f p ss = render p ++ g ss + g [Zero] = " = 0" + g [Pos] = " > 0" + g [Neg] = " < 0" + g xs + | Set.fromList xs == Set.fromList [Pos,Neg] = "/= 0" + | Set.fromList xs == Set.fromList [Zero,Pos] = ">= 0" + | Set.fromList xs == Set.fromList [Zero,Neg] = "<= 0" + | otherwise = error "showDNF: should not happen" + +dumpSignConf + :: forall v. + (Ord v, RenderVar v, Show v) + => [(SignConf (Polynomial Rational v), Map.Map (Polynomial Rational v) (Set.Set Sign))] + -> IO () +dumpSignConf x = + forM_ x $ \(conf, as) -> do + putStrLn "============" + mapM_ putStrLn $ showSignConf conf + forM_ (Map.toList as) $ \(p, sign) -> + printf "%s %s\n" (render p) (show sign) + +-- --------------------------------------------------------------------------- + +test1a :: IO () +test1a = mapM_ putStrLn $ showSignConf conf + where + x = var () + ps :: [UPolynomial (Polynomial Rational Int)] + ps = [x + 1, -2*x + 3, x] + [(conf, _)] = runM $ buildSignConf ps + +test1b :: Bool +test1b = isJust $ solve cs + where + x = var () + cs = [x + 1 .>. 0, -2*x + 3 .>. 0, x .>. 0] + +test1c :: Bool +test1c = isJust $ do + m <- solve' cs + guard $ and $ do + (p, ss) <- cs + let val = eval (m Map.!) (mapCoeff fromRational p) + return $ signOfConst val `elem` ss + where + x = var () + cs = [(x + 1, [Pos]), (-2*x + 3, [Pos]), (x, [Pos])] + +test2a :: IO () +test2a = mapM_ putStrLn $ showSignConf conf + where + x = var () + ps :: [UPolynomial (Polynomial Rational Int)] + ps = [x^(2::Int)] + [(conf, _)] = runM $ buildSignConf ps + +test2b :: Bool +test2b = isNothing $ solve cs + where + x = var () + cs = [x^(2::Int) .<. 0] + +test = and [test1b, test1c, test2b] + +test_project :: DNF (Polynomial Rational Int, [Sign]) +test_project = DNF $ map fst $ project [(p', [Zero])] + where + a = var 0 + b = var 1 + c = var 2 + x = var 3 + p :: Polynomial Rational Int + p = a*x^(2::Int) + b*x + c + p' = toUPolynomialOf p 3 + +test_project_print :: IO () +test_project_print = putStrLn $ showDNF $ test_project + +test_project_2 = project [(p, [Zero]), (x, [Pos])] + where + x = var () + p :: UPolynomial (Polynomial Rational Int) + p = x^(2::Int) + 4*x - 10 + +test_project_3_print = dumpProjection $ project [(toUPolynomialOf p 0, [Neg])] + where + a = var 0 + b = var 1 + c = var 2 + p :: Polynomial Rational Int + p = a^(2::Int) + b^(2::Int) + c^(2::Int) - 1 + +test_solve = solve [p .<. 0] + where + a = var 0 + b = var 1 + c = var 2 + p :: Polynomial Rational Int + p = a^(2::Int) + b^(2::Int) + c^(2::Int) - 1 + +test_collectPolynomials + :: [( Set.Set (UPolynomial (Polynomial Rational Int)) + , Map.Map (Polynomial Rational Int) (Set.Set Sign) + )] +test_collectPolynomials = runM $ collectPolynomials (Set.singleton p') + where + a = var 0 + b = var 1 + c = var 2 + x = var 3 + p :: Polynomial Rational Int + p = a*x^(2::Int) + b*x + c + p' = toUPolynomialOf p 3 + +test_collectPolynomials_print :: IO () +test_collectPolynomials_print = do + forM_ test_collectPolynomials $ \(ps,s) -> do + putStrLn "============" + mapM_ (putStrLn . render) (Set.toList ps) + forM_ (Map.toList s) $ \(p, sign) -> + printf "%s %s\n" (render p) (show sign) + +test_buildSignConf :: [(SignConf (Polynomial Rational Int), Map.Map (Polynomial Rational Int) (Set.Set Sign))] +test_buildSignConf = runM $ buildSignConf [toUPolynomialOf p 3] + where + a = var 0 + b = var 1 + c = var 2 + x = var 3 + p :: Polynomial Rational Int + p = a*x^(2::Int) + b*x + c + +test_buildSignConf_print :: IO () +test_buildSignConf_print = dumpSignConf test_buildSignConf + +test_buildSignConf_2 :: [(SignConf (Polynomial Rational Int), Map.Map (Polynomial Rational Int) (Set.Set Sign))] +test_buildSignConf_2 = runM $ buildSignConf [toUPolynomialOf p 0 | p <- ps] + where + x = var 0 + ps :: [Polynomial Rational Int] + ps = [x + 1, -2*x + 3, x] + +test_buildSignConf_2_print :: IO () +test_buildSignConf_2_print = dumpSignConf test_buildSignConf_2 + +test_buildSignConf_3 :: [(SignConf (Polynomial Rational Int), Map.Map (Polynomial Rational Int) (Set.Set Sign))] +test_buildSignConf_3 = runM $ buildSignConf [toUPolynomialOf p 0 | p <- ps] + where + x = var 0 + ps :: [Polynomial Rational Int] + ps = [x, 2*x] + +test_buildSignConf_3_print :: IO () +test_buildSignConf_3_print = dumpSignConf test_buildSignConf_3 + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/CongruenceClosure.hs b/src/Algorithm/CongruenceClosure.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/CongruenceClosure.hs @@ -0,0 +1,203 @@ +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.CongruenceClosure +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : portable +-- +-- References: +-- +-- * R. Nieuwenhuis and A. Oliveras, "Fast congruence closure and extensions," +-- Information and Computation, vol. 205, no. 4, pp. 557-580, Apr. 2007. +-- +-- +----------------------------------------------------------------------------- +module Algorithm.CongruenceClosure + ( Solver + , Var + , FlatTerm (..) + , newSolver + , newVar + , merge + , areCongruent + ) where + +import Prelude hiding (lookup) + +import Control.Monad +import Data.IORef +import Data.Maybe +import qualified Data.IntMap as IM + +type Var = Int + +data FlatTerm + = FTConst Var + | FTApp Var Var + deriving (Ord, Eq, Show) + +type Eqn1 = (FlatTerm, Var) +type PendingEqn = Either (Var,Var) (Eqn1, Eqn1) + +data Solver + = Solver + { svVarCounter :: IORef Int + , svPending :: IORef [PendingEqn] + , svRepresentativeTable :: IORef (IM.IntMap Var) -- 本当は配列が良い + , svClassList :: IORef (IM.IntMap [Var]) + , svUseList :: IORef (IM.IntMap [Eqn1]) + , svLookupTable :: IORef (IM.IntMap (IM.IntMap Eqn1)) + } + +newSolver :: IO Solver +newSolver = do + vcnt <- newIORef 0 + pending <- newIORef [] + rep <- newIORef IM.empty + classes <- newIORef IM.empty + useList <- newIORef IM.empty + lookup <- newIORef IM.empty + return $ + Solver + { svVarCounter = vcnt + , svPending = pending + , svRepresentativeTable = rep + , svClassList = classes + , svUseList = useList + , svLookupTable = lookup + } + +newVar :: Solver -> IO Var +newVar solver = do + v <- readIORef (svVarCounter solver) + writeIORef (svVarCounter solver) $! v + 1 + modifyIORef (svRepresentativeTable solver) (IM.insert v v) + modifyIORef (svClassList solver) (IM.insert v [v]) + modifyIORef (svUseList solver) (IM.insert v []) + return v + +merge :: Solver -> (FlatTerm, Var) -> IO () +merge solver (s, a) = do + case s of + FTConst c -> do + addToPending solver (Left (c, a)) + propagate solver + FTApp a1 a2 -> do + a1' <- getRepresentative solver a1 + a2' <- getRepresentative solver a2 + ret <- lookup solver a1' a2' + case ret of + Just (FTApp b1 b2, b) -> do + addToPending solver $ Right ((FTApp a1 a2, a), (FTApp b1 b2, b)) + propagate solver + Nothing -> do + setLookup solver a1' a2' (FTApp a1 a2, a) + modifyIORef (svUseList solver) $ + IM.alter (Just . ((FTApp a1 a2, a) :) . fromMaybe []) a1' . + IM.alter (Just . ((FTApp a1 a2, a) :) . fromMaybe []) a2' + +propagate :: Solver -> IO () +propagate solver = go + where + go = do + ps <- readIORef (svPending solver) + case ps of + [] -> return () + (p:ps') -> do + writeIORef (svPending solver) ps' + processEqn p + go + + processEqn p = do + let (a,b) = case p of + Left (a,b) -> (a,b) + Right ((_, a), (_, b)) -> (a,b) + a' <- getRepresentative solver a + b' <- getRepresentative solver b + if a' == b' + then return () + else do + clist <- readIORef (svClassList solver) + let classA = clist IM.! a' + classB = clist IM.! b' + if length classA < length classB + then update a' b' classA classB + else update b' a' classB classA + + update a' b' classA classB = do + modifyIORef (svRepresentativeTable solver) $ + IM.union (IM.fromList [(c,b') | c <- classA]) + modifyIORef (svClassList solver) $ + IM.insert b' (classA ++ classB) . IM.delete a' + + useList <- readIORef (svUseList solver) + forM_ (useList IM.! a') $ \(FTApp c1 c2, c) -> do -- FIXME: not exhaustive + c1' <- getRepresentative solver c1 + c2' <- getRepresentative solver c2 + ret <- lookup solver c1' c2' + case ret of + Just (FTApp d1 d2, d) -> do -- FIXME: not exhaustive + addToPending solver $ Right ((FTApp c1 c2, c), (FTApp d1 d2, d)) + Nothing -> do + return () + writeIORef (svUseList solver) $ IM.delete a' useList + +areCongruent :: Solver -> FlatTerm -> FlatTerm -> IO Bool +areCongruent solver t1 t2 = do + u1 <- normalize solver t1 + u2 <- normalize solver t2 + return $ u1 == u2 + +normalize :: Solver -> FlatTerm -> IO FlatTerm +normalize solver (FTConst c) = liftM FTConst $ getRepresentative solver c +normalize solver (FTApp t1 t2) = do + u1 <- getRepresentative solver t1 + u2 <- getRepresentative solver t2 + ret <- lookup solver u1 u2 + case ret of + Just (FTApp _ _, a) -> liftM FTConst $ getRepresentative solver a + Nothing -> return $ FTApp u1 u2 + +{-------------------------------------------------------------------- + Helper funcions +--------------------------------------------------------------------} + +lookup :: Solver -> Var -> Var -> IO (Maybe Eqn1) +lookup solver c1 c2 = do + tbl <- readIORef $ svLookupTable solver + return $ do + m <- IM.lookup c1 tbl + IM.lookup c2 m + +setLookup :: Solver -> Var -> Var -> Eqn1 -> IO () +setLookup solver a1 a2 eqn = do + modifyIORef (svLookupTable solver) $ + IM.insertWith IM.union a1 (IM.singleton a2 eqn) + +addToPending :: Solver -> PendingEqn -> IO () +addToPending solver eqn = modifyIORef (svPending solver) (eqn :) + +getRepresentative :: Solver -> Var -> IO Var +getRepresentative solver c = do + m <- readIORef $ svRepresentativeTable solver + return $ m IM.! c + +{-------------------------------------------------------------------- + Test +--------------------------------------------------------------------} + +test = do + solver <- newSolver + a <- newVar solver + b <- newVar solver + c <- newVar solver + d <- newVar solver + merge solver (FTConst a, c) + print =<< areCongruent solver (FTApp a b) (FTApp c d) -- False + merge solver (FTConst b, d) + print =<< areCongruent solver (FTApp a b) (FTApp c d) -- True + diff --git a/src/Algorithm/ContiTraverso.hs b/src/Algorithm/ContiTraverso.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/ContiTraverso.hs @@ -0,0 +1,122 @@ +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.ContiTraverso +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : portable +-- +-- References: +-- +-- * P. Conti and C. Traverso, "Buchberger algorithm and integer programming," +-- Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, +-- Lecture Notes in Computer Science Volume 539, 1991, pp 130-139 +-- +-- +-- +-- * IKEGAMI Daisuke, "数列と多項式の愛しい関係," 2011, +-- +-- +-- * 伊藤雅史, , 平林 隆一, "整数計画問題のための b-Gröbner 基底変換アルゴリズム," +-- +-- +-- +----------------------------------------------------------------------------- +module Algorithm.ContiTraverso + ( solve + , solve' + ) where + +import Data.Function +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.List +import Data.Monoid +import Data.Ratio + +import Data.ArithRel +import Data.Linear +import qualified Data.LA as LA +import Data.Expr (Var, VarSet, Variables (..), Model) +import Data.OptDir +import Data.Polynomial +import Data.Polynomial.GBase +import qualified Algorithm.LPUtil as LPUtil + +solve :: MonomialOrder Var -> OptDir -> LA.Expr Rational -> [LA.Atom Rational] -> Maybe (Model Integer) +solve cmp dir obj cs = do + m <- solve' cmp obj3 cs3 + return . IM.map round . mt . IM.map fromInteger $ m + where + ((obj2,cs2), mt) = LPUtil.toStandardForm (if dir == OptMin then obj else lnegate obj, cs) + obj3 = LA.mapCoeff g obj2 + where + g = round . (c*) + c = fromInteger $ foldl' lcm 1 [denominator c | (c,_) <- LA.terms obj] + cs3 = map f cs2 + f (lhs,rhs) = (LA.mapCoeff g lhs, g rhs) + where + g = round . (c*) + c = fromInteger $ foldl' lcm 1 [denominator c | (c,_) <- LA.terms lhs] + +solve' :: MonomialOrder Var -> LA.Expr Integer -> [(LA.Expr Integer, Integer)] -> Maybe (Model Integer) +solve' cmp obj cs + | or [c < 0 | (c,x) <- LA.terms obj, x /= LA.unitVar] = error "all coefficient of cost function should be non-negative" + | otherwise = + if IM.keysSet (IM.filter (/= 0) m) `IS.isSubsetOf` vs' + then Just $ IM.filterWithKey (\y _ -> y `IS.member` vs') m + else Nothing + + where + vs :: [Var] + vs = IS.toList vs' + + vs' :: VarSet + vs' = vars $ obj : [lhs | (lhs,_) <- cs] + + v2 :: Var + v2 = if IS.null vs' then 0 else IS.findMax vs' + 1 + + vs2 :: [Var] + vs2 = [v2 .. v2 + length cs - 1] + + vs2' :: IS.IntSet + vs2' = IS.fromList vs2 + + t :: Var + t = v2 + length cs + + cmp2 :: MonomialOrder Var + cmp2 = elimOrdering (IS.fromList vs2) `mappend` elimOrdering (IS.singleton t) `mappend` costOrdering obj `mappend` cmp + + gbase :: [Polynomial Rational Var] + gbase = buchberger cmp2 (product (map var (t:vs2)) - 1 : phi) + where + phi = do + xj <- vs + let aj = [(yi, aij) | (yi,(ai,_)) <- zip vs2 cs, let aij = LA.coeff xj ai] + return $ product [var yi ^ aij | (yi, aij) <- aj, aij > 0] + - product [var yi ^ (-aij) | (yi, aij) <- aj, aij < 0] * var xj + + yb = product [var yi ^ bi | ((_,bi),yi) <- zip cs vs2] + + [(_,z)] = terms (reduce cmp2 yb gbase) + + m = mkModel (vs++vs2++[t]) z + +mkModel :: [Var] -> MonicMonomial Var -> Model Integer +mkModel vs xs = mmToIntMap xs `IM.union` IM.fromList [(x, 0) | x <- vs] +-- IM.union is left-biased + +costOrdering :: LA.Expr Integer -> MonomialOrder Var +costOrdering obj = compare `on` f + where + vs = vars obj + f xs = LA.evalExpr (mkModel (IS.toList vs) xs) obj + +elimOrdering :: IS.IntSet -> MonomialOrder Var +elimOrdering xs = compare `on` f + where + f ys = not (IS.null (xs `IS.intersection` IM.keysSet (mmToIntMap ys))) diff --git a/src/Algorithm/Cooper.hs b/src/Algorithm/Cooper.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/Cooper.hs @@ -0,0 +1,444 @@ +{-# OPTIONS_GHC -Wall #-} +{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.Cooper +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (FlexibleInstances) +-- +-- Naive implementation of Cooper's algorithm +-- +-- Reference: +-- +-- * +-- +-- * +-- +-- See also: +-- +-- * +-- +----------------------------------------------------------------------------- +module Algorithm.Cooper + ( + -- * Language of presburger arithmetics + ExprZ + , Lit (..) + , QFFormula (..) + , (.|.) + , Model + + -- * Projection + , project + , projectCases + , projectCases' + , projectCasesN + + -- * Quantifier elimination + , eliminateQuantifiers + + -- * Constraint solving + , solveFormula + , solveQFFormula + , solveConj + , solveQFLA + ) where + +import Control.Monad +import Data.List +import Data.Maybe +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.Ratio + +import Data.ArithRel +import Data.Expr +import Data.Formula +import Data.Linear +import qualified Data.LA as LA +import qualified Algorithm.FourierMotzkin as FM + +-- --------------------------------------------------------------------------- + +-- | Linear arithmetic expression over integers. +type ExprZ = LA.Expr Integer + +atomZ :: RelOp -> Expr Rational -> Expr Rational -> Maybe QFFormula +atomZ op a b = do + (e1,c1) <- FM.termR a + (e2,c2) <- FM.termR b + let a' = c2 .*. e1 + b' = c1 .*. e2 + case op of + Le -> return $ Lit $ a' `leZ` b' + Lt -> return $ Lit $ a' `ltZ` b' + Ge -> return $ Lit $ a' `geZ` b' + Gt -> return $ Lit $ a' `gtZ` b' + Eql -> return $ eqZ a' b' + NEq -> liftM notB (atomZ Eql a b) + +leZ, ltZ, geZ, gtZ :: ExprZ -> ExprZ -> Lit +leZ e1 e2 = e1 `ltZ` (e2 .+. LA.constant 1) +ltZ e1 e2 = Pos $ (e2 .-. e1) +geZ = flip leZ +gtZ = flip gtZ + +eqZ :: ExprZ -> ExprZ -> QFFormula +eqZ e1 e2 = Lit (e1 `leZ` e2) .&&. Lit (e1 `geZ` e2) + +-- | Literal +-- +-- * @Pos e@ means @e > 0@ +-- +-- * @Divisible True d e@ means @e@ can be divided by @d@ (i.e. @d|e@) +-- +-- * @Divisible False d e@ means @e@ can not be divided by @d@ (i.e. @¬(d|e)@) +data Lit + = Pos ExprZ + | Divisible Bool Integer ExprZ + deriving (Show, Eq, Ord) + +instance Variables Lit where + vars (Pos t) = vars t + vars (Divisible _ _ t) = vars t + +instance Complement Lit where + notB (Pos e) = e `leZ` LA.constant 0 + notB (Divisible b c e) = Divisible (not b) c e + +-- | quantifier-free negation normal form +data QFFormula + = T' + | F' + | And' QFFormula QFFormula + | Or' QFFormula QFFormula + | Lit Lit + deriving (Show, Eq, Ord) + +instance Complement QFFormula where + notB T' = F' + notB F' = T' + notB (And' a b) = Or' (notB a) (notB b) + notB (Or' a b) = And' (notB a) (notB b) + notB (Lit lit) = Lit (notB lit) + +instance Lattice QFFormula where + top = T' + bottom = F' + meet = And' + join = Or' + +instance Boolean QFFormula + +instance Variables QFFormula where + vars T' = IS.empty + vars F' = IS.empty + vars (And' a b) = vars a `IS.union` vars b + vars (Or' a b) = vars a `IS.union` vars b + vars (Lit l) = vars l + +instance IsRel (LA.Expr Integer) QFFormula where + rel op lhs rhs = + case op of + Le -> Lit $ leZ lhs rhs + Ge -> Lit $ geZ lhs rhs + Lt -> Lit $ ltZ lhs rhs + Gt -> Lit $ gtZ lhs rhs + Eql -> eqZ lhs rhs + NEq -> notB $ rel Eql lhs rhs + +(.|.) :: Integer -> ExprZ -> QFFormula +n .|. e = Lit $ Divisible True n e + +subst1 :: Var -> ExprZ -> QFFormula -> QFFormula +subst1 x e = go + where + go T' = T' + go F' = F' + go (And' a b) = And' (go a) (go b) + go (Or' a b) = Or' (go a) (go b) + go (Lit (Divisible b c e1)) = Lit $ Divisible b c $ LA.applySubst1 x e e1 + go (Lit (Pos e1)) = Lit $ Pos $ LA.applySubst1 x e e1 + +simplify :: QFFormula -> QFFormula +simplify (And' a b) = simplify1 $ And' (simplify a) (simplify b) +simplify (Or' a b) = simplify1 $ Or' (simplify a) (simplify b) +simplify formula = simplify1 formula + +simplify1 :: QFFormula -> QFFormula +simplify1 T' = T' +simplify1 F' = F' +simplify1 (And' a b) = + case (a, b) of + (T', b') -> b' + (a', T') -> a' + (F', _) -> false + (_, F') -> false + (a',b') -> a' .&&. b' +simplify1 (Or' a b) = + case (a, b) of + (F', b') -> b' + (a', F') -> a' + (T', _) -> true + (_, T') -> true + (a',b') -> a' .||. b' +simplify1 (Lit lit) = simplifyLit lit + +simplifyLit :: Lit -> QFFormula +simplifyLit (Pos e) = + case LA.asConst e of + Just c -> if c > 0 then true else false + Nothing -> + -- e > 0 <=> e - 1 >= 0 + -- <=> LA.mapCoeff (`div` d) (e - 1) >= 0 + -- <=> LA.mapCoeff (`div` d) (e - 1) + 1 > 0 + Lit $ Pos $ LA.mapCoeff (`div` d) (e .-. LA.constant 1) .+. LA.constant 1 + where + d = if null cs then 1 else abs $ foldl1' gcd cs + cs = [c | (c,x) <- LA.terms e, x /= LA.unitVar] +simplifyLit lit@(Divisible b c e) + | LA.coeff LA.unitVar e `mod` d /= 0 = if b then false else true + | c' == 1 = if b then true else false + | d == 1 = Lit lit + | otherwise = Lit $ Divisible b c' e' + where + d = abs $ foldl' gcd c [c2 | (c2,x) <- LA.terms e, x /= LA.unitVar] + c' = c `div` d + e' = LA.mapCoeff (`div` d) e + +-- --------------------------------------------------------------------------- + +data Witness = WCase1 Integer ExprZ | WCase2 Integer Integer Integer [ExprZ] + +evalWitness :: Model Integer -> Witness -> Integer +evalWitness model (WCase1 c e) = LA.evalExpr model e `div` c +evalWitness model (WCase2 c j delta us) + | null us' = j `div` c + | otherwise = (j + (((u - delta - 1) `div` delta) * delta)) `div` c + where + us' = map (LA.evalExpr model) us + u = minimum us' + +-- --------------------------------------------------------------------------- + +project :: Var -> QFFormula -> QFFormula +project x formula = simplify $ orB [phi | (phi,_) <- projectCases' x formula, phi /= F'] + +projectCases :: Var -> QFFormula -> [(QFFormula, Model Integer -> Model Integer)] +projectCases x formula = do + (phi, wit) <- projectCases' x formula + return (phi, \m -> IM.insert x (evalWitness m wit) m) + +projectCases' :: Var -> QFFormula -> [(QFFormula, Witness)] +projectCases' x formula = [(simplify phi, w) | (phi,w) <- case1 ++ case2] + where + -- xの係数の最小公倍数 + c :: Integer + c = f formula + where + f :: QFFormula -> Integer + f T' = 1 + f F' = 1 + f (And' a b) = lcm (f a) (f b) + f (Or' a b) = lcm (f a) (f b) + f (Lit (Pos e)) = fromMaybe 1 (LA.lookupCoeff x e) + f (Lit (Divisible _ _ e)) = fromMaybe 1 (LA.lookupCoeff x e) + + -- 式をスケールしてxの係数の絶対値をcへと変換し、その後cxをxで置き換え、 + -- xがcで割り切れるという制約を追加した論理式 + formula1 :: QFFormula + formula1 = simplify $ f formula .&&. Lit (Divisible True c (LA.var x)) + where + f :: QFFormula -> QFFormula + f T' = T' + f F' = F' + f (And' a b) = f a .&&. f b + f (Or' a b) = f a .||. f b + f lit@(Lit (Pos e)) = + case LA.lookupCoeff x e of + Nothing -> lit + Just a -> + let s = abs (c `div` a) + in Lit $ Pos $ g s e + f lit@(Lit (Divisible b d e)) = + case LA.lookupCoeff x e of + Nothing -> lit + Just a -> + let s = abs (c `div` a) + in Lit $ Divisible b (s*d) $ g s e + + g :: Integer -> ExprZ -> ExprZ + g s = LA.mapCoeffWithVar (\c' x' -> if x==x' then signum c' else s*c') + + -- d|x+t という形の論理式の d の最小公倍数 + delta :: Integer + delta = f formula1 + where + f :: QFFormula -> Integer + f T' = 1 + f F' = 1 + f (And' a b) = lcm (f a) (f b) + f (Or' a b) = lcm (f a) (f b) + f (Lit (Divisible _ d _)) = d + f (Lit (Pos _)) = 1 + + -- ts = {t | t < x は formula1 に現れる原子論理式} + ts :: [ExprZ] + ts = f formula1 + where + f :: QFFormula -> [ExprZ] + f T' = [] + f F' = [] + f (And' a b) = f a ++ f b + f (Or' a b) = f a ++ f b + f (Lit (Divisible _ _ _)) = [] + f (Lit (Pos e)) = + case LA.extractMaybe x e of + Nothing -> [] + Just (1, e') -> [lnegate e'] -- Pos e <=> (x + e' > 0) <=> (-e' < x) + Just (-1, _) -> [] -- Pos e <=> (-x + e' > 0) <=> (x < e') + _ -> error "should not happen" + + -- formula1を真にする最小のxが存在する場合 + case1 :: [(QFFormula, Witness)] + case1 = [ (subst1 x e formula1, WCase1 c e) + | j <- [1..delta], t <- ts, let e = t .+. LA.constant j ] + + -- formula1のなかの x < t を真に t < x を偽に置き換えた論理式 + formula2 :: QFFormula + formula2 = simplify $ f formula1 + where + f :: QFFormula -> QFFormula + f T' = T' + f F' = F' + f (And' a b) = f a .&&. f b + f (Or' a b) = f a .||. f b + f lit@(Lit (Pos e)) = + case LA.lookupCoeff x e of + Nothing -> lit + Just 1 -> F' -- Pos e <=> ( x + e' > 0) <=> -e' < x + Just (-1) -> T' -- Pos e <=> (-x + e' > 0) <=> x < e' + _ -> error "should not happen" + f lit@(Lit (Divisible _ _ _)) = lit + + -- us = {u | x < u は formula1 に現れる原子論理式} + us :: [ExprZ] + us = f formula1 + where + f :: QFFormula -> [ExprZ] + f T' = [] + f F' = [] + f (And' a b) = f a ++ f b + f (Or' a b) = f a ++ f b + f (Lit (Pos e)) = + case LA.extractMaybe x e of + Nothing -> [] + Just (1, _) -> [] -- Pos e <=> ( x + e' > 0) <=> -e' < x + Just (-1, e') -> [e'] -- Pos e <=> (-x + e' > 0) <=> x < e' + _ -> error "should not happen" + f (Lit (Divisible _ _ _)) = [] + + -- formula1を真にする最小のxが存在しない場合 + case2 :: [(QFFormula, Witness)] + case2 = [(subst1 x (LA.constant j) formula2, WCase2 c j delta us) | j <- [1..delta]] + +projectCasesN :: VarSet -> QFFormula -> [(QFFormula, Model Integer -> Model Integer)] +projectCasesN vs2 = f (IS.toList vs2) + where + f :: [Var] -> QFFormula -> [(QFFormula, Model Integer -> Model Integer)] + f [] formula = return (formula, id) + f (v:vs) formula = do + (formula2, mt1) <- projectCases v formula + (formula3, mt2) <- f vs formula2 + return (formula3, mt1 . mt2) + +-- --------------------------------------------------------------------------- + +-- | eliminate quantifiers and returns equivalent quantifier-free formula. +eliminateQuantifiers :: Formula (Atom Rational) -> Maybe QFFormula +eliminateQuantifiers = f + where + f T = return T' + f F = return F' + f (Atom (Rel e1 op e2)) = atomZ op e1 e2 + f (And a b) = liftM2 (.&&.) (f a) (f b) + f (Or a b) = liftM2 (.||.) (f a) (f b) + f (Not a) = f (pushNot a) + f (Imply a b) = f $ Or (Not a) b + f (Equiv a b) = f $ And (Imply a b) (Imply b a) + f (Forall x body) = liftM notB $ f $ Exists x $ Not body + f (Exists x body) = liftM (project x) (f body) + +-- --------------------------------------------------------------------------- + +solveFormula :: Formula (Atom Rational) -> SatResult Integer +solveFormula formula = + case eliminateQuantifiers formula of + Nothing -> Unknown + Just formula' -> + case solveQFFormula formula' of + Nothing -> Unsat + Just m -> Sat m + +solveQFFormula :: QFFormula -> Maybe (Model Integer) +solveQFFormula formula = listToMaybe $ do + (formula2, mt) <- projectCasesN (vars formula) formula + case formula2 of + T' -> return $ mt IM.empty + _ -> mzero + +-- | solve a (open) quantifier-free formula +solveConj :: [LA.Atom Rational] -> Maybe (Model Integer) +solveConj cs = solveQFFormula formula + where + formula = andB [rel op (f (lhs .-. rhs)) (LA.constant 0) | Rel lhs op rhs <- cs] + f e = LA.mapCoeff (round . (s*)) e + where + s = fromInteger $ foldl' lcm 1 [denominator c | (c,_) <- LA.terms e] + +-- | solve a (open) quantifier-free formula +solveQFLA :: [LA.Atom Rational] -> VarSet -> Maybe (Model Rational) +solveQFLA cs ivs = listToMaybe $ do + (cs2, mt) <- FM.projectN rvs cs + m <- maybeToList $ solveConj cs2 + return $ mt $ IM.map fromInteger m + where + rvs = vars cs `IS.difference` ivs + +-- --------------------------------------------------------------------------- + +testHagiya :: QFFormula +testHagiya = project 1 $ andB [c1, c2, c3] + where + [x,y,z] = map LA.var [1..3] + c1 = x .<. (y .+. y) + c2 = z .<. x + c3 = 3 .|. x + +{- +∃ x. 0 < y+y ∧ z 0 ∧ 3|z+1) ∨ (2y-z > -2 ∧ 3|z+2) ∨ (2y-z > -3 ∧ 3|z+3) +-} + +test3 :: QFFormula +test3 = project 1 $ andB [p1,p2,p3,p4] + where + x = LA.var 0 + y = LA.var 1 + p1 = LA.constant 0 .<. y + p2 = 2 .*. x .<. y + p3 = y .<. x .+. LA.constant 2 + p4 = 2 .|. y + +{- +∃ y. 0 < y ∧ 2x +-- +----------------------------------------------------------------------------- +module Algorithm.FOLModelFinder + ( + -- * Formula types + Var + , FSym + , PSym + , GenLit (..) + , Term (..) + , Atom (..) + , Lit + , Clause + , Formula + , GenFormula (..) + , toSkolemNF + + -- * Model types + , Model (..) + , Entity + , showModel + , showEntity + + -- * Main function + , findModel + ) where + +import Control.Monad +import Control.Monad.State +import Data.Array.IArray +import Data.IORef +import Data.List +import Data.Maybe +import qualified Data.Map as Map +import qualified Data.Set as Set +import Text.Printf + +import qualified SAT + +-- --------------------------------------------------------------------------- + +-- | Variable +type Var = String + +-- | Function Symbol +type FSym = String + +-- | Predicate Symbol +type PSym = String + +class Vars a where + vars :: a -> Set.Set Var + +instance Vars a => Vars [a] where + vars = Set.unions . map vars + +-- | Generalized literal type parameterized by atom type +data GenLit a + = Pos a + | Neg a + deriving (Show, Eq, Ord) + +instance Vars a => Vars (GenLit a) where + vars (Pos a) = vars a + vars (Neg a) = vars a + +-- --------------------------------------------------------------------------- + +-- | Term +data Term + = TmApp FSym [Term] + | TmVar Var + deriving (Show, Eq, Ord) + +data Atom = PApp PSym [Term] + deriving (Show, Eq, Ord) + +type Lit = GenLit Atom + +type Clause = [Lit] + +instance Vars Term where + vars (TmVar v) = Set.singleton v + vars (TmApp _ ts) = vars ts + +instance Vars Atom where + vars (PApp _ ts) = vars ts + +-- --------------------------------------------------------------------------- + +-- Formula type +type Formula = GenFormula Atom + +-- Generalized formula parameterized by atom type +data GenFormula a + = T + | F + | Atom a + | And (GenFormula a) (GenFormula a) + | Or (GenFormula a) (GenFormula a) + | Not (GenFormula a) + | Imply (GenFormula a) (GenFormula a) + | Equiv (GenFormula a) (GenFormula a) + | Forall Var (GenFormula a) + | Exists Var (GenFormula a) + deriving (Show, Eq, Ord) + +instance Vars a => Vars (GenFormula a) where + vars T = Set.empty + vars F = Set.empty + vars (Atom a) = vars a + vars (And phi psi) = vars phi `Set.union` vars psi + vars (Or phi psi) = vars phi `Set.union` vars psi + vars (Not phi) = vars phi + vars (Imply phi psi) = vars phi `Set.union` vars psi + vars (Equiv phi psi) = vars phi `Set.union` vars psi + vars (Forall v phi) = Set.delete v (vars phi) + vars (Exists v phi) = Set.delete v (vars phi) + +toNNF :: Formula -> Formula +toNNF = f + where + f (And phi psi) = f phi `And` f psi + f (Or phi psi) = f phi `Or` f psi + f (Not phi) = g phi + f (Imply phi psi) = g phi `Or` f psi + f (Equiv phi psi) = f (And (Imply phi psi) (Imply psi phi)) + f (Forall v phi) = Forall v (f phi) + f (Exists v phi) = Exists v (f phi) + f phi = phi + + g :: Formula -> Formula + g T = F + g F = T + g (And phi psi) = g phi `Or` g psi + g (Or phi psi) = g phi `And` g psi + g (Not phi) = f phi + g (Imply phi psi) = f phi `And` g psi + g (Equiv phi psi) = g (And (Imply phi psi) (Imply psi phi)) + g (Forall v phi) = Exists v (g phi) + g (Exists v phi) = Forall v (g phi) + g (Atom a) = Not (Atom a) + +-- | normalize a formula into a skolem normal form. +-- +-- TODO: +-- +-- * Tseitin encoding +toSkolemNF :: forall m. Monad m => (String -> Int -> m FSym) -> Formula -> m [Clause] +toSkolemNF skolem phi = f [] Map.empty (toNNF phi) + where + f :: [Var] -> Map.Map Var Term -> Formula -> m [Clause] + f _ _ T = return [] + f _ _ F = return [[]] + f _ s (Atom a) = return [[Pos (substAtom s a)]] + f _ s (Not (Atom a)) = return [[Neg (substAtom s a)]] + f uvs s (And phi psi) = do + phi' <- f uvs s phi + psi' <- f uvs s psi + return $ phi' ++ psi' + f uvs s (Or phi psi) = do + phi' <- f uvs s phi + psi' <- f uvs s psi + return $ [c1++c2 | c1 <- phi', c2 <- psi'] + f uvs s psi@(Forall v phi) = do + let v' = gensym v (vars psi `Set.union` Set.fromList uvs) + f (v' : uvs) (Map.insert v (TmVar v') s) phi + f uvs s (Exists v phi) = do + fsym <- skolem v (length uvs) + f uvs (Map.insert v (TmApp fsym [TmVar v | v <- reverse uvs]) s) phi + f _ _ _ = error "toSkolemNF: should not happen" + + gensym :: String -> Set.Set Var -> Var + gensym template vs = head [name | name <- names, Set.notMember name vs] + where + names = template : [template ++ show n | n <-[1..]] + + substAtom :: Map.Map Var Term -> Atom -> Atom + substAtom s (PApp p ts) = PApp p (map (substTerm s) ts) + + substTerm :: Map.Map Var Term -> Term -> Term + substTerm s (TmVar v) = fromMaybe (TmVar v) (Map.lookup v s) + substTerm s (TmApp f ts) = TmApp f (map (substTerm s) ts) + +test_toSkolemNF = do + ref <- newIORef 0 + let skolem name _ = do + n <- readIORef ref + let fsym = name ++ "#" ++ show n + writeIORef ref (n+1) + return fsym + + -- ∀x. animal(a) → (∃y. heart(y) ∧ has(x,y)) + let phi = Forall "x" $ + Imply + (Atom (PApp "animal" [TmVar "x"])) + (Exists "y" $ + And (Atom (PApp "heart" [TmVar "y"])) + (Atom (PApp "has" [TmVar "x", TmVar "y"]))) + + phi' <- toSkolemNF skolem phi + + print phi' +{- +[[Neg (PApp "animal" [TmVar "x"]),Pos (PApp "heart" [TmApp "y#0" [TmVar "x"]])],[Neg (PApp "animal" [TmVar "x"]),Pos (PApp "has" [TmVar "x",TmApp "y#0" [TmVar "x"]])]] + +{¬animal(x) ∨ heart(y#1(x)), ¬animal(x) ∨ has(x1, y#0(x))} +-} + +-- --------------------------------------------------------------------------- + +-- | Shallow term +data SGenTerm v + = STmApp FSym [v] + | STmVar v + deriving (Show, Eq, Ord) + +-- | Shallow atom +data SGenAtom v + = SPApp PSym [v] + | SEq (SGenTerm v) v + deriving (Show, Eq, Ord) + +type STerm = SGenTerm Var +type SAtom = SGenAtom Var +type SLit = GenLit SAtom +type SClause = [SLit] + +instance Vars STerm where + vars (STmApp _ xs) = Set.fromList xs + vars (STmVar v) = Set.singleton v + +instance Vars SAtom where + vars (SPApp _ xs) = Set.fromList xs + vars (SEq t v) = Set.insert v (vars t) + +-- --------------------------------------------------------------------------- + +type M = State (Set.Set Var, Int, [SLit]) + +flatten :: Clause -> SClause +flatten c = + case runState (mapM flattenLit c) (vars c, 0, []) of + (c, (_,_,ls)) -> removeNegEq $ ls ++ c + where + gensym :: M Var + gensym = do + (vs, n, ls) <- get + let go m = do + let v = "#" ++ show m + if v `Set.member` vs + then go (m+1) + else do + put (Set.insert v vs, m+1, ls) + return v + go n + + flattenLit :: Lit -> M SLit + flattenLit (Pos a) = liftM Pos $ flattenAtom a + flattenLit (Neg a) = liftM Neg $ flattenAtom a + + flattenAtom :: Atom -> M SAtom + flattenAtom (PApp "=" [TmVar x, TmVar y]) = return $ SEq (STmVar x) y + flattenAtom (PApp "=" [TmVar x, TmApp f ts]) = do + xs <- mapM flattenTerm ts + return $ SEq (STmApp f xs) x + flattenAtom (PApp "=" [TmApp f ts, TmVar x]) = do + xs <- mapM flattenTerm ts + return $ SEq (STmApp f xs) x + flattenAtom (PApp "=" [TmApp f ts, t2]) = do + xs <- mapM flattenTerm ts + x <- flattenTerm t2 + return $ SEq (STmApp f xs) x + flattenAtom (PApp p ts) = do + xs <- mapM flattenTerm ts + return $ SPApp p xs + + flattenTerm :: Term -> M Var + flattenTerm (TmVar x) = return x + flattenTerm (TmApp f ts) = do + xs <- mapM flattenTerm ts + x <- gensym + (vs, n, ls) <- get + put (vs, n, Neg (SEq (STmApp f xs) x) : ls) + return x + + removeNegEq :: SClause -> SClause + removeNegEq = go [] + where + go r [] = r + go r (Neg (SEq (STmVar x) y) : ls) = go (map (substLit x y) r) (map (substLit x y) ls) + go r (l : ls) = go (l : r) ls + + substLit :: Var -> Var -> SLit -> SLit + substLit x y (Pos a) = Pos $ substAtom x y a + substLit x y (Neg a) = Neg $ substAtom x y a + + substAtom :: Var -> Var -> SAtom -> SAtom + substAtom x y (SPApp p xs) = SPApp p (map (substVar x y) xs) + substAtom x y (SEq t v) = SEq (substTerm x y t) (substVar x y v) + + substTerm :: Var -> Var -> STerm -> STerm + substTerm x y (STmApp f xs) = STmApp f (map (substVar x y) xs) + substTerm x y (STmVar v) = STmVar (substVar x y v) + + substVar :: Var -> Var -> Var -> Var + substVar x y v + | v==x = y + | otherwise = v + +test_flatten = flatten [Pos $ PApp "P" [TmApp "a" [], TmApp "f" [TmVar "x"]]] + +{- +[Pos $ PApp "P" [TmApp "a" [], TmApp "f" [TmVar "x"]]] + +P(a, f(x)) + +[Pos (SPApp "P" ["#0","#1"]),Neg (SEq (STmApp "a" []) "#0"),Neg (SEq (STmApp "f" ["x"]) "#1")] + +f(x) ≠ z ∨ a ≠ y ∨ P(y,z) +(f(x) = z ∧ a = y) → P(y,z) +-} + +-- --------------------------------------------------------------------------- + +-- | Element of model. +type Entity = Int + +-- | print entity +showEntity :: Entity -> String +showEntity e = "$" ++ show e + +showEntityTuple :: [Entity] -> String +showEntityTuple xs = printf "(%s)" $ intercalate ", " $ map showEntity xs + +-- --------------------------------------------------------------------------- + +type GroundTerm = SGenTerm Entity +type GroundAtom = SGenAtom Entity +type GroundLit = GenLit GroundAtom +type GroundClause = [GroundLit] + +type Subst = Map.Map Var Entity + +enumSubst :: Set.Set Var -> [Entity] -> [Subst] +enumSubst vs univ = do + ps <- sequence [[(v,e) | e <- univ] | v <- Set.toList vs] + return $ Map.fromList ps + +applySubst :: Subst -> SClause -> GroundClause +applySubst s = map substLit + where + substLit :: SLit -> GroundLit + substLit (Pos a) = Pos $ substAtom a + substLit (Neg a) = Neg $ substAtom a + + substAtom :: SAtom -> GroundAtom + substAtom (SPApp p xs) = SPApp p (map substVar xs) + substAtom (SEq t v) = SEq (substTerm t) (substVar v) + + substTerm :: STerm -> GroundTerm + substTerm (STmApp f xs) = STmApp f (map substVar xs) + substTerm (STmVar v) = STmVar (substVar v) + + substVar :: Var -> Entity + substVar = (s Map.!) + +simplifyGroundClause :: GroundClause -> Maybe GroundClause +simplifyGroundClause = liftM concat . mapM f + where + f :: GroundLit -> Maybe [GroundLit] + f (Pos (SEq (STmVar x) y)) = if x==y then Nothing else return [] + f lit = return [lit] + +collectFSym :: SClause -> Set.Set (FSym, Int) +collectFSym = Set.unions . map f + where + f :: SLit -> Set.Set (FSym, Int) + f (Pos a) = g a + f (Neg a) = g a + + g :: SAtom -> Set.Set (FSym, Int) + g (SEq (STmApp f xs) _) = Set.singleton (f, length xs) + g _ = Set.empty + +collectPSym :: SClause -> Set.Set (PSym, Int) +collectPSym = Set.unions . map f + where + f :: SLit -> Set.Set (PSym, Int) + f (Pos a) = g a + f (Neg a) = g a + + g :: SAtom -> Set.Set (PSym, Int) + g (SPApp p xs) = Set.singleton (p, length xs) + g _ = Set.empty + +-- --------------------------------------------------------------------------- + +data Model + = Model + { mUniverse :: [Entity] + , mRelations :: Map.Map PSym [[Entity]] + , mFunctions :: Map.Map FSym [([Entity], Entity)] + } + +showModel :: Model -> [String] +showModel m = + printf "DOMAIN = {%s}" (intercalate ", " (map showEntity (mUniverse m))) : + [ printf "%s = { %s }" p s + | (p, xss) <- Map.toList (mRelations m) + , let s = intercalate ", " [if length xs == 1 then showEntity (head xs) else showEntityTuple xs | xs <- xss] + ] ++ + [ printf "%s%s = %s" f (if length xs == 0 then "" else showEntityTuple xs) (showEntity y) + | (f, xss) <- Map.toList (mFunctions m) + , (xs, y) <- xss + ] + +-- --------------------------------------------------------------------------- + +findModel :: Int -> [Clause] -> IO (Maybe Model) +findModel size cs = do + let univ = [0..size-1] + + let cs2 = map flatten cs + fs = Set.unions $ map collectFSym cs2 + ps = Set.unions $ map collectPSym cs2 + + solver <- SAT.newSolver + + ref <- newIORef Map.empty + + let translateAtom :: GroundAtom -> IO SAT.Var + translateAtom (SEq (STmVar _) _) = error "should not happen" + translateAtom a = do + m <- readIORef ref + case Map.lookup a m of + Just b -> return b + Nothing -> do + b <- SAT.newVar solver + writeIORef ref (Map.insert a b m) + return b + + translateLit :: GroundLit -> IO SAT.Lit + translateLit (Pos a) = translateAtom a + translateLit (Neg a) = liftM negate $ translateAtom a + + translateClause :: GroundClause -> IO SAT.Clause + translateClause = mapM translateLit + + -- Instances + forM_ cs2 $ \c -> do + forM_ (enumSubst (vars c) univ) $ \s -> do + case simplifyGroundClause (applySubst s c) of + Nothing -> return () + Just c' -> SAT.addClause solver =<< translateClause c' + + -- Functional definitions + forM_ (Set.toList fs) $ \(f, arity) -> do + forM_ (replicateM arity univ) $ \args -> + forM_ [(y1,y2) | y1 <- univ, y2 <- univ, y1 < y2] $ \(y1,y2) -> do + let c = [Neg (SEq (STmApp f args) y1), Neg (SEq (STmApp f args) y2)] + c' <- translateClause c + SAT.addClause solver c' + + -- Totality definitions + forM_ (Set.toList fs) $ \(f, arity) -> do + forM_ (replicateM arity univ) $ \args -> do + let c = [Pos (SEq (STmApp f args) y) | y <- univ] + c' <- translateClause c + SAT.addClause solver c' + + ret <- SAT.solve solver + if ret + then do + bmodel <- SAT.model solver + m <- readIORef ref + + let rels = Map.fromList $ do + (p,_) <- Set.toList ps + let tbl = sort [xs | (SPApp p' xs, b) <- Map.toList m, p == p', bmodel ! b] + return (p, tbl) + let funs = Map.fromList $ do + (f,_) <- Set.toList fs + let tbl = sort [(xs, y) | (SEq (STmApp f' xs) y, b) <- Map.toList m, f == f', bmodel ! b] + return (f, tbl) + + let model = Model + { mUniverse = univ + , mRelations = rels + , mFunctions = funs + } + + return (Just model) + else do + return Nothing + +-- --------------------------------------------------------------------------- + +{- +∀x. ∃y. x≠y && f(y)=x +∀x. x≠g(x) ∧ f(g(x))=x +-} + +test = do + let c1 = [Pos $ PApp "=" [TmApp "f" [TmApp "g" [TmVar "x"]], TmVar "x"]] + c2 = [Neg $ PApp "=" [TmVar "x", TmApp "g" [TmVar "x"]]] + ret <- findModel 3 [c1, c2] + case ret of + Nothing -> putStrLn "=== NO MODEL FOUND ===" + Just m -> do + putStrLn "=== A MODEL FOUND ===" + mapM_ putStrLn $ showModel m + +test2 = do + let phi = Forall "x" $ Exists "y" $ + And (Not (Atom (PApp "=" [TmVar "x", TmVar "y"]))) + (Atom (PApp "=" [TmApp "f" [TmVar "y"], TmVar "x"])) + + ref <- newIORef 0 + let skolem name _ = do + n <- readIORef ref + let fsym = name ++ "#" ++ show n + writeIORef ref (n+1) + return fsym + cs <- toSkolemNF skolem phi + + ret <- findModel 3 cs + case ret of + Nothing -> putStrLn "=== NO MODEL FOUND ===" + Just m -> do + putStrLn "=== A MODEL FOUND ===" + mapM_ putStrLn $ showModel m + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/FourierMotzkin.hs b/src/Algorithm/FourierMotzkin.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/FourierMotzkin.hs @@ -0,0 +1,284 @@ +{-# OPTIONS_GHC -Wall #-} +{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.FourierMotzkin +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (MultiParamTypeClasses, FunctionalDependencies) +-- +-- Naïve implementation of Fourier-Motzkin Variable Elimination +-- +-- Reference: +-- +-- * +-- +----------------------------------------------------------------------------- +module Algorithm.FourierMotzkin + ( Lit (..) + , project + , projectN + , eliminateQuantifiers + , solve + , solveConj + + -- Functions for internal use in OmegaTest + , termR + , Rat + , constraintsToDNF + ) where + +import Control.Monad +import Data.List +import Data.Maybe +import Data.Ratio +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS + +import Data.ArithRel +import Data.Expr +import Data.Formula +import Data.Linear +import qualified Data.LA as LA +import qualified Data.Interval as Interval + +-- --------------------------------------------------------------------------- + +type ExprZ = LA.Expr Integer + +-- | (t,c) represents t/c, and c must be >0. +type Rat = (ExprZ, Integer) + +evalRat :: Model Rational -> Rat -> Rational +evalRat model (e, d) = LA.lift1 1 (model IM.!) (LA.mapCoeff fromIntegral e) / (fromIntegral d) + +-- | Literal +data Lit = Nonneg ExprZ | Pos ExprZ deriving (Show, Eq, Ord) + +instance Variables Lit where + vars (Pos t) = vars t + vars (Nonneg t) = vars t + +instance Complement Lit where + notB (Pos t) = Nonneg (lnegate t) + notB (Nonneg t) = Pos (lnegate t) + +-- 制約集合の単純化 +-- It returns Nothing when a inconsistency is detected. +simplify :: [Lit] -> Maybe [Lit] +simplify = fmap concat . mapM f + where + f :: Lit -> Maybe [Lit] + f lit@(Pos e) = + case LA.asConst e of + Just x -> guard (x > 0) >> return [] + Nothing -> return [lit] + f lit@(Nonneg e) = + case LA.asConst e of + Just x -> guard (x >= 0) >> return [] + Nothing -> return [lit] + +-- --------------------------------------------------------------------------- + +atomR :: RelOp -> Expr Rational -> Expr Rational -> Maybe (DNF Lit) +atomR op a b = do + a' <- termR a + b' <- termR b + return $ atomR' op a' b' + +atomR' :: RelOp -> Rat -> Rat -> DNF Lit +atomR' op a b = + case op of + Le -> DNF [[a `leR` b]] + Lt -> DNF [[a `ltR` b]] + Ge -> DNF [[a `geR` b]] + Gt -> DNF [[a `gtR` b]] + Eql -> DNF [[a `leR` b, a `geR` b]] + NEq -> DNF [[a `ltR` b], [a `gtR` b]] + +termR :: Expr Rational -> Maybe Rat +termR (Const c) = return (LA.constant (numerator c), denominator c) +termR (Var v) = return (LA.var v, 1) +termR (a :+: b) = do + (t1,c1) <- termR a + (t2,c2) <- termR b + return (c2 .*. t1 .+. c1 .*. t2, c1*c2) +termR (a :*: b) = do + (t1,c1) <- termR a + (t2,c2) <- termR b + msum [ do{ c <- LA.asConst t1; return (c .*. t2, c1*c2) } + , do{ c <- LA.asConst t2; return (c .*. t1, c1*c2) } + ] +termR (a :/: b) = do + (t1,c1) <- termR a + (t2,c2) <- termR b + c3 <- LA.asConst t2 + guard $ c3 /= 0 + return (c2 .*. t1, c1*c3) + +leR, ltR, geR, gtR :: Rat -> Rat -> Lit +leR (e1,c) (e2,d) = Nonneg $ normalizeExprR $ c .*. e2 .-. d .*. e1 +ltR (e1,c) (e2,d) = Pos $ normalizeExprR $ c .*. e2 .-. d .*. e1 +geR = flip leR +gtR = flip gtR + +normalizeExprR :: ExprZ -> ExprZ +normalizeExprR e = LA.mapCoeff (`div` d) e + where d = abs $ gcd' $ map fst $ LA.terms e + +litToLAAtom :: Lit -> LA.Atom Rational +litToLAAtom (Nonneg e) = LA.mapCoeff fromInteger e .>=. LA.constant 0 +litToLAAtom (Pos e) = LA.mapCoeff fromInteger e .>. LA.constant 0 + +-- --------------------------------------------------------------------------- + +{- +(ls1,ls2,us1,us2) represents +{ x | ∀(M,c)∈ls1. M/c≤x, ∀(M,c)∈ls2. M/c [LA.Atom Rational] -> [([LA.Atom Rational], Model Rational -> Model Rational)] +project v xs = do + ys <- unDNF $ constraintsToDNF xs + (zs, mt) <- project' v ys + return (map litToLAAtom zs, mt) + +project' :: Var -> [Lit] -> [([Lit], Model Rational -> Model Rational)] +project' v xs = do + case collectBounds v xs of + (bnd, rest) -> do + cond <- unDNF $ boundConditions bnd + let mt m = + case Interval.pickup (evalBounds m bnd) of + Nothing -> error "FourierMotzkin.project: should not happen" + Just val -> IM.insert v val m + return (rest ++ cond, mt) + +projectN :: VarSet -> [LA.Atom Rational] -> [([LA.Atom Rational], Model Rational -> Model Rational)] +projectN vs xs = do + ys <- unDNF $ constraintsToDNF xs + (zs, mt) <- projectN' vs ys + return (map litToLAAtom zs, mt) + +projectN' :: VarSet -> [Lit] -> [([Lit], Model Rational -> Model Rational)] +projectN' vs2 xs2 = do + (zs, mt) <- f (IS.toList vs2) xs2 + return (zs, mt) + where + f [] xs = return (xs, id) + f (v:vs) xs = do + (ys, mt1) <- project' v xs + (zs, mt2) <- f vs ys + return (zs, mt1 . mt2) + +collectBounds :: Var -> [Lit] -> (BoundsR, [Lit]) +collectBounds v = foldr phi (([],[],[],[]),[]) + where + phi :: Lit -> (BoundsR, [Lit]) -> (BoundsR, [Lit]) + phi lit@(Nonneg t) x = f False lit t x + phi lit@(Pos t) x = f True lit t x + + f :: Bool -> Lit -> ExprZ -> (BoundsR, [Lit]) -> (BoundsR, [Lit]) + f strict lit t (bnd@(ls1,ls2,us1,us2), xs) = + case LA.extract v t of + (c,t') -> + case c `compare` 0 of + EQ -> (bnd, lit : xs) + GT -> + if strict + then ((ls1, (lnegate t', c) : ls2, us1, us2), xs) -- 0 < cx + M ⇔ -M/c < x + else (((lnegate t', c) : ls1, ls2, us1, us2), xs) -- 0 ≤ cx + M ⇔ -M/c ≤ x + LT -> + if strict + then ((ls1, ls2, us1, (t', negate c) : us2), xs) -- 0 < cx + M ⇔ x < M/-c + else ((ls1, ls2, (t', negate c) : us1, us2), xs) -- 0 ≤ cx + M ⇔ x ≤ M/-c + +boundConditions :: BoundsR -> DNF Lit +boundConditions (ls1, ls2, us1, us2) = DNF $ maybeToList $ simplify $ + [ x `leR` y | x <- ls1, y <- us1 ] ++ + [ x `ltR` y | x <- ls1, y <- us2 ] ++ + [ x `ltR` y | x <- ls2, y <- us1 ] ++ + [ x `ltR` y | x <- ls2, y <- us2 ] + +eliminateQuantifiers :: Formula (Atom Rational) -> Maybe (DNF Lit) +eliminateQuantifiers = f + where + f T = return true + f F = return false + f (Atom (Rel a op b)) = atomR op a b + f (And a b) = liftM2 (.&&.) (f a) (f b) + f (Or a b) = liftM2 (.||.) (f a) (f b) + f (Not a) = f (pushNot a) + f (Imply a b) = f (Or (Not a) b) + f (Equiv a b) = f (And (Imply a b) (Imply b a)) + f (Forall v a) = do + dnf <- f (Exists v (pushNot a)) + return (notB dnf) + f (Exists v a) = do + dnf <- f a + return $ orB [DNF $ map fst $ project' v xs | xs <- unDNF dnf] + +solve :: Formula (Atom Rational) -> SatResult Rational +solve formula = + case eliminateQuantifiers formula of + Nothing -> Unknown + Just dnf -> + case msum [solve' vs xs | xs <- unDNF dnf] of + Nothing -> Unsat + Just m -> Sat m + where + vs = IS.toList (vars formula) + +solveConj :: [LA.Atom Rational] -> Maybe (Model Rational) +solveConj cs = msum [solve' vs cs2 | cs2 <- unDNF (constraintsToDNF cs)] + where + vs = IS.toList (vars cs) + +solve' :: [Var] -> [Lit] -> Maybe (Model Rational) +solve' vs xs = listToMaybe $ do + (ys,mt) <- projectN' (IS.fromList vs) =<< maybeToList (simplify xs) + guard $ Just [] == simplify ys + return $ mt IM.empty + +evalBounds :: Model Rational -> BoundsR -> Interval.Interval Rational +evalBounds model (ls1,ls2,us1,us2) = + foldl' Interval.intersection Interval.univ $ + [ Interval.interval (Just (True, evalRat model x)) Nothing | x <- ls1 ] ++ + [ Interval.interval (Just (False, evalRat model x)) Nothing | x <- ls2 ] ++ + [ Interval.interval Nothing (Just (True, evalRat model x)) | x <- us1 ] ++ + [ Interval.interval Nothing (Just (False, evalRat model x)) | x <- us2 ] + +-- --------------------------------------------------------------------------- + +constraintsToDNF :: [LA.Atom Rational] -> DNF Lit +constraintsToDNF = andB . map constraintToDNF + +constraintToDNF :: LA.Atom Rational -> DNF Lit +constraintToDNF (Rel lhs op rhs) = DNF $ + case op of + Eql -> [[Nonneg lhs', Nonneg (lnegate lhs')]] + NEq -> [[Pos lhs'], [Pos (lnegate lhs')]] + Ge -> [[Nonneg lhs']] + Le -> [[Nonneg (lnegate lhs')]] + Gt -> [[Pos lhs']] + Lt -> [[Pos (lnegate lhs')]] + where + lhs' = normalize (lhs .-. rhs) + + normalize :: LA.Expr Rational -> ExprZ + normalize e = LA.mapCoeff (round . (*c)) e + where + c = fromIntegral $ foldl' lcm 1 ds + ds = [denominator d | (d,_) <- LA.terms e] + +-- --------------------------------------------------------------------------- + +gcd' :: [Integer] -> Integer +gcd' [] = 1 +gcd' xs = foldl1' gcd xs + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/LPSolver.hs b/src/Algorithm/LPSolver.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/LPSolver.hs @@ -0,0 +1,249 @@ +{-# LANGUAGE ScopedTypeVariables #-} +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.LPSolver +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (ScopedTypeVariables) +-- +-- Naïve implementation of Simplex method +-- +-- Reference: +-- +-- * +-- +----------------------------------------------------------------------------- + +module Algorithm.LPSolver where + +import Control.Monad +import Control.Monad.State +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.OptDir + +import Data.Expr +import Data.ArithRel +import Data.Linear +import qualified Data.LA as LA +import qualified Data.Interval as Interval +import qualified Algorithm.Simplex as Simplex +import qualified Algorithm.BoundsInference as BI + +-- --------------------------------------------------------------------------- +-- LP Monad + +type Solver r = (Var, Simplex.Tableau r, VarSet, VarMap (LA.Expr r)) +type LP r = State (Solver r) + +emptySolver :: VarSet -> Solver r +emptySolver vs = (1 + maximum ((-1) : IS.toList vs), IM.empty, IS.empty, IM.empty) + +gensym :: LP r Var +gensym = do + (x,tbl,avs,defs) <- get + put (x+1,tbl,avs,defs) + return x + +getTableau :: LP r (Simplex.Tableau r) +getTableau = do + (_,tbl,_,_) <- get + return tbl + +putTableau :: Simplex.Tableau r -> LP r () +putTableau tbl = do + (x,_,avs,defs) <- get + put (x,tbl,avs,defs) + +addArtificialVariable :: Var -> LP r () +addArtificialVariable v = do + (x,tbl,avs,defs) <- get + put (x, tbl, IS.insert v avs, defs) + +getArtificialVariables :: LP r VarSet +getArtificialVariables = do + (_,_,avs,_) <- get + return avs + +clearArtificialVariables :: LP r () +clearArtificialVariables = do + (x,tbl,_,defs) <- get + put (x, tbl, IS.empty, defs) + +define :: Var -> LA.Expr r -> LP r () +define v e = do + (x,tbl,avs,defs) <- get + put (x,tbl,avs, IM.insert v e defs) + +getDefs :: LP r (VarMap (LA.Expr r)) +getDefs = do + (_,_,_,defs) <- get + return defs + +-- --------------------------------------------------------------------------- + +addConstraint :: Real r => LA.Atom r -> LP r () +addConstraint c = do + c2 <- expandDefs' c + let (e, rop, b) = normalizeConstraint c2 + tbl <- getTableau + case rop of + -- x≥b で b≤0 なら追加しない。ad hoc なので一般化したい。 + Ge | isSingleVar e && b<=0 -> return () + + Le -> do + v <- gensym -- slack variable + putTableau $ Simplex.setRow v tbl (LA.coeffMap e, b) + Ge -> do + v1 <- gensym -- surplus variable + v2 <- gensym -- artificial variable + putTableau $ Simplex.setRow v2 tbl (LA.coeffMap (e .-. LA.var v1), b) + addArtificialVariable v2 + Eql -> do + v <- gensym -- artificial variable + putTableau $ Simplex.setRow v tbl (LA.coeffMap e, b) + addArtificialVariable v + _ -> error $ "addConstraint does not support " ++ show rop + where + isSingleVar e = + case LA.terms e of + [(1,_)] -> True + _ -> False + +addConstraint2 :: Real r => LA.Atom r -> LP r () +addConstraint2 c = do + Rel lhs rop rhs <- expandDefs' c + let + (b', e) = LA.extract LA.unitVar (lhs .-. rhs) + b = - b' + case rop of + Le -> f e b + Ge -> f (lnegate e) (negate b) + Eql -> do + f e b + f (lnegate e) (negate b) + _ -> error $ "addConstraint does not support " ++ show rop + where + -- -x≤b で -b≤0 なら追加しない。ad hoc なので一般化したい。 + f e b | isSingleNegatedVar e && -b <= 0 = return () + f e b = do + tbl <- getTableau + v <- gensym -- slack variable + putTableau $ Simplex.setRow v tbl (LA.coeffMap e, b) + + isSingleNegatedVar e = + case LA.terms e of + [(-1,_)] -> True + _ -> False + +expandDefs :: (Num r, Eq r) => LA.Expr r -> LP r (LA.Expr r) +expandDefs e = do + defs <- getDefs + return $ LA.applySubst defs e + +expandDefs' :: (Num r, Eq r) => LA.Atom r -> LP r (LA.Atom r) +expandDefs' (Rel lhs op rhs) = do + lhs' <- expandDefs lhs + rhs' <- expandDefs rhs + return $ Rel lhs' op rhs' + +tableau :: (RealFrac r) => [LA.Atom r] -> LP r () +tableau cs = do + let (nonnegVars, cs') = collectNonnegVars cs IS.empty + fvs = vars cs `IS.difference` nonnegVars + forM_ (IS.toList fvs) $ \v -> do + v1 <- gensym + v2 <- gensym + define v (LA.var v1 .-. LA.var v2) + mapM_ addConstraint cs' + +getModel :: Fractional r => VarSet -> LP r (Model r) +getModel vs = do + tbl <- getTableau + defs <- getDefs + let bs = IM.map snd (IM.delete Simplex.objRow tbl) + vs' = vs `IS.union` IS.fromList [v | e <- IM.elems defs, v <- IS.toList (vars e)] + -- Note that IM.union is left-biased + m0 = bs `IM.union` IM.fromList [(v,0) | v <- IS.toList vs'] + return $ IM.filterWithKey (\k _ -> k `IS.member` vs) $ IM.map (LA.evalExpr m0) defs `IM.union` m0 + +phaseI :: (Fractional r, Real r) => LP r Bool +phaseI = do + tbl <- getTableau + avs <- getArtificialVariables + let (ret, tbl') = Simplex.phaseI tbl avs + putTableau tbl' + when ret clearArtificialVariables + return ret + +simplex :: (Fractional r, Real r) => OptDir -> LA.Expr r -> LP r Bool +simplex optdir obj = do + tbl <- getTableau + defs <- getDefs + let (ret, tbl') = Simplex.simplex optdir (Simplex.setObjFun tbl (LA.applySubst defs obj)) + putTableau tbl' + return ret + +dualSimplex :: (Fractional r, Real r) => OptDir -> LA.Expr r -> LP r Bool +dualSimplex optdir obj = do + tbl <- getTableau + defs <- getDefs + let (ret, tbl') = Simplex.dualSimplex optdir (Simplex.setObjFun tbl (LA.applySubst defs obj)) + putTableau tbl' + return ret + +-- --------------------------------------------------------------------------- + +normalizeConstraint :: forall r. Real r => LA.Atom r -> (LA.Expr r, RelOp, r) +normalizeConstraint (Rel a op b) + | rhs < 0 = (lnegate lhs, flipOp op, negate rhs) + | otherwise = (lhs, op, rhs) + where + (c, lhs) = LA.extract LA.unitVar (a .-. b) + rhs = - c + +collectNonnegVars :: forall r. (RealFrac r) => [LA.Atom r] -> VarSet -> (VarSet, [LA.Atom r]) +collectNonnegVars cs ivs = (nonnegVars, cs) + where + vs = vars cs + bounds = BI.inferBounds initialBounds cs ivs 1000 + where + initialBounds = IM.fromList [(v, Interval.univ) | v <- IS.toList vs] + nonnegVars = IS.filter f vs + where + f v = case Interval.lowerBound (bounds IM.! v) of + Just (_, lb) | 0 <= lb -> True + _ -> False + + isTriviallyTrue :: LA.Atom r -> Bool + isTriviallyTrue (Rel a op b) = + case op of + Le -> + case ub of + Nothing -> False + Just (_, val) -> val <= 0 + Ge -> + case lb of + Nothing -> False + Just (_, val) -> val >= 0 + Lt -> + case ub of + Nothing -> False + Just (incl, val) -> val < 0 || (not incl && val <= 0) + Gt -> + case lb of + Nothing -> False + Just (incl, val) -> val > 0 || (not incl && val >= 0) + Eql -> isTriviallyTrue (c .<=. lzero) && isTriviallyTrue (c .>=. lzero) + NEq -> isTriviallyTrue (c .<. lzero) || isTriviallyTrue (c .>. lzero) + where + c = a .-. b + i = LA.computeInterval bounds c + lb = Interval.lowerBound i + ub = Interval.upperBound i + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/LPSolverHL.hs b/src/Algorithm/LPSolverHL.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/LPSolverHL.hs @@ -0,0 +1,289 @@ +{-# LANGUAGE ScopedTypeVariables #-} +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.LPSolverHL +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (ScopedTypeVariables) +-- +-- High-Level API for LPSolver.hs +-- +----------------------------------------------------------------------------- + +module Algorithm.LPSolverHL + ( module Data.Expr + , module Data.Formula + , minimize + , maximize + , optimize + , solve + ) where + +import Control.Monad.State +import Data.Maybe (fromMaybe) +import Data.Ratio +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.OptDir + +import Data.Expr +import Data.ArithRel +import Data.Formula (Atom) +import qualified Data.LA as LA +import qualified Algorithm.Simplex as Simplex +import Algorithm.LPSolver + +-- --------------------------------------------------------------------------- + +maximize :: (RealFrac r) => Expr r -> [Atom r] -> OptResult r +maximize = optimize OptMax + +minimize :: (RealFrac r) => Expr r -> [Atom r] -> OptResult r +minimize = optimize OptMin + +optimize :: (RealFrac r) => OptDir -> Expr r -> [Atom r] -> OptResult r +optimize optdir obj2 cs2 = fromMaybe OptUnknown $ do + obj <- LA.compileExpr obj2 + cs <- mapM LA.compileAtom cs2 + return (optimize' optdir obj cs) + +solve :: (RealFrac r) => [Atom r] -> SatResult r +solve cs2 = fromMaybe Unknown $ do + cs <- mapM LA.compileAtom cs2 + return (solve' cs) + +-- --------------------------------------------------------------------------- + +solve' :: (RealFrac r) => [LA.Atom r] -> SatResult r +solve' cs = + flip evalState (emptySolver vs) $ do + tableau cs + ret <- phaseI + if not ret + then return Unsat + else do + m <- getModel vs + return (Sat m) + where + vs = vars cs + +optimize' :: (RealFrac r) => OptDir -> LA.Expr r -> [LA.Atom r] -> OptResult r +optimize' optdir obj cs = + flip evalState (emptySolver vs) $ do + tableau cs + ret <- phaseI + if not ret + then return OptUnsat + else do + ret2 <- simplex optdir obj + if not ret2 + then return Unbounded + else do + m <- getModel vs + tbl <- getTableau + return $ Optimum (Simplex.currentObjValue tbl) m + where + vs = vars cs `IS.union` vars obj + +-- --------------------------------------------------------------------------- +-- Test cases + +example_3_2 :: (Expr Rational, [Atom Rational]) +example_3_2 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + x3 = var 3 + obj = 3*x1 + 2*x2 + 3*x3 + cond = [ 2*x1 + x2 + x3 .<=. 2 + , x1 + 2*x2 + 3*x3 .<=. 5 + , 2*x1 + 2*x2 + x3 .<=. 6 + , x1 .>=. 0 + , x2 .>=. 0 + , x3 .>=. 0 + ] + +test_3_2 :: Bool +test_3_2 = + uncurry maximize example_3_2 == + Optimum (27/5) (IM.fromList [(1,1/5),(2,0),(3,8/5)]) + +example_3_5 :: (Expr Rational, [Atom Rational]) +example_3_5 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + x3 = var 3 + x4 = var 4 + x5 = var 5 + obj = -2*x1 + 4*x2 + 7*x3 + x4 + 5*x5 + cond = [ -x1 + x2 + 2*x3 + x4 + 2*x5 .==. 7 + , -x1 + 2*x2 + 3*x3 + x4 + x5 .==. 6 + , -x1 + x2 + x3 + 2*x4 + x5 .==. 4 + , x2 .>=. 0 + , x3 .>=. 0 + , x4 .>=. 0 + , x5 .>=. 0 + ] + +test_3_5 :: Bool +test_3_5 = + uncurry minimize example_3_5 == + Optimum 19 (IM.fromList [(1,-1),(2,0),(3,1),(4,0),(5,2)]) + +example_4_1 :: (Expr Rational, [Atom Rational]) +example_4_1 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + obj = 2*x1 + x2 + cond = [ -x1 + x2 .>=. 2 + , x1 + x2 .<=. 1 + , x1 .>=. 0 + , x2 .>=. 0 + ] + +test_4_1 :: Bool +test_4_1 = + uncurry maximize example_4_1 == + OptUnsat + +example_4_2 :: (Expr Rational, [Atom Rational]) +example_4_2 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + obj = 2*x1 + x2 + cond = [ - x1 - x2 .<=. 10 + , 2*x1 - x2 .<=. 40 + , x1 .>=. 0 + , x2 .>=. 0 + ] + +test_4_2 :: Bool +test_4_2 = + uncurry maximize example_4_2 == + Unbounded + +example_4_3 :: (Expr Rational, [Atom Rational]) +example_4_3 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + obj = 6*x1 - 2*x2 + cond = [ 2*x1 - x2 .<=. 2 + , x1 .<=. 4 + , x1 .>=. 0 + , x2 .>=. 0 + ] + +test_4_3 :: Bool +test_4_3 = + uncurry maximize example_4_3 == + Optimum 12 (IM.fromList [(1,4),(2,6)]) + +example_4_5 :: (Expr Rational, [Atom Rational]) +example_4_5 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + obj = 2*x1 + x2 + cond = [ 4*x1 + 3*x2 .<=. 12 + , 4*x1 + x2 .<=. 8 + , 4*x1 - x2 .<=. 8 + , x1 .>=. 0 + , x2 .>=. 0 + ] + +test_4_5 :: Bool +test_4_5 = + uncurry maximize example_4_5 == + Optimum 5 (IM.fromList [(1,3/2),(2,2)]) + +example_4_6 :: (Expr Rational, [Atom Rational]) +example_4_6 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + x3 = var 3 + x4 = var 4 + obj = 20*x1 + (1/2)*x2 - 6*x3 + (3/4)*x4 + cond = [ x1 .<=. 2 + , 8*x1 - x2 + 9*x3 + (1/4)*x4 .<=. 16 + , 12*x1 - (1/2)*x2 + 3*x3 + (1/2)*x4 .<=. 24 + , x2 .<=. 1 + , x1 .>=. 0 + , x2 .>=. 0 + , x3 .>=. 0 + , x4 .>=. 0 + ] + +test_4_6 :: Bool +test_4_6 = + uncurry maximize example_4_6 == + Optimum (165/4) (IM.fromList [(1,2),(2,1),(3,0),(4,1)]) + +example_4_7 :: (Expr Rational, [Atom Rational]) +example_4_7 = (obj, cond) + where + x1 = var 1 + x2 = var 2 + x3 = var 3 + x4 = var 4 + obj = x1 + 1.5*x2 + 5*x3 + 2*x4 + cond = [ 3*x1 + 2*x2 + x3 + 4*x4 .<=. 6 + , 2*x1 + x2 + 5*x3 + x4 .<=. 4 + , 2*x1 + 6*x2 - 4*x3 + 8*x4 .==. 0 + , x1 + 3*x2 - 2*x3 + 4*x4 .==. 0 + , x1 .>=. 0 + , x2 .>=. 0 + , x3 .>=. 0 + , x4 .>=. 0 + ] + +test_4_7 :: Bool +test_4_7 = + uncurry maximize example_4_7 == + Optimum (48/11) (IM.fromList [(1,0),(2,0),(3,81),(4,41)]) + +-- 退化して巡回の起こるKuhnの7変数3制約の例 +kuhn_7_3 :: (Expr Rational, [Atom Rational]) +kuhn_7_3 = (obj, cond) + where + [x1,x2,x3,x4,x5,x6,x7] = map var [1..7] + obj = -2*x4-3*x5+x6+12*x7 + cond = [ x1 - 2*x4 - 9*x5 + x6 + 9*x7 .==. 0 + , x2 + (1/3)*x4 + x5 - (1/3)*x6 - 2*x7 .==. 0 + , x3 + 2*x4 + 3*x5 - x6 - 12*x7 .==. 2 + , x1 .>=. 0 + , x2 .>=. 0 + , x3 .>=. 0 + , x4 .>=. 0 + , x5 .>=. 0 + , x6 .>=. 0 + , x7 .>=. 0 + ] + +test_kuhn_7_3 :: Bool +test_kuhn_7_3 = + uncurry minimize kuhn_7_3 == + Optimum (-2) (IM.fromList [(1,2),(2,0),(3,0),(4,2),(5,0),(6,2),(7,0)]) + +testAll :: Bool +testAll = and + [ test_3_2 + , test_3_5 + , test_4_1 + , test_4_2 + , test_4_3 + , test_4_5 + , test_4_6 + , test_4_7 + , test_kuhn_7_3 + ] + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/LPUtil.hs b/src/Algorithm/LPUtil.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/LPUtil.hs @@ -0,0 +1,91 @@ +module Algorithm.LPUtil + ( toStandardForm + , toStandardForm' + ) where + +import Control.Exception +import Control.Monad +import Control.Monad.State +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.Maybe + +import Data.Expr (Var, VarSet, VarMap, Variables (..), Model (..)) +import Data.ArithRel +import Data.Linear +import qualified Data.LA as LA +import qualified Data.Interval as Interval +import qualified Algorithm.BoundsInference as BI + +toStandardForm + :: (LA.Expr Rational, [Rel (LA.Expr Rational)]) + -> ( (LA.Expr Rational, [(LA.Expr Rational, Rational)]) + , Model Rational -> Model Rational + ) +toStandardForm prob1@(obj, cs) = (prob2, mt) + where + vs = vars obj `IS.union` vars cs + (prob2,s) = toStandardForm' prob1 + mt m = IM.fromAscList $ do + v <- IS.toAscList vs + case IM.lookup v s of + Just def -> return (v, LA.evalExpr m def) + Nothing -> return (v, m IM.! v) + +type M = State Var + +toStandardForm' + :: (LA.Expr Rational, [Rel (LA.Expr Rational)]) + -> ( (LA.Expr Rational, [(LA.Expr Rational, Rational)]) + , VarMap (LA.Expr Rational) + ) +toStandardForm' (obj, cs) = m + where + vs = vars obj `IS.union` vars cs + v1 = if IS.null vs then 0 else IS.findMax vs + 1 + initialBounds = IM.fromList [(v, Interval.univ) | v <- IS.toList vs] + bounds = BI.inferBounds initialBounds cs IS.empty 10 + + gensym :: M Var + gensym = do + v <- get + put $ v+1 + return v + + m = flip evalState v1 $ do + s <- liftM IM.unions $ forM (IM.toList bounds) $ \(v,i) -> do + case Interval.lowerBound i of + Nothing -> do + v1 <- gensym + v2 <- gensym + return $ IM.singleton v (LA.var v1 .-. LA.var v2) + Just (_,lb) + | lb >= 0 -> return IM.empty + | otherwise -> do + v1 <- gensym + return $ IM.singleton v (LA.var v1 .-. LA.constant lb) + let obj2 = LA.applySubst s obj + + cs2 <- liftM concat $ forM cs $ \(Rel lhs op rhs) -> do + case LA.extract LA.unitVar (LA.applySubst s (lhs .-. rhs)) of + (c,e) -> do + let (lhs2,op2,rhs2) = + if -c >= 0 + then (e,op,-c) + else (lnegate e, flipOp op, c) + case op2 of + Eql -> return [(lhs2,rhs2)] + Le -> do + v <- gensym + return [(lhs2 .+. LA.var v, rhs2)] + Ge -> do + case LA.terms lhs2 of + [(1,_)] | rhs2<=0 -> return [] + _ -> do + v <- gensym + return [(lhs2 .-. LA.var v, rhs2)] + _ -> error $ "LPUtil.toStandardForm: " ++ show op2 ++ " is not supported" + + assert (and [isNothing $ LA.lookupCoeff LA.unitVar c | (c,_) <- cs2]) $ return () + + return ((obj2,cs2),s) diff --git a/src/Algorithm/MIPSolver2.hs b/src/Algorithm/MIPSolver2.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/MIPSolver2.hs @@ -0,0 +1,490 @@ +{-# LANGUAGE ScopedTypeVariables, Rank2Types #-} +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.MIPSolver2 +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable +-- +-- Naïve implementation of MIP solver based on Simplex2 module +-- +-- Reference: +-- +-- * +-- +-- * Ralph E. Gomory. +-- \"An Algorithm for the Mixed Integer Problem\", Technical Report +-- RM-2597, 1960, The Rand Corporation, Santa Monica, CA. +-- +-- +-- * Ralph E. Gomory. +-- \"Outline of an algorithm for integer solutions to linear programs\". +-- Bull. Amer. Math. Soc., Vol. 64, No. 5. (1958), pp. 275-278. +-- +-- +-- * R. C. Daniel and Martyn Jeffreys. +-- \"Unboundedness in Integer and Discrete Programming L.P. Relaxations\" +-- The Journal of the Operational Research Society, Vol. 30, No. 12. (1979) +-- +-- +----------------------------------------------------------------------------- +module Algorithm.MIPSolver2 + ( + -- * The @Solver@ type + Solver + , newSolver + + -- * Solving + , optimize + + -- * Extract results + , model + , getObjValue + + -- * Configulation + , setNThread + , setLogger + , setShowRational + ) where + +import Prelude hiding (log) + +import Control.Monad +import Control.Exception +import Control.Concurrent +import Control.Concurrent.STM +import Data.List +import Data.OptDir +import Data.Ord +import Data.IORef +import Data.Maybe +import qualified Data.IntSet as IS +import qualified Data.IntMap as IM +import qualified Data.Map as Map +import qualified Data.Sequence as Seq +import qualified Data.Foldable as F +import Data.Time +import System.CPUTime +import System.Timeout +import Text.Printf + +import qualified Data.LA as LA +import Data.ArithRel ((.<=.), (.>=.)) +import qualified Algorithm.Simplex2 as Simplex2 +import Algorithm.Simplex2 (OptResult (..), Var, Model) +import Data.Linear +import Util (isInteger, fracPart) + +data Solver + = MIP + { mipRootLP :: Simplex2.Solver + , mipIVs :: IS.IntSet + , mipBest :: TVar (Maybe Node) + + , mipNThread :: IORef Int + , mipLogger :: IORef (Maybe (String -> IO ())) + , mipShowRational :: IORef Bool + } + +data Node = + Node + { ndLP :: Simplex2.Solver + , ndDepth :: {-# UNPACK #-} !Int + , ndValue :: Rational + } + +newSolver :: Simplex2.Solver -> IS.IntSet -> IO Solver +newSolver lp ivs = do + lp2 <- Simplex2.cloneSolver lp + + forM_ (IS.toList ivs) $ \v -> do + lb <- Simplex2.getLB lp2 v + case lb of + Just l | not (isInteger l) -> + Simplex2.assertLower lp2 v (fromInteger (ceiling l)) + _ -> return () + ub <- Simplex2.getUB lp2 v + case ub of + Just u | not (isInteger u) -> + Simplex2.assertLower lp2 v (fromInteger (floor u)) + _ -> return () + + bestRef <- newTVarIO Nothing + + nthreadRef <- newIORef 0 + logRef <- newIORef Nothing + showRef <- newIORef False + + return $ + MIP + { mipRootLP = lp2 + , mipIVs = ivs + , mipBest = bestRef + + , mipNThread = nthreadRef + , mipLogger = logRef + , mipShowRational = showRef + } + +optimize :: Solver -> (Model -> Rational -> IO ()) -> IO OptResult +optimize solver update = do + let lp = mipRootLP solver + log solver "MIP: Solving LP relaxation..." + ret <- Simplex2.check lp + if not ret + then return Unsat + else do + s0 <- showValue solver =<< Simplex2.getObjValue lp + log solver (printf "MIP: LP relaxation is satisfiable with obj = %s" s0) + log solver "MIP: Optimizing LP relaxation" + ret2 <- Simplex2.optimize lp Simplex2.defaultOptions + case ret2 of + Unsat -> error "should not happen" + ObjLimit -> error "should not happen" + Unbounded -> do + log solver "MIP: LP relaxation is unbounded" + let ivs = mipIVs solver + if IS.null ivs + then return Unbounded + else do + {- + * In general, original problem may have optimal + solution even though LP relaxiation is unbounded. + * But if restricted to rational numbers, the + original problem is unbounded or unsatisfiable + when LP relaxation is unbounded. + -} + origObj <- Simplex2.getObj lp + lp2 <- Simplex2.cloneSolver lp + Simplex2.clearLogger lp2 + Simplex2.setObj lp2 (LA.constant 0) + branchAndBound solver lp2 $ \m _ -> do + update m (LA.evalExpr m origObj) + best <- readTVarIO (mipBest solver) + case best of + Just nd -> do + m <- Simplex2.model (ndLP nd) + atomically $ writeTVar (mipBest solver) $ Just nd{ ndValue = LA.evalExpr m origObj } + return Unbounded + Nothing -> return Unsat + Optimum -> do + s1 <- showValue solver =<< Simplex2.getObjValue lp + log solver $ "MIP: LP relaxation optimum is " ++ s1 + log solver "MIP: Integer optimization begins..." + Simplex2.clearLogger lp + branchAndBound solver lp update + m <- readTVarIO (mipBest solver) + case m of + Nothing -> return Unsat + Just _ -> return Optimum + +branchAndBound :: Solver -> Simplex2.Solver -> (Model -> Rational -> IO ()) -> IO () +branchAndBound solver rootLP update = do + dir <- Simplex2.getOptDir rootLP + rootVal <- Simplex2.getObjValue rootLP + let root = Node{ ndLP = rootLP, ndDepth = 0, ndValue = rootVal } + + pool <- newTVarIO (Seq.singleton root) + activeThreads <- newTVarIO (Map.empty) + visitedNodes <- newTVarIO 0 + solchan <- newTChanIO + + let addNode :: Node -> STM () + addNode nd = do + modifyTVar pool (Seq.|> nd) + + pickNode :: IO (Maybe Node) + pickNode = do + self <- myThreadId + atomically $ modifyTVar activeThreads (Map.delete self) + atomically $ do + s <- readTVar pool + case Seq.viewl s of + nd Seq.:< s2 -> do + writeTVar pool s2 + modifyTVar activeThreads (Map.insert self nd) + return (Just nd) + Seq.EmptyL -> do + ths <- readTVar activeThreads + if Map.null ths + then return Nothing + else retry + + processNode :: Node -> IO () + processNode node = do + let lp = ndLP node + lim <- liftM (fmap ndValue) $ readTVarIO (mipBest solver) + ret <- Simplex2.dualSimplex lp Simplex2.defaultOptions{ Simplex2.objLimit = lim } + + case ret of + Unbounded -> error "should not happen" + Unsat -> return () + ObjLimit -> return () + Optimum -> do + val <- Simplex2.getObjValue lp + p <- prune solver val + unless p $ do + xs <- violated node (mipIVs solver) + case xs of + [] -> atomically $ writeTChan solchan $ node { ndValue = val } + _ -> do + r <- if ndDepth node `mod` 100 /= 0 + then return Nothing + else liftM listToMaybe $ filterM (canDeriveGomoryCut lp) $ map fst xs + case r of + Nothing -> do -- branch + let (v0,val0) = fst $ maximumBy (comparing snd) + [((v,vval), abs (fromInteger (round vval) - vval)) | (v,vval) <- xs] + let lp1 = lp + lp2 <- Simplex2.cloneSolver lp + Simplex2.assertAtom lp1 (LA.var v0 .<=. LA.constant (fromInteger (floor val0))) + Simplex2.assertAtom lp2 (LA.var v0 .>=. LA.constant (fromInteger (ceiling val0))) + atomically $ do + addNode $ Node lp1 (ndDepth node + 1) val + addNode $ Node lp2 (ndDepth node + 1) val + modifyTVar visitedNodes (+1) + Just v -> do -- cut + atom <- deriveGomoryCut lp (mipIVs solver) v + Simplex2.assertAtom lp atom + atomically $ do + addNode $ Node lp (ndDepth node + 1) val + + let isCompleted = do + nodes <- readTVar pool + threads <- readTVar activeThreads + return $ Seq.null nodes && Map.null threads + + -- fork worker threads + nthreads <- liftM (max 1) $ readIORef (mipNThread solver) + + log solver $ printf "MIP: forking %d worker threads..." nthreads + + startCPU <- getCPUTime + startWC <- getCurrentTime + ex <- newEmptyTMVarIO + + let printStatus :: Seq.Seq Node -> Int -> IO () + printStatus nodes visited + | Seq.null nodes = return () -- should not happen + | otherwise = do + nowCPU <- getCPUTime + nowWC <- getCurrentTime + let spentCPU = (nowCPU - startCPU) `div` 10^(12::Int) + let spentWC = round (nowWC `diffUTCTime` startWC) :: Int + + let vs = map ndValue (F.toList nodes) + dualBound = + case dir of + OptMin -> minimum vs + OptMax -> maximum vs + + primalBound <- do + x <- readTVarIO (mipBest solver) -- TODO: 引数にするようにした方が良い? + return $ case x of + Nothing -> Nothing + Just node -> Just (ndValue node) + + (p,g) <- case primalBound of + Nothing -> return ("not yet found", "--") + Just val -> do + p <- showValue solver val + let g = if val == 0 + then "inf" + else printf "%.2f%%" (fromRational (abs (dualBound - val) * 100 / abs val) :: Double) + return (p, g) + d <- showValue solver dualBound + + let range = + case dir of + OptMin -> p ++ " >= " ++ d + OptMax -> p ++ " <= " ++ d + + log solver $ printf "cpu time = %d sec; wc time = %d sec; active nodes = %d; visited nodes = %d; %s; gap = %s" + spentCPU spentWC (Seq.length nodes) visited range g + + mask $ \(restore :: forall a. IO a -> IO a) -> do + threads <- replicateM nthreads $ do + forkIO $ do + let loop = do + m <- pickNode + case m of + Nothing -> return () + Just node -> processNode node >> loop + ret <- try $ restore loop + case ret of + Left e -> atomically (putTMVar ex e) + Right _ -> return () + + let propagateException :: SomeException -> IO () + propagateException e = do + mapM_ (\t -> throwTo t e) threads + throwIO e + + let loop = do + ret <- try $ timeout (2*1000*1000) $ restore $ atomically $ msum + [ do node <- readTChan solchan + ret <- do + old <- readTVar (mipBest solver) + case old of + Nothing -> do + writeTVar (mipBest solver) (Just node) + return True + Just best -> do + let isBetter = if dir==OptMin then ndValue node < ndValue best else ndValue node > ndValue best + when isBetter $ writeTVar (mipBest solver) (Just node) + return isBetter + return $ do + when ret $ do + let lp = ndLP node + m <- Simplex2.model lp + update m (ndValue node) + loop + , do b <- isCompleted + guard b + return $ return () + , do e <- readTMVar ex + return $ propagateException e + ] + + case ret of + Left (e::SomeException) -> propagateException e + Right (Just m) -> m + Right Nothing -> do -- timeout + (nodes, visited) <- atomically $ do + nodes <- readTVar pool + athreads <- readTVar activeThreads + visited <- readTVar visitedNodes + return (Seq.fromList (Map.elems athreads) Seq.>< nodes, visited) + printStatus nodes visited + loop + + loop + +model :: Solver -> IO Model +model solver = do + m <- readTVarIO (mipBest solver) + case m of + Nothing -> error "no model" + Just node -> Simplex2.model (ndLP node) + +getObjValue :: Solver -> IO Rational +getObjValue solver = do + m <- readTVarIO (mipBest solver) + case m of + Nothing -> error "no model" + Just node -> return $ ndValue node + +violated :: Node -> IS.IntSet -> IO [(Var, Rational)] +violated node ivs = do + m <- Simplex2.model (ndLP node) + let p (v,val) = v `IS.member` ivs && not (isInteger val) + return $ filter p (IM.toList m) + +prune :: Solver -> Rational -> IO Bool +prune solver lb = do + b <- readTVarIO (mipBest solver) + case b of + Nothing -> return False + Just node -> do + dir <- Simplex2.getOptDir (mipRootLP solver) + return $ if dir==OptMin then ndValue node <= lb else ndValue node >= lb + +showValue :: Solver -> Rational -> IO String +showValue solver v = do + printRat <- readIORef (mipShowRational solver) + return $ Simplex2.showValue printRat v + +setShowRational :: Solver -> Bool -> IO () +setShowRational solver = writeIORef (mipShowRational solver) + +setNThread :: Solver -> Int -> IO () +setNThread solver = writeIORef (mipNThread solver) + +{-------------------------------------------------------------------- + Logging +--------------------------------------------------------------------} + +-- | set callback function for receiving messages. +setLogger :: Solver -> (String -> IO ()) -> IO () +setLogger solver logger = do + writeIORef (mipLogger solver) (Just logger) + +log :: Solver -> String -> IO () +log solver msg = logIO solver (return msg) + +logIO :: Solver -> IO String -> IO () +logIO solver action = do + m <- readIORef (mipLogger solver) + case m of + Nothing -> return () + Just logger -> action >>= logger + +{-------------------------------------------------------------------- + GomoryCut +--------------------------------------------------------------------} + +deriveGomoryCut :: Simplex2.Solver -> IS.IntSet -> Var -> IO (LA.Atom Rational) +deriveGomoryCut lp ivs xi = do + v0 <- Simplex2.getValue lp xi + let f0 = fracPart v0 + assert (0 < f0 && f0 < 1) $ return () + + row <- Simplex2.getRow lp xi + + -- remove fixed variables + let p (_,xj) = do + lb <- Simplex2.getLB lp xj + ub <- Simplex2.getUB lp xj + case (lb,ub) of + (Just l, Just u) -> return (l < u) + _ -> return True + ns <- filterM p $ LA.terms row + + js <- flip filterM ns $ \(_, xj) -> do + vj <- Simplex2.getValue lp xj + lb <- Simplex2.getLB lp xj + return $ Just vj == lb + ks <- flip filterM ns $ \(_, xj) -> do + vj <- Simplex2.getValue lp xj + ub <- Simplex2.getUB lp xj + return $ Just vj == ub + + xs1 <- forM js $ \(aij, xj) -> do + let fj = fracPart aij + Just lj <- Simplex2.getLB lp xj + let c = if xj `IS.member` ivs + then (if fj <= 1 - f0 then fj / (1 - f0) else ((1 - fj) / f0)) + else (if aij > 0 then aij / (1 - f0) else (-aij / f0)) + return $ c .*. (LA.var xj .-. LA.constant lj) + xs2 <- forM ks $ \(aij, xj) -> do + let fj = fracPart aij + Just uj <- Simplex2.getUB lp xj + let c = if xj `IS.member` ivs + then (if fj <= f0 then fj / f0 else ((1 - fj) / (1 - f0))) + else (if aij > 0 then aij / f0 else (-aij / (1 - f0))) + return $ c .*. (LA.constant uj .-. LA.var xj) + + return $ lsum xs1 .+. lsum xs2 .>=. LA.constant 1 + +-- TODO: Simplex2をδに対応させたら、xi, xj がδを含まない有理数であるという条件も必要 +canDeriveGomoryCut :: Simplex2.Solver -> Var -> IO Bool +canDeriveGomoryCut lp xi = do + b <- Simplex2.isBasicVariable lp xi + if not b + then return False + else do + val <- Simplex2.getValue lp xi + if isInteger val + then return False + else do + row <- Simplex2.getRow lp xi + ys <- forM (LA.terms row) $ \(_,xj) -> do + vj <- Simplex2.getValue lp xj + lb <- Simplex2.getLB lp xj + ub <- Simplex2.getUB lp xj + return $ Just vj == lb || Just vj == ub + return (and ys) diff --git a/src/Algorithm/MIPSolverHL.hs b/src/Algorithm/MIPSolverHL.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/MIPSolverHL.hs @@ -0,0 +1,304 @@ +{-# LANGUAGE ScopedTypeVariables #-} +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.MIPSolverHL +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (ScopedTypeVariables) +-- +-- References: +-- +-- * [Gomory1960] +-- Ralph E. Gomory. +-- An Algorithm for the Mixed Integer Problem, Technical Report +-- RM-2597, 1960, The Rand Corporation, Santa Monica, CA. +-- +-- +-- * [Gomory1958] +-- Ralph E. Gomory. +-- Outline of an algorithm for integer solutions to linear programs. +-- Bull. Amer. Math. Soc., Vol. 64, No. 5. (1958), pp. 275-278. +-- +----------------------------------------------------------------------------- + +module Algorithm.MIPSolverHL + ( module Data.Expr + , module Data.Formula + , module Data.OptDir + , minimize + , maximize + , optimize +-- , solve + ) where + +import Control.Exception +import Control.Monad.State +import Data.Ord +import Data.Maybe +import Data.List (maximumBy) +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.Ratio +import Data.OptDir + +import Data.Expr +import Data.ArithRel +import Data.Formula (Atom) +import Data.Linear +import qualified Data.LA as LA +import qualified Algorithm.Simplex as Simplex +import qualified Algorithm.LPSolver as LPSolver +import Algorithm.LPSolver +import qualified Algorithm.OmegaTest as OmegaTest +import Util (isInteger, fracPart) + +-- --------------------------------------------------------------------------- + +maximize :: RealFrac r => Expr r -> [Atom r] -> VarSet -> OptResult r +maximize = optimize OptMax + +minimize :: RealFrac r => Expr r -> [Atom r] -> VarSet -> OptResult r +minimize = optimize OptMin + +optimize :: RealFrac r => OptDir -> Expr r -> [Atom r] -> VarSet -> OptResult r +optimize optdir obj2 cs2 ivs = fromMaybe OptUnknown $ do + obj <- LA.compileExpr obj2 + cs <- mapM LA.compileAtom cs2 + return (optimize' optdir obj cs ivs) + +{- +solve :: RealFrac r => [Atom r] -> VarSet -> SatResult r +solve cs2 ivs = fromMaybe Unknown $ do + cs <- mapM compileAtom cs2 + return (solve' cs ivs) +-} + +-- --------------------------------------------------------------------------- + +data Node r + = Node + { ndSolver :: LPSolver.Solver r + , ndDepth :: {-# UNPACK #-} !Int +-- , ndCutSlackVariables :: VarSet + } + +ndTableau :: Node r -> Simplex.Tableau r +ndTableau node = evalState getTableau (ndSolver node) + +ndLowerBound :: (Num r, Eq r) => Node r -> r +ndLowerBound node = evalState (liftM Simplex.currentObjValue getTableau) (ndSolver node) + +data Err = ErrUnbounded | ErrUnsat deriving (Ord, Eq, Show, Enum, Bounded) + +optimize' :: RealFrac r => OptDir -> LA.Expr r -> [LA.Atom r] -> VarSet -> OptResult r +optimize' optdir obj cs ivs = + case mkInitialNode optdir obj cs ivs of + Left err -> + case err of + ErrUnsat -> OptUnsat + ErrUnbounded -> + if IS.null ivs + then Unbounded + else + {- + Fallback to Fourier-Motzkin + OmegaTest + * In general, original problem may have optimal + solution even though LP relaxiation is unbounded. + * But if restricted to rational numbers, the + original problem is unbounded or unsatisfiable + when LP relaxation is unbounded. + -} + case OmegaTest.solveQFLA (map conv cs) ivs of + Nothing -> OptUnsat + Just _ -> Unbounded + Right (node0, ivs2) -> + case traverse optdir obj ivs2 node0 of + Left ErrUnbounded -> error "shoud not happen" + Left ErrUnsat -> OptUnsat + Right node -> flip evalState (ndSolver node) $ do + tbl <- getTableau + model <- getModel vs + return $ Optimum (Simplex.currentObjValue tbl) model + where + vs = vars cs `IS.union` vars obj + +tableau' :: (RealFrac r) => [LA.Atom r] -> VarSet -> LP r VarSet +tableau' cs ivs = do + let (nonnegVars, cs') = collectNonnegVars cs ivs + fvs = vars cs `IS.difference` nonnegVars + ivs2 <- liftM IS.unions $ forM (IS.toList fvs) $ \v -> do + v1 <- gensym + v2 <- gensym + define v (LA.var v1 .-. LA.var v2) + return $ if v `IS.member` ivs then IS.fromList [v1,v2] else IS.empty + mapM_ addConstraint cs' + return ivs2 + +conv :: RealFrac r => LA.Atom r -> LA.Atom Rational +conv (Rel a op b) = Rel (f a) op (f b) + where + f = LA.mapCoeff toRational + +mkInitialNode :: RealFrac r => OptDir -> LA.Expr r -> [LA.Atom r] -> VarSet -> Either Err (Node r, VarSet) +mkInitialNode optdir obj cs ivs = + flip evalState (emptySolver vs) $ do + ivs2 <- tableau' cs ivs + ret <- phaseI + if not ret + then return (Left ErrUnsat) + else do + ret2 <- simplex optdir obj + if ret2 + then do + solver <- get + return $ Right $ + ( Node{ ndSolver = solver + , ndDepth = 0 +-- , ndCutSlackVariables = IS.empty + } + , ivs `IS.union` ivs2 + ) + else return (Left ErrUnbounded) + where + vs = vars cs `IS.union` vars obj + +isStrictlyBetter :: RealFrac r => OptDir -> r -> r -> Bool +isStrictlyBetter optdir = if optdir==OptMin then (<) else (>) + +traverse :: forall r. RealFrac r => OptDir -> LA.Expr r -> VarSet -> Node r -> Either Err (Node r) +traverse optdir obj ivs node0 = loop [node0] Nothing + where + loop :: [Node r] -> Maybe (Node r) -> Either Err (Node r) + loop [] (Just best) = Right best + loop [] Nothing = Left ErrUnsat + loop (n:ns) Nothing = + case children n of + Nothing -> loop ns (Just n) + Just cs -> loop (cs++ns) Nothing + loop (n:ns) (Just best) + | isStrictlyBetter optdir (ndLowerBound n) (ndLowerBound best) = + case children n of + Nothing -> loop ns (Just n) + Just cs -> loop (cs++ns) (Just best) + | otherwise = loop ns (Just best) + + reopt :: Solver r -> Maybe (Solver r) + reopt s = flip evalState s $ do + ret <- dualSimplex optdir obj + if ret + then liftM Just get + else return Nothing + + children :: Node r -> Maybe [Node r] + children node + | null xs = Nothing -- no violation + | ndDepth node `mod` 100 == 0 = -- cut + let + (f0, m0) = maximumBy (comparing fst) [(fracPart val, m) | (_,m,val) <- xs] + sv = flip execState (ndSolver node) $ do + s <- gensym + let g j x = assert (a >= 0) a + where + a | j `IS.member` ivs = + if fracPart x <= f0 + then fracPart x + else (f0 / (f0 - 1)) * (fracPart x - 1) + -- [Gomory1960] では (f0 / (1 - f0)) * (fracPart x - 1) としているが、 + -- これは誤り + | otherwise = + if x >= 0 + then x + else (f0 / (f0 - 1)) * x + putTableau $ IM.insert s (IM.mapWithKey (\j x -> negate (g j x)) m0, negate f0) tbl + in Just $ [node{ ndSolver = sv2, ndDepth = ndDepth node + 1 } | sv2 <- maybeToList (reopt sv)] + | otherwise = -- branch + let (v0, val0) = snd $ maximumBy (comparing fst) [(fracPart val, (v, val)) | (v,_,val) <- xs] + cs = [ LA.var v0 .>=. LA.constant (fromIntegral (ceiling val0 :: Integer)) + , LA.var v0 .<=. LA.constant (fromIntegral (floor val0 :: Integer)) + ] + svs = [execState (addConstraint2 c) (ndSolver node) | c <- cs] + in Just $ [node{ ndSolver = sv, ndDepth = ndDepth node + 1 } | Just sv <- map reopt svs] + + where + tbl :: Simplex.Tableau r + tbl = ndTableau node + + xs :: [(Var, VarMap r, r)] + xs = [ (v, m, val) + | v <- IS.toList ivs + , Just (m, val) <- return (IM.lookup v tbl) + , not (isInteger val) + ] + +-- --------------------------------------------------------------------------- + +example1 :: (Fractional r, Eq r) => (OptDir, LA.Expr r, [LA.Atom r], VarSet) +example1 = (optdir, obj, cs, ivs) + where + optdir = OptMax + x1 = LA.var 1 + x2 = LA.var 2 + x3 = LA.var 3 + x4 = LA.var 4 + obj = x1 .+. 2 .*. x2 .+. 3 .*. x3 .+. x4 + cs = + [ (-1) .*. x1 .+. x2 .+. x3 .+. 10.*.x4 .<=. LA.constant 20 + , x1 .-. 3 .*. x2 .+. x3 .<=. LA.constant 30 + , x2 .-. 3.5 .*. x4 .==. LA.constant 0 + , LA.constant 0 .<=. x1 + , x1 .<=. LA.constant 40 + , LA.constant 0 .<=. x2 + , LA.constant 0 .<=. x3 + , LA.constant 2 .<=. x4 + , x4 .<=. LA.constant 3 + ] + ivs = IS.singleton 4 + +test1 :: Bool +test1 = result==expected + where + (optdir, obj, cs, ivs) = example1 + result, expected :: OptResult Rational + result = optimize' optdir obj cs ivs + expected = Optimum (245/2) (IM.fromList [(1,40),(2,21/2),(3,39/2),(4,3)]) + +test1' :: Bool +test1' = result==expected + where + (optdir, obj, cs, ivs) = example1 + f OptMin = OptMax + f OptMax = OptMin + result, expected :: OptResult Rational + result = optimize' (f optdir) (lnegate obj) cs ivs + expected = Optimum (-245/2) (IM.fromList [(1,40),(2,21/2),(3,39/2),(4,3)]) + +-- 『数理計画法の基礎』(坂和 正敏) p.109 例 3.8 +example2 :: (Fractional r, Eq r) => (OptDir, LA.Expr r, [LA.Atom r], VarSet) +example2 = (optdir, obj, cs, ivs) + where + optdir = OptMin + [x1,x2,x3] = map LA.var [1..3] + obj = (-1) .*. x1 .-. 3 .*. x2 .-. 5 .*. x3 + cs = + [ 3 .*. x1 .+. 4 .*. x2 .<=. LA.constant 10 + , 2 .*. x1 .+. x2 .+. x3 .<=. LA.constant 7 + , 3.*.x1 .+. x2 .+. 4 .*. x3 .==. LA.constant 12 + , LA.constant 0 .<=. x1 + , LA.constant 0 .<=. x2 + , LA.constant 0 .<=. x3 + ] + ivs = IS.fromList [1,2] + +test2 :: Bool +test2 = result == expected + where + result, expected :: OptResult Rational + result = optimize' optdir obj cs ivs + expected = Optimum (-37/2) (IM.fromList [(1,0),(2,2),(3,5/2)]) + (optdir, obj, cs, ivs) = example2 + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/OmegaTest.hs b/src/Algorithm/OmegaTest.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/OmegaTest.hs @@ -0,0 +1,265 @@ +{-# OPTIONS_GHC -Wall #-} +{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.OmegaTest +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (MultiParamTypeClasses, FunctionalDependencies) +-- +-- (incomplete) implementation of Omega Test +-- +-- References: +-- +-- * William Pugh. The Omega test: a fast and practical integer +-- programming algorithm for dependence analysis. In Proceedings of +-- the 1991 ACM/IEEE conference on Supercomputing (1991), pp. 4-13. +-- +-- * +-- +-- See also: +-- +-- * +-- +----------------------------------------------------------------------------- +module Algorithm.OmegaTest + ( Model + , solve + , solveQFLA + ) where + +import Control.Monad +import Data.List +import Data.Maybe +import Data.Ord +import Data.Ratio +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS + +import Data.Expr +import Data.Formula +import Data.Linear +import qualified Data.LA as LA +import Util (combineMaybe) +import qualified Algorithm.FourierMotzkin as FM +import Algorithm.FourierMotzkin (Lit (..), Rat) + +-- --------------------------------------------------------------------------- + +type ExprZ = LA.Expr Integer + +-- 制約集合の単純化 +-- It returns Nothing when a inconsistency is detected. +simplify :: [Lit] -> Maybe [Lit] +simplify = fmap concat . mapM f + where + f :: Lit -> Maybe [Lit] + f lit@(Pos e) = + case LA.asConst e of + Just x -> guard (x > 0) >> return [] + Nothing -> return [lit] + f lit@(Nonneg e) = + case LA.asConst e of + Just x -> guard (x >= 0) >> return [] + Nothing -> return [lit] + +-- --------------------------------------------------------------------------- + +leZ, ltZ, geZ, gtZ :: ExprZ -> ExprZ -> Lit +-- Note that constants may be floored by division +leZ e1 e2 = Nonneg (LA.mapCoeff (`div` d) e) + where + e = e2 .-. e1 + d = abs $ gcd' [c | (c,v) <- LA.terms e, v /= LA.unitVar] +ltZ e1 e2 = (e1 .+. LA.constant 1) `leZ` e2 +geZ = flip leZ +gtZ = flip gtZ + +eqZ :: ExprZ -> ExprZ -> (DNF Lit) +eqZ e1 e2 + = if LA.coeff LA.unitVar e3 `mod` d == 0 + then DNF [[Nonneg e, Nonneg (lnegate e)]] + else false + where + e = LA.mapCoeff (`div` d) e3 + e3 = e1 .-. e2 + d = abs $ gcd' [c | (c,v) <- LA.terms e3, v /= LA.unitVar] + +-- --------------------------------------------------------------------------- + +{- +(ls,us) represents +{ x | ∀(M,c)∈ls. M/c≤x, ∀(M,c)∈us. x≤M/c } +-} +type BoundsZ = ([Rat],[Rat]) + +collectBoundsZ :: Var -> [Lit] -> (BoundsZ,[Lit]) +collectBoundsZ v = foldr phi (([],[]),[]) + where + phi :: Lit -> (BoundsZ,[Lit]) -> (BoundsZ,[Lit]) + phi (Pos t) x = phi (Nonneg (t .-. LA.constant 1)) x + phi lit@(Nonneg t) ((ls,us),xs) = + case LA.extract v t of + (c,t') -> + case c `compare` 0 of + EQ -> ((ls, us), lit : xs) + GT -> (((lnegate t', c) : ls, us), xs) -- 0 ≤ cx + M ⇔ -M/c ≤ x + LT -> ((ls, (t', negate c) : us), xs) -- 0 ≤ cx + M ⇔ x ≤ M/-c + +isExact :: BoundsZ -> Bool +isExact (ls,us) = and [a==1 || b==1 | (_,a)<-ls , (_,b)<-us] + +solve' :: [Var] -> [Lit] -> Maybe (Model Integer) +solve' vs2 xs = simplify xs >>= go vs2 + where + go :: [Var] -> [Lit] -> Maybe (Model Integer) + go [] [] = return IM.empty + go [] _ = mzero + go vs ys = + if isExact bnd + then case1 + else case1 `mplus` case2 + where + (v,vs',bnd@(ls,us),rest) = chooseVariable vs ys + + case1 = do + let zs = [ LA.constant ((a-1)*(b-1)) `leZ` (a .*. d .-. b .*. c) + | (c,a)<-ls , (d,b)<-us ] + model <- go vs' =<< simplify (zs ++ rest) + case pickupZ (evalBoundsZ model bnd) of + Nothing -> error "solve': should not happen" + Just val -> return $ IM.insert v val model + + case2 = msum + [ do eq <- isZero $ a' .*. LA.var v .-. (c' .+. LA.constant k) + let (vs'', lits'', mt) = elimEq eq (v:vs') ys + model <- go vs'' =<< simplify lits'' + return $ mt model + | let m = maximum [b | (_,b)<-us] + , (c',a') <- ls + , k <- [0 .. (m*a'-a'-m) `div` m] + ] + +chooseVariable :: [Var] -> [Lit] -> (Var, [Var], BoundsZ, [Lit]) +chooseVariable vs xs = head $ [e | e@(_,_,bnd,_) <- table, isExact bnd] ++ table + where + table = [ (v, vs', bnd, rest) + | (v,vs') <- pickup vs, let (bnd, rest) = collectBoundsZ v xs + ] + +evalBoundsZ :: Model Integer -> BoundsZ -> IntervalZ +evalBoundsZ model (ls,us) = + foldl' intersectZ univZ $ + [ (Just (ceiling (LA.evalExpr model x % c)), Nothing) | (x,c) <- ls ] ++ + [ (Nothing, Just (floor (LA.evalExpr model x % c))) | (x,c) <- us ] + +elimEq :: ExprZ -> [Var] -> [Lit] -> ([Var], [Lit], Model Integer -> Model Integer) +elimEq e vs lits = + if abs ak == 1 + then + case LA.extract xk e of + (_, e') -> + let xk_def = signum ak .*. lnegate e' + in ( vs + , [applySubst1Lit xk xk_def lit | lit <- lits] + , \model -> IM.insert xk (LA.evalExpr model xk_def) model + ) + else + let m = abs ak + 1 + xk_def = (- signum ak * m) .*. LA.var sigma .+. + LA.fromTerms [(signum ak * (a `zmod` m), x) | (a,x) <- LA.terms e, x /= xk] + e2 = (- abs ak) .*. LA.var sigma .+. + LA.fromTerms [((floor (a%m + 1/2) + (a `zmod` m)), x) | (a,x) <- LA.terms e, x /= xk] + -- LA.applySubst1 xk xk_def e を normalize したもの + in case elimEq e2 (sigma : vs) [applySubst1Lit xk xk_def lit | lit <- lits] of + (vs2, lits2, mt) -> + ( vs2 + , lits2 + , \model -> + let model2 = mt model + in IM.delete sigma $ IM.insert xk (LA.evalExpr model2 xk_def) model2 + ) + where + (ak,xk) = minimumBy (comparing (abs . fst)) [(a,x) | (a,x) <- LA.terms e, x /= LA.unitVar] + sigma = maximum (-1 : vs) + 1 + +applySubst1Lit :: Var -> ExprZ -> Lit -> Lit +applySubst1Lit v e (Nonneg e2) = LA.applySubst1 v e e2 `geZ` LA.constant 0 + +-- --------------------------------------------------------------------------- + +isZero :: ExprZ -> Maybe ExprZ +isZero e + = if LA.coeff LA.unitVar e `mod` d == 0 + then Just $ e2 + else Nothing + where + e2 = LA.mapCoeff (`div` d) e + d = abs $ gcd' [c | (c,v) <- LA.terms e, v /= LA.unitVar] + +-- --------------------------------------------------------------------------- + +type IntervalZ = (Maybe Integer, Maybe Integer) + +univZ :: IntervalZ +univZ = (Nothing, Nothing) + +intersectZ :: IntervalZ -> IntervalZ -> IntervalZ +intersectZ (l1,u1) (l2,u2) = (combineMaybe max l1 l2, combineMaybe min u1 u2) + +pickupZ :: IntervalZ -> Maybe Integer +pickupZ (Nothing,Nothing) = return 0 +pickupZ (Just x, Nothing) = return x +pickupZ (Nothing, Just x) = return x +pickupZ (Just x, Just y) = if x <= y then return x else mzero + +-- --------------------------------------------------------------------------- + +solve :: [LA.Atom Rational] -> Maybe (Model Integer) +solve cs = msum [solve' (IS.toList vs) lits | lits <- unDNF dnf] + where + dnf = andB (map f cs) + vs = vars cs + f (Rel lhs op rhs) = + case op of + Lt -> DNF [[a `ltZ` b]] + Le -> DNF [[a `leZ` b]] + Gt -> DNF [[a `gtZ` b]] + Ge -> DNF [[a `geZ` b]] + Eql -> eqZ a b + NEq -> DNF [[a `ltZ` b], [a `gtZ` b]] + where + (e1,c1) = g lhs + (e2,c2) = g rhs + a = c2 .*. e1 + b = c1 .*. e2 + g :: LA.Expr Rational -> (ExprZ, Integer) + g a = (LA.mapCoeff (\c -> floor (c * fromInteger d)) a, d) + where + d = foldl' lcm 1 [denominator c | (c,_) <- LA.terms a] + +solveQFLA :: [LA.Atom Rational] -> VarSet -> Maybe (Model Rational) +solveQFLA cs ivs = listToMaybe $ do + (cs2, mt) <- FM.projectN rvs cs + m <- maybeToList $ solve cs2 + return $ mt $ IM.map fromInteger m + where + rvs = vars cs `IS.difference` ivs + +-- --------------------------------------------------------------------------- + +zmod :: Integer -> Integer -> Integer +a `zmod` b = a - b * floor (a % b + 1 / 2) + +gcd' :: [Integer] -> Integer +gcd' [] = 1 +gcd' xs = foldl1' gcd xs + +pickup :: [a] -> [(a,[a])] +pickup [] = [] +pickup (x:xs) = (x,xs) : [(y,x:ys) | (y,ys) <- pickup xs] + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/Simplex.hs b/src/Algorithm/Simplex.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/Simplex.hs @@ -0,0 +1,309 @@ +{-# LANGUAGE ScopedTypeVariables #-} +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.Simplex +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (ScopedTypeVariables) +-- +-- Naïve implementation of Simplex method +-- +-- Reference: +-- +-- * +-- +----------------------------------------------------------------------------- +module Algorithm.Simplex + ( module Data.OptDir + , Tableau + , RowIndex + , ColIndex + , Row + , PivotResult + , objRow + , pivot + , lookupRow + , setRow + , setObjFun + , currentObjValue + , simplex + , dualSimplex + , phaseI + , toCSV + ) where + +import Data.Ord +import Data.List (intersperse, minimumBy, foldl') +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Data.OptDir +import Control.Exception + +import Data.Expr +import Data.Linear +import qualified Data.LA as LA + +-- --------------------------------------------------------------------------- + +type Tableau r = VarMap (Row r) +{- +tbl ! v == (m, val) +==> +var v .+. m .==. constant val +-} + +type RowIndex = Int +type ColIndex = Int +type Row r = (VarMap r, r) +data PivotResult r = PivotUnbounded | PivotFinished | PivotSuccess (Tableau r) + deriving (Show, Eq, Ord) + +objRow :: RowIndex +objRow = -1 + +pivot :: (Fractional r, Eq r) => RowIndex -> ColIndex -> Tableau r -> Tableau r +{-# INLINE pivot #-} +{-# SPECIALIZE pivot :: RowIndex -> ColIndex -> Tableau Rational -> Tableau Rational #-} +{-# SPECIALIZE pivot :: RowIndex -> ColIndex -> Tableau Double -> Tableau Double #-} +pivot r s tbl = + assert (validTableau tbl) $ -- precondition + assert (validTableau tbl') $ -- postcondition + tbl' + where + tbl' = IM.insert s row_s $ IM.map f $ IM.delete r $ tbl + f orig@(row_i, row_i_val) = + case IM.lookup s row_i of + Nothing -> orig + Just c -> + ( IM.filter (0/=) $ IM.unionWith (+) (IM.delete s row_i) (IM.map (negate c *) row_r') + , row_i_val - c*row_r_val' + ) + (row_r, row_r_val) = lookupRow r tbl + a_rs = row_r IM.! s + row_r' = IM.map (/ a_rs) $ IM.insert r 1 $ IM.delete s row_r + row_r_val' = row_r_val / a_rs + row_s = (row_r', row_r_val') + +lookupRow :: RowIndex -> Tableau r -> Row r +lookupRow r m = m IM.! r + +-- 行の基底変数の列が0になるように変形 +normalizeRow :: (Num r, Eq r) => Tableau r -> Row r -> Row r +normalizeRow a (row0,val0) = obj' + where + obj' = g $ foldl' f (IM.empty, val0) $ + [ case IM.lookup j a of + Nothing -> (IM.singleton j x, 0) + Just (row,val) -> (IM.map ((-x)*) (IM.delete j row), -x*val) + | (j,x) <- IM.toList row0 ] + f (m1,v1) (m2,v2) = (IM.unionWith (+) m1 m2, v1+v2) + g (m,v) = (IM.filter (0/=) m, v) + +setRow :: (Num r, Eq r) => RowIndex -> Tableau r -> Row r -> Tableau r +setRow i tbl row = assert (validTableau tbl) $ assert (validTableau tbl') $ tbl' + where + tbl' = IM.insert i (normalizeRow tbl row) tbl + +setObjFun :: (Num r, Eq r) => Tableau r -> LA.Expr r -> Tableau r +setObjFun tbl e = setRow objRow tbl row + where + row = + case LA.extract LA.unitVar e of + (c, e') -> (LA.coeffMap (lnegate e'), c) + +copyObjRow :: (Num r, Eq r) => Tableau r -> Tableau r -> Tableau r +copyObjRow from to = + case IM.lookup objRow from of + Nothing -> IM.delete objRow to + Just row -> setRow objRow to row + +currentObjValue :: (Num r, Eq r) => Tableau r -> r +currentObjValue = snd . lookupRow objRow + +validTableau :: Tableau r -> Bool +validTableau tbl = + and [v `IM.notMember` m | (v, (m,_)) <- IM.toList tbl, v /= objRow] && + and [IS.null (IM.keysSet m `IS.intersection` vs) | (m,_) <- IM.elems tbl'] + where + tbl' = IM.delete objRow tbl + vs = IM.keysSet tbl' + +isFeasible :: Real r => Tableau r -> Bool +isFeasible tbl = + and [val >= 0 | (v, (_,val)) <- IM.toList tbl, v /= objRow] + +isOptimal :: Real r => OptDir -> Tableau r -> Bool +isOptimal optdir tbl = + and [not (cmp cj) | cj <- IM.elems (fst (lookupRow objRow tbl))] + where + cmp = case optdir of + OptMin -> (0<) + OptMax -> (0>) + +isImproving :: Real r => OptDir -> Tableau r -> Tableau r -> Bool +isImproving OptMin from to = currentObjValue to <= currentObjValue from +isImproving OptMax from to = currentObjValue to >= currentObjValue from + +-- --------------------------------------------------------------------------- +-- primal simplex + +simplex :: (Real r, Fractional r) => OptDir -> Tableau r -> (Bool, Tableau r) +{-# SPECIALIZE simplex :: OptDir -> Tableau Rational -> (Bool, Tableau Rational) #-} +{-# SPECIALIZE simplex :: OptDir -> Tableau Double -> (Bool, Tableau Double) #-} +simplex optdir = go + where + go tbl = assert (isFeasible tbl) $ + case primalPivot optdir tbl of + PivotFinished -> assert (isOptimal optdir tbl) (True, tbl) + PivotUnbounded -> (False, tbl) + PivotSuccess tbl' -> assert (isImproving optdir tbl tbl') $ go tbl' + +primalPivot :: (Real r, Fractional r) => OptDir -> Tableau r -> PivotResult r +{-# INLINE primalPivot #-} +primalPivot optdir tbl + | null cs = PivotFinished + | null rs = PivotUnbounded + | otherwise = PivotSuccess (pivot r s tbl) + where + cmp = case optdir of + OptMin -> (0<) + OptMax -> (0>) + cs = [(j,cj) | (j,cj) <- IM.toList (fst (lookupRow objRow tbl)), cmp cj] + -- smallest subscript rule + s = fst $ head cs + -- classical rule + --s = fst $ (if optdir==OptMin then maximumBy else minimumBy) (compare `on` snd) cs + rs = [ (i, y_i0 / y_is) + | (i, (row_i, y_i0)) <- IM.toList tbl, i /= objRow + , let y_is = IM.findWithDefault 0 s row_i, y_is > 0 + ] + r = fst $ minimumBy (comparing snd) rs + +-- --------------------------------------------------------------------------- +-- dual simplex + +dualSimplex :: (Real r, Fractional r) => OptDir -> Tableau r -> (Bool, Tableau r) +{-# SPECIALIZE dualSimplex :: OptDir -> Tableau Rational -> (Bool, Tableau Rational) #-} +{-# SPECIALIZE dualSimplex :: OptDir -> Tableau Double -> (Bool, Tableau Double) #-} +dualSimplex optdir = go + where + go tbl = assert (isOptimal optdir tbl) $ + case dualPivot optdir tbl of + PivotFinished -> assert (isFeasible tbl) $ (True, tbl) + PivotUnbounded -> (False, tbl) + PivotSuccess tbl' -> assert (isImproving optdir tbl' tbl) $ go tbl' + +dualPivot :: (Real r, Fractional r) => OptDir -> Tableau r -> PivotResult r +{-# INLINE dualPivot #-} +dualPivot optdir tbl + | null rs = PivotFinished + | null cs = PivotUnbounded + | otherwise = PivotSuccess (pivot r s tbl) + where + rs = [(i, row_i) | (i, (row_i, y_i0)) <- IM.toList tbl, i /= objRow, 0 > y_i0] + (r, row_r) = head rs + cs = [ (j, if optdir==OptMin then y_0j / y_rj else - y_0j / y_rj) + | (j, y_rj) <- IM.toList row_r + , y_rj < 0 + , let y_0j = IM.findWithDefault 0 j obj + ] + s = fst $ minimumBy (comparing snd) cs + (obj,_) = lookupRow objRow tbl + +-- --------------------------------------------------------------------------- +-- phase I of the two-phased method + +phaseI :: (Real r, Fractional r) => Tableau r -> VarSet -> (Bool, Tableau r) +{-# SPECIALIZE phaseI :: Tableau Rational -> VarSet -> (Bool, Tableau Rational) #-} +{-# SPECIALIZE phaseI :: Tableau Double -> VarSet -> (Bool, Tableau Double) #-} +phaseI tbl avs + | currentObjValue tbl1' /= 0 = (False, tbl1') + | otherwise = (True, copyObjRow tbl $ removeArtificialVariables avs $ tbl1') + where + optdir = OptMax + tbl1 = setObjFun tbl $ lnegate $ lsum [LA.var v | v <- IS.toList avs] + tbl1' = go tbl1 + go tbl2 + | currentObjValue tbl2 == 0 = tbl2 + | otherwise = + case primalPivot optdir tbl2 of + PivotSuccess tbl2' -> assert (isImproving optdir tbl2 tbl2') $ go tbl2' + PivotFinished -> assert (isOptimal optdir tbl2) tbl2 + PivotUnbounded -> error "phaseI: should not happen" + +-- post-processing of phaseI +-- pivotを使ってartificial variablesを基底から除いて、削除 +removeArtificialVariables :: (Real r, Fractional r) => VarSet -> Tableau r -> Tableau r +removeArtificialVariables avs tbl0 = tbl2 + where + tbl1 = foldl' f (IM.delete objRow tbl0) (IS.toList avs) + tbl2 = IM.map (\(row,val) -> (IM.filterWithKey (\j _ -> j `IS.notMember` avs) row, val)) tbl1 + f tbl i = + case IM.lookup i tbl of + Nothing -> tbl + Just row -> + case [j | (j,c) <- IM.toList (fst row), c /= 0, j `IS.notMember` avs] of + [] -> IM.delete i tbl + j:_ -> pivot i j tbl + + +-- --------------------------------------------------------------------------- + +toCSV :: (Num r, Eq r, Show r) => (r -> String) -> Tableau r -> String +toCSV showCell tbl = unlines . map (concat . intersperse ",") $ header : body + where + header :: [String] + header = "" : map colName cols ++ [""] + + body :: [[String]] + body = [showRow i (lookupRow i tbl) | i <- rows] + + rows :: [RowIndex] + rows = IM.keys (IM.delete objRow tbl) ++ [objRow] + + cols :: [ColIndex] + cols = [0..colMax] + where + colMax = maximum (-1 : [c | (row, _) <- IM.elems tbl, c <- IM.keys row]) + + rowName :: RowIndex -> String + rowName i = if i==objRow then "obj" else "x" ++ show i + + colName :: ColIndex -> String + colName j = "x" ++ show j + + showRow i (row, row_val) = rowName i : [showCell (IM.findWithDefault 0 j row') | j <- cols] ++ [showCell row_val] + where row' = IM.insert i 1 row + +-- --------------------------------------------------------------------------- + +-- 退化して巡回の起こるKuhnの7変数3制約の例 + +kuhn_7_3 :: Tableau Rational +kuhn_7_3 = IM.fromList + [ (1, (IM.fromList [(4,-2), (5,-9), (6,1), (7,9)], 0)) + , (2, (IM.fromList [(4,1/3), (5,1), (6,-1/3), (7,-2)], 0)) + , (3, (IM.fromList [(4,2), (5,3), (6,-1), (7,-12)], 2)) + , (objRow, (IM.fromList [(4,2), (5,3), (6,-1), (7,-12)], 0)) + ] + +test_kuhn_7_3 :: (Bool, Tableau Rational) +test_kuhn_7_3 = simplex OptMin kuhn_7_3 + +-- from http://www.math.cuhk.edu.hk/~wei/lpch5.pdf +example_5_7 :: Tableau Rational +example_5_7 = IM.fromList + [ (4, (IM.fromList [(1,-1), (2,-2), (3,-3)], -5)) + , (5, (IM.fromList [(1,-2), (2,-2), (3,-1)], -6)) + , (objRow, (IM.fromList [(1,3),(2,4),(3,5)], 0)) + ] + +test_example_5_7 :: (Bool, Tableau Rational) +test_example_5_7 = dualSimplex OptMax example_5_7 +-- optimal value should be -11 + +-- --------------------------------------------------------------------------- diff --git a/src/Algorithm/Simplex2.hs b/src/Algorithm/Simplex2.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/Simplex2.hs @@ -0,0 +1,1023 @@ +{-# LANGUAGE DoAndIfThenElse, TypeSynonymInstances, FlexibleContexts, FlexibleInstances #-} +----------------------------------------------------------------------------- +-- | +-- Module : Algorithm.Simplex2 +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (DoAndIfThenElse, TypeSynonymInstances, FlexibleContexts, FlexibleInstances) +-- +-- Naïve implementation of Simplex method +-- +-- Reference: +-- +-- * +-- +-- * Bruno Dutertre and Leonardo de Moura. +-- A Fast Linear-Arithmetic Solver for DPLL(T). +-- Computer Aided Verification In Computer Aided Verification, Vol. 4144 (2006), pp. 81-94. +-- +-- +-- * Bruno Dutertre and Leonardo de Moura. +-- Integrating Simplex with DPLL(T). +-- CSL Technical Report SRI-CSL-06-01. 2006. +-- +-- +----------------------------------------------------------------------------- +module Algorithm.Simplex2 + ( + -- * The @Solver@ type + Solver + , GenericSolver + , SolverValue (..) + , newSolver + , cloneSolver + + -- * Problem specification + , Var + , newVar + , RelOp (..) + , (.<=.), (.>=.), (.==.), (.<.), (.>.) + , Atom (..) + , assertAtom + , assertAtomEx + , assertLower + , assertUpper + , setObj + , getObj + , OptDir (..) + , setOptDir + , getOptDir + + -- * Solving + , check + , Options (..) + , defaultOptions + , OptResult (..) + , optimize + , dualSimplex + + -- * Extract results + , Model + , model + , RawModel + , rawModel + , getValue + , getObjValue + + -- * Reading status + , getTableau + , getRow + , getCol + , getCoeff + , nVars + , isBasicVariable + , isNonBasicVariable + , isFeasible + , isOptimal + , getLB + , getUB + + -- * Configulation + , setLogger + , clearLogger + , PivotStrategy (..) + , setPivotStrategy + + -- * Debug + , dump + ) where + +import Prelude hiding (log) +import Control.Exception +import Control.Monad +import Data.Ord +import Data.IORef +import Data.List +import Data.Maybe +import Data.Ratio +import qualified Data.Map as Map +import qualified Data.IntMap as IM +import Text.Printf +import Data.Time +import Data.OptDir +import System.CPUTime + +import qualified Data.LA as LA +import Data.LA (Atom (..)) +import Data.ArithRel +import Data.Linear +import Data.Delta +import Util (showRational) + +{-------------------------------------------------------------------- + The @Solver@ type +--------------------------------------------------------------------} + +type Var = Int + +data GenericSolver v + = GenericSolver + { svTableau :: !(IORef (IM.IntMap (LA.Expr Rational))) + , svLB :: !(IORef (IM.IntMap v)) + , svUB :: !(IORef (IM.IntMap v)) + , svModel :: !(IORef (IM.IntMap v)) + , svVCnt :: !(IORef Int) + , svOk :: !(IORef Bool) + , svOptDir :: !(IORef OptDir) + + , svDefDB :: !(IORef (Map.Map (LA.Expr Rational) Var)) + + , svLogger :: !(IORef (Maybe (String -> IO ()))) + , svPivotStrategy :: !(IORef PivotStrategy) + , svNPivot :: !(IORef Int) + } + +type Solver = GenericSolver Rational + +-- special basic variable +objVar :: Int +objVar = -1 + +newSolver :: SolverValue v => IO (GenericSolver v) +newSolver = do + t <- newIORef (IM.singleton objVar lzero) + l <- newIORef IM.empty + u <- newIORef IM.empty + m <- newIORef (IM.singleton objVar lzero) + v <- newIORef 0 + ok <- newIORef True + dir <- newIORef OptMin + defs <- newIORef Map.empty + logger <- newIORef Nothing + pivot <- newIORef PivotStrategyBlandRule + npivot <- newIORef 0 + return $ + GenericSolver + { svTableau = t + , svLB = l + , svUB = u + , svModel = m + , svVCnt = v + , svOk = ok + , svOptDir = dir + , svDefDB = defs + , svLogger = logger + , svNPivot = npivot + , svPivotStrategy = pivot + } + +cloneSolver :: GenericSolver v -> IO (GenericSolver v) +cloneSolver solver = do + t <- newIORef =<< readIORef (svTableau solver) + l <- newIORef =<< readIORef (svLB solver) + u <- newIORef =<< readIORef (svUB solver) + m <- newIORef =<< readIORef (svModel solver) + v <- newIORef =<< readIORef (svVCnt solver) + ok <- newIORef =<< readIORef (svOk solver) + dir <- newIORef =<< readIORef (svOptDir solver) + defs <- newIORef =<< readIORef (svDefDB solver) + logger <- newIORef =<< readIORef (svLogger solver) + pivot <- newIORef =<< readIORef (svPivotStrategy solver) + npivot <- newIORef =<< readIORef (svNPivot solver) + return $ + GenericSolver + { svTableau = t + , svLB = l + , svUB = u + , svModel = m + , svVCnt = v + , svOk = ok + , svOptDir = dir + , svDefDB = defs + , svLogger = logger + , svNPivot = npivot + , svPivotStrategy = pivot + } + +class (Linear Rational v, Ord v) => SolverValue v where + toValue :: Rational -> v + showValue :: Bool -> v -> String + model :: GenericSolver v -> IO Model + +instance SolverValue Rational where + toValue = id + showValue = showRational + model = rawModel + +instance SolverValue (Delta Rational) where + toValue = fromReal + showValue = showDelta + model solver = do + xs <- variables solver + ys <- liftM concat $ forM xs $ \x -> do + Delta p q <- getValue solver x + lb <- getLB solver x + ub <- getUB solver x + return $ + [(p - c) / (k - q) | Just (Delta c k) <- return lb, c < p, k > q] ++ + [(d - p) / (q - h) | Just (Delta d h) <- return ub, p < d, q > h] + let delta0 :: Rational + delta0 = if null ys then 0.1 else minimum ys + f :: Delta Rational -> Rational + f (Delta r k) = r + k * delta0 + liftM (IM.map f) $ readIORef (svModel solver) + +{- +Largest coefficient rule: original rule suggested by G. Dantzig. +Largest increase rule: computationally more expensive in comparison with Largest coefficient, but locally maximizes the progress. +Steepest edge rule: best pivot rule in practice, an efficient approximate implementation is "Devex". +Bland’s rule: avoids cycling but one of the slowest rules. +Random edge rule: Randomized have lead to the current best provable bounds for the number of pivot steps of the simplex method. +Lexicographic rule: used for avoiding cyclying. +-} +data PivotStrategy + = PivotStrategyBlandRule + | PivotStrategyLargestCoefficient +-- | PivotStrategySteepestEdge + deriving (Eq, Ord, Enum, Show, Read) + +setPivotStrategy :: GenericSolver v -> PivotStrategy -> IO () +setPivotStrategy solver ps = writeIORef (svPivotStrategy solver) ps + +{-------------------------------------------------------------------- + problem description +--------------------------------------------------------------------} + +newVar :: SolverValue v => GenericSolver v -> IO Var +newVar solver = do + v <- readIORef (svVCnt solver) + writeIORef (svVCnt solver) $! v+1 + modifyIORef (svModel solver) (IM.insert v lzero) + return v + +assertAtom :: Solver -> LA.Atom Rational -> IO () +assertAtom solver atom = do + (v,op,rhs') <- simplifyAtom solver atom + case op of + Le -> assertUpper solver v (toValue rhs') + Ge -> assertLower solver v (toValue rhs') + Eql -> do + assertLower solver v (toValue rhs') + assertUpper solver v (toValue rhs') + _ -> error "unsupported" + return () + +assertAtomEx :: GenericSolver (Delta Rational) -> LA.Atom Rational -> IO () +assertAtomEx solver atom = do + (v,op,rhs') <- simplifyAtom solver atom + case op of + Le -> assertUpper solver v (toValue rhs') + Ge -> assertLower solver v (toValue rhs') + Lt -> assertUpper solver v (toValue rhs' .-. delta) + Gt -> assertLower solver v (toValue rhs' .+. delta) + Eql -> do + assertLower solver v (toValue rhs') + assertUpper solver v (toValue rhs') + return () + +simplifyAtom :: SolverValue v => GenericSolver v -> LA.Atom Rational -> IO (Var, RelOp, Rational) +simplifyAtom solver (Rel lhs op rhs) = do + let (lhs',rhs') = + case LA.extract LA.unitVar (lhs .-. rhs) of + (n,e) -> (e, -n) + case LA.terms lhs' of + [(1,v)] -> return (v, op, rhs') + [(-1,v)] -> return (v, flipOp op, -rhs') + _ -> do + defs <- readIORef (svDefDB solver) + let (c,lhs'') = scale lhs' -- lhs' = lhs'' / c = rhs' + rhs'' = c .*. rhs' + op'' = if c < 0 then flipOp op else op + case Map.lookup lhs'' defs of + Just v -> do + return (v,op'',rhs'') + Nothing -> do + v <- newVar solver + setRow solver v lhs'' + modifyIORef (svDefDB solver) $ Map.insert lhs'' v + return (v,op'',rhs'') + where + scale :: LA.Expr Rational -> (Rational, LA.Expr Rational) + scale e = (c, c .*. e) + where + c = c1 * c2 + c1 = fromIntegral $ foldl' lcm 1 [denominator c | (c, _) <- LA.terms e] + c2 = signum $ head ([c | (c,x) <- LA.terms e] ++ [1]) + +assertLower :: SolverValue v => GenericSolver v -> Var -> v -> IO () +assertLower solver x l = do + l0 <- getLB solver x + u0 <- getUB solver x + case (l0,u0) of + (Just l0', _) | l <= l0' -> return () + (_, Just u0') | u0' < l -> markBad solver + _ -> do + modifyIORef (svLB solver) (IM.insert x l) + b <- isNonBasicVariable solver x + v <- getValue solver x + when (b && not (l <= v)) $ update solver x l + checkNBFeasibility solver + +assertUpper :: SolverValue v => GenericSolver v -> Var -> v -> IO () +assertUpper solver x u = do + l0 <- getLB solver x + u0 <- getUB solver x + case (l0,u0) of + (_, Just u0') | u0' <= u -> return () + (Just l0', _) | u < l0' -> markBad solver + _ -> do + modifyIORef (svUB solver) (IM.insert x u) + b <- isNonBasicVariable solver x + v <- getValue solver x + when (b && not (v <= u)) $ update solver x u + checkNBFeasibility solver + +-- FIXME: 式に定数項が含まれる可能性を考えるとこれじゃまずい? +setObj :: SolverValue v => GenericSolver v -> LA.Expr Rational -> IO () +setObj solver e = setRow solver objVar e + +getObj :: SolverValue v => GenericSolver v -> IO (LA.Expr Rational) +getObj solver = getRow solver objVar + +setRow :: SolverValue v => GenericSolver v -> Var -> LA.Expr Rational -> IO () +setRow solver v e = do + modifyIORef (svTableau solver) $ \t -> + IM.insert v (LA.applySubst t e) t + modifyIORef (svModel solver) $ \m -> + IM.insert v (LA.evalLinear m (toValue 1) e) m + +setOptDir :: GenericSolver v -> OptDir -> IO () +setOptDir solver dir = writeIORef (svOptDir solver) dir + +getOptDir :: GenericSolver v -> IO OptDir +getOptDir solver = readIORef (svOptDir solver) + +{-------------------------------------------------------------------- + Status +--------------------------------------------------------------------} + +nVars :: GenericSolver v -> IO Int +nVars solver = readIORef (svVCnt solver) + +isBasicVariable :: GenericSolver v -> Var -> IO Bool +isBasicVariable solver v = do + t <- readIORef (svTableau solver) + return $ v `IM.member` t + +isNonBasicVariable :: GenericSolver v -> Var -> IO Bool +isNonBasicVariable solver x = liftM not (isBasicVariable solver x) + +isFeasible :: SolverValue v => GenericSolver v -> IO Bool +isFeasible solver = do + xs <- variables solver + liftM and $ forM xs $ \x -> do + v <- getValue solver x + l <- getLB solver x + u <- getUB solver x + return (testLB l v && testUB u v) + +isOptimal :: SolverValue v => GenericSolver v -> IO Bool +isOptimal solver = do + obj <- getRow solver objVar + ret <- selectEnteringVariable solver + return $! isNothing ret + +{-------------------------------------------------------------------- + Satisfiability solving +--------------------------------------------------------------------} + +check :: SolverValue v => GenericSolver v -> IO Bool +check solver = do + let + loop :: IO Bool + loop = do + m <- selectViolatingBasicVariable solver + + case m of + Nothing -> return True + Just xi -> do + li <- getLB solver xi + ui <- getUB solver xi + isLBViolated <- do + vi <- getValue solver xi + return $ not (testLB li vi) + let q = if isLBViolated + then -- select the smallest non-basic variable xj such that + -- (aij > 0 and β(xj) < uj) or (aij < 0 and β(xj) > lj) + canIncrease solver + else -- select the smallest non-basic variable xj such that + -- (aij < 0 and β(xj) < uj) or (aij > 0 and β(xj) > lj) + canDecrease solver + xi_def <- getRow solver xi + r <- liftM (fmap snd) $ findM q (LA.terms xi_def) + case r of + Nothing -> markBad solver >> return False + Just xj -> do + pivotAndUpdate solver xi xj (fromJust (if isLBViolated then li else ui)) + loop + + ok <- readIORef (svOk solver) + if not ok + then return False + else do + log solver "check" + result <- recordTime solver loop + when result $ checkFeasibility solver + return result + +selectViolatingBasicVariable :: SolverValue v => GenericSolver v -> IO (Maybe Var) +selectViolatingBasicVariable solver = do + let + p :: Var -> IO Bool + p x | x == objVar = return False + p xi = do + li <- getLB solver xi + ui <- getUB solver xi + vi <- getValue solver xi + return $ not (testLB li vi) || not (testUB ui vi) + vs <- basicVariables solver + + ps <- readIORef (svPivotStrategy solver) + case ps of + PivotStrategyBlandRule -> + findM p vs + PivotStrategyLargestCoefficient -> do + xs <- filterM p vs + case xs of + [] -> return Nothing + _ -> do + xs2 <- forM xs $ \xi -> do + vi <- getValue solver xi + li <- getLB solver xi + ui <- getUB solver xi + if not (testLB li vi) + then return (xi, fromJust li .-. vi) + else return (xi, vi .-. fromJust ui) + return $ Just $ fst $ maximumBy (comparing snd) xs2 + +{-------------------------------------------------------------------- + Optimization +--------------------------------------------------------------------} + +-- | results of optimization +data OptResult = Optimum | Unsat | Unbounded | ObjLimit + deriving (Show, Eq, Ord) + +data Options + = Options + { objLimit :: Maybe Rational + } + deriving (Show, Eq, Ord) + +defaultOptions :: Options +defaultOptions + = Options + { objLimit = Nothing + } + +optimize :: Solver -> Options -> IO OptResult +optimize solver opt = do + ret <- do + is_fea <- isFeasible solver + if is_fea then return True else check solver + if not ret + then return Unsat -- unsat + else do + log solver "optimize" + result <- recordTime solver loop + when (result == Optimum) $ checkOptimality solver + return result + where + loop :: IO OptResult + loop = do + checkFeasibility solver + ret <- selectEnteringVariable solver + case ret of + Nothing -> return Optimum + Just (c,xj) -> do + dir <- getOptDir solver + r <- if dir==OptMin + then if c > 0 + then decreaseNB solver xj -- xj を小さくして目的関数を小さくする + else increaseNB solver xj -- xj を大きくして目的関数を小さくする + else if c > 0 + then increaseNB solver xj -- xj を大きくして目的関数を大きくする + else decreaseNB solver xj -- xj を小さくして目的関数を大きくする + if r + then loop + else return Unbounded + +selectEnteringVariable :: SolverValue v => GenericSolver v -> IO (Maybe (Rational, Var)) +selectEnteringVariable solver = do + ps <- readIORef (svPivotStrategy solver) + obj_def <- getRow solver objVar + case ps of + PivotStrategyBlandRule -> + findM canEnter (LA.terms obj_def) + PivotStrategyLargestCoefficient -> do + ts <- filterM canEnter (LA.terms obj_def) + case ts of + [] -> return Nothing + _ -> return $ Just $ snd $ maximumBy (comparing fst) [(abs c, (c,xj)) | (c,xj) <- ts] + where + canEnter :: (Rational, Var) -> IO Bool + canEnter (_,xj) | xj == LA.unitVar = return False + canEnter (c,xj) = do + dir <- getOptDir solver + if dir==OptMin + then canDecrease solver (c,xj) + else canIncrease solver (c,xj) + +canIncrease :: SolverValue v => GenericSolver v -> (Rational,Var) -> IO Bool +canIncrease solver (a,x) = + case compare a 0 of + EQ -> return False + GT -> canIncrease1 solver x + LT -> canDecrease1 solver x + +canDecrease :: SolverValue v => GenericSolver v -> (Rational,Var) -> IO Bool +canDecrease solver (a,x) = + case compare a 0 of + EQ -> return False + GT -> canDecrease1 solver x + LT -> canIncrease1 solver x + +canIncrease1 :: SolverValue v => GenericSolver v -> Var -> IO Bool +canIncrease1 solver x = do + u <- getUB solver x + v <- getValue solver x + case u of + Nothing -> return True + Just uv -> return $! (v < uv) + +canDecrease1 :: SolverValue v => GenericSolver v -> Var -> IO Bool +canDecrease1 solver x = do + l <- getLB solver x + v <- getValue solver x + case l of + Nothing -> return True + Just lv -> return $! (lv < v) + +-- | feasibility を保ちつつ non-basic variable xj の値を大きくする +increaseNB :: Solver -> Var -> IO Bool +increaseNB solver xj = do + col <- getCol solver xj + + -- Upper bounds of θ + -- NOTE: xj 自体の上限も考慮するのに注意 + ubs <- liftM concat $ forM ((xj,1) : IM.toList col) $ \(xi,aij) -> do + v1 <- getValue solver xi + li <- getLB solver xi + ui <- getUB solver xi + return [ assert (theta >= lzero) ((xi,v2), theta) + | Just v2 <- [ui | aij > 0] ++ [li | aij < 0] + , let theta = (v2 .-. v1) ./. aij ] + + -- β(xj) := β(xj) + θ なので θ を大きく + case ubs of + [] -> return False -- unbounded + _ -> do + let (xi, v) = fst $ minimumBy (comparing snd) ubs + pivotAndUpdate solver xi xj v + return True + +-- | feasibility を保ちつつ non-basic variable xj の値を小さくする +decreaseNB :: Solver -> Var -> IO Bool +decreaseNB solver xj = do + col <- getCol solver xj + + -- Lower bounds of θ + -- NOTE: xj 自体の下限も考慮するのに注意 + lbs <- liftM concat $ forM ((xj,1) : IM.toList col) $ \(xi,aij) -> do + v1 <- getValue solver xi + li <- getLB solver xi + ui <- getUB solver xi + return [ assert (theta <= lzero) ((xi,v2), theta) + | Just v2 <- [li | aij > 0] ++ [ui | aij < 0] + , let theta = (v2 .-. v1) ./. aij ] + + -- β(xj) := β(xj) + θ なので θ を小さく + case lbs of + [] -> return False -- unbounded + _ -> do + let (xi, v) = fst $ maximumBy (comparing snd) lbs + pivotAndUpdate solver xi xj v + return True + +dualSimplex :: Solver -> Options -> IO OptResult +dualSimplex solver opt = do + let + loop :: IO OptResult + loop = do + checkOptimality solver + + p <- prune solver opt + if p + then return ObjLimit + else do + m <- selectViolatingBasicVariable solver + case m of + Nothing -> return Optimum + Just xi -> do + xi_def <- getRow solver xi + li <- getLB solver xi + ui <- getUB solver xi + isLBViolated <- do + vi <- getValue solver xi + return $ not (testLB li vi) + r <- dualRTest solver xi_def isLBViolated + case r of + Nothing -> markBad solver >> return Unsat -- dual unbounded + Just xj -> do + pivotAndUpdate solver xi xj (fromJust (if isLBViolated then li else ui)) + loop + + ok <- readIORef (svOk solver) + if not ok + then return Unsat + else do + log solver "dual simplex" + result <- recordTime solver loop + when (result == Optimum) $ checkFeasibility solver + return result + +dualRTest :: Solver -> LA.Expr Rational -> Bool -> IO (Maybe Var) +dualRTest solver row isLBViolated = do + -- normalize to the cases of minimization + obj_def <- do + def <- getRow solver objVar + dir <- getOptDir solver + return $ + case dir of + OptMin -> def + OptMax -> lnegate def + -- normalize to the cases of lower bound violation + let xi_def = + if isLBViolated + then row + else lnegate row + ws <- do + -- select non-basic variable xj such that + -- (aij > 0 and β(xj) < uj) or (aij < 0 and β(xj) > lj) + liftM concat $ forM (LA.terms xi_def) $ \(aij, xj) -> do + b <- canIncrease solver (aij, xj) + if b + then do + let cj = LA.coeff xj obj_def + let ratio = cj / aij + return [(xj, ratio) | ratio >= 0] + else + return [] + case ws of + [] -> return Nothing + _ -> return $ Just $ fst $ minimumBy (comparing snd) ws + +prune :: Solver -> Options -> IO Bool +prune solver opt = + case objLimit opt of + Nothing -> return False + Just lim -> do + o <- getObjValue solver + dir <- getOptDir solver + case dir of + OptMin -> return $! (lim <= o) + OptMax -> return $! (lim >= o) + +{-------------------------------------------------------------------- + Extract results +--------------------------------------------------------------------} + +type RawModel v = IM.IntMap v + +rawModel :: GenericSolver v -> IO (RawModel v) +rawModel solver = do + xs <- variables solver + liftM IM.fromList $ forM xs $ \x -> do + val <- getValue solver x + return (x,val) + +getObjValue :: GenericSolver v -> IO v +getObjValue solver = getValue solver objVar + +type Model = IM.IntMap Rational + +{-------------------------------------------------------------------- + major function +--------------------------------------------------------------------} + +update :: SolverValue v => GenericSolver v -> Var -> v -> IO () +update solver xj v = do + -- log solver $ printf "before update x%d (%s)" xj (show v) + -- dump solver + + v0 <- getValue solver xj + let diff = v .-. v0 + + aj <- getCol solver xj + modifyIORef (svModel solver) $ \m -> + let m2 = IM.map (\aij -> aij .*. diff) aj + in IM.insert xj v $ IM.unionWith (.+.) m2 m + + -- log solver $ printf "after update x%d (%s)" xj (show v) + -- dump solver + +pivot :: SolverValue v => GenericSolver v -> Var -> Var -> IO () +pivot solver xi xj = do + modifyIORef' (svNPivot solver) (+1) + modifyIORef' (svTableau solver) $ \defs -> + case LA.solveFor (LA.var xi .==. (defs IM.! xi)) xj of + Just (Eql, xj_def) -> + IM.insert xj xj_def . IM.map (LA.applySubst1 xj xj_def) . IM.delete xi $ defs + _ -> error "pivot: should not happen" + +pivotAndUpdate :: SolverValue v => GenericSolver v -> Var -> Var -> v -> IO () +pivotAndUpdate solver xi xj v | xi == xj = update solver xi v -- xi = xj is non-basic variable +pivotAndUpdate solver xi xj v = do + -- xi is basic variable + -- xj is non-basic varaible + + -- log solver $ printf "before pivotAndUpdate x%d x%d (%s)" xi xj (show v) + -- dump solver + + m <- readIORef (svModel solver) + + aj <- getCol solver xj + let aij = aj IM.! xi + let theta = (v .-. (m IM.! xi)) ./. aij + + let m' = IM.fromList $ + [(xi, v), (xj, (m IM.! xj) .+. theta)] ++ + [(xk, (m IM.! xk) .+. (akj .*. theta)) | (xk, akj) <- IM.toList aj, xk /= xi] + writeIORef (svModel solver) (IM.union m' m) -- note that 'IM.union' is left biased. + + pivot solver xi xj + + -- log solver $ printf "after pivotAndUpdate x%d x%d (%s)" xi xj (show v) + -- dump solver + +getLB :: GenericSolver v -> Var -> IO (Maybe v) +getLB solver x = do + lb <- readIORef (svLB solver) + return $ IM.lookup x lb + +getUB :: GenericSolver v -> Var -> IO (Maybe v) +getUB solver x = do + ub <- readIORef (svUB solver) + return $ IM.lookup x ub + +getTableau :: GenericSolver v -> IO (IM.IntMap (LA.Expr Rational)) +getTableau solver = do + t <- readIORef (svTableau solver) + return $ IM.delete objVar t + +getValue :: GenericSolver v -> Var -> IO v +getValue solver x = do + m <- readIORef (svModel solver) + return $ m IM.! x + +getRow :: GenericSolver v -> Var -> IO (LA.Expr Rational) +getRow solver x = do + -- x should be basic variable or 'objVar' + t <- readIORef (svTableau solver) + return $! (t IM.! x) + +-- aijが非ゼロの列も全部探しているのは効率が悪い +getCol :: SolverValue v => GenericSolver v -> Var -> IO (IM.IntMap Rational) +getCol solver xj = do + t <- readIORef (svTableau solver) + return $ IM.mapMaybe (LA.lookupCoeff xj) t + +getCoeff :: GenericSolver v -> Var -> Var -> IO Rational +getCoeff solver xi xj = do + xi_def <- getRow solver xi + return $! LA.coeff xj xi_def + +markBad :: GenericSolver v -> IO () +markBad solver = writeIORef (svOk solver) False + +{-------------------------------------------------------------------- + utility +--------------------------------------------------------------------} + +findM :: Monad m => (a -> m Bool) -> [a] -> m (Maybe a) +findM _ [] = return Nothing +findM p (x:xs) = do + r <- p x + if r + then return (Just x) + else findM p xs + +testLB :: SolverValue v => Maybe v -> v -> Bool +testLB Nothing _ = True +testLB (Just l) x = l <= x + +testUB :: SolverValue v => Maybe v -> v -> Bool +testUB Nothing _ = True +testUB (Just u) x = x <= u + +variables :: GenericSolver v -> IO [Var] +variables solver = do + vcnt <- nVars solver + return [0..vcnt-1] + +basicVariables :: GenericSolver v -> IO [Var] +basicVariables solver = do + t <- readIORef (svTableau solver) + return (IM.keys t) + +modifyIORef' :: IORef a -> (a -> a) -> IO () +modifyIORef' ref f = do + x <- readIORef ref + writeIORef ref $! f x + +recordTime :: SolverValue v => GenericSolver v -> IO a -> IO a +recordTime solver act = do + dumpSize solver + writeIORef (svNPivot solver) 0 + + startCPU <- getCPUTime + startWC <- getCurrentTime + + result <- act + + endCPU <- getCPUTime + endWC <- getCurrentTime + + (log solver . printf "cpu time = %.3fs") (fromIntegral (endCPU - startCPU) / 10^(12::Int) :: Double) + (log solver . printf "wall clock time = %.3fs") (realToFrac (endWC `diffUTCTime` startWC) :: Double) + (log solver . printf "#pivot = %d") =<< readIORef (svNPivot solver) + return result + +showDelta :: Bool -> Delta Rational -> String +showDelta asRatio v = + case v of + (Delta r k) -> + f r ++ + case compare k 0 of + EQ -> "" + GT -> " + " ++ f k ++ " delta" + LT -> " - " ++ f (abs k) ++ " delta" + where + f = showRational asRatio + +{-------------------------------------------------------------------- + Logging +--------------------------------------------------------------------} + +-- | set callback function for receiving messages. +setLogger :: GenericSolver v -> (String -> IO ()) -> IO () +setLogger solver logger = do + writeIORef (svLogger solver) (Just logger) + +clearLogger :: GenericSolver v -> IO () +clearLogger solver = writeIORef (svLogger solver) Nothing + +log :: GenericSolver v -> String -> IO () +log solver msg = logIO solver (return msg) + +logIO :: GenericSolver v -> IO String -> IO () +logIO solver action = do + m <- readIORef (svLogger solver) + case m of + Nothing -> return () + Just logger -> action >>= logger + +{-------------------------------------------------------------------- + debug and tests +--------------------------------------------------------------------} + +test4 :: IO () +test4 = do + solver <- newSolver + setLogger solver putStrLn + x0 <- newVar solver + x1 <- newVar solver + + writeIORef (svTableau solver) (IM.fromList [(x1, LA.var x0)]) + writeIORef (svLB solver) (IM.fromList [(x0, toValue 0), (x1, toValue 0)]) + writeIORef (svUB solver) (IM.fromList [(x0, toValue 2), (x1, toValue 3)]) + setObj solver (LA.fromTerms [(-1, x0)]) + + ret <- optimize solver defaultOptions + print ret + dump solver + +test5 :: IO () +test5 = do + solver <- newSolver + setLogger solver putStrLn + x0 <- newVar solver + x1 <- newVar solver + + writeIORef (svTableau solver) (IM.fromList [(x1, LA.var x0)]) + writeIORef (svLB solver) (IM.fromList [(x0, toValue 0), (x1, toValue 0)]) + writeIORef (svUB solver) (IM.fromList [(x0, toValue 2), (x1, toValue 0)]) + setObj solver (LA.fromTerms [(-1, x0)]) + + checkFeasibility solver + + ret <- optimize solver defaultOptions + print ret + dump solver + +test6 :: IO () +test6 = do + solver <- newSolver + setLogger solver putStrLn + x0 <- newVar solver + + assertAtom solver (LA.constant 1 .<. LA.var x0) + assertAtom solver (LA.constant 2 .>. LA.var x0) + + ret <- check solver + print ret + dump solver + + m <- model solver + print m + +dumpSize :: SolverValue v => GenericSolver v -> IO () +dumpSize solver = do + t <- readIORef (svTableau solver) + let nrows = IM.size t - 1 -- -1 is objVar + xs <- variables solver + let ncols = length xs - nrows + let nnz = sum [IM.size $ LA.coeffMap xi_def | (xi,xi_def) <- IM.toList t, xi /= objVar] + log solver $ printf "%d rows, %d columns, %d non-zeros" nrows ncols nnz + +dump :: SolverValue v => GenericSolver v -> IO () +dump solver = do + log solver "=============" + + log solver "Tableau:" + t <- readIORef (svTableau solver) + log solver $ printf "obj = %s" (show (t IM.! objVar)) + forM_ (IM.toList t) $ \(xi, e) -> do + when (xi /= objVar) $ log solver $ printf "x%d = %s" xi (show e) + + log solver "" + + log solver "Assignments and Bounds:" + objVal <- getValue solver objVar + log solver $ printf "beta(obj) = %s" (showValue True objVal) + xs <- variables solver + forM_ xs $ \x -> do + l <- getLB solver x + u <- getUB solver x + v <- getValue solver x + let f Nothing = "Nothing" + f (Just x) = showValue True x + log solver $ printf "beta(x%d) = %s; %s <= x%d <= %s" x (showValue True v) (f l) x (f u) + + log solver "" + log solver "Status:" + is_fea <- isFeasible solver + is_opt <- isOptimal solver + log solver $ printf "Feasible: %s" (show is_fea) + log solver $ printf "Optimal: %s" (show is_opt) + + log solver "=============" + +checkFeasibility :: SolverValue v => GenericSolver v -> IO () +checkFeasibility _ | True = return () +checkFeasibility solver = do + xs <- variables solver + forM_ xs $ \x -> do + v <- getValue solver x + l <- getLB solver x + u <- getUB solver x + let f Nothing = "Nothing" + f (Just x) = showValue True x + unless (testLB l v) $ + error (printf "(%s) <= x%d is violated; x%d = (%s)" (f l) x x (showValue True v)) + unless (testUB u v) $ + error (printf "x%d <= (%s) is violated; x%d = (%s)" x (f u) x (showValue True v)) + return () + +checkNBFeasibility :: SolverValue v => GenericSolver v -> IO () +checkNBFeasibility _ | True = return () +checkNBFeasibility solver = do + xs <- variables solver + forM_ xs $ \x -> do + b <- isNonBasicVariable solver x + when b $ do + v <- getValue solver x + l <- getLB solver x + u <- getUB solver x + let f Nothing = "Nothing" + f (Just x) = showValue True x + unless (testLB l v) $ + error (printf "checkNBFeasibility: (%s) <= x%d is violated; x%d = (%s)" (f l) x x (showValue True v)) + unless (testUB u v) $ + error (printf "checkNBFeasibility: x%d <= (%s) is violated; x%d = (%s)" x (f u) x (showValue True v)) + +checkOptimality :: Solver -> IO () +checkOptimality _ | True = return () +checkOptimality solver = do + ret <- selectEnteringVariable solver + case ret of + Nothing -> return () -- optimal + Just (_,x) -> error (printf "checkOptimality: not optimal (x%d can be changed)" x) diff --git a/src/Algorithm/Wang.hs b/src/Algorithm/Wang.hs new file mode 100644 --- /dev/null +++ b/src/Algorithm/Wang.hs @@ -0,0 +1,46 @@ +import Control.Monad (guard,msum) +import Data.List (intersect) +import Data.Maybe (isJust, listToMaybe) + +data Formula x + = Atom x + | Not !(Formula x) + | Imply !(Formula x) !(Formula x) + | And !(Formula x) !(Formula x) + | Or !(Formula x) !(Formula x) + deriving Eq + +type Sequent x = ([Formula x], [Formula x]) + +isValid :: Eq x => Sequent x -> Bool +isValid = isJust . isValid' + +isValid' :: Eq x => Sequent x -> Maybe () +isValid' (l,r) = + do xs <- listToMaybe $ msum $ + [ do let i = intersect l r + guard $ not $ null i + return [] + , do (Not p, r) <- pick r + return [(p:l,r)] + , do (Not p, l) <- pick l + return [(l,p:r)] + , do (Imply p q, r) <- pick r + return [(p:l,q:r)] + , do (Or p q, r) <- pick r + return [(l,p:q:r)] + , do (And p q, l) <- pick l + return [(p:q:l,r)] + , do (Or p q, l) <- pick l + return [(p:l,r), (q:l,r)] + , do (And p q, r) <- pick r + return [(l,p:r), (l,q:r)] + , do (Imply p q, l) <- pick l + return [(q:l,r), (l,p:r)] + ] + mapM_ isValid' xs + return () + +pick :: [x] -> [(x,[x])] +pick [] = [] +pick (x:xs) = (x,xs) : [(y,x:ys) | (y,ys) <- pick xs] diff --git a/src/BenchmarkSATLIB.hs b/src/BenchmarkSATLIB.hs deleted file mode 100644 --- a/src/BenchmarkSATLIB.hs +++ /dev/null @@ -1,39 +0,0 @@ -module Main where - -import Control.Monad -import Data.Array.IArray -import Text.Printf -import Criterion.Main -import qualified Language.CNF.Parse.ParseDIMACS as DIMACS -import qualified SAT - -solve :: FilePath -> IO () -solve fname = do - ret <- DIMACS.parseFile fname - case ret of - Left err -> error $ show err - Right cnf -> do - solver <- SAT.newSolver - SAT.setRandomFreq solver 0 - _ <- replicateM (DIMACS.numVars cnf) (SAT.newVar solver) - forM_ (DIMACS.clauses cnf) $ \clause -> - SAT.addClause solver (elems clause) - SAT.solve solver - return () - -main :: IO () -main = do - Criterion.Main.defaultMain - [ bgroup "uf250-1065" - [ bench fname (solve path) - | i <- [(1::Int)..100] - , let fname = printf "uf250-0%d.cnf" i - , let path = "benchmarks/UF250.1065.100/" ++ fname - ] - , bgroup "uuf250-1065" - [ bench fname (solve path) - | i <- [(1::Int)..100] - , let fname = printf "uuf250-0%d.cnf" i - , let path = "benchmarks/UUF250.1065.100/" ++ fname - ] - ] diff --git a/src/BoundsInference.hs b/src/BoundsInference.hs deleted file mode 100644 --- a/src/BoundsInference.hs +++ /dev/null @@ -1,85 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables, BangPatterns #-} ------------------------------------------------------------------------------ --- | --- Module : BoundsInference --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (ScopedTypeVariables, BangPatterns) --- --- Tightening variable bounds by constraint propagation. --- ------------------------------------------------------------------------------ -module BoundsInference - ( BoundsEnv - , inferBounds - , LA.computeInterval - ) where - -import Control.Monad -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS - -import Data.Expr -import Data.Formula -import Data.Linear -import Data.Interval -import Data.LA (BoundsEnv) -import qualified Data.LA as LA -import Util (isInteger) - -type C r = (RelOp, LA.Expr r) - --- | tightening variable bounds by constraint propagation. -inferBounds :: forall r. (RealFrac r) - => LA.BoundsEnv r -- ^ initial bounds - -> [LA.Atom r] -- ^ constraints - -> VarSet -- ^ integral variables - -> Int -- ^ limit of iterations - -> LA.BoundsEnv r -inferBounds bounds constraints ivs limit = loop 0 bounds - where - cs :: VarMap [C r] - cs = IM.fromListWith (++) $ do - LA.Atom lhs op rhs <- constraints - let m = LA.coeffMap (lhs .-. rhs) - (v,c) <- IM.toList m - guard $ v /= LA.unitVar - let op' = if c < 0 then flipOp op else op - rhs' = (-1/c) .*. LA.fromCoeffMap (IM.delete v m) - return (v, [(op', rhs')]) - - loop :: Int -> LA.BoundsEnv r -> LA.BoundsEnv r - loop !i b = if (limit>=0 && i>=limit) || b==b' then b else loop (i+1) b' - where - b' = refine b - - refine :: LA.BoundsEnv r -> LA.BoundsEnv r - refine b = IM.mapWithKey (\v i -> tighten v $ f b (IM.findWithDefault [] v cs) i) b - - -- tighten bounds of integer variables - tighten :: Var -> Interval r -> Interval r - tighten v x = - if v `IS.notMember` ivs - then x - else tightenToInteger x - -f :: (Real r, Fractional r) => LA.BoundsEnv r -> [C r] -> Interval r -> Interval r -f b cs i = foldr intersection i $ do - (op, rhs) <- cs - let i' = LA.computeInterval b rhs - lb = lowerBound i' - ub = upperBound i' - case op of - Eql -> return i' - Le -> return $ interval Nothing ub - Ge -> return $ interval lb Nothing - Lt -> return $ interval Nothing (strict ub) - Gt -> return $ interval (strict lb) Nothing - NEq -> [] - -strict :: EndPoint r -> EndPoint r -strict Nothing = Nothing -strict (Just (_,val)) = Just (False,val) diff --git a/src/CongruenceClosure.hs b/src/CongruenceClosure.hs deleted file mode 100644 --- a/src/CongruenceClosure.hs +++ /dev/null @@ -1,203 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : CongruenceClosure --- Copyright : (c) Masahiro Sakai 2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : portable --- --- References: --- --- * R. Nieuwenhuis and A. Oliveras, "Fast congruence closure and extensions," --- Information and Computation, vol. 205, no. 4, pp. 557-580, Apr. 2007. --- --- ------------------------------------------------------------------------------ -module CongruenceClosure - ( Solver - , Var - , FlatTerm (..) - , newSolver - , newVar - , merge - , areCongruent - ) where - -import Prelude hiding (lookup) - -import Control.Monad -import Data.IORef -import Data.Maybe -import qualified Data.IntMap as IM - -type Var = Int - -data FlatTerm - = FTConst Var - | FTApp Var Var - deriving (Ord, Eq, Show) - -type Eqn1 = (FlatTerm, Var) -type PendingEqn = Either (Var,Var) (Eqn1, Eqn1) - -data Solver - = Solver - { svVarCounter :: IORef Int - , svPending :: IORef [PendingEqn] - , svRepresentativeTable :: IORef (IM.IntMap Var) -- 本当は配列が良い - , svClassList :: IORef (IM.IntMap [Var]) - , svUseList :: IORef (IM.IntMap [Eqn1]) - , svLookupTable :: IORef (IM.IntMap (IM.IntMap Eqn1)) - } - -newSolver :: IO Solver -newSolver = do - vcnt <- newIORef 0 - pending <- newIORef [] - rep <- newIORef IM.empty - classes <- newIORef IM.empty - useList <- newIORef IM.empty - lookup <- newIORef IM.empty - return $ - Solver - { svVarCounter = vcnt - , svPending = pending - , svRepresentativeTable = rep - , svClassList = classes - , svUseList = useList - , svLookupTable = lookup - } - -newVar :: Solver -> IO Var -newVar solver = do - v <- readIORef (svVarCounter solver) - writeIORef (svVarCounter solver) $! v + 1 - modifyIORef (svRepresentativeTable solver) (IM.insert v v) - modifyIORef (svClassList solver) (IM.insert v [v]) - modifyIORef (svUseList solver) (IM.insert v []) - return v - -merge :: Solver -> (FlatTerm, Var) -> IO () -merge solver (s, a) = do - case s of - FTConst c -> do - addToPending solver (Left (c, a)) - propagate solver - FTApp a1 a2 -> do - a1' <- getRepresentative solver a1 - a2' <- getRepresentative solver a2 - ret <- lookup solver a1' a2' - case ret of - Just (FTApp b1 b2, b) -> do - addToPending solver $ Right ((FTApp a1 a2, a), (FTApp b1 b2, b)) - propagate solver - Nothing -> do - setLookup solver a1' a2' (FTApp a1 a2, a) - modifyIORef (svUseList solver) $ - IM.alter (Just . ((FTApp a1 a2, a) :) . fromMaybe []) a1' . - IM.alter (Just . ((FTApp a1 a2, a) :) . fromMaybe []) a2' - -propagate :: Solver -> IO () -propagate solver = go - where - go = do - ps <- readIORef (svPending solver) - case ps of - [] -> return () - (p:ps') -> do - writeIORef (svPending solver) ps' - processEqn p - go - - processEqn p = do - let (a,b) = case p of - Left (a,b) -> (a,b) - Right ((_, a), (_, b)) -> (a,b) - a' <- getRepresentative solver a - b' <- getRepresentative solver b - if a' == b' - then return () - else do - clist <- readIORef (svClassList solver) - let classA = clist IM.! a' - classB = clist IM.! b' - if length classA < length classB - then update a' b' classA classB - else update b' a' classB classA - - update a' b' classA classB = do - modifyIORef (svRepresentativeTable solver) $ - IM.union (IM.fromList [(c,b') | c <- classA]) - modifyIORef (svClassList solver) $ - IM.insert b' (classA ++ classB) . IM.delete a' - - useList <- readIORef (svUseList solver) - forM_ (useList IM.! a') $ \(FTApp c1 c2, c) -> do -- FIXME: not exhaustive - c1' <- getRepresentative solver c1 - c2' <- getRepresentative solver c2 - ret <- lookup solver c1' c2' - case ret of - Just (FTApp d1 d2, d) -> do -- FIXME: not exhaustive - addToPending solver $ Right ((FTApp c1 c2, c), (FTApp d1 d2, d)) - Nothing -> do - return () - writeIORef (svUseList solver) $ IM.delete a' useList - -areCongruent :: Solver -> FlatTerm -> FlatTerm -> IO Bool -areCongruent solver t1 t2 = do - u1 <- normalize solver t1 - u2 <- normalize solver t2 - return $ u1 == u2 - -normalize :: Solver -> FlatTerm -> IO FlatTerm -normalize solver (FTConst c) = liftM FTConst $ getRepresentative solver c -normalize solver (FTApp t1 t2) = do - u1 <- getRepresentative solver t1 - u2 <- getRepresentative solver t2 - ret <- lookup solver u1 u2 - case ret of - Just (FTApp _ _, a) -> liftM FTConst $ getRepresentative solver a - Nothing -> return $ FTApp u1 u2 - -{-------------------------------------------------------------------- - Helper funcions ---------------------------------------------------------------------} - -lookup :: Solver -> Var -> Var -> IO (Maybe Eqn1) -lookup solver c1 c2 = do - tbl <- readIORef $ svLookupTable solver - return $ do - m <- IM.lookup c1 tbl - IM.lookup c2 m - -setLookup :: Solver -> Var -> Var -> Eqn1 -> IO () -setLookup solver a1 a2 eqn = do - modifyIORef (svLookupTable solver) $ - IM.insertWith IM.union a1 (IM.singleton a2 eqn) - -addToPending :: Solver -> PendingEqn -> IO () -addToPending solver eqn = modifyIORef (svPending solver) (eqn :) - -getRepresentative :: Solver -> Var -> IO Var -getRepresentative solver c = do - m <- readIORef $ svRepresentativeTable solver - return $ m IM.! c - -{-------------------------------------------------------------------- - Test ---------------------------------------------------------------------} - -test = do - solver <- newSolver - a <- newVar solver - b <- newVar solver - c <- newVar solver - d <- newVar solver - merge solver (FTConst a, c) - print =<< areCongruent solver (FTApp a b) (FTApp c d) -- False - merge solver (FTConst b, d) - print =<< areCongruent solver (FTApp a b) (FTApp c d) -- True - diff --git a/src/ContiTraverso.hs b/src/ContiTraverso.hs deleted file mode 100644 --- a/src/ContiTraverso.hs +++ /dev/null @@ -1,114 +0,0 @@ -{- -http://posso.dm.unipi.it/users/traverso/conti-traverso-ip.ps -http://madscientist.jp/~ikegami/articles/IntroSequencePolynomial.html -http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1295-27.pdf --} -module ContiTraverso where - -import Data.Function -import Data.Monoid -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS - -import qualified Data.LA as LA -import Data.Expr (Variables (..)) -import Data.Polynomial -import Data.Polynomial.GBase - -type Var = Int - -type Model = IM.IntMap Integer - -solve :: MonomialOrder Var -> [Var] -> [(LA.Expr Integer, Integer)] -> LA.Expr Integer -> Maybe Model -solve cmp vs cs obj = - if IM.keysSet (IM.filter (/= 0) m) `IS.isSubsetOf` vs' - then Just $ IM.filterWithKey (\y _ -> y `IS.member` vs') m - else Nothing - - where - vs' :: IS.IntSet - vs' = IS.fromList vs - - v2 :: Var - v2 = if null vs then 0 else maximum vs + 1 - - vs2 :: [Var] - vs2 = [v2 .. v2 + length cs - 1] - - vs2' :: IS.IntSet - vs2' = IS.fromList vs2 - - t :: Var - t = v2 + length cs - - cmp2 :: MonomialOrder Var - cmp2 = elimOrdering (IS.fromList vs2) `mappend` elimOrdering (IS.singleton t) `mappend` costOrdering obj `mappend` cmp - - gbase :: [Polynomial Rational Var] - gbase = buchberger cmp2 (product (map var (t:vs2)) - 1 : phi) - where - phi = do - xj <- vs - let aj = [(yi, aij) | (yi,(ai,_)) <- zip vs2 cs, let aij = LA.coeff xj ai] - return $ product [var yi ^ aij | (yi, aij) <- aj, aij > 0] - - product [var yi ^ (-aij) | (yi, aij) <- aj, aij < 0] * var xj - - yb = product [var yi ^ bi | ((_,bi),yi) <- zip cs vs2] - - [(_,z)] = terms (reduce cmp2 yb gbase) - - m = mkModel (vs++vs2++[t]) z - -mkModel :: [Var] -> MonicMonomial Var -> Model -mkModel vs xs = mmToIntMap xs `IM.union` IM.fromList [(x, 0) | x <- vs] --- IM.union is left-biased - -costOrdering :: LA.Expr Integer -> MonomialOrder Var -costOrdering obj = compare `on` f - where - vs = vars obj - f xs = LA.evalExpr (mkModel (IS.toList vs) xs) obj - -elimOrdering :: IS.IntSet -> MonomialOrder Var -elimOrdering xs = compare `on` f - where - f ys = not (IS.null (xs `IS.intersection` IM.keysSet (mmToIntMap ys))) - --- http://madscientist.jp/~ikegami/articles/IntroSequencePolynomial.html --- optimum is (3,2,0) -test_ikegami = solve grlex vs cs obj - where - [x,y,z] = vs - vs = [1..3] - cs = [ (LA.fromTerms [(2,x),(2,y),(2,z)], 10) - , (LA.fromTerms [(3,x),(1,y),(1,z)], 11) - ] - obj = LA.fromTerms [(1,x),(2,y),(3,z)] - --- http://posso.dm.unipi.it/users/traverso/conti-traverso-ip.ps --- optimum is (39, 75, 1, 8, 122) -test_1 = solve grlex vs cs obj - where - [x1,x2,x3,x4,x5] = vs - vs = [1..5] - cs = [ (LA.fromTerms [(2, x1), ( 5, x2), (-3, x3), ( 1,x4), (-2, x5)], 214) - , (LA.fromTerms [(1, x1), ( 7, x2), ( 2, x3), ( 3,x4), ( 1, x5)], 712) - , (LA.fromTerms [(4, x1), (-2, x2), (-1, x3), (-5,x4), ( 3, x5)], 331) - ] - obj = LA.fromTerms [(1,x1),(1,x2),(1,x3),(1,x4),(1,x5)] - --- optimum is (0,2,2) -test_2 = solve grlex vs cs obj - where - [x1,x2,x3] = vs - vs = [1..3] - cs = [ (LA.fromTerms [(2, x1), (3, x2), (-1, x3)], 4) ] - obj = LA.fromTerms [(2,x1),(1,x2)] - --- infeasible -test_3 = solve grlex vs cs obj - where - [x1,x2,x3] = vs - vs = [1..3] - cs = [ (LA.fromTerms [(2, x1), (2, x2), (2, x3)], 3) ] - obj = LA.fromTerms [(1,x1)] diff --git a/src/Converter/CNF2LP.hs b/src/Converter/CNF2LP.hs --- a/src/Converter/CNF2LP.hs +++ b/src/Converter/CNF2LP.hs @@ -32,10 +32,16 @@ , LPFile.dir = dir , LPFile.objectiveFunction = (Nothing, obj) , LPFile.constraints = cs - , LPFile.bounds = Map.empty - , LPFile.integerVariables = Set.empty - , LPFile.binaryVariables = Set.fromList vs - , LPFile.semiContinuousVariables = Set.empty + , LPFile.varInfo = Map.fromList + [ ( v + , LPFile.VarInfo + { LPFile.varName = v + , LPFile.varType = LPFile.IntegerVariable + , LPFile.varBounds = (LPFile.Finite 0, LPFile.Finite 1) + } + ) + | v <- vs + ] , LPFile.sos = [] } mtrans m = diff --git a/src/Converter/LP2SMT.hs b/src/Converter/LP2SMT.hs new file mode 100644 --- /dev/null +++ b/src/Converter/LP2SMT.hs @@ -0,0 +1,303 @@ +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Converter.LP2SMT +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : experimental +-- Portability : portable +-- +----------------------------------------------------------------------------- +module Converter.LP2SMT + ( convert + , Options (..) + , defaultOptions + , Language (..) + ) where + +import Data.Char +import Data.Ord +import Data.List +import Data.Ratio +import qualified Data.Set as Set +import qualified Data.Map as Map +import System.IO +import Text.Printf +import qualified Text.LPFile as LP +import Util (showRationalAsFiniteDecimal) + +data Options + = Options + { optLanguage :: Language + , optCheckSAT :: Bool + , optProduceModel :: Bool + , optOptimize :: Bool + } + deriving (Show, Eq, Ord) + +defaultOptions :: Options +defaultOptions + = Options + { optLanguage = SMTLIB2 + , optCheckSAT = True + , optProduceModel = True + , optOptimize = False + } + +data Language + = SMTLIB2 + | YICES + deriving (Show, Eq, Ord, Enum) + +-- ------------------------------------------------------------------------ + +type Var = String +type Env = Map.Map LP.Var Var + +concatS :: [ShowS] -> ShowS +concatS = foldr (.) id + +unlinesS :: [ShowS] -> ShowS +unlinesS = concatS . map (. showChar '\n') + +list :: [ShowS] -> ShowS +list xs = showParen True $ concatS (intersperse (showChar ' ') xs) + +and' :: [ShowS] -> ShowS +and' [] = showString "true" +and' [x] = x +and' xs = list (showString "and" : xs) + +or' :: [ShowS] -> ShowS +or' [] = showString "false" +or' [x] = x +or' xs = list (showString "or" : xs) + +not' :: ShowS -> ShowS +not' x = list [showString "not", x] + +expr :: Options -> Env -> LP.LP -> LP.Expr -> ShowS +expr opt env lp e = + case e of + [] -> showChar '0' + _ -> list (showChar '+' : map f e) + where + f (LP.Term c []) = realNum opt c + f (LP.Term c vs) = + case xs of + [] -> realNum opt 1 + [x] -> x + _ -> list (showChar '*' : xs) + where + xs = [realNum opt c | c /= 1] ++ + [ v3 + | v <- vs + , let v2 = env Map.! v + , let v3 = if LP.getVarType lp v == LP.IntegerVariable + then toReal opt (showString v2) + else showString v2 + ] + +realNum :: Options -> Rational -> ShowS +realNum opt r = + case optLanguage opt of + SMTLIB2 + | r < 0 -> list [showChar '-', f (negate r)] + | otherwise -> f r + YICES -> + if denominator r == 1 + then shows (numerator r) + else shows (numerator r) . showChar '/' . shows (denominator r) + where + f r = case showRationalAsFiniteDecimal r of + Just s -> showString s + Nothing -> list [showChar '/', shows (numerator r) . showString ".0", shows (denominator r) . showString ".0"] + +rel :: Bool -> LP.RelOp -> ShowS -> ShowS -> ShowS +rel True LP.Eql x y = and' [rel False LP.Le x y, rel False LP.Ge x y] +rel _ LP.Eql x y = list [showString "=", x, y] +rel _ LP.Le x y = list [showString "<=", x, y] +rel _ LP.Ge x y = list [showString ">=", x, y] + +toReal :: Options -> ShowS -> ShowS +toReal opt x = + case optLanguage opt of + SMTLIB2 -> list [showString "to_real", x] + YICES -> x + +assert :: Options -> (ShowS, Maybe String) -> ShowS +assert opt (x, label) = list [showString "assert", x'] + where + x' = case label of + Just name | optLanguage opt == SMTLIB2 -> + list [ showString "!" + , x + , showString ":named" + , showString (encode opt name) + ] + _ -> x + +constraint :: Options -> Bool -> Env -> LP.LP -> LP.Constraint -> (ShowS, Maybe String) +constraint opt q env lp + LP.Constraint + { LP.constrLabel = label + , LP.constrIndicator = g + , LP.constrBody = (e, op, b) + } = (c1, label) + where + c0 = rel q op (expr opt env lp e) (realNum opt b) + c1 = case g of + Nothing -> c0 + Just (var,val) -> + list [ showString "=>" + , rel q LP.Eql (expr opt env lp [LP.Term 1 [var]]) (realNum opt val) + , c0 + ] + +conditions :: Options -> Bool -> Env -> LP.LP -> [(ShowS, Maybe String)] +conditions opt q env lp = bnds ++ cs ++ ss + where + vs = LP.variables lp + bnds = map bnd (Set.toList vs) + bnd v = (c1, Nothing) + where + v2 = env Map.! v + v3 = if LP.getVarType lp v == LP.IntegerVariable + then toReal opt (showString v2) + else showString v2 + (lb,ub) = LP.getBounds lp v + s1 = case lb of + LP.NegInf -> [] + LP.PosInf -> [showString "false"] + LP.Finite x -> [list [showString "<=", realNum opt x, v3]] + s2 = case ub of + LP.NegInf -> [showString "false"] + LP.PosInf -> [] + LP.Finite x -> [list [showString "<=", v3, realNum opt x]] + c0 = and' (s1 ++ s2) + c1 = if LP.getVarType lp v == LP.SemiContinuousVariable + then or' [list [showString "=", showString v2, realNum opt 0], c0] + else c0 + cs = map (constraint opt q env lp) (LP.constraints lp) + ss = concatMap sos (LP.sos lp) + sos (label, typ, xs) = do + (x1,x2) <- case typ of + LP.S1 -> pairs $ map fst xs + LP.S2 -> nonAdjacentPairs $ map fst $ sortBy (comparing snd) $ xs + let c = not' $ and' + [ list [showString "/=", v3, realNum opt 0] + | v<-[x1,x2] + , let v2 = env Map.! v + , let v3 = if LP.getVarType lp v == LP.IntegerVariable + then toReal opt (showString v2) + else showString v2 + ] + return (c, label) + +pairs :: [a] -> [(a,a)] +pairs [] = [] +pairs (x:xs) = [(x,x2) | x2 <- xs] ++ pairs xs + +nonAdjacentPairs :: [a] -> [(a,a)] +nonAdjacentPairs (x1:x2:xs) = [(x1,x3) | x3 <- xs] ++ nonAdjacentPairs (x2:xs) +nonAdjacentPairs _ = [] + +convert :: Options -> LP.LP -> ShowS +convert opt lp = + unlinesS $ defs ++ map (assert opt) (conditions opt False env lp) + ++ [ assert opt (optimality, Nothing) | optOptimize opt ] + ++ [ case optLanguage opt of + SMTLIB2 -> list [showString "set-option", showString ":produce-models", showString "true"] + YICES -> list [showString "set-evidence!", showString "true"] + | optProduceModel opt ] + ++ [ case optLanguage opt of + SMTLIB2 -> list [showString "check-sat"] + YICES -> list [showString "check"] + | optCheckSAT opt ] + where + vs = LP.variables lp + real_vs = vs `Set.difference` int_vs + int_vs = LP.integerVariables lp + realType = + case optLanguage opt of + SMTLIB2 -> "Real" + YICES -> "real" + intType = + case optLanguage opt of + SMTLIB2 -> "Int" + YICES -> "int" + ts = [(v, realType) | v <- Set.toList real_vs] ++ [(v, intType) | v <- Set.toList int_vs] + obj = snd (LP.objectiveFunction lp) + env = Map.fromList [(v, encode opt v) | v <- Set.toList vs] + -- Note that identifiers of LPFile does not contain '-'. + -- So that there are no name crash. + env2 = Map.fromList [(v, encode opt (v ++ "-2")) | v <- Set.toList vs] + + defs = do + (v,t) <- ts + let v2 = env Map.! v + return $ showString $ + case optLanguage opt of + SMTLIB2 -> printf "(declare-fun %s () %s)" v2 t + YICES -> printf "(define %s::%s) ; %s" v2 t v + + optimality = list [showString "forall", decl, body] + where + decl = + case optLanguage opt of + SMTLIB2 -> list [list [showString (env2 Map.! v), showString t] | (v,t) <- ts] + YICES -> list [showString $ printf "%s::%s" (env2 Map.! v) t | (v,t) <- ts] + body = list [showString "=>" + , and' (map fst (conditions opt True env2 lp)) + , list [ showString $ if LP.dir lp == LP.OptMin then "<=" else ">=" + , expr opt env lp obj, expr opt env2 lp obj + ] + ] + +encode :: Options -> String -> String +encode opt s = + case optLanguage opt of + SMTLIB2 + | all p s -> s + | any q s -> error $ "cannot encode " ++ show s + | otherwise -> "|" ++ s ++ "|" + YICES -> concatMap f s + where + p c = isAscii c && (isAlpha c || isDigit c || c `elem` "~!@$%^&*_-+=<>.?/") + q c = c == '|' && c == '\\' + + -- Note that '[', ']', '\\' does not appear in identifiers of LP file. + f '(' = "[" + f ')' = "]" + f c | c `elem` "/\";" = printf "\\x%02d" (fromEnum c :: Int) + f c = [c] + +-- ------------------------------------------------------------------------ + +testFile :: FilePath -> IO () +testFile fname = do + result <- LP.parseFile fname + case result of + Right lp -> putStrLn $ convert defaultOptions lp "" + Left err -> hPrint stderr err + +test :: IO () +test = putStrLn $ convert defaultOptions testdata "" + +testdata :: LP.LP +Right testdata = LP.parseString "test" $ unlines + [ "Maximize" + , " obj: x1 + 2 x2 + 3 x3 + x4" + , "Subject To" + , " c1: - x1 + x2 + x3 + 10 x4 <= 20" + , " c2: x1 - 3 x2 + x3 <= 30" + , " c3: x2 - 3.5 x4 = 0" + , "Bounds" + , " 0 <= x1 <= 40" + , " 2 <= x4 <= 3" + , "General" + , " x4" + , "End" + ] diff --git a/src/Converter/MaxSAT2LP.hs b/src/Converter/MaxSAT2LP.hs --- a/src/Converter/MaxSAT2LP.hs +++ b/src/Converter/MaxSAT2LP.hs @@ -22,17 +22,28 @@ import SAT.Types convert :: MaxSAT.WCNF -> (LPFile.LP, Map.Map LPFile.Var Rational -> Model) -convert (nvar, top, ls) = (lp, mtrans) +convert + MaxSAT.WCNF + { MaxSAT.numVars = nvar + , MaxSAT.topCost = top + , MaxSAT.clauses = ls + } = (lp, mtrans) where lp = LPFile.LP { LPFile.variables = Set.fromList vs , LPFile.dir = LPFile.OptMin , LPFile.objectiveFunction = (Nothing, obj) , LPFile.constraints = cs - , LPFile.bounds = Map.empty - , LPFile.integerVariables = Set.empty - , LPFile.binaryVariables = Set.fromList vs - , LPFile.semiContinuousVariables = Set.empty + , LPFile.varInfo = Map.fromList + [ ( v + , LPFile.VarInfo + { LPFile.varName = v + , LPFile.varType = LPFile.IntegerVariable + , LPFile.varBounds = (LPFile.Finite 0, LPFile.Finite 1) + } + ) + | v <- vs + ] , LPFile.sos = [] } mtrans m = diff --git a/src/Converter/PB2LP.hs b/src/Converter/PB2LP.hs --- a/src/Converter/PB2LP.hs +++ b/src/Converter/PB2LP.hs @@ -35,10 +35,16 @@ , LPFile.dir = dir , LPFile.objectiveFunction = (Nothing, obj2) , LPFile.constraints = cs2 - , LPFile.bounds = Map.empty - , LPFile.integerVariables = Set.empty - , LPFile.binaryVariables = vs2 - , LPFile.semiContinuousVariables = Set.empty + , LPFile.varInfo = Map.fromAscList + [ ( v + , LPFile.VarInfo + { LPFile.varName = v + , LPFile.varType = LPFile.IntegerVariable + , LPFile.varBounds = (LPFile.Finite 0, LPFile.Finite 1) + } + ) + | v <- Set.toAscList vs2 + ] , LPFile.sos = [] } @@ -105,10 +111,16 @@ , LPFile.dir = LPFile.OptMin , LPFile.objectiveFunction = (Nothing, obj2) , LPFile.constraints = topConstr ++ map snd cs2 - , LPFile.bounds = Map.empty - , LPFile.integerVariables = Set.empty - , LPFile.binaryVariables = vs2 - , LPFile.semiContinuousVariables = Set.empty + , LPFile.varInfo = Map.fromAscList + [ ( v + , LPFile.VarInfo + { LPFile.varName = v + , LPFile.varType = LPFile.IntegerVariable + , LPFile.varBounds = (LPFile.Finite 0, LPFile.Finite 1) + } + ) + | v <- Set.toAscList vs2 + ] , LPFile.sos = [] } diff --git a/src/Cooper.hs b/src/Cooper.hs deleted file mode 100644 --- a/src/Cooper.hs +++ /dev/null @@ -1,449 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : Cooper --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : portable --- --- Naive implementation of Cooper's algorithm --- --- Reference: --- --- * --- --- * --- --- See also: --- --- * --- ------------------------------------------------------------------------------ -module Cooper - ( module Data.Expr - , module Data.Formula - , ExprZ - , Lit (..) - , Formula' (..) - , eliminateQuantifiers - , solve - , solveQFLA - , Model - ) where - -import Control.Monad -import Data.List -import Data.Maybe -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS - -import Data.Expr -import Data.Formula -import Data.Linear -import qualified Data.LA as LA -import qualified FourierMotzkin as FM -import qualified Data.Interval as Interval - --- --------------------------------------------------------------------------- - --- | Linear arithmetic expression over integers. -type ExprZ = LA.Expr Integer - -atomZ :: RelOp -> Expr Rational -> Expr Rational -> Maybe Formula' -atomZ op a b = do - (e1,c1) <- FM.termR a - (e2,c2) <- FM.termR b - let a' = c2 .*. e1 - b' = c1 .*. e2 - case op of - Le -> return $ Lit $ a' `leZ` b' - Lt -> return $ Lit $ a' `ltZ` b' - Ge -> return $ Lit $ a' `geZ` b' - Gt -> return $ Lit $ a' `gtZ` b' - Eql -> return $ eqZ a' b' - NEq -> liftM notB (atomZ Eql a b) - -leZ, ltZ, geZ, gtZ :: ExprZ -> ExprZ -> Lit -leZ e1 e2 = e1 `ltZ` (e2 .+. LA.constant 1) -ltZ e1 e2 = Pos $ (e2 .-. e1) -geZ = flip leZ -gtZ = flip gtZ - -eqZ :: ExprZ -> ExprZ -> Formula' -eqZ e1 e2 = Lit (e1 `leZ` e2) .&&. Lit (e1 `geZ` e2) - --- | Literal --- --- * @Pos e@ means @e > 0@ --- --- * @Divisible True d e@ means @e@ can be divided by @d@ (i.e. @d|e@) --- --- * @Divisible False d e@ means @e@ can not be divided by @d@ (i.e. @¬(d|e)@) -data Lit - = Pos ExprZ - | Divisible Bool Integer ExprZ - deriving (Show, Eq, Ord) - -instance Variables Lit where - vars (Pos t) = vars t - vars (Divisible _ _ t) = vars t - -instance Complement Lit where - notB (Pos e) = e `leZ` LA.constant 0 - notB (Divisible b c e) = Divisible (not b) c e - --- | quantifier-free negation normal form -data Formula' - = T' - | F' - | And' Formula' Formula' - | Or' Formula' Formula' - | Lit Lit - deriving (Show, Eq, Ord) - -instance Complement Formula' where - notB T' = F' - notB F' = T' - notB (And' a b) = Or' (notB a) (notB b) - notB (Or' a b) = And' (notB a) (notB b) - notB (Lit lit) = Lit (notB lit) - -instance Lattice Formula' where - top = T' - bottom = F' - meet = And' - join = Or' - -instance Boolean Formula' - -subst1 :: Var -> ExprZ -> Formula' -> Formula' -subst1 x e = go - where - go T' = T' - go F' = F' - go (And' a b) = And' (go a) (go b) - go (Or' a b) = Or' (go a) (go b) - go (Lit (Divisible b c e1)) = Lit $ Divisible b c $ LA.applySubst1 x e e1 - go (Lit (Pos e1)) = Lit $ Pos $ LA.applySubst1 x e e1 - -simplify :: Formula' -> Formula' -simplify T' = T' -simplify F' = F' -simplify (And' a b) = - case (simplify a, simplify b) of - (T', b') -> b' - (a', T') -> a' - (F', _) -> false - (_, F') -> false - (a',b') -> a' .&&. b' -simplify (Or' a b) = - case (simplify a, simplify b) of - (F', b') -> b' - (a', F') -> a' - (T', _) -> true - (_, T') -> true - (a',b') -> a' .||. b' -simplify (Lit lit) = simplifyLit lit - -simplifyLit :: Lit -> Formula' -simplifyLit lit@(Pos e) = - case LA.asConst e of - Just c -> if c > 0 then true else false - Nothing -> - -- e > 0 <=> e - 1 >= 0 - -- <=> LA.mapCoeff (`div` d) (e - 1) >= 0 - -- <=> LA.mapCoeff (`div` d) (e - 1) + 1 > 0 - Lit $ Pos $ LA.mapCoeff (`div` d) (e .-. LA.constant 1) .+. LA.constant 1 - where - d = if null cs then 1 else abs $ foldl1' gcd cs - cs = [c | (c,x) <- LA.terms e, x /= LA.unitVar] -simplifyLit lit@(Divisible b c e) - | LA.coeff LA.unitVar e `mod` d /= 0 = if b then false else true - | c' == 1 = if b then true else false - | d == 1 = Lit lit - | otherwise = Lit $ Divisible b c' e' - where - d = abs $ foldl' gcd c [c | (c,x) <- LA.terms e, x /= LA.unitVar] - c' = c `div` d - e' = LA.mapCoeff (`div` d) e - --- --------------------------------------------------------------------------- - -data Witness = WCase1 Integer ExprZ | WCase2 Integer Integer Integer [ExprZ] - -eliminateZ :: Var -> Formula' -> Formula' -eliminateZ x formula = simplify $ orB $ map fst $ eliminateZ' x formula - -eliminateZ' :: Var -> Formula' -> [(Formula', Witness)] -eliminateZ' x formula = case1 ++ case2 - where - -- xの係数の最小公倍数 - c :: Integer - c = f formula - where - f :: Formula' -> Integer - f T' = 1 - f F' = 1 - f (And' a b) = lcm (f a) (f b) - f (Or' a b) = lcm (f a) (f b) - f (Lit (Pos e)) = fromMaybe 1 (LA.lookupCoeff x e) - f (Lit (Divisible _ _ e)) = fromMaybe 1 (LA.lookupCoeff x e) - - -- 式をスケールしてxの係数の絶対値をcへと変換し、その後cxをxで置き換え、 - -- xがcで割り切れるという制約を追加した論理式 - formula1 :: Formula' - formula1 = simplify $ f formula .&&. Lit (Divisible True c (LA.var x)) - where - f :: Formula' -> Formula' - f T' = T' - f F' = F' - f (And' a b) = f a .&&. f b - f (Or' a b) = f a .||. f b - f lit@(Lit (Pos e)) = - case LA.lookupCoeff x e of - Nothing -> lit - Just a -> - let s = abs (c `div` a) - in Lit $ Pos $ g s e - f lit@(Lit (Divisible b d e)) = - case LA.lookupCoeff x e of - Nothing -> lit - Just a -> - let s = abs (c `div` a) - in Lit $ Divisible b (s*d) $ g s e - - g :: Integer -> ExprZ -> ExprZ - g s = LA.mapCoeffWithVar (\c' x' -> if x==x' then signum c' else s*c') - - -- d|x+t という形の論理式の d の最小公倍数 - delta :: Integer - delta = f formula1 - where - f :: Formula' -> Integer - f T' = 1 - f F' = 1 - f (And' a b) = lcm (f a) (f b) - f (Or' a b) = lcm (f a) (f b) - f (Lit (Divisible _ d _)) = d - f (Lit (Pos _)) = 1 - - -- ts = {t | t < x は formula1 に現れる原子論理式} - ts :: [ExprZ] - ts = f formula1 - where - f :: Formula' -> [ExprZ] - f T' = [] - f F' = [] - f (And' a b) = f a ++ f b - f (Or' a b) = f a ++ f b - f (Lit (Divisible _ _ _)) = [] - f (Lit (Pos e)) = - case LA.extractMaybe x e of - Nothing -> [] - Just (1, e') -> [lnegate e'] -- Pos e <=> (x + e' > 0) <=> (-e' < x) - Just (-1, e') -> [] -- Pos e <=> (-x + e' > 0) <=> (x < e') - _ -> error "should not happen" - - -- formula1を真にする最小のxが存在する場合 - case1 :: [(Formula', Witness)] - case1 = [ (subst1 x e formula1, WCase1 c e) - | j <- [1..delta], t <- ts, let e = t .+. LA.constant j ] - - -- formula1のなかの x < t を真に t < x を偽に置き換えた論理式 - formula2 :: Formula' - formula2 = simplify $ f formula1 - where - f :: Formula' -> Formula' - f T' = T' - f F' = F' - f (And' a b) = f a .&&. f b - f (Or' a b) = f a .||. f b - f lit@(Lit (Pos e)) = - case LA.lookupCoeff x e of - Nothing -> lit - Just 1 -> F' -- Pos e <=> ( x + e' > 0) <=> -e' < x - Just (-1) -> T' -- Pos e <=> (-x + e' > 0) <=> x < e' - _ -> error "should not happen" - f lit@(Lit (Divisible _ _ _)) = lit - - -- us = {u | x < u は formula1 に現れる原子論理式} - us :: [ExprZ] - us = f formula1 - where - f :: Formula' -> [ExprZ] - f T' = [] - f F' = [] - f (And' a b) = f a ++ f b - f (Or' a b) = f a ++ f b - f (Lit (Pos e)) = - case LA.extractMaybe x e of - Nothing -> [] - Just (1, e') -> [] -- Pos e <=> ( x + e' > 0) <=> -e' < x - Just (-1, e') -> [e'] -- Pos e <=> (-x + e' > 0) <=> x < e' - _ -> error "should not happen" - f (Lit (Divisible _ _ _)) = [] - - -- formula1を真にする最小のxが存在しない場合 - case2 :: [(Formula', Witness)] - case2 = [(subst1 x (LA.constant j) formula2, WCase2 c j delta us) | j <- [1..delta]] - -evalWitness :: Model Integer -> Witness -> Integer -evalWitness model (WCase1 c e) = LA.evalExpr model e `div` c -evalWitness model (WCase2 c j delta us) - | null us' = j `div` c - | otherwise = (j + (((u - delta - 1) `div` delta) * delta)) `div` c - where - us' = map (LA.evalExpr model) us - u = minimum us' - --- --------------------------------------------------------------------------- - --- | eliminate quantifiers and returns equivalent quantifier-free formula. -eliminateQuantifiers :: Formula Rational -> Maybe Formula' -eliminateQuantifiers = f - where - f T = return T' - f F = return F' - f (Atom (Rel e1 op e2)) = atomZ op e1 e2 - f (And a b) = liftM2 (.&&.) (f a) (f b) - f (Or a b) = liftM2 (.||.) (f a) (f b) - f (Not a) = f (pushNot a) - f (Imply a b) = f $ Or (Not a) b - f (Equiv a b) = f $ And (Imply a b) (Imply b a) - f (Forall x body) = liftM notB $ f $ Exists x $ pushNot body - f (Exists x body) = liftM (eliminateZ x) (f body) - --- --------------------------------------------------------------------------- - --- | solve a formula and returns assignment of outer-most existential quantified --- variables. -solve :: Formula Rational -> SatResult Integer -solve formula = - case eliminateQuantifiers formula of - Nothing -> Unknown - Just formula' -> - case solve' vs formula' of - Nothing -> Unsat - Just m -> Sat m - where - vs = IS.toList (vars formula) - -solve' :: [Var] -> Formula' -> Maybe (Model Integer) -solve' vs formula = go vs (simplify formula) - where - go [] T' = return IM.empty - go [] _ = mzero - go (v:vs) formula = do - let xs = eliminateZ' v formula - msum $ flip map xs $ \(formula', witness) -> do - model <- go vs (simplify formula') - let val = evalWitness model witness - return $ IM.insert v val model - --- --------------------------------------------------------------------------- - --- | solve a (open) quantifier-free formula -solveQFLA :: [LA.Atom Rational] -> VarSet -> Maybe (Model Rational) -solveQFLA cs ivs = msum [ FM.simplify xs >>= go (IS.toList rvs) | xs <- unDNF dnf ] - where - vs = vars cs - rvs = vs `IS.difference` ivs - dnf = FM.constraintsToDNF cs - - go :: [Var] -> [FM.Lit] -> Maybe (Model Rational) - go [] xs = fmap (fmap fromIntegral) $ solve' (IS.toList ivs) (foldr And' T' (map f xs)) - go (v:vs) ys = msum (map f (unDNF (FM.boundConditions bnd))) - where - (bnd, rest) = FM.collectBounds v ys - f zs = do - model <- go vs (zs ++ rest) - val <- Interval.pickup (FM.evalBounds model bnd) - return $ IM.insert v val model - - f :: FM.Lit -> Formula' - f (FM.Nonneg e) = Lit $ e `geZ` (LA.constant 0) - f (FM.Pos e) = Lit $ e `gtZ` (LA.constant 0) - --- --------------------------------------------------------------------------- - -{- -7x + 12y + 31z = 17 -3x + 5y + 14z = 7 -1 ≤ x ≤ 40 --50 ≤ y ≤ 50 - -satisfiable in R -but unsatisfiable in Z --} -test1 :: Formula Rational -test1 = c1 .&&. c2 .&&. c3 .&&. c4 - where - x = Var 0 - y = Var 1 - z = Var 2 - c1 = 7*x + 12*y + 31*z .==. 17 - c2 = 3*x + 5*y + 14*z .==. 7 - c3 = 1 .<=. x .&&. x .<=. 40 - c4 = (-50) .<=. y .&&. y .<=. 50 - -test1' :: Formula Rational -test1' = Exists 0 $ Exists 1 $ Exists 2 $ test1 - -{- -27 ≤ 11x+13y ≤ 45 --10 ≤ 7x-9y ≤ 4 - -satisfiable in R -but unsatisfiable in Z --} -test2 :: Formula Rational -test2 = c1 .&&. c2 - where - x = Var 0 - y = Var 1 - t1 = 11*x + 13*y - t2 = 7*x - 9*y - c1 = 27 .<=. t1 .&&. t1 .<=. 45 - c2 = (-10) .<=. t2 .&&. t2 .<=. 4 - -test2' :: Formula Rational -test2' = Exists 0 $ Exists 1 $ test2 - -testHagiya :: Formula' -testHagiya = eliminateZ 1 $ c1 .&&. c2 .&&. c3 - where - [x,y,z] = map LA.var [1..3] - c1 = Lit $ x `ltZ` (y .+. y) -- x < y+y - c2 = Lit $ z `ltZ` x -- z < x - c3 = Lit $ Divisible True 3 x -- 3 | x - -{- -Or' (And' (Lit (Pos (Expr {coeffMap = fromList [(-1,-1),(2,2),(3,-1)]}))) (Lit (Divisible True 3 (Expr {coeffMap = fromList [(-1,1),(3,1)]})))) - (Or' (And' (Lit (Pos (Expr {coeffMap = fromList [(-1,-2),(2,2),(3,-1)]}))) (Lit (Divisible True 3 (Expr {coeffMap = fromList [(-1,2),(3,1)]})))) - (And' (Lit (Pos (Expr {coeffMap = fromList [(-1,-3),(2,2),(3,-1)]}))) (Lit (Divisible True 3 (Expr {coeffMap = fromList [(-1,3),(3,1)]}))))) - -(2y-z > 0 && 3|z+1) || -(2y-z > -2 && 3|z+2) || -(2y-z > -3 && 3|z+3) || --} - -test3 :: Formula' -test3 = eliminateZ 1 (andB [p1,p2,p3,p4]) - where - x = LA.var 0 - y = LA.var 1 - p1 = Lit $ Pos y - p2 = Lit $ Pos (y .-. 2 .*. x) - p3 = Lit $ Pos (x .+. LA.constant 2 .-. y) - p4 = Lit $ Divisible True 2 y - -{- -∃ y. 0 < y ∧ 2x Rational -> Rational -toRational' (RealRoot p i) epsilon = Sturm.approx p i epsilon +instance Real AReal where + toRational x + | Data.AlgebraicNumber.deg x == 1 = + let p = minimalPolynomial x + a = P.coeff (P.mmVar ()) p + b = P.coeff P.mmOne p + in - b / a + | otherwise = error "toRational: proper algebraic number" + +instance RealFrac AReal where + properFraction = properFraction' + truncate = truncate' + round = round' + ceiling = ceiling' + floor = floor' + +approx :: AReal -> Rational -> Rational +approx x@(RealRoot p i) epsilon = + if isRational x + then toRational x + else Sturm.approx p i epsilon -- | Same as 'properFraction'. properFraction' :: Integral b => AReal -> (b, AReal) diff --git a/src/Data/AlgebraicNumber/RealInstance.hs b/src/Data/AlgebraicNumber/RealInstance.hs deleted file mode 100644 --- a/src/Data/AlgebraicNumber/RealInstance.hs +++ /dev/null @@ -1,20 +0,0 @@ -module Data.AlgebraicNumber.RealInstance where - -import Data.Polynomial as P -import Data.AlgebraicNumber - -instance Real AReal where - toRational x - | Data.AlgebraicNumber.deg x == 1 = - let p = minimalPolynomial x - a = P.coeff (P.mmVar ()) p - b = P.coeff P.mmOne p - in - b / a - | otherwise = error "toRational: proper algebraic number" - -instance RealFrac AReal where - properFraction = properFraction' - truncate = truncate' - round = round' - ceiling = ceiling' - floor = floor' diff --git a/src/Data/ArithRel.hs b/src/Data/ArithRel.hs new file mode 100644 --- /dev/null +++ b/src/Data/ArithRel.hs @@ -0,0 +1,130 @@ +{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, FunctionalDependencies #-} +----------------------------------------------------------------------------- +-- | +-- Module : Data.ArithRel +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable (FlexibleInstances, MultiParamTypeClasses, FunctionalDependencies) +-- +-- Arithmetic relations +-- +----------------------------------------------------------------------------- +module Data.ArithRel + ( + -- * Relational operators + RelOp (..) + , flipOp + , negOp + , showOp + , evalOp + + -- * Relation + , Rel (..) + + -- * DSL + , IsRel (..) + , (.<.), (.<=.), (.>=.), (.>.), (.==.), (./=.) + ) where + +import qualified Data.IntSet as IS +import Data.Expr (Variables (..)) +import Data.Lattice (Complement (..)) + +infix 4 .<., .<=., .>=., .>., .==., ./=. + +-- --------------------------------------------------------------------------- + +-- | relational operators +data RelOp = Lt | Le | Ge | Gt | Eql | NEq + deriving (Show, Eq, Ord) + + +-- | flipping relational operator +-- +-- @rel (flipOp op) a b@ is equivalent to @rel op b a@ +flipOp :: RelOp -> RelOp +flipOp Le = Ge +flipOp Ge = Le +flipOp Lt = Gt +flipOp Gt = Lt +flipOp Eql = Eql +flipOp NEq = NEq + +-- | negating relational operator +-- +-- @rel (negOp op) a b@ is equivalent to @notB (rel op a b)@ +negOp :: RelOp -> RelOp +negOp Lt = Ge +negOp Le = Gt +negOp Ge = Lt +negOp Gt = Le +negOp Eql = NEq +negOp NEq = Eql + +-- | operator symbol +showOp :: RelOp -> String +showOp Lt = "<" +showOp Le = "<=" +showOp Ge = ">=" +showOp Gt = ">" +showOp Eql = "=" +showOp NEq = "/=" + +-- | evaluate an operator into a comparision function +evalOp :: Ord a => RelOp -> a -> a -> Bool +evalOp Lt = (<) +evalOp Le = (<=) +evalOp Ge = (>=) +evalOp Gt = (>) +evalOp Eql = (==) +evalOp NEq = (/=) + +-- --------------------------------------------------------------------------- + +-- | type class for constructing relational formula +class IsRel e r | r -> e where + rel :: RelOp -> e -> e -> r + +-- | constructing relational formula +(.<.) :: IsRel e r => e -> e -> r +a .<. b = rel Lt a b + +-- | constructing relational formula +(.<=.) :: IsRel e r => e -> e -> r +a .<=. b = rel Le a b + +-- | constructing relational formula +(.>.) :: IsRel e r => e -> e -> r +a .>. b = rel Gt a b + +-- | constructing relational formula +(.>=.) :: IsRel e r => e -> e -> r +a .>=. b = rel Ge a b + +-- | constructing relational formula +(.==.) :: IsRel e r => e -> e -> r +a .==. b = rel Eql a b + +-- | constructing relational formula +(./=.) :: IsRel e r => e -> e -> r +a ./=. b = rel NEq a b + +-- --------------------------------------------------------------------------- + +-- | Atomic formula +data Rel e = Rel e RelOp e + deriving (Show, Eq, Ord) + +instance Complement (Rel c) where + notB (Rel lhs op rhs) = Rel lhs (negOp op) rhs + +instance IsRel e (Rel e) where + rel op a b = Rel a op b + +instance Variables e => Variables (Rel e) where + vars (Rel a _ b) = vars a `IS.union` vars b + +-- --------------------------------------------------------------------------- diff --git a/src/Data/Formula.hs b/src/Data/Formula.hs --- a/src/Data/Formula.hs +++ b/src/Data/Formula.hs @@ -1,4 +1,4 @@ -{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-} +{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Formula @@ -7,7 +7,7 @@ -- -- Maintainer : masahiro.sakai@gmail.com -- Stability : provisional --- Portability : non-portable (MultiParamTypeClasses, FunctionalDependencies) +-- Portability : non-portable (MultiParamTypeClasses, FlexibleInstances) -- -- Formula of first order logic. -- @@ -18,12 +18,7 @@ module Data.Lattice -- * Relational operators - , RelOp (..) - , Rel (..) - , (.<.), (.<=.), (.>=.), (.>.), (.==.), (./=.) - , flipOp - , negOp - , showOp + , module Data.ArithRel -- * Concrete formula , Atom (..) @@ -35,111 +30,33 @@ import qualified Data.IntSet as IS import Data.Expr import Data.Lattice - --- --------------------------------------------------------------------------- - -infix 4 .<., .<=., .>=., .>., .==., ./=. - --- --------------------------------------------------------------------------- - --- | relational operators -data RelOp = Lt | Le | Ge | Gt | Eql | NEq - deriving (Show, Eq, Ord) - --- | type class for constructing relational formula -class Rel e r | r -> e where - rel :: RelOp -> e -> e -> r - --- | constructing relational formula -(.<.) :: Rel e r => e -> e -> r -a .<. b = rel Lt a b - --- | constructing relational formula -(.<=.) :: Rel e r => e -> e -> r -a .<=. b = rel Le a b - --- | constructing relational formula -(.>.) :: Rel e r => e -> e -> r -a .>. b = rel Gt a b - --- | constructing relational formula -(.>=.) :: Rel e r => e -> e -> r -a .>=. b = rel Ge a b - --- | constructing relational formula -(.==.) :: Rel e r => e -> e -> r -a .==. b = rel Eql a b - --- | constructing relational formula -(./=.) :: Rel e r => e -> e -> r -a ./=. b = rel NEq a b - --- | flipping relational operator --- --- @rel (flipOp op) a b@ is equivalent to @rel op b a@ -flipOp :: RelOp -> RelOp -flipOp Le = Ge -flipOp Ge = Le -flipOp Lt = Gt -flipOp Gt = Lt -flipOp Eql = Eql -flipOp NEq = NEq - --- | negating relational operator --- --- @rel (negOp op) a b@ is equivalent to @notB (rel op a b)@ -negOp :: RelOp -> RelOp -negOp Lt = Ge -negOp Le = Gt -negOp Ge = Lt -negOp Gt = Le -negOp Eql = NEq -negOp NEq = Eql - --- | operator symbol -showOp :: RelOp -> String -showOp Lt = "<" -showOp Le = "<=" -showOp Ge = ">=" -showOp Gt = ">" -showOp Eql = "=" -showOp NEq = "/=" +import Data.ArithRel -- --------------------------------------------------------------------------- -- | Atomic formula -data Atom c = Rel (Expr c) RelOp (Expr c) - deriving (Show, Eq, Ord) - -instance Complement (Atom c) where - notB (Rel lhs op rhs) = Rel lhs (negOp op) rhs - -instance Variables (Atom c) where - vars (Rel a _ b) = vars a `IS.union` vars b - -instance Rel (Expr c) (Atom c) where - rel op a b = Rel a op b +type Atom c = Rel (Expr c) -- --------------------------------------------------------------------------- -- | formulas of first order logic -data Formula c +data Formula a = T | F - | Atom (Atom c) - | And (Formula c) (Formula c) - | Or (Formula c) (Formula c) - | Not (Formula c) - | Imply (Formula c) (Formula c) - | Equiv (Formula c) (Formula c) - | Forall Var (Formula c) - | Exists Var (Formula c) + | Atom a + | And (Formula a) (Formula a) + | Or (Formula a) (Formula a) + | Not (Formula a) + | Imply (Formula a) (Formula a) + | Equiv (Formula a) (Formula a) + | Forall Var (Formula a) + | Exists Var (Formula a) deriving (Show, Eq, Ord) -instance Variables (Formula c) where +instance Variables a => Variables (Formula a) where vars T = IS.empty vars F = IS.empty - vars (Atom atom) = vars atom + vars (Atom a) = vars a vars (And a b) = vars a `IS.union` vars b vars (Or a b) = vars a `IS.union` vars b vars (Not a) = vars a @@ -148,7 +65,7 @@ vars (Forall v a) = IS.delete v (vars a) vars (Exists v a) = IS.delete v (vars a) -instance Complement (Formula c) where +instance Complement (Formula a) where notB = Not instance Lattice (Formula c) where @@ -161,14 +78,14 @@ (.=>.) = Imply (.<=>.) = Equiv -instance Rel (Expr c) (Formula c) where +instance IsRel (Expr c) (Formula (Atom c)) where rel op a b = Atom $ rel op a b -- | convert a formula into negation normal form -pushNot :: Formula c -> Formula c +pushNot :: Complement a => Formula a -> Formula a pushNot T = F pushNot F = T -pushNot (Atom (Rel a op b)) = Atom $ Rel a (negOp op) b +pushNot (Atom a) = Atom $ notB a pushNot (And a b) = Or (pushNot a) (pushNot b) pushNot (Or a b) = And (pushNot a) (pushNot b) pushNot (Not a) = a diff --git a/src/Data/LA.hs b/src/Data/LA.hs --- a/src/Data/LA.hs +++ b/src/Data/LA.hs @@ -47,6 +47,7 @@ -- * Atomic formula of linear arithmetics , Atom (..) , showAtom + , evalAtom , solveFor -- * misc @@ -64,6 +65,7 @@ import qualified Data.IntSet as IS import qualified Data.Expr as Expr import Data.Expr (Var, VarMap, VarSet, Variables, Model) +import qualified Data.ArithRel as ArithRel import qualified Data.Formula as Formula import Data.Linear import Data.Interval @@ -248,29 +250,23 @@ ----------------------------------------------------------------------------- -- | Atomic Formula of Linear Arithmetics -data Atom r = Atom (Expr r) Formula.RelOp (Expr r) - deriving (Show, Eq, Ord) - -instance Formula.Complement (Atom r) where - notB (Atom lhs op rhs) = Atom lhs (Formula.negOp op) rhs - -instance Variables (Atom r) where - vars (Atom a _ b) = Expr.vars a `IS.union` Expr.vars b - -instance Formula.Rel (Expr r) (Atom r) where - rel op a b = Atom a op b +type Atom r = ArithRel.Rel (Expr r) showAtom :: (Num r, Eq r, Show r) => Atom r -> String -showAtom (Atom lhs op rhs) = showExpr lhs ++ Formula.showOp op ++ showExpr rhs +showAtom (ArithRel.Rel lhs op rhs) = showExpr lhs ++ ArithRel.showOp op ++ showExpr rhs +-- | evaluate the formula under the model. +evalAtom :: (Num r, Ord r) => Model r -> Atom r -> Bool +evalAtom m (ArithRel.Rel lhs op rhs) = ArithRel.evalOp op (evalExpr m lhs) (evalExpr m rhs) + -- | Solve linear (in)equation for the given variable. -- -- @solveFor a v@ returns @Just (op, e)@ such that @Atom v op e@ -- is equivalent to @a@. -solveFor :: (Real r, Fractional r) => Atom r -> Var -> Maybe (Formula.RelOp, Expr r) -solveFor (Atom lhs op rhs) v = do +solveFor :: (Real r, Fractional r) => Atom r -> Var -> Maybe (ArithRel.RelOp, Expr r) +solveFor (ArithRel.Rel lhs op rhs) v = do (c,e) <- extractMaybe v (lhs .-. rhs) - return ( if c < 0 then Formula.flipOp op else op + return ( if c < 0 then ArithRel.flipOp op else op , (1/c) .*. lnegate e ) @@ -300,9 +296,9 @@ return $ (1/c) .*. x compileAtom :: (Real r, Fractional r) => Formula.Atom r -> Maybe (Atom r) -compileAtom (Formula.Rel a op b) = do +compileAtom (ArithRel.Rel a op b) = do a' <- compileExpr a b' <- compileExpr b - return $ Atom a' op b' + return $ ArithRel.rel op a' b' ----------------------------------------------------------------------------- diff --git a/src/Data/Polyhedron.hs b/src/Data/Polyhedron.hs --- a/src/Data/Polyhedron.hs +++ b/src/Data/Polyhedron.hs @@ -28,7 +28,7 @@ import qualified Data.Interval as Interval import Data.Expr (Variables (..)) -import Data.Formula (RelOp (..), flipOp) +import Data.ArithRel import qualified Data.LA as LA import Data.Linear import Data.Lattice @@ -84,9 +84,9 @@ map (foldl' intersection univ) $ transpose $ map fromAtom cs fromAtom :: AtomR -> [Polyhedron] -fromAtom (LA.Atom lhs NEq rhs) = - fromAtom (LA.Atom lhs Lt rhs) ++ fromAtom (LA.Atom lhs Gt rhs) -fromAtom (LA.Atom lhs op rhs) = +fromAtom (Rel lhs NEq rhs) = + fromAtom (lhs .<. rhs) ++ fromAtom (lhs .>. rhs) +fromAtom (Rel lhs op rhs) = case LA.extract LA.unitVar (lhs .-. rhs) of (c, e1) -> case toRat e1 of @@ -108,18 +108,18 @@ -- | Convert the polyhedron to a list of linear (in)equalities. toConstraints :: Polyhedron -> [AtomR] -toConstraints Empty = [LA.Atom (LA.constant 0) Lt (LA.constant 0)] +toConstraints Empty = [LA.constant 0 .<. LA.constant 0] toConstraints (Polyhedron m) = do (e, ival) <- Map.toList m let e' = LA.mapCoeff fromIntegral e xs = case Interval.lowerBound ival of Nothing -> [] - Just (True,c) -> [LA.Atom (LA.constant c) Le e'] - Just (False,c) -> [LA.Atom (LA.constant c) Lt e'] + Just (True,c) -> [LA.constant c .<=. e'] + Just (False,c) -> [LA.constant c .<. e'] ys = case Interval.upperBound ival of Nothing -> [] - Just (True,c) -> [LA.Atom e' Le (LA.constant c)] - Just (False,c) -> [LA.Atom e' Lt (LA.constant c)] + Just (True,c) -> [e' .<=. LA.constant c] + Just (False,c) -> [e' .<. LA.constant c] xs ++ ys p :: ExprZ -> Bool diff --git a/src/Data/Polynomial.hs b/src/Data/Polynomial.hs --- a/src/Data/Polynomial.hs +++ b/src/Data/Polynomial.hs @@ -48,6 +48,7 @@ , deg , coeff , lookupCoeff + , variables -- * Operations , deriv @@ -60,6 +61,7 @@ , mapCoeff , toMonic , toZ + , toUPolynomialOf , polyDiv , polyMod , polyDivMod @@ -82,7 +84,10 @@ , mmVar , mmOne , mmFromList + , mmFromMap + , mmFromIntMap , mmToList + , mmToMap , mmToIntMap , mmDegree , mmProd @@ -196,6 +201,9 @@ lookupCoeff :: Ord v => MonicMonomial v -> Polynomial k v -> Maybe k lookupCoeff xs (Polynomial m) = Map.lookup xs m +variables :: Ord v => Polynomial k v -> Set.Set v +variables p = Set.unions $ [Map.keysSet (mmToMap mm) | (_, mm) <- terms p] + -- | Formal derivative of polynomials deriv :: (Eq k, Num k, Ord v, Show v) => Polynomial k v -> v -> Polynomial k v deriv p x = sum [fromMonomial (monomialDeriv m x) | m <- terms p] @@ -242,6 +250,14 @@ ts = [(toRational c, xs) | (c,xs) <- terms p] s = foldl' lcm 1 (map (denominator . fst) ts) +toUPolynomialOf :: (Eq k, Ord k, Num k, Ord v, Show v) => Polynomial k v -> v -> UPolynomial (Polynomial k v) +toUPolynomialOf p v = fromTerms $ do + (c,mm) <- terms p + let m = mmToMap mm + return ( fromTerms [(c, mmFromMap (Map.delete v m))] + , mmFromList [((), Map.findWithDefault 0 v m)] + ) + -- | Multivariate division algorithm polyMDivMod :: forall k v. (Eq k, Fractional k, Ord v, Show v) @@ -324,6 +340,12 @@ ratioPrec1 = ratioPrec + 1 isNegativeCoeff = (0>) +instance (Num c, Ord c, RenderCoeff c, Ord v, RenderVar v) => RenderCoeff (Polynomial c v) where + renderCoeff _prec c = showChar '(' . showString (render c) . showChar ')' + isNegativeCoeff p = isNegativeCoeff c + where + (c,_) = leadingTerm grlex p + class RenderVar v where renderVar :: Int -> v -> ShowS @@ -410,7 +432,7 @@ -- 本当は変数の型に応じて type family で表現を変えたい -- | Monic monomials -newtype MonicMonomial v = MonicMonomial (Map.Map v Integer) +newtype MonicMonomial v = MonicMonomial{ mmToMap :: Map.Map v Integer } deriving (Eq, Ord) instance (Ord v, Show v) => Show (MonicMonomial v) where @@ -430,6 +452,14 @@ mmFromList xs | any (\(x,e) -> 0>e) xs = error "mmFromList: negative exponent" | otherwise = MonicMonomial $ Map.fromListWith (+) [(x,e) | (x,e) <- xs, e > 0] + +mmFromMap :: Ord v => Map.Map v Integer -> MonicMonomial v +mmFromMap m + | any (\(x,e) -> 0>e) (Map.toList m) = error "mmFromFromMap: negative exponent" + | otherwise = MonicMonomial $ Map.filter (>0) m + +mmFromIntMap :: IM.IntMap Integer -> MonicMonomial Int +mmFromIntMap = mmFromMap . Map.fromDistinctAscList . IM.toAscList mmToList :: Ord v => MonicMonomial v -> [(v, Integer)] mmToList (MonicMonomial m) = Map.toAscList m diff --git a/src/Data/Polynomial/Graeffe.hs b/src/Data/Polynomial/Graeffe.hs deleted file mode 100644 --- a/src/Data/Polynomial/Graeffe.hs +++ /dev/null @@ -1,75 +0,0 @@ ------------------------------------------------------------------------------ --- | --- Module : Data.Polynomial.Graeffe --- Copyright : (c) Masahiro Sakai 2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : portable --- --- Graeffe's Method --- --- Reference: --- --- * --- --- * --- ------------------------------------------------------------------------------ - -module Data.Polynomial.Graeffe - ( NthRoot (..) - , graeffesMethod - ) where - -import Control.Exception -import qualified Data.IntMap as IM -import Data.Polynomial - -data NthRoot = NthRoot !Integer !Rational - deriving (Show) - -graeffesMethod :: UPolynomial Rational -> Int -> [NthRoot] -graeffesMethod p v = xs !! (v - 1) - where - xs = map (uncurry g) $ zip [1..] (tail $ iterate f $ toMonic p) - - n = deg p - - g :: Int -> UPolynomial Rational -> [NthRoot] - g v p = do - i <- [1::Int .. fromInteger n] - let yi = if i == 1 then - (b i) else - (b i / b (i-1)) - return $ NthRoot (2 ^ fromIntegral v) yi - where - bs = IM.fromList [(fromInteger i, b) | (b,ys) <- terms p, let i = n - mmDegree ys, i /= 0] - b i = IM.findWithDefault 0 i bs - -f :: UPolynomial Rational -> UPolynomial Rational -f p = (-1) ^ (deg p) * - fromTerms [ (c, mmFromList [assert (e `mod` 2 == 0) (x, e `div` 2) | (x,e) <- mmToList xs]) - | (c,xs) <- terms (p * subst p (\_ -> - var ())) ] - -f' :: UPolynomial Rational -> UPolynomial Rational -f' p = fromTerms [(b k, mmFromList [((), n - k)]) | k <- [0..n]] - where - n = deg p - - a :: Integer -> Rational - a k - | n >= k = coeff (mmFromList [((), n - k)]) p - | otherwise = 0 - - b :: Integer -> Rational - b k = (-1)^k * (a k)^2 + 2 * sum [(-1)^j * (a j) * (a (2*k-j)) | j <- [0..k-1]] - -test v = graeffesMethod p v - where - x = var () - p = x^2 - 2 - -test2 v = graeffesMethod p v - where - x = var () - p = x^5 - 3*x - 1 diff --git a/src/FourierMotzkin.hs b/src/FourierMotzkin.hs deleted file mode 100644 --- a/src/FourierMotzkin.hs +++ /dev/null @@ -1,301 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} -{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-} ------------------------------------------------------------------------------ --- | --- Module : FourierMotzkin --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (MultiParamTypeClasses, FunctionalDependencies) --- --- Naïve implementation of Fourier-Motzkin Variable Elimination --- --- Reference: --- --- * --- ------------------------------------------------------------------------------ -module FourierMotzkin - ( module Data.Expr - , module Data.Formula - , Lit (..) - , eliminateQuantifiers - , solve - - -- FIXME - , termR - , Rat - , collectBounds - , boundConditions - , evalBounds - , simplify - , constraintsToDNF - ) where - -import Control.Monad -import Data.List -import Data.Maybe -import Data.Ratio -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS - -import Data.Expr -import Data.Formula -import Data.Linear -import qualified Data.LA as LA -import qualified Data.Interval as Interval - --- --------------------------------------------------------------------------- - -type ExprZ = LA.Expr Integer - --- | (t,c) represents t/c, and c must be >0. -type Rat = (ExprZ, Integer) - -evalRat :: Model Rational -> Rat -> Rational -evalRat model (e, d) = LA.lift1 1 (model IM.!) (LA.mapCoeff fromIntegral e) / (fromIntegral d) - --- | Literal -data Lit = Nonneg ExprZ | Pos ExprZ deriving (Show, Eq, Ord) - -instance Variables Lit where - vars (Pos t) = vars t - vars (Nonneg t) = vars t - -instance Complement Lit where - notB (Pos t) = Nonneg (lnegate t) - notB (Nonneg t) = Pos (lnegate t) - --- 制約集合の単純化 --- It returns Nothing when a inconsistency is detected. -simplify :: [Lit] -> Maybe [Lit] -simplify = fmap concat . mapM f - where - f :: Lit -> Maybe [Lit] - f lit@(Pos e) = - case LA.asConst e of - Just x -> guard (x > 0) >> return [] - Nothing -> return [lit] - f lit@(Nonneg e) = - case LA.asConst e of - Just x -> guard (x >= 0) >> return [] - Nothing -> return [lit] - --- --------------------------------------------------------------------------- - -atomR :: RelOp -> Expr Rational -> Expr Rational -> Maybe (DNF Lit) -atomR op a b = do - a' <- termR a - b' <- termR b - return $ case op of - Le -> DNF [[a' `leR` b']] - Lt -> DNF [[a' `ltR` b']] - Ge -> DNF [[a' `geR` b']] - Gt -> DNF [[a' `gtR` b']] - Eql -> DNF [[a' `leR` b', a' `geR` b']] - NEq -> DNF [[a' `ltR` b'], [a' `gtR` b']] - -termR :: Expr Rational -> Maybe Rat -termR (Const c) = return (LA.constant (numerator c), denominator c) -termR (Var v) = return (LA.var v, 1) -termR (a :+: b) = do - (t1,c1) <- termR a - (t2,c2) <- termR b - return (c2 .*. t1 .+. c1 .*. t2, c1*c2) -termR (a :*: b) = do - (t1,c1) <- termR a - (t2,c2) <- termR b - msum [ do{ c <- LA.asConst t1; return (c .*. t2, c1*c2) } - , do{ c <- LA.asConst t2; return (c .*. t1, c1*c2) } - ] -termR (a :/: b) = do - (t1,c1) <- termR a - (t2,c2) <- termR b - c3 <- LA.asConst t2 - guard $ c3 /= 0 - return (c2 .*. t1, c1*c3) - -leR, ltR, geR, gtR :: Rat -> Rat -> Lit -leR (e1,c) (e2,d) = Nonneg $ normalizeExprR $ c .*. e2 .-. d .*. e1 -ltR (e1,c) (e2,d) = Pos $ normalizeExprR $ c .*. e2 .-. d .*. e1 -geR = flip leR -gtR = flip gtR - -normalizeExprR :: ExprZ -> ExprZ -normalizeExprR e = LA.mapCoeff (`div` d) e - where d = abs $ gcd' $ map fst $ LA.terms e - --- --------------------------------------------------------------------------- - -{- -(ls1,ls2,us1,us2) represents -{ x | ∀(M,c)∈ls1. M/c≤x, ∀(M,c)∈ls2. M/c [Lit] -> DNF Lit -eliminate v xs = DNF [rest] .&&. boundConditions bnd - where - (bnd, rest) = collectBounds v xs - -collectBounds :: Var -> [Lit] -> (BoundsR, [Lit]) -collectBounds v = foldr phi (([],[],[],[]),[]) - where - phi :: Lit -> (BoundsR, [Lit]) -> (BoundsR, [Lit]) - phi lit@(Nonneg t) x = f False lit t x - phi lit@(Pos t) x = f True lit t x - - f :: Bool -> Lit -> ExprZ -> (BoundsR, [Lit]) -> (BoundsR, [Lit]) - f strict lit t (bnd@(ls1,ls2,us1,us2), xs) = - case LA.extract v t of - (c,t') -> - case c `compare` 0 of - EQ -> (bnd, lit : xs) - GT -> - if strict - then ((ls1, (lnegate t', c) : ls2, us1, us2), xs) -- 0 < cx + M ⇔ -M/c < x - else (((lnegate t', c) : ls1, ls2, us1, us2), xs) -- 0 ≤ cx + M ⇔ -M/c ≤ x - LT -> - if strict - then ((ls1, ls2, us1, (t', negate c) : us2), xs) -- 0 < cx + M ⇔ x < M/-c - else ((ls1, ls2, (t', negate c) : us1, us2), xs) -- 0 ≤ cx + M ⇔ x ≤ M/-c - -boundConditions :: BoundsR -> DNF Lit -boundConditions (ls1, ls2, us1, us2) = DNF $ maybeToList $ simplify $ - [ x `leR` y | x <- ls1, y <- us1 ] ++ - [ x `ltR` y | x <- ls1, y <- us2 ] ++ - [ x `ltR` y | x <- ls2, y <- us1 ] ++ - [ x `ltR` y | x <- ls2, y <- us2 ] - -eliminateQuantifiers :: Formula Rational -> Maybe (DNF Lit) -eliminateQuantifiers = f - where - f T = return true - f F = return false - f (Atom (Rel a op b)) = atomR op a b - f (And a b) = liftM2 (.&&.) (f a) (f b) - f (Or a b) = liftM2 (.||.) (f a) (f b) - f (Not a) = f (pushNot a) - f (Imply a b) = f (Or (Not a) b) - f (Equiv a b) = f (And (Imply a b) (Imply b a)) - f (Forall v a) = do - dnf <- f (Exists v (pushNot a)) - return (notB dnf) - f (Exists v a) = do - dnf <- f a - return $ orB [eliminate v xs | xs <- unDNF dnf] - -solve :: Formula Rational -> SatResult Rational -solve formula = - case eliminateQuantifiers formula of - Nothing -> Unknown - Just dnf -> - case msum [solve' vs xs | xs <- unDNF dnf] of - Nothing -> Unsat - Just m -> Sat m - where - vs = IS.toList (vars formula) - -solve' :: [Var] -> [Lit] -> Maybe (Model Rational) -solve' vs xs = simplify xs >>= go vs - where - go [] [] = return IM.empty - go [] _ = mzero - go (v:vs) ys = msum (map f (unDNF (boundConditions bnd))) - where - (bnd, rest) = collectBounds v ys - f zs = do - model <- go vs (zs ++ rest) - val <- Interval.pickup (evalBounds model bnd) - return $ IM.insert v val model - -evalBounds :: Model Rational -> BoundsR -> Interval.Interval Rational -evalBounds model (ls1,ls2,us1,us2) = - foldl' Interval.intersection Interval.univ $ - [ Interval.interval (Just (True, evalRat model x)) Nothing | x <- ls1 ] ++ - [ Interval.interval (Just (False, evalRat model x)) Nothing | x <- ls2 ] ++ - [ Interval.interval Nothing (Just (True, evalRat model x)) | x <- us1 ] ++ - [ Interval.interval Nothing (Just (False, evalRat model x)) | x <- us2 ] - --- --------------------------------------------------------------------------- - -constraintsToDNF :: [LA.Atom Rational] -> DNF Lit -constraintsToDNF = andB . map constraintToDNF - -constraintToDNF :: LA.Atom Rational -> DNF Lit -constraintToDNF (LA.Atom a op b) = DNF $ - case op of - Eql -> [[Nonneg c, Nonneg (lnegate c)]] - NEq -> [[Pos c], [Pos (lnegate c)]] - Ge -> [[Nonneg c]] - Le -> [[Nonneg (lnegate c)]] - Gt -> [[Pos c]] - Lt -> [[Pos (lnegate c)]] - where - c = normalize (a .-. b) - - normalize :: LA.Expr Rational -> ExprZ - normalize e = LA.mapCoeff (round . (*c)) e - where - c = fromIntegral $ foldl' lcm 1 ds - ds = [denominator c | (c,v) <- LA.terms e] - --- --------------------------------------------------------------------------- - -gcd' :: [Integer] -> Integer -gcd' [] = 1 -gcd' xs = foldl1' gcd xs - --- --------------------------------------------------------------------------- - -{- -7x + 12y + 31z = 17 -3x + 5y + 14z = 7 -1 ≤ x ≤ 40 --50 ≤ y ≤ 50 - -satisfiable in R -but unsatisfiable in Z --} -test1 :: Formula Rational -test1 = c1 .&&. c2 .&&. c3 .&&. c4 - where - x = Var 0 - y = Var 1 - z = Var 2 - c1 = 7*x + 12*y + 31*z .==. 17 - c2 = 3*x + 5*y + 14*z .==. 7 - c3 = 1 .<=. x .&&. x .<=. 40 - c4 = (-50) .<=. y .&&. y .<=. 50 - -test1' :: [LA.Atom Rational] -test1' = [c1, c2] ++ c3 ++ c4 - where - x = LA.var 0 - y = LA.var 1 - z = LA.var 2 - c1 = 7.*.x .+. 12.*.y .+. 31.*.z .==. LA.constant 17 - c2 = 3.*.x .+. 5.*.y .+. 14.*.z .==. LA.constant 7 - c3 = [LA.constant 1 .<=. x, x .<=. LA.constant 40] - c4 = [LA.constant (-50) .<=. y, y .<=. LA.constant 50] - -{- -27 ≤ 11x+13y ≤ 45 --10 ≤ 7x-9y ≤ 4 - -satisfiable in R -but unsatisfiable in Z --} -test2 :: Formula Rational -test2 = c1 .&&. c2 - where - x = Var 0 - y = Var 1 - t1 = 11*x + 13*y - t2 = 7*x - 9*y - c1 = 27 .<=. t1 .&&. t1 .<=. 45 - c2 = (-10) .<=. t2 .&&. t2 .<=. 4 - --- --------------------------------------------------------------------------- diff --git a/src/LPSolver.hs b/src/LPSolver.hs deleted file mode 100644 --- a/src/LPSolver.hs +++ /dev/null @@ -1,250 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables #-} -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : LPSolver --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (ScopedTypeVariables) --- --- Naïve implementation of Simplex method --- --- Reference: --- --- * --- ------------------------------------------------------------------------------ - -module LPSolver where - -import Control.Monad -import Control.Monad.State -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS -import Data.OptDir - -import Data.Expr -import Data.Formula -import Data.Linear -import qualified Data.LA as LA -import qualified Data.Interval as Interval -import qualified Simplex -import qualified BoundsInference as BI - --- --------------------------------------------------------------------------- --- LP Monad - -type Solver r = (Var, Simplex.Tableau r, VarSet, VarMap (LA.Expr r)) -type LP r = State (Solver r) - -emptySolver :: VarSet -> Solver r -emptySolver vs = (1 + maximum ((-1) : IS.toList vs), IM.empty, IS.empty, IM.empty) - -gensym :: LP r Var -gensym = do - (x,tbl,avs,defs) <- get - put (x+1,tbl,avs,defs) - return x - -getTableau :: LP r (Simplex.Tableau r) -getTableau = do - (_,tbl,_,_) <- get - return tbl - -putTableau :: Simplex.Tableau r -> LP r () -putTableau tbl = do - (x,_,avs,defs) <- get - put (x,tbl,avs,defs) - -addArtificialVariable :: Var -> LP r () -addArtificialVariable v = do - (x,tbl,avs,defs) <- get - put (x, tbl, IS.insert v avs, defs) - -getArtificialVariables :: LP r VarSet -getArtificialVariables = do - (_,_,avs,_) <- get - return avs - -clearArtificialVariables :: LP r () -clearArtificialVariables = do - (x,tbl,_,defs) <- get - put (x, tbl, IS.empty, defs) - -define :: Var -> LA.Expr r -> LP r () -define v e = do - (x,tbl,avs,defs) <- get - put (x,tbl,avs, IM.insert v e defs) - -getDefs :: LP r (VarMap (LA.Expr r)) -getDefs = do - (_,_,_,defs) <- get - return defs - --- --------------------------------------------------------------------------- - -addConstraint :: Real r => LA.Atom r -> LP r () -addConstraint c = do - c <- expandDefs' c - let (e, rop, b) = normalizeConstraint c - tbl <- getTableau - case rop of - -- x≥b で b≤0 なら追加しない。ad hoc なので一般化したい。 - Ge | isSingleVar e && b<=0 -> return () - - Le -> do - v <- gensym -- slack variable - putTableau $ Simplex.setRow v tbl (LA.coeffMap e, b) - Ge -> do - v1 <- gensym -- surplus variable - v2 <- gensym -- artificial variable - putTableau $ Simplex.setRow v2 tbl (LA.coeffMap (e .-. LA.var v1), b) - addArtificialVariable v2 - Eql -> do - v <- gensym -- artificial variable - putTableau $ Simplex.setRow v tbl (LA.coeffMap e, b) - addArtificialVariable v - _ -> error $ "addConstraint does not support " ++ show rop - where - isSingleVar e = - case LA.terms e of - [(1,_)] -> True - _ -> False - -addConstraint2 :: Real r => LA.Atom r -> LP r () -addConstraint2 c = do - (LA.Atom lhs rop rhs) <- expandDefs' c - let - (b', e) = LA.extract LA.unitVar (lhs .-. rhs) - b = - b' - tbl <- getTableau - case rop of - Le -> f e b - Ge -> f (lnegate e) (negate b) - Eql -> do - f e b - f (lnegate e) (negate b) - _ -> error $ "addConstraint does not support " ++ show rop - where - -- -x≤b で -b≤0 なら追加しない。ad hoc なので一般化したい。 - f e b | isSingleNegatedVar e && -b <= 0 = return () - f e b = do - tbl <- getTableau - v <- gensym -- slack variable - putTableau $ Simplex.setRow v tbl (LA.coeffMap e, b) - - isSingleNegatedVar e = - case LA.terms e of - [(-1,_)] -> True - _ -> False - -expandDefs :: (Num r, Eq r) => LA.Expr r -> LP r (LA.Expr r) -expandDefs e = do - defs <- getDefs - return $ LA.applySubst defs e - -expandDefs' :: (Num r, Eq r) => LA.Atom r -> LP r (LA.Atom r) -expandDefs' (LA.Atom lhs op rhs) = do - lhs' <- expandDefs lhs - rhs' <- expandDefs rhs - return $ LA.Atom lhs' op rhs' - -tableau :: (RealFrac r) => [LA.Atom r] -> LP r () -tableau cs = do - let (nonnegVars, cs') = collectNonnegVars cs IS.empty - fvs = vars cs `IS.difference` nonnegVars - forM_ (IS.toList fvs) $ \v -> do - v1 <- gensym - v2 <- gensym - define v (LA.var v1 .-. LA.var v2) - mapM_ addConstraint cs' - -getModel :: Fractional r => VarSet -> LP r (Model r) -getModel vs = do - tbl <- getTableau - defs <- getDefs - let bs = IM.map snd (IM.delete Simplex.objRow tbl) - vs' = vs `IS.union` IS.fromList [v | e <- IM.elems defs, v <- IS.toList (vars e)] - -- Note that IM.union is left-biased - m0 = bs `IM.union` IM.fromList [(v,0) | v <- IS.toList vs'] - return $ IM.filterWithKey (\k _ -> k `IS.member` vs) $ IM.map (LA.evalExpr m0) defs `IM.union` m0 - -phaseI :: (Fractional r, Real r) => LP r Bool -phaseI = do - tbl <- getTableau - avs <- getArtificialVariables - let (ret, tbl') = Simplex.phaseI tbl avs - putTableau tbl' - when ret clearArtificialVariables - return ret - -simplex :: (Fractional r, Real r) => OptDir -> LA.Expr r -> LP r Bool -simplex optdir obj = do - tbl <- getTableau - defs <- getDefs - let (ret, tbl') = Simplex.simplex optdir (Simplex.setObjFun tbl (LA.applySubst defs obj)) - putTableau tbl' - return ret - -dualSimplex :: (Fractional r, Real r) => OptDir -> LA.Expr r -> LP r Bool -dualSimplex optdir obj = do - tbl <- getTableau - defs <- getDefs - let (ret, tbl') = Simplex.dualSimplex optdir (Simplex.setObjFun tbl (LA.applySubst defs obj)) - putTableau tbl' - return ret - --- --------------------------------------------------------------------------- - -normalizeConstraint :: forall r. Real r => LA.Atom r -> (LA.Expr r, RelOp, r) -normalizeConstraint (LA.Atom a op b) - | rhs < 0 = (lnegate lhs, flipOp op, negate rhs) - | otherwise = (lhs, op, rhs) - where - (c, lhs) = LA.extract LA.unitVar (a .-. b) - rhs = - c - -collectNonnegVars :: forall r. (RealFrac r) => [LA.Atom r] -> VarSet -> (VarSet, [LA.Atom r]) -collectNonnegVars cs ivs = (nonnegVars, cs) - where - vs = vars cs - bounds = BI.inferBounds initialBounds cs ivs 1000 - where - initialBounds = IM.fromList [(v, Interval.univ) | v <- IS.toList vs] - nonnegVars = IS.filter f vs - where - f v = case Interval.lowerBound (bounds IM.! v) of - Just (_, lb) | 0 <= lb -> True - _ -> False - - isTriviallyTrue :: LA.Atom r -> Bool - isTriviallyTrue (LA.Atom a op b) = - case op of - Le -> - case ub of - Nothing -> False - Just (_, val) -> val <= 0 - Ge -> - case lb of - Nothing -> False - Just (_, val) -> val >= 0 - Lt -> - case ub of - Nothing -> False - Just (incl, val) -> val < 0 || (not incl && val <= 0) - Gt -> - case lb of - Nothing -> False - Just (incl, val) -> val > 0 || (not incl && val >= 0) - Eql -> isTriviallyTrue (LA.Atom c Le lzero) && isTriviallyTrue (LA.Atom c Ge lzero) - NEq -> isTriviallyTrue (LA.Atom c Lt lzero) && isTriviallyTrue (LA.Atom c Gt lzero) - where - c = a .-. b - i = LA.computeInterval bounds c - lb = Interval.lowerBound i - ub = Interval.upperBound i - --- --------------------------------------------------------------------------- diff --git a/src/LPSolverHL.hs b/src/LPSolverHL.hs deleted file mode 100644 --- a/src/LPSolverHL.hs +++ /dev/null @@ -1,288 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables #-} -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : LPSolverHL --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (ScopedTypeVariables) --- --- High-Level API for LPSolver.hs --- ------------------------------------------------------------------------------ - -module LPSolverHL - ( module Data.Expr - , module Data.Formula - , minimize - , maximize - , optimize - , solve - ) where - -import Control.Monad.State -import Data.Maybe (fromMaybe) -import Data.Ratio -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS -import Data.OptDir - -import Data.Expr -import Data.Formula -import qualified Data.LA as LA -import qualified Simplex -import LPSolver - --- --------------------------------------------------------------------------- - -maximize :: (RealFrac r) => Expr r -> [Atom r] -> OptResult r -maximize = optimize OptMax - -minimize :: (RealFrac r) => Expr r -> [Atom r] -> OptResult r -minimize = optimize OptMin - -optimize :: (RealFrac r) => OptDir -> Expr r -> [Atom r] -> OptResult r -optimize optdir obj2 cs2 = fromMaybe OptUnknown $ do - obj <- LA.compileExpr obj2 - cs <- mapM LA.compileAtom cs2 - return (optimize' optdir obj cs) - -solve :: (RealFrac r) => [Atom r] -> SatResult r -solve cs2 = fromMaybe Unknown $ do - cs <- mapM LA.compileAtom cs2 - return (solve' cs) - --- --------------------------------------------------------------------------- - -solve' :: (RealFrac r) => [LA.Atom r] -> SatResult r -solve' cs = - flip evalState (emptySolver vs) $ do - tableau cs - ret <- phaseI - if not ret - then return Unsat - else do - m <- getModel vs - return (Sat m) - where - vs = vars cs - -optimize' :: (RealFrac r) => OptDir -> LA.Expr r -> [LA.Atom r] -> OptResult r -optimize' optdir obj cs = - flip evalState (emptySolver vs) $ do - tableau cs - ret <- phaseI - if not ret - then return OptUnsat - else do - ret2 <- simplex optdir obj - if not ret2 - then return Unbounded - else do - m <- getModel vs - tbl <- getTableau - return $ Optimum (Simplex.currentObjValue tbl) m - where - vs = vars cs `IS.union` vars obj - --- --------------------------------------------------------------------------- --- Test cases - -example_3_2 :: (Expr Rational, [Atom Rational]) -example_3_2 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - x3 = var 3 - obj = 3*x1 + 2*x2 + 3*x3 - cond = [ 2*x1 + x2 + x3 .<=. 2 - , x1 + 2*x2 + 3*x3 .<=. 5 - , 2*x1 + 2*x2 + x3 .<=. 6 - , x1 .>=. 0 - , x2 .>=. 0 - , x3 .>=. 0 - ] - -test_3_2 :: Bool -test_3_2 = - uncurry maximize example_3_2 == - Optimum (27 % 5) (IM.fromList [(1,1 % 5),(2,0 % 1),(3,8 % 5)]) - -example_3_5 :: (Expr Rational, [Atom Rational]) -example_3_5 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - x3 = var 3 - x4 = var 4 - x5 = var 5 - obj = -2*x1 + 4*x2 + 7*x3 + x4 + 5*x5 - cond = [ -x1 + x2 + 2*x3 + x4 + 2*x5 .==. 7 - , -x1 + 2*x2 + 3*x3 + x4 + x5 .==. 6 - , -x1 + x2 + x3 + 2*x4 + x5 .==. 4 - , x2 .>=. 0 - , x3 .>=. 0 - , x4 .>=. 0 - , x5 .>=. 0 - ] - -test_3_5 :: Bool -test_3_5 = - uncurry minimize example_3_5 == - Optimum (19 % 1) (IM.fromList [(1,(-1) % 1),(2,0 % 1),(3,1 % 1),(4,0 % 1),(5,2 % 1)]) - -example_4_1 :: (Expr Rational, [Atom Rational]) -example_4_1 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - obj = 2*x1 + x2 - cond = [ -x1 + x2 .>=. 2 - , x1 + x2 .<=. 1 - , x1 .>=. 0 - , x2 .>=. 0 - ] - -test_4_1 :: Bool -test_4_1 = - uncurry maximize example_4_1 == - OptUnsat - -example_4_2 :: (Expr Rational, [Atom Rational]) -example_4_2 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - obj = 2*x1 + x2 - cond = [ - x1 - x2 .<=. 10 - , 2*x1 - x2 .<=. 40 - , x1 .>=. 0 - , x2 .>=. 0 - ] - -test_4_2 :: Bool -test_4_2 = - uncurry maximize example_4_2 == - Unbounded - -example_4_3 :: (Expr Rational, [Atom Rational]) -example_4_3 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - obj = 6*x1 - 2*x2 - cond = [ 2*x1 - x2 .<=. 2 - , x1 .<=. 4 - , x1 .>=. 0 - , x2 .>=. 0 - ] - -test_4_3 :: Bool -test_4_3 = - uncurry maximize example_4_3 == - Optimum (12 % 1) (IM.fromList [(1,4 % 1),(2,6 % 1)]) - -example_4_5 :: (Expr Rational, [Atom Rational]) -example_4_5 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - obj = 2*x1 + x2 - cond = [ 4*x1 + 3*x2 .<=. 12 - , 4*x1 + x2 .<=. 8 - , 4*x1 - x2 .<=. 8 - , x1 .>=. 0 - , x2 .>=. 0 - ] - -test_4_5 :: Bool -test_4_5 = - uncurry maximize example_4_5 == - Optimum (5 % 1) (IM.fromList [(1,3 % 2),(2,2 % 1)]) - -example_4_6 :: (Expr Rational, [Atom Rational]) -example_4_6 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - x3 = var 3 - x4 = var 4 - obj = 20*x1 + (1/2)*x2 - 6*x3 + (3/4)*x4 - cond = [ x1 .<=. 2 - , 8*x1 - x2 + 9*x3 + (1/4)*x4 .<=. 16 - , 12*x1 - (1/2)*x2 + 3*x3 + (1/2)*x4 .<=. 24 - , x2 .<=. 1 - , x1 .>=. 0 - , x2 .>=. 0 - , x3 .>=. 0 - , x4 .>=. 0 - ] - -test_4_6 :: Bool -test_4_6 = - uncurry maximize example_4_6 == - Optimum (165 % 4) (IM.fromList [(1,2 % 1),(2,1 % 1),(3,0 % 1),(4,1 % 1)]) - -example_4_7 :: (Expr Rational, [Atom Rational]) -example_4_7 = (obj, cond) - where - x1 = var 1 - x2 = var 2 - x3 = var 3 - x4 = var 4 - obj = x1 + 1.5*x2 + 5*x3 + 2*x4 - cond = [ 3*x1 + 2*x2 + x3 + 4*x4 .<=. 6 - , 2*x1 + x2 + 5*x3 + x4 .<=. 4 - , 2*x1 + 6*x2 - 4*x3 + 8*x4 .==. 0 - , x1 + 3*x2 - 2*x3 + 4*x4 .==. 0 - , x1 .>=. 0 - , x2 .>=. 0 - , x3 .>=. 0 - , x4 .>=. 0 - ] - -test_4_7 :: Bool -test_4_7 = - uncurry maximize example_4_7 == - Optimum (48 % 11) (IM.fromList [(1,0 % 1),(2,0 % 1),(3,8 % 11),(4,4 % 11)]) - --- 退化して巡回の起こるKuhnの7変数3制約の例 -kuhn_7_3 :: (Expr Rational, [Atom Rational]) -kuhn_7_3 = (obj, cond) - where - [x1,x2,x3,x4,x5,x6,x7] = map var [1..7] - obj = -2*x4-3*x5+x6+12*x7 - cond = [ x1 - 2*x4 - 9*x5 + x6 + 9*x7 .==. 0 - , x2 + (1/3)*x4 + x5 - (1/3)*x6 - 2*x7 .==. 0 - , x3 + 2*x4 + 3*x5 - x6 - 12*x7 .==. 2 - , x1 .>=. 0 - , x2 .>=. 0 - , x3 .>=. 0 - , x4 .>=. 0 - , x5 .>=. 0 - , x6 .>=. 0 - , x7 .>=. 0 - ] - -test_kuhn_7_3 :: Bool -test_kuhn_7_3 = - uncurry minimize kuhn_7_3 == - Optimum ((-2) % 1) (IM.fromList [(1,2 % 1),(2,0 % 1),(3,0 % 1),(4,2 % 1),(5,0 % 1),(6,2 % 1),(7,0 % 1)]) - -testAll :: Bool -testAll = and - [ test_3_2 - , test_3_5 - , test_4_1 - , test_4_2 - , test_4_3 - , test_4_5 - , test_4_6 - , test_4_7 - , test_kuhn_7_3 - ] - --- --------------------------------------------------------------------------- diff --git a/src/MIPSolver2.hs b/src/MIPSolver2.hs deleted file mode 100644 --- a/src/MIPSolver2.hs +++ /dev/null @@ -1,480 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables, Rank2Types #-} -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : MIPSolver2 --- Copyright : (c) Masahiro Sakai 2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable --- --- Naïve implementation of MIP solver based on Simplex2 module --- --- Reference: --- --- * --- --- * Ralph E. Gomory. --- \"An Algorithm for the Mixed Integer Problem\", Technical Report --- RM-2597, 1960, The Rand Corporation, Santa Monica, CA. --- --- --- * Ralph E. Gomory. --- \"Outline of an algorithm for integer solutions to linear programs\". --- Bull. Amer. Math. Soc., Vol. 64, No. 5. (1958), pp. 275-278. --- --- --- * R. C. Daniel and Martyn Jeffreys. --- \"Unboundedness in Integer and Discrete Programming L.P. Relaxations\" --- The Journal of the Operational Research Society, Vol. 30, No. 12. (1979) --- --- ------------------------------------------------------------------------------ -module MIPSolver2 - ( - -- * The @Solver@ type - Solver - , newSolver - - -- * Solving - , optimize - - -- * Extract results - , model - , getObjValue - - -- * Configulation - , setNThread - , setLogger - , setShowRational - ) where - -import Prelude hiding (log) - -import Control.Monad -import Control.Exception -import Control.Concurrent -import Control.Concurrent.STM -import Data.List -import Data.OptDir -import Data.Ord -import Data.IORef -import Data.Maybe -import qualified Data.IntSet as IS -import qualified Data.IntMap as IM -import qualified Data.Map as Map -import qualified Data.Sequence as Seq -import qualified Data.Foldable as F -import System.CPUTime -import Text.Printf - -import qualified Data.LA as LA -import Data.Formula ((.<=.), (.>=.), (.==.)) -import qualified Simplex2 -import Simplex2 (OptResult (..), Var, Model) -import qualified OmegaTest -import Data.Linear -import Util (isInteger, fracPart) - -data Solver - = MIP - { mipRootLP :: Simplex2.Solver - , mipIVs :: IS.IntSet - , mipBest :: TVar (Maybe Node) - - , mipNThread :: IORef Int - , mipLogger :: IORef (Maybe (String -> IO ())) - , mipShowRational :: IORef Bool - } - -data Node = - Node - { ndLP :: Simplex2.Solver - , ndDepth :: {-# UNPACK #-} !Int - , ndValue :: Rational - } - -newSolver :: Simplex2.Solver -> IS.IntSet -> IO Solver -newSolver lp ivs = do - lp2 <- Simplex2.cloneSolver lp - - forM_ (IS.toList ivs) $ \v -> do - lb <- Simplex2.getLB lp2 v - case lb of - Just l | not (isInteger l) -> - Simplex2.assertLower lp2 v (fromInteger (ceiling l)) - _ -> return () - ub <- Simplex2.getUB lp2 v - case ub of - Just u | not (isInteger u) -> - Simplex2.assertLower lp2 v (fromInteger (floor u)) - _ -> return () - - bestRef <- newTVarIO Nothing - - nthreadRef <- newIORef 0 - logRef <- newIORef Nothing - showRef <- newIORef False - - return $ - MIP - { mipRootLP = lp2 - , mipIVs = ivs - , mipBest = bestRef - - , mipNThread = nthreadRef - , mipLogger = logRef - , mipShowRational = showRef - } - -optimize :: Solver -> (Model -> Rational -> IO ()) -> IO OptResult -optimize solver update = do - let lp = mipRootLP solver - log solver "MIP: Solving LP relaxation..." - ret <- Simplex2.check lp - if not ret - then return Unsat - else do - s0 <- showValue solver =<< Simplex2.getObjValue lp - log solver (printf "MIP: LP relaxation is satisfiable with obj = %s" s0) - log solver "MIP: Optimizing LP relaxation" - ret2 <- Simplex2.optimize lp Simplex2.defaultOptions - case ret2 of - Unsat -> error "should not happen" - Unbounded -> do - log solver "MIP: LP relaxation is unbounded" - let ivs = mipIVs solver - if IS.null ivs - then return Unbounded - else do - {- - Fallback to Fourier-Motzkin + OmegaTest - * In general, original problem may have optimal - solution even though LP relaxiation is unbounded. - * But if restricted to rational numbers, the - original problem is unbounded or unsatisfiable - when LP relaxation is unbounded. - -} - log solver "MIP: falling back to Fourier-Motzkin + OmegaTest" - t <- Simplex2.getTableau lp - let ds = [LA.var v .==. def | (v, def) <- IM.toList t] - n <- Simplex2.nVars lp - bs <- liftM concat $ forM [0..n-1] $ \v -> do - lb <- Simplex2.getLB lp v - ub <- Simplex2.getUB lp v - return $ [LA.var v .>=. LA.constant (fromJust lb) | isJust lb] ++ - [LA.var v .<=. LA.constant (fromJust ub) | isJust ub] - case OmegaTest.solveQFLA (bs ++ ds) ivs of - Just _ -> return Unbounded - Nothing -> return Unsat - Optimum -> do - s0 <- showValue solver =<< Simplex2.getObjValue lp - log solver $ "MIP: LP relaxation optimum is " ++ s0 - log solver "MIP: Integer optimization begins..." - Simplex2.clearLogger lp - branchAndBound solver update - m <- readTVarIO (mipBest solver) - case m of - Nothing -> return Unsat - Just _ -> return Optimum - -branchAndBound :: Solver -> (Model -> Rational -> IO ()) -> IO () -branchAndBound solver update = do - dir <- Simplex2.getOptDir (mipRootLP solver) - rootVal <- Simplex2.getObjValue (mipRootLP solver) - let root = Node{ ndLP = mipRootLP solver, ndDepth = 0, ndValue = rootVal } - - pool <- newTVarIO (Seq.singleton root) - activeThreads <- newTVarIO (Map.empty) - visitedNodes <- newTVarIO 0 - - let addNode :: Node -> STM () - addNode nd = do - modifyTVar pool (Seq.|> nd) - - pickNode :: IO (Maybe Node) - pickNode = do - self <- myThreadId - atomically $ modifyTVar activeThreads (Map.delete self) - atomically $ do - s <- readTVar pool - case Seq.viewl s of - nd Seq.:< s2 -> do - writeTVar pool s2 - modifyTVar activeThreads (Map.insert self nd) - return (Just nd) - Seq.EmptyL -> do - ths <- readTVar activeThreads - if Map.null ths - then return Nothing - else retry - - updateBest :: Node -> IO () - updateBest node = do - let lp = ndLP node - m <- Simplex2.model lp - ret <- atomically $ do - old <- readTVar (mipBest solver) - case old of - Nothing -> do - writeTVar (mipBest solver) (Just node) - return True - Just best -> do - let isBetter = if dir==OptMin then ndValue node < ndValue best else ndValue node > ndValue best - when isBetter $ writeTVar (mipBest solver) (Just node) - return isBetter - when ret $ update m (ndValue node) -- 複数スレッドからupdateが同時に呼ばれてまずい可能性がある - - processNode :: Node -> IO () - processNode node = do - let lp = ndLP node - lim <- liftM (fmap ndValue) $ readTVarIO (mipBest solver) - ret <- Simplex2.dualSimplex lp Simplex2.defaultOptions{ Simplex2.objLimit = lim } - - case ret of - Unbounded -> error "should not happen" - Unsat -> return () - ObjLimit -> return () - Optimum -> do - val <- Simplex2.getObjValue lp - p <- prune solver val - unless p $ do - xs <- violated node (mipIVs solver) - case xs of - [] -> updateBest (node { ndValue = val }) - _ -> do - r <- if ndDepth node `mod` 100 /= 0 - then return Nothing - else liftM listToMaybe $ filterM (canDeriveGomoryCut lp) $ map fst xs - case r of - Nothing -> do -- branch - let (v0,val0) = fst $ maximumBy (comparing snd) - [((v,val), abs (fromInteger (round val) - val)) | (v,val) <- xs] - let lp1 = lp - lp2 <- Simplex2.cloneSolver lp - Simplex2.assertAtom lp1 (LA.var v0 .<=. LA.constant (fromInteger (floor val0))) - Simplex2.assertAtom lp2 (LA.var v0 .>=. LA.constant (fromInteger (ceiling val0))) - atomically $ do - addNode $ Node lp1 (ndDepth node + 1) val - addNode $ Node lp2 (ndDepth node + 1) val - modifyTVar visitedNodes (+1) - Just v -> do -- cut - atom <- deriveGomoryCut lp (mipIVs solver) v - Simplex2.assertAtom lp atom - atomically $ do - addNode $ Node lp (ndDepth node + 1) val - - let isCompleted = do - nodes <- readTVar pool - threads <- readTVar activeThreads - return $ Seq.null nodes && Map.null threads - - -- fork worker threads - nthreads <- do - n <- readIORef (mipNThread solver) - if n >= 1 - then return n - else return 1 -- getNumCapabilities -- base-4.4.0.0以降にしか存在しない - - let child = do - m <- pickNode - case m of - Nothing -> return () - Just node -> processNode node >> child - - log solver $ printf "MIP: forking %d worker threads..." nthreads - start <- getCPUTime - ex <- newEmptyTMVarIO - threads <- replicateM nthreads $ do - mask $ \restore -> forkIO $ do - ret <- try (restore child) - case ret of - Left e -> atomically (putTMVar ex e) - Right _ -> return () - - th <- forkIO $ do - let loop = do - (nodes, visited::Int) <- atomically $ do - nodes <- readTVar pool - athreads <- readTVar activeThreads - visited <- readTVar visitedNodes - return (Seq.fromList (Map.elems athreads) Seq.>< nodes, visited) - if Seq.null nodes - then return () - else do - now <- getCPUTime - let spent = (now - start) `div` 10^(12::Int) - - let vs = map ndValue (F.toList nodes) - dualBound = - case dir of - OptMin -> minimum vs - OptMax -> maximum vs - - primalBound <- do - x <- readTVarIO (mipBest solver) - return $ case x of - Nothing -> Nothing - Just node -> Just (ndValue node) - - (p,g) <- case primalBound of - Nothing -> return ("not yet found", "--") - Just val -> do - p <- showValue solver val - let g = if val == 0 - then "inf" - else printf "%.2f%%" (fromRational (abs (dualBound - val) * 100 / abs val) :: Double) - return (p, g) - d <- showValue solver dualBound - - let range = - case dir of - OptMin -> p ++ " >= " ++ d - OptMax -> p ++ " <= " ++ d - - log solver $ printf "time = %d sec; active nodes = %d; visited nodes = %d; %s; gap = %s" spent (Seq.length nodes) visited range g - threadDelay (2*1000*1000) -- 2s - loop - loop - - -- join - let wait = isCompleted >>= guard >> return Nothing - let loop :: (forall a. IO a -> IO a) -> IO () - loop restore = do - ret <- try $ restore $ atomically $ wait `orElse` (liftM Just (readTMVar ex)) - case ret of - Right Nothing -> return () - Right (Just (e::SomeException)) -> do - mapM_ (\t -> throwTo t e) (th:threads) - throwIO e - Left (e::SomeException) -> do - mapM_ (\t -> throwTo t e) (th:threads) - throwIO e - mask loop - -model :: Solver -> IO Model -model solver = do - m <- readTVarIO (mipBest solver) - case m of - Nothing -> error "no model" - Just node -> Simplex2.model (ndLP node) - -getObjValue :: Solver -> IO Rational -getObjValue solver = do - m <- readTVarIO (mipBest solver) - case m of - Nothing -> error "no model" - Just node -> return $ ndValue node - -violated :: Node -> IS.IntSet -> IO [(Var, Rational)] -violated node ivs = do - m <- Simplex2.model (ndLP node) - let p (v,val) = v `IS.member` ivs && not (isInteger val) - return $ filter p (IM.toList m) - -prune :: Solver -> Rational -> IO Bool -prune solver lb = do - b <- readTVarIO (mipBest solver) - case b of - Nothing -> return False - Just node -> do - dir <- Simplex2.getOptDir (mipRootLP solver) - return $ if dir==OptMin then ndValue node <= lb else ndValue node >= lb - -showValue :: Solver -> Rational -> IO String -showValue solver v = do - printRat <- readIORef (mipShowRational solver) - return $ Simplex2.showValue printRat v - -setShowRational :: Solver -> Bool -> IO () -setShowRational solver = writeIORef (mipShowRational solver) - -setNThread :: Solver -> Int -> IO () -setNThread solver = writeIORef (mipNThread solver) - -{-------------------------------------------------------------------- - Logging ---------------------------------------------------------------------} - --- | set callback function for receiving messages. -setLogger :: Solver -> (String -> IO ()) -> IO () -setLogger solver logger = do - writeIORef (mipLogger solver) (Just logger) - -log :: Solver -> String -> IO () -log solver msg = logIO solver (return msg) - -logIO :: Solver -> IO String -> IO () -logIO solver action = do - m <- readIORef (mipLogger solver) - case m of - Nothing -> return () - Just logger -> action >>= logger - -{-------------------------------------------------------------------- - GomoryCut ---------------------------------------------------------------------} - -deriveGomoryCut :: Simplex2.Solver -> IS.IntSet -> Var -> IO (LA.Atom Rational) -deriveGomoryCut lp ivs xi = do - v0 <- Simplex2.getValue lp xi - let f0 = fracPart v0 - assert (0 < f0 && f0 < 1) $ return () - - row <- Simplex2.getRow lp xi - - -- remove fixed variables - let p (_,xj) = do - lb <- Simplex2.getLB lp xj - ub <- Simplex2.getUB lp xj - case (lb,ub) of - (Just l, Just u) -> return (l < u) - _ -> return True - ns <- filterM p $ LA.terms row - - js <- flip filterM ns $ \(_, xj) -> do - vj <- Simplex2.getValue lp xj - lb <- Simplex2.getLB lp xj - return $ Just vj == lb - ks <- flip filterM ns $ \(_, xj) -> do - vj <- Simplex2.getValue lp xj - ub <- Simplex2.getUB lp xj - return $ Just vj == ub - - xs1 <- forM js $ \(aij, xj) -> do - let fj = fracPart aij - Just lj <- Simplex2.getLB lp xj - let c = if xj `IS.member` ivs - then (if fj <= 1 - f0 then fj / (1 - f0) else ((1 - fj) / f0)) - else (if aij > 0 then aij / (1 - f0) else (-aij / f0)) - return $ c .*. (LA.var xj .-. LA.constant lj) - xs2 <- forM ks $ \(aij, xj) -> do - let fj = fracPart aij - Just uj <- Simplex2.getUB lp xj - let c = if xj `IS.member` ivs - then (if fj <= f0 then fj / f0 else ((1 - fj) / (1 - f0))) - else (if aij > 0 then aij / f0 else (-aij / (1 - f0))) - return $ c .*. (LA.constant uj .-. LA.var xj) - - return $ lsum xs1 .+. lsum xs2 .>=. LA.constant 1 - --- TODO: Simplex2をδに対応させたら、xi, xj がδを含まない有理数であるという条件も必要 -canDeriveGomoryCut :: Simplex2.Solver -> Var -> IO Bool -canDeriveGomoryCut lp xi = do - b <- Simplex2.isBasicVariable lp xi - if not b - then return False - else do - val <- Simplex2.getValue lp xi - if isInteger val - then return False - else do - row <- Simplex2.getRow lp xi - ys <- forM (LA.terms row) $ \(_,xj) -> do - vj <- Simplex2.getValue lp xj - lb <- Simplex2.getLB lp xj - ub <- Simplex2.getUB lp xj - return $ Just vj == lb || Just vj == ub - return (and ys) diff --git a/src/MIPSolverHL.hs b/src/MIPSolverHL.hs deleted file mode 100644 --- a/src/MIPSolverHL.hs +++ /dev/null @@ -1,300 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables #-} -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : MIPSolverHL --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (ScopedTypeVariables) --- --- References: --- --- * [Gomory1960] --- Ralph E. Gomory. --- An Algorithm for the Mixed Integer Problem, Technical Report --- RM-2597, 1960, The Rand Corporation, Santa Monica, CA. --- --- --- * [Gomory1958] --- Ralph E. Gomory. --- Outline of an algorithm for integer solutions to linear programs. --- Bull. Amer. Math. Soc., Vol. 64, No. 5. (1958), pp. 275-278. --- ------------------------------------------------------------------------------ - -module MIPSolverHL - ( module Data.Expr - , module Data.Formula - , module Data.OptDir - , minimize - , maximize - , optimize --- , solve - ) where - -import Control.Exception -import Control.Monad.State -import Data.Ord -import Data.Maybe -import Data.List (maximumBy) -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS -import Data.Ratio -import Data.OptDir - -import Data.Expr -import Data.Formula -import Data.Linear -import qualified Data.LA as LA -import qualified Simplex -import Util (isInteger, fracPart) -import LPSolver -import qualified OmegaTest - --- --------------------------------------------------------------------------- - -maximize :: RealFrac r => Expr r -> [Atom r] -> VarSet -> OptResult r -maximize = optimize OptMax - -minimize :: RealFrac r => Expr r -> [Atom r] -> VarSet -> OptResult r -minimize = optimize OptMin - -optimize :: RealFrac r => OptDir -> Expr r -> [Atom r] -> VarSet -> OptResult r -optimize optdir obj2 cs2 ivs = fromMaybe OptUnknown $ do - obj <- LA.compileExpr obj2 - cs <- mapM LA.compileAtom cs2 - return (optimize' optdir obj cs ivs) - -{- -solve :: RealFrac r => [Atom r] -> VarSet -> SatResult r -solve cs2 ivs = fromMaybe Unknown $ do - cs <- mapM compileAtom cs2 - return (solve' cs ivs) --} - --- --------------------------------------------------------------------------- - -data Node r - = Node - { ndSolver :: LPSolver.Solver r - , ndDepth :: {-# UNPACK #-} !Int --- , ndCutSlackVariables :: VarSet - } - -ndTableau :: Node r -> Simplex.Tableau r -ndTableau node = evalState getTableau (ndSolver node) - -ndLowerBound :: (Num r, Eq r) => Node r -> r -ndLowerBound node = evalState (liftM Simplex.currentObjValue getTableau) (ndSolver node) - -data Err = ErrUnbounded | ErrUnsat deriving (Ord, Eq, Show, Enum, Bounded) - -optimize' :: RealFrac r => OptDir -> LA.Expr r -> [LA.Atom r] -> VarSet -> OptResult r -optimize' optdir obj cs ivs = - case mkInitialNode optdir obj cs ivs of - Left err -> - case err of - ErrUnsat -> OptUnsat - ErrUnbounded -> - if IS.null ivs - then Unbounded - else - {- - Fallback to Fourier-Motzkin + OmegaTest - * In general, original problem may have optimal - solution even though LP relaxiation is unbounded. - * But if restricted to rational numbers, the - original problem is unbounded or unsatisfiable - when LP relaxation is unbounded. - -} - case OmegaTest.solveQFLA (map conv cs) ivs of - Nothing -> OptUnsat - Just _ -> Unbounded - Right (node0, ivs2) -> - case traverse optdir obj ivs2 node0 of - Left ErrUnbounded -> error "shoud not happen" - Left ErrUnsat -> OptUnsat - Right node -> flip evalState (ndSolver node) $ do - tbl <- getTableau - model <- getModel vs - return $ Optimum (Simplex.currentObjValue tbl) model - where - vs = vars cs `IS.union` vars obj - -tableau' :: (RealFrac r) => [LA.Atom r] -> VarSet -> LP r VarSet -tableau' cs ivs = do - let (nonnegVars, cs') = collectNonnegVars cs ivs - fvs = vars cs `IS.difference` nonnegVars - ivs2 <- liftM IS.unions $ forM (IS.toList fvs) $ \v -> do - v1 <- gensym - v2 <- gensym - define v (LA.var v1 .-. LA.var v2) - return $ if v `IS.member` ivs then IS.fromList [v1,v2] else IS.empty - mapM_ addConstraint cs' - return ivs2 - -conv :: RealFrac r => LA.Atom r -> LA.Atom Rational -conv (LA.Atom a op b) = LA.Atom (f a) op (f b) - where - f = LA.mapCoeff toRational - -mkInitialNode :: RealFrac r => OptDir -> LA.Expr r -> [LA.Atom r] -> VarSet -> Either Err (Node r, VarSet) -mkInitialNode optdir obj cs ivs = - flip evalState (emptySolver vs) $ do - ivs2 <- tableau' cs ivs - ret <- phaseI - if not ret - then return (Left ErrUnsat) - else do - ret2 <- simplex optdir obj - if ret2 - then do - solver <- get - return $ Right $ - ( Node{ ndSolver = solver - , ndDepth = 0 --- , ndCutSlackVariables = IS.empty - } - , ivs `IS.union` ivs2 - ) - else return (Left ErrUnbounded) - where - vs = vars cs `IS.union` vars obj - -isStrictlyBetter :: RealFrac r => OptDir -> r -> r -> Bool -isStrictlyBetter optdir = if optdir==OptMin then (<) else (>) - -traverse :: forall r. RealFrac r => OptDir -> LA.Expr r -> VarSet -> Node r -> Either Err (Node r) -traverse optdir obj ivs node0 = loop [node0] Nothing - where - loop :: [Node r] -> Maybe (Node r) -> Either Err (Node r) - loop [] (Just best) = Right best - loop [] Nothing = Left ErrUnsat - loop (n:ns) Nothing = - case children n of - Nothing -> loop ns (Just n) - Just cs -> loop (cs++ns) Nothing - loop (n:ns) (Just best) - | isStrictlyBetter optdir (ndLowerBound n) (ndLowerBound best) = - case children n of - Nothing -> loop ns (Just n) - Just cs -> loop (cs++ns) (Just best) - | otherwise = loop ns (Just best) - - reopt :: Solver r -> Maybe (Solver r) - reopt s = flip evalState s $ do - ret <- dualSimplex optdir obj - if ret - then liftM Just get - else return Nothing - - children :: Node r -> Maybe [Node r] - children node - | null xs = Nothing -- no violation - | ndDepth node `mod` 100 == 0 = -- cut - let - (f0, m0) = maximumBy (comparing fst) [(fracPart val, m) | (_,m,val) <- xs] - sv = flip execState (ndSolver node) $ do - s <- gensym - let g j x = assert (a >= 0) a - where - a | j `IS.member` ivs = - if fracPart x <= f0 - then fracPart x - else (f0 / (f0 - 1)) * (fracPart x - 1) - -- [Gomory1960] では (f0 / (1 - f0)) * (fracPart x - 1) としているが、 - -- これは誤り - | otherwise = - if x >= 0 - then x - else (f0 / (f0 - 1)) * x - putTableau $ IM.insert s (IM.mapWithKey (\j x -> negate (g j x)) m0, negate f0) tbl - in Just $ [node{ ndSolver = sv2, ndDepth = ndDepth node + 1 } | sv2 <- maybeToList (reopt sv)] - | otherwise = -- branch - let (v0, val0) = snd $ maximumBy (comparing fst) [(fracPart val, (v, val)) | (v,_,val) <- xs] - cs = [ LA.Atom (LA.var v0) Ge (LA.constant (fromIntegral (ceiling val0 :: Integer))) - , LA.Atom (LA.var v0) Le (LA.constant (fromIntegral (floor val0 :: Integer))) - ] - svs = [execState (addConstraint2 c) (ndSolver node) | c <- cs] - in Just $ [node{ ndSolver = sv, ndDepth = ndDepth node + 1 } | Just sv <- map reopt svs] - - where - tbl :: Simplex.Tableau r - tbl = ndTableau node - - xs :: [(Var, VarMap r, r)] - xs = [ (v, m, val) - | v <- IS.toList ivs - , Just (m, val) <- return (IM.lookup v tbl) - , not (isInteger val) - ] - --- --------------------------------------------------------------------------- - -example1 = (optdir, obj, cs, ivs) - where - optdir = OptMax - x1 = LA.var 1 - x2 = LA.var 2 - x3 = LA.var 3 - x4 = LA.var 4 - obj = x1 .+. 2 .*. x2 .+. 3 .*. x3 .+. x4 - cs = - [ LA.Atom ((-1) .*. x1 .+. x2 .+. x3 .+. 10.*.x4) Le (LA.constant 20) - , LA.Atom (x1 .-. 3 .*. x2 .+. x3) Le (LA.constant 30) - , LA.Atom (x2 .-. 3.5 .*. x4) Eql (LA.constant 0) - , LA.Atom (LA.constant 0) Le x1 - , LA.Atom x1 Le (LA.constant 40) - , LA.Atom (LA.constant 0) Le x2 - , LA.Atom (LA.constant 0) Le x3 - , LA.Atom (LA.constant 2) Le x4 - , LA.Atom x4 Le (LA.constant 3) - ] - ivs = IS.singleton 4 - -test1 :: Bool -test1 = result==expected - where - (optdir, obj, cs, ivs) = example1 - result, expected :: OptResult Rational - result = optimize' optdir obj cs ivs - expected = Optimum (245 % 2) (IM.fromList [(1,40 % 1),(2,21 % 2),(3,39 % 2),(4,3 % 1)]) - -test1' :: Bool -test1' = result==expected - where - (optdir, obj, cs, ivs) = example1 - f OptMin = OptMax - f OptMax = OptMin - result, expected :: OptResult Rational - result = optimize' (f optdir) (lnegate obj) cs ivs - expected = Optimum (-245 % 2) (IM.fromList [(1,40 % 1),(2,21 % 2),(3,39 % 2),(4,3 % 1)]) - --- 『数理計画法の基礎』(坂和 正敏) p.109 例 3.8 -example2 = (optdir, obj, cs, ivs) - where - optdir = OptMin - [x1,x2,x3] = map LA.var [1..3] - obj = (-1) .*. x1 .-. 3 .*. x2 .-. 5 .*. x3 - cs = - [ LA.Atom (3 .*. x1 .+. 4 .*. x2) Le (LA.constant 10) - , LA.Atom (2 .*. x1 .+. x2 .+. x3) Le (LA.constant 7) - , LA.Atom (3.*.x1 .+. x2 .+. 4 .*. x3) Eql (LA.constant 12) - , LA.Atom (LA.constant 0) Le x1 - , LA.Atom (LA.constant 0) Le x2 - , LA.Atom (LA.constant 0) Le x3 - ] - ivs = IS.fromList [1,2] - -test2 :: Bool -test2 = result == expected - where - result, expected :: OptResult Rational - result = optimize' optdir obj cs ivs - expected = Optimum ((-37) % 2) (IM.fromList [(1,0 % 1),(2,2 % 1),(3,5 % 2)]) - (optdir, obj, cs, ivs) = example2 - --- --------------------------------------------------------------------------- diff --git a/src/OmegaTest.hs b/src/OmegaTest.hs deleted file mode 100644 --- a/src/OmegaTest.hs +++ /dev/null @@ -1,310 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} -{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-} ------------------------------------------------------------------------------ --- | --- Module : OmegaTest --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (MultiParamTypeClasses, FunctionalDependencies) --- --- (incomplete) implementation of Omega Test --- --- References: --- --- * William Pugh. The Omega test: a fast and practical integer --- programming algorithm for dependence analysis. In Proceedings of --- the 1991 ACM/IEEE conference on Supercomputing (1991), pp. 4-13. --- --- * --- --- See also: --- --- * --- ------------------------------------------------------------------------------ -module OmegaTest - ( module Data.Expr - , module Data.Formula - , Lit (..) - , eliminateQuantifiers - , solve - , solveQFLA - ) where - -import Control.Monad -import Data.List -import Data.Maybe -import Data.Ratio -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS - -import Data.Expr -import Data.Formula -import Data.Linear -import qualified Data.LA as LA -import qualified Data.Interval as Interval -import Util (combineMaybe) -import qualified FourierMotzkin as FM -import FourierMotzkin (Lit (..), Rat (..)) - --- --------------------------------------------------------------------------- - -type ExprZ = LA.Expr Integer - --- 制約集合の単純化 --- It returns Nothing when a inconsistency is detected. -simplify :: [Lit] -> Maybe [Lit] -simplify = fmap concat . mapM f - where - f :: Lit -> Maybe [Lit] - f lit@(Pos e) = - case LA.asConst e of - Just x -> guard (x > 0) >> return [] - Nothing -> return [lit] - f lit@(Nonneg e) = - case LA.asConst e of - Just x -> guard (x >= 0) >> return [] - Nothing -> return [lit] - --- --------------------------------------------------------------------------- - -atomZ :: RelOp -> Expr Rational -> Expr Rational -> Maybe (DNF Lit) -atomZ op a b = do - (e1,c1) <- FM.termR a - (e2,c2) <- FM.termR b - let a' = c2 .*. e1 - b' = c1 .*. e2 - return $ case op of - Le -> DNF [[a' `leZ` b']] - Lt -> DNF [[a' `ltZ` b']] - Ge -> DNF [[a' `geZ` b']] - Gt -> DNF [[a' `gtZ` b']] - Eql -> eqZ a' b' - NEq -> DNF [[a' `ltZ` b'], [a' `gtZ` b']] - -leZ, ltZ, geZ, gtZ :: ExprZ -> ExprZ -> Lit --- Note that constants may be floored by division -leZ e1 e2 = Nonneg (LA.mapCoeff (`div` d) e) - where - e = e2 .-. e1 - d = abs $ gcd' [c | (c,v) <- LA.terms e, v /= LA.unitVar] -ltZ e1 e2 = (e1 .+. LA.constant 1) `leZ` e2 -geZ = flip leZ -gtZ = flip gtZ - -eqZ :: ExprZ -> ExprZ -> (DNF Lit) -eqZ e1 e2 - = if LA.coeff LA.unitVar e3 `mod` d == 0 - then DNF [[Nonneg e, Nonneg (lnegate e)]] - else false - where - e = LA.mapCoeff (`div` d) e3 - e3 = e1 .-. e2 - d = abs $ gcd' [c | (c,v) <- LA.terms e3, v /= LA.unitVar] - --- --------------------------------------------------------------------------- - -{- -(ls,us) represents -{ x | ∀(M,c)∈ls. M/c≤x, ∀(M,c)∈us. x≤M/c } --} -type BoundsZ = ([Rat],[Rat]) - -eliminate :: Var -> [Lit] -> DNF Lit -eliminate v xs = DNF [rest] .&&. boundConditionsZ bnd - where - (bnd,rest) = collectBoundsZ v xs - -collectBoundsZ :: Var -> [Lit] -> (BoundsZ,[Lit]) -collectBoundsZ v = foldr phi (([],[]),[]) - where - phi :: Lit -> (BoundsZ,[Lit]) -> (BoundsZ,[Lit]) - phi (Pos t) x = phi (Nonneg (t .-. LA.constant 1)) x - phi lit@(Nonneg t) ((ls,us),xs) = - case LA.extract v t of - (c,t') -> - case c `compare` 0 of - EQ -> ((ls, us), lit : xs) - GT -> (((lnegate t', c) : ls, us), xs) -- 0 ≤ cx + M ⇔ -M/c ≤ x - LT -> ((ls, (t', negate c) : us), xs) -- 0 ≤ cx + M ⇔ x ≤ M/-c - -boundConditionsZ :: BoundsZ -> DNF Lit -boundConditionsZ (ls,us) = DNF $ catMaybes $ map simplify $ - if isExact (ls,us) - then [cond1] - else cond1 : cond2 - where - cond1 = - [ LA.constant ((a-1)*(b-1)) `leZ` (a .*. d .-. b .*. c) - | (c,a)<-ls , (d,b)<-us ] - cond2 = - [ [(a' .*. c) `leZ` (a .*. val) | (c,a)<-ls] ++ - [(b .*. val) `geZ` (a' .*. d) | (d,b)<-us] - | not (null us) - , let m = maximum [b | (_,b)<-us] - , (c',a') <- ls - , k <- [0 .. (m*a'-a'-m) `div` m] - , let val = c' .+. LA.constant k - -- x = val / a' - -- c / a ≤ x ⇔ c / a ≤ val / a' ⇔ a' c ≤ a val - -- x ≤ d / b ⇔ val / a' ≤ d / b ⇔ b val ≤ a' d - ] - -isExact :: BoundsZ -> Bool -isExact (ls,us) = and [a==1 || b==1 | (c,a)<-ls , (d,b)<-us] - -eliminateQuantifiers :: Formula Rational -> Maybe (DNF Lit) -eliminateQuantifiers = f - where - f T = return true - f F = return false - f (Atom (Rel a op b)) = atomZ op a b - f (And a b) = liftM2 (.&&.) (f a) (f b) - f (Or a b) = liftM2 (.||.) (f a) (f b) - f (Not a) = f (pushNot a) - f (Imply a b) = f (Or (Not a) b) - f (Equiv a b) = f (And (Imply a b) (Imply b a)) - f (Forall v a) = do - dnf <- f (Exists v (pushNot a)) - return $ notB dnf - f (Exists v a) = do - dnf <- f a - return $ orB [eliminate v xs | xs <- unDNF dnf] - -solve :: Formula Rational -> SatResult Integer -solve formula = - case eliminateQuantifiers formula of - Nothing -> Unknown - Just dnf -> - case msum [solve' vs xs | xs <- unDNF dnf] of - Nothing -> Unsat - Just m -> Sat m - where - vs = IS.toList (vars formula) - -solve' :: [Var] -> [Lit] -> Maybe (Model Integer) -solve' vs xs = simplify xs >>= go vs - where - go :: [Var] -> [Lit] -> Maybe (Model Integer) - go [] [] = return IM.empty - go [] _ = mzero - go vs ys = msum (map f (unDNF (boundConditionsZ bnd))) - where - (v,vs',bnd,rest) = chooseVariable vs ys - f zs = do - model <- go vs' (zs ++ rest) - val <- pickupZ (evalBoundsZ model bnd) - return $ IM.insert v val model - -chooseVariable :: [Var] -> [Lit] -> (Var, [Var], BoundsZ, [Lit]) -chooseVariable vs xs = head $ [e | e@(_,_,bnd,_) <- table, isExact bnd] ++ table - where - table = [ (v, vs', bnd, rest) - | (v,vs') <- pickup vs, let (bnd, rest) = collectBoundsZ v xs - ] - -evalBoundsZ :: Model Integer -> BoundsZ -> IntervalZ -evalBoundsZ model (ls,us) = - foldl' intersectZ univZ $ - [ (Just (ceiling (LA.evalExpr model x % c)), Nothing) | (x,c) <- ls ] ++ - [ (Nothing, Just (floor (LA.evalExpr model x % c))) | (x,c) <- us ] - --- --------------------------------------------------------------------------- - -type IntervalZ = (Maybe Integer, Maybe Integer) - -univZ :: IntervalZ -univZ = (Nothing, Nothing) - -intersectZ :: IntervalZ -> IntervalZ -> IntervalZ -intersectZ (l1,u1) (l2,u2) = (combineMaybe max l1 l2, combineMaybe min u1 u2) - -pickupZ :: IntervalZ -> Maybe Integer -pickupZ (Nothing,Nothing) = return 0 -pickupZ (Just x, Nothing) = return x -pickupZ (Nothing, Just x) = return x -pickupZ (Just x, Just y) = if x <= y then return x else mzero - --- --------------------------------------------------------------------------- - -solveQFLA :: [LA.Atom Rational] -> VarSet -> Maybe (Model Rational) -solveQFLA cs ivs = msum [ FM.simplify xs >>= go (IS.toList rvs) | xs <- unDNF dnf ] - where - vs = vars cs - rvs = vs `IS.difference` ivs - dnf = FM.constraintsToDNF cs - - go :: [Var] -> [Lit] -> Maybe (Model Rational) - go [] xs = fmap (fmap fromIntegral) $ solve' (IS.toList ivs) xs - go (v:vs) ys = msum (map f (unDNF (FM.boundConditions bnd))) - where - (bnd, rest) = FM.collectBounds v ys - f zs = do - model <- go vs (zs ++ rest) - val <- Interval.pickup (FM.evalBounds model bnd) - return $ IM.insert v val model - --- --------------------------------------------------------------------------- - -gcd' :: [Integer] -> Integer -gcd' [] = 1 -gcd' xs = foldl1' gcd xs - -pickup :: [a] -> [(a,[a])] -pickup [] = [] -pickup (x:xs) = (x,xs) : [(y,x:ys) | (y,ys) <- pickup xs] - --- --------------------------------------------------------------------------- - -{- -7x + 12y + 31z = 17 -3x + 5y + 14z = 7 -1 ≤ x ≤ 40 --50 ≤ y ≤ 50 - -satisfiable in R -but unsatisfiable in Z --} -test1 :: Formula Rational -test1 = c1 .&&. c2 .&&. c3 .&&. c4 - where - x = Var 0 - y = Var 1 - z = Var 2 - c1 = 7*x + 12*y + 31*z .==. 17 - c2 = 3*x + 5*y + 14*z .==. 7 - c3 = 1 .<=. x .&&. x .<=. 40 - c4 = (-50) .<=. y .&&. y .<=. 50 - -test1' :: [LA.Atom Rational] -test1' = [c1, c2] ++ c3 ++ c4 - where - x = LA.var 0 - y = LA.var 1 - z = LA.var 2 - c1 = 7.*.x .+. 12.*.y .+. 31.*.z .==. LA.constant 17 - c2 = 3.*.x .+. 5.*.y .+. 14.*.z .==. LA.constant 7 - c3 = [LA.constant 1 .<=. x, x .<=. LA.constant 40] - c4 = [LA.constant (-50) .<=. y, y .<=. LA.constant 50] - -{- -27 ≤ 11x+13y ≤ 45 --10 ≤ 7x-9y ≤ 4 - -satisfiable in R -but unsatisfiable in Z --} -test2 :: Formula Rational -test2 = c1 .&&. c2 - where - x = Var 0 - y = Var 1 - t1 = 11*x + 13*y - t2 = 7*x - 9*y - c1 = 27 .<=. t1 .&&. t1 .<=. 45 - c2 = (-10) .<=. t2 .&&. t2 .<=. 4 - --- --------------------------------------------------------------------------- diff --git a/src/SAT.hs b/src/SAT.hs --- a/src/SAT.hs +++ b/src/SAT.hs @@ -38,6 +38,8 @@ -- * Problem specification , newVar + , newVars + , newVars_ , addClause , addAtLeast , addAtMost @@ -56,6 +58,7 @@ -- * Extract results , Model , model + , failedAssumptions -- * Solver configulation , RestartStrategy (..) @@ -65,6 +68,8 @@ , defaultRestartFirst , setRestartInc , defaultRestartInc + , setLearntSizeFirst + , defaultLearntSizeFirst , setLearntSizeInc , defaultLearntSizeInc , setCCMin @@ -109,6 +114,7 @@ import qualified Data.Set as Set import qualified Data.IndexedPriorityQueue as PQ import qualified Data.SeqQueue as SQ +import Data.Time import System.CPUTime import qualified System.Random as Rand import Text.Printf @@ -258,10 +264,15 @@ -- | The factor with which the restart limit is multiplied in each restart. (default 1.5) , svRestartInc :: !(IORef Double) + -- | The initial limit for learnt clauses. + , svLearntSizeFirst :: !(IORef Int) + -- | The limit for learnt clauses is multiplied with this factor periodically. (default 1.1) , svLearntSizeInc :: !(IORef Double) - , svLearntLim :: !(IORef Int) + , svLearntLim :: !(IORef Int) + , svLearntLimAdjCnt :: !(IORef Int) + , svLearntLimSeq :: !(IORef [(Int,Int)]) -- | Controls conflict clause minimization (0=none, 1=local, 2=recursive) , svCCMin :: !(IORef Int) @@ -274,6 +285,8 @@ , svRandomFreq :: !(IORef Double) , svRandomGen :: !(IORef Rand.StdGen) + + , svFailedAssumptions :: !(IORef [Lit]) } markBad :: Solver -> IO () @@ -500,17 +513,22 @@ restartFirst <- newIORef defaultRestartFirst restartInc <- newIORef defaultRestartInc learning <- newIORef defaultLearningStrategy + learntSizeFirst <- newIORef defaultLearntSizeFirst learntSizeInc <- newIORef defaultLearntSizeInc ccMin <- newIORef defaultCCMin checkModel <- newIORef False - learntLim <- newIORef undefined + learntLim <- newIORef undefined + learntLimAdjCnt <- newIORef (-1) + learntLimSeq <- newIORef undefined logger <- newIORef Nothing randfreq <- newIORef defaultRandomFreq randgen <- newIORef =<< Rand.newStdGen + failed <- newIORef [] + let solver = Solver { svOk = ok @@ -537,13 +555,17 @@ , svRestartFirst = restartFirst , svRestartInc = restartInc , svLearningStrategy = learning + , svLearntSizeFirst = learntSizeFirst , svLearntSizeInc = learntSizeInc , svCCMin = ccMin - , svLearntLim = learntLim + , svLearntLim = learntLim + , svLearntLimAdjCnt = learntLimAdjCnt + , svLearntLimSeq = learntLimSeq , svLogger = logger , svCheckModel = checkModel , svRandomFreq = randfreq , svRandomGen = randgen + , svFailedAssumptions = failed } return solver @@ -580,6 +602,14 @@ PQ.enqueue (svVarQueue s) v return v +-- |Add variables. @newVars solver n = replicateM n (newVar solver)@ +newVars :: Solver -> Int -> IO [Var] +newVars s n = replicateM n (newVar s) + +-- |Add variables. @newVars_ solver n >> return () = newVars_ solver n@ +newVars_ :: Solver -> Int -> IO () +newVars_ s n = replicateM_ n (newVar s) + -- |Add a clause to the solver. addClause :: Solver -> Clause -> IO () addClause solver lits = do @@ -759,6 +789,7 @@ solve_ solver = do log solver "Solving starts ..." writeIORef (svModel solver) Nothing + writeIORef (svFailedAssumptions solver) [] ok <- readIORef (svOk solver) if not ok @@ -773,27 +804,27 @@ restartInc <- readIORef (svRestartInc solver) let restartSeq = mkRestartSeq restartStrategy restartFirst restartInc - learntSizeInc <- readIORef (svLearntSizeInc solver) - nc <- nClauses solver - nv <- nVars solver - let learntSizeSeq = iterate (ceiling . (learntSizeInc*) . fromIntegral) (max ((nc + nv) `div` 3) 16) - let learntSizeAdjSeq = iterate (\x -> (x * 3) `div` 2) (100::Int) - nextLearntSize <- gen learntSizeSeq - nextLearntSizeAdj <- gen learntSizeAdjSeq - - learntSizeAdjCnt <- newIORef undefined let learntSizeAdj = do - size <- nextLearntSize - adj <- nextLearntSizeAdj + (size,adj) <- shift (svLearntLimSeq solver) writeIORef (svLearntLim solver) size - writeIORef learntSizeAdjCnt adj + writeIORef (svLearntLimAdjCnt solver) adj onConflict = do - cnt <- readIORef learntSizeAdjCnt + cnt <- readIORef (svLearntLimAdjCnt solver) if (cnt==0) then learntSizeAdj - else writeIORef (learntSizeAdjCnt) $! cnt-1 + else writeIORef (svLearntLimAdjCnt solver) $! cnt-1 - learntSizeAdj + cnt <- readIORef (svLearntLimAdjCnt solver) + when (cnt == -1) $ do + learntSizeFirst <- readIORef (svLearntSizeFirst solver) + learntSizeInc <- readIORef (svLearntSizeInc solver) + nc <- nClauses solver + nv <- nVars solver + let initialLearntLim = if learntSizeFirst > 0 then learntSizeFirst else max ((nc + nv) `div` 3) 16 + learntSizeSeq = iterate (ceiling . (learntSizeInc*) . fromIntegral) initialLearntLim + learntSizeAdjSeq = iterate (\x -> (x * 3) `div` 2) (100::Int) + writeIORef (svLearntLimSeq solver) (zip learntSizeSeq learntSizeAdjSeq) + learntSizeAdj let loop [] = error "solve_: should not happen" loop (conflict_lim:rs) = do @@ -805,9 +836,11 @@ backtrackTo solver levelRoot loop rs - start <- getCPUTime + startCPU <- getCPUTime + startWC <- getCurrentTime result <- loop restartSeq - end <- getCPUTime + endCPU <- getCPUTime + endWC <- getCurrentTime when result $ do checkModel <- readIORef (svCheckModel solver) @@ -818,7 +851,8 @@ when debugMode $ dumpVarActivity solver when debugMode $ dumpClaActivity solver - (log solver . printf "solving time = %.3fs") (fromIntegral (end - start) / 10^(12::Int) :: Double) + (log solver . printf "#cpu_time = %.3fs") (fromIntegral (endCPU - startCPU) / 10^(12::Int) :: Double) + (log solver . printf "#wall_clock_time = %.3fs") (realToFrac (endWC `diffUTCTime` startWC) :: Double) (log solver . printf "#decision = %d") =<< readIORef (svNDecision solver) (log solver . printf "#random_decision = %d") =<< readIORef (svNRandomDecision solver) (log solver . printf "#conflict = %d") =<< readIORef (svNConflict solver) @@ -837,6 +871,9 @@ case conflict of Nothing -> do + lv <- readIORef (svLevel solver) + when (lv == levelRoot) $ simplify solver + n <- nLearnt solver m <- nAssigns solver learnt_lim <- readIORef (svLearntLim solver) @@ -866,7 +903,7 @@ return $ printf "conflict(level=%d): %s" d str if d == levelRoot - then return (Just False) + then markBad solver >> return (Just False) else if conflict_lim >= 0 && c+1 >= conflict_lim then return Nothing else do @@ -890,8 +927,10 @@ -- dummy decision level modifyIORef' (svLevel solver) (+1) go - else if val == lFalse then + else if val == lFalse then do -- conflict with assumption + core <- analyzeFinal solver l + writeIORef (svFailedAssumptions solver) core return Nothing else return (Just l) @@ -956,6 +995,30 @@ m <- readIORef (svModel solver) return (fromJust m) +-- | After 'solveWith' returns False, it returns a set of assumptions +-- that leads to contradiction. In particular, if it returns an empty +-- set, the problem is unsatisiable without any assumptions. +failedAssumptions :: Solver -> IO [Lit] +failedAssumptions solver = readIORef (svFailedAssumptions solver) + +-- | Simplify the clause database according to the current top-level assigment. +simplify :: Solver -> IO () +simplify solver = do + xs <- readIORef (svClauseDB solver) + let loop [] rs !n = return (rs,n) + loop (y:ys) rs !n = do + b1 <- isSatisfied solver y + b2 <- isLocked solver y + if b1 && not b2 + then do + detach solver y + loop ys rs (n+1) + else loop ys (y:rs) n + (ys,n) <- loop xs [] (0::Int) + when (n > 0) $ + log solver $ printf "simplify: %d satisfied constraints are removed" n + writeIORef (svClauseDB solver) ys + {-------------------------------------------------------------------- Parameter settings. --------------------------------------------------------------------} @@ -994,6 +1057,14 @@ defaultLearningStrategy :: LearningStrategy defaultLearningStrategy = LearningClause +-- | The initial limit for learnt clauses. +setLearntSizeFirst :: Solver -> Int -> IO () +setLearntSizeFirst solver !x = writeIORef (svLearntSizeFirst solver) x + +-- | default value for @LearntSizeFirst@. +defaultLearntSizeFirst :: Int +defaultLearntSizeFirst = -1 + -- | The limit for learnt clauses is multiplied with this factor each restart. (default 1.1) setLearntSizeInc :: Solver -> Double -> IO () setLearntSizeInc solver !r = writeIORef (svLearntSizeInc solver) r @@ -1072,23 +1143,23 @@ m <- PQ.dequeue vqueue case m of Nothing -> return litUndef - Just var -> do - val <- varValue solver var - if val /= lUndef + Just var2 -> do + val2 <- varValue solver var2 + if val2 /= lUndef then loop - else return var - var <- + else return var2 + var2 <- if var==litUndef then loop else return var - if var==litUndef + if var2==litUndef then return litUndef else do - vd <- varData solver var + vd <- varData solver var2 -- TODO: random polarity p <- readIORef (vdPolarity vd) - return $! literal var p + return $! literal var2 p decide :: Solver -> Lit -> IO () decide solver !lit = do @@ -1198,6 +1269,30 @@ _:(_,lv):_ -> lv return (map fst xs, level) +-- { p } ∪ { pにfalseを割り当てる原因のassumption } +analyzeFinal :: Solver -> Lit -> IO [Lit] +analyzeFinal solver p = do + lits <- readIORef (svTrail solver) + let go :: [Lit] -> VarSet -> [Lit] -> IO [Lit] + go [] _ result = return result + go (l:ls) seen result = do + lv <- litLevel solver l + if lv == levelRoot then + return result + else if litVar l `IS.member` seen then do + r <- varReason solver (litVar l) + case r of + Nothing -> do + let seen' = IS.delete (litVar l) seen + go ls seen' (l : result) + Just constr -> do + c <- reasonOf solver constr (Just l) + let seen' = IS.delete (litVar l) seen `IS.union` IS.fromList [litVar l2 | l2 <- c] + go ls seen' result + else + go ls seen result + go lits (IS.singleton (litVar p)) [p] + analyzeConflictHybrid :: Constraint c => Solver -> c -> IO (Clause, Level, ([(Integer,Lit)], Integer)) analyzeConflictHybrid solver constr = do d <- readIORef (svLevel solver) @@ -2120,13 +2215,11 @@ x <- readIORef ref writeIORef ref $! f x -gen :: [a] -> IO (IO a) -gen xs = do - ref <- newIORef xs - return $ do - (y:ys) <- readIORef ref - writeIORef ref ys - return y +shift :: IORef [a] -> IO a +shift ref = do + (x:xs) <- readIORef ref + writeIORef ref xs + return x {-------------------------------------------------------------------- debug diff --git a/src/SAT/CAMUS.hs b/src/SAT/CAMUS.hs new file mode 100644 --- /dev/null +++ b/src/SAT/CAMUS.hs @@ -0,0 +1,128 @@ +----------------------------------------------------------------------------- +-- | +-- Module : SAT.CAMUS +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : portable +-- +----------------------------------------------------------------------------- +module SAT.CAMUS + ( MUS + , MCS + , Options (..) + , defaultOptions + , allMCSAssumptions + , allMUSAssumptions + , enumMCSAssumptions + , hittingSetDual + ) where + +import Control.Monad +import Data.Array.IArray +import qualified Data.IntSet as IS +import Data.List +import Data.IORef +import SAT + +type MUS = [Lit] +type MCS = [Lit] + +-- | Options for 'enumMCSAssumptions', 'allMCSAssumptions', 'allMUSAssumptions' +data Options + = Options + { optLogger :: String -> IO () + , optCallback :: MCS -> IO () + } + +-- | default 'Options' value +defaultOptions :: Options +defaultOptions = + Options + { optLogger = \_ -> return () + , optCallback = \_ -> return () + } + +enumMCSAssumptions :: SAT.Solver -> [Lit] -> Options -> IO () +enumMCSAssumptions solver sels opt = loop 1 + where + log :: String -> IO () + log = optLogger opt + + callback :: MCS -> IO () + callback = optCallback opt + + loop :: Integer -> IO () + loop k = do + log $ "CAMUS: k = " ++ show k + ret <- SAT.solve solver + when ret $ do + vk <- SAT.newVar solver + SAT.addPBAtMostSoft solver vk [(1,-sel) | sel <- sels] k + let loop2 = do + ret2 <- SAT.solveWith solver [vk] + when ret2 $ do + m <- SAT.model solver + let mcs = [sel | sel <- sels, not (evalLit sel m)] + callback mcs + SAT.addClause solver mcs + loop2 + loop2 + SAT.addClause solver [-vk] + loop (k+1) + +evalLit :: Lit -> Model -> Bool +evalLit l m = m ! SAT.litVar l == SAT.litPolarity l + +allMCSAssumptions :: SAT.Solver -> [Lit] -> Options -> IO [MCS] +allMCSAssumptions solver sels opt = do + ref <- newIORef [] + let opt2 = + opt + { optCallback = \mcs -> do + modifyIORef ref (mcs:) + optCallback opt mcs + } + enumMCSAssumptions solver sels opt2 + readIORef ref + +allMUSAssumptions :: SAT.Solver -> [Lit] -> Options -> IO [MCS] +allMUSAssumptions solver sels opt = do + log "CAMUS: MCS enumeration begins" + mcses <- allMCSAssumptions solver sels opt + log "CAMUS: MCS enumeration done" + return $ hittingSetDual mcses + where + log :: String -> IO () + log = optLogger opt + +-- FIXME: remove nub +hittingSetDual :: [MCS] -> [MUS] +hittingSetDual mcses = nub $ f (map IS.fromList mcses) [] + where + f :: [IS.IntSet] -> [Int] -> [MUS] + f [] mus = return mus + f mcses mus = do + sel <- IS.toList $ IS.unions mcses + let mus' = sel:mus + mcs <- mcses + guard $ sel `IS.member` mcs + let mcses' = propagateChoice mcses sel mcs + f mcses' mus' + +propagateChoice :: [IS.IntSet] -> Lit -> IS.IntSet -> [IS.IntSet] +propagateChoice mcses sel mcs = zs + where + xs = filter (sel `IS.notMember`) mcses + ys = map (IS.filter (sel <) . (`IS.difference` mcs)) xs + zs = maintainNoSupersets ys + +maintainNoSupersets :: [IS.IntSet] -> [IS.IntSet] +maintainNoSupersets xss = go [] xss + where + go yss [] = yss + go yss (xs:xss) = go (xs : filter p yss) (filter p xss) + where + p zs = not (xs `IS.isSubsetOf` zs) diff --git a/src/SAT/Integer.hs b/src/SAT/Integer.hs --- a/src/SAT/Integer.hs +++ b/src/SAT/Integer.hs @@ -1,61 +1,89 @@ {-# LANGUAGE MultiParamTypeClasses #-} -module SAT.Integer where +module SAT.Integer + ( Expr (..) + , newVar + , linearize + , addConstraint + , addConstraintSoft + , eval + ) where import Control.Monad import Data.Array.IArray import Text.Printf -import SAT + +import Data.ArithRel import Data.Linear +import qualified SAT +import qualified SAT.TseitinEncoder as TseitinEncoder -data Expr = Expr [(Integer, SAT.Lit)] Integer +data Expr = Expr [(Integer, [SAT.Lit])] newVar :: SAT.Solver -> Integer -> Integer -> IO Expr newVar solver lo hi = do when (lo > hi) $ error $ printf "SAT.Integer.newVar: inconsistent bounds given [%d, %d]" lo hi let hi' = hi - lo bitWidth = head $ [w | w <- [1..], let mx = 2 ^ w - 1, hi' <= mx] - vs <- replicateM bitWidth (SAT.newVar solver) + vs <- SAT.newVars solver bitWidth let xs = zip (iterate (2*) 1) vs SAT.addPBAtMost solver xs hi' - return $ Expr xs lo - -constant :: Integer -> Expr -constant c = Expr [] c + return $ Expr ((lo,[]) : [(c,[x]) | (c,x) <- xs]) instance Module Integer Expr where - n .*. Expr xs c = Expr [(n*m,lit) | (m,lit) <- xs] (n*c) - Expr xs1 c1 .+. Expr xs2 c2 = Expr (xs1++xs2) (c1+c2) - lzero = Expr [] 0 - -addLe :: SAT.Solver -> Expr -> Expr -> IO () -addLe solver lhs rhs = do - let Expr xs c = lhs .-. rhs - SAT.addPBAtMost solver xs (-c) - -addGe :: SAT.Solver -> Expr -> Expr -> IO () -addGe solver lhs rhs = do - let Expr xs c = lhs .-. rhs - SAT.addPBAtLeast solver xs (-c) + n .*. Expr xs = Expr [(n*m,lits) | (m,lits) <- xs] + Expr xs1 .+. Expr xs2 = Expr (xs1++xs2) + lzero = Expr [] -addEq :: SAT.Solver -> Expr -> Expr -> IO () -addEq solver lhs rhs = do - let Expr xs c = lhs .-. rhs - SAT.addPBExactly solver xs (-c) +instance Num Expr where + Expr xs1 + Expr xs2 = Expr (xs1++xs2) + Expr xs1 * Expr xs2 = Expr [(c1*c2, lits1++lits2) | (c1,lits1) <- xs1, (c2,lits2) <- xs2] + negate (Expr xs) = Expr [(-c,lits) | (c,lits) <- xs] + abs = id + signum _ = 1 + fromInteger c = Expr [(c,[])] -addLeSoft :: SAT.Solver -> SAT.Lit -> Expr -> Expr -> IO () -addLeSoft solver ind lhs rhs = do - let Expr xs c = lhs .-. rhs - SAT.addPBAtMostSoft solver ind xs (-c) +linearize :: TseitinEncoder.Encoder -> Expr -> IO ([(Integer,SAT.Lit)], Integer) +linearize enc (Expr xs) = do + let ys = [(c,lits) | (c,lits@(_:_)) <- xs] + c = sum [c | (c,[]) <- xs] + zs <- forM ys $ \(c,lits) -> do + l <- TseitinEncoder.encodeConj enc lits + return (c,l) + return (zs, c) -addGeSoft :: SAT.Solver -> SAT.Lit -> Expr -> Expr -> IO () -addGeSoft solver ind lhs rhs = do - let Expr xs c = lhs .-. rhs - SAT.addPBAtLeastSoft solver ind xs (-c) +addConstraint :: TseitinEncoder.Encoder -> Rel Expr -> IO () +addConstraint enc (Rel lhs op rhs) = do + let solver = TseitinEncoder.encSolver enc + (lhs2,c) <- linearize enc (lhs - rhs) + let rhs2 = -c + case op of + Le -> SAT.addPBAtMost solver lhs2 rhs2 + Lt -> SAT.addPBAtMost solver lhs2 (rhs2-1) + Ge -> SAT.addPBAtLeast solver lhs2 rhs2 + Gt -> SAT.addPBAtLeast solver lhs2 (rhs2+1) + Eql -> SAT.addPBExactly solver lhs2 rhs2 + NEq -> do + sel <- SAT.newVar solver + SAT.addPBAtLeastSoft solver sel lhs2 (rhs2+1) + SAT.addPBAtMostSoft solver (-sel) lhs2 (rhs2-1) -addEqSoft :: SAT.Solver -> SAT.Lit -> Expr -> Expr -> IO () -addEqSoft solver ind lhs rhs = do - let Expr xs c = lhs .-. rhs - SAT.addPBExactlySoft solver ind xs (-c) +addConstraintSoft :: TseitinEncoder.Encoder -> SAT.Lit -> Rel Expr -> IO () +addConstraintSoft enc sel (Rel lhs op rhs) = do + let solver = TseitinEncoder.encSolver enc + (lhs2,c) <- linearize enc (lhs - rhs) + let rhs2 = -c + case op of + Le -> SAT.addPBAtMostSoft solver sel lhs2 rhs2 + Lt -> SAT.addPBAtMostSoft solver sel lhs2 (rhs2-1) + Ge -> SAT.addPBAtLeastSoft solver sel lhs2 rhs2 + Gt -> SAT.addPBAtLeastSoft solver sel lhs2 (rhs2+1) + Eql -> SAT.addPBExactlySoft solver sel lhs2 rhs2 + NEq -> do + sel2 <- SAT.newVar solver + sel3 <- TseitinEncoder.encodeConj enc [sel,sel2] + sel4 <- TseitinEncoder.encodeConj enc [sel,-sel2] + SAT.addPBAtLeastSoft solver sel3 lhs2 (rhs2+1) + SAT.addPBAtMostSoft solver sel4 lhs2 (rhs2-1) eval :: SAT.Model -> Expr -> Integer -eval m (Expr ts c) = sum [if m ! SAT.litVar lit == SAT.litPolarity lit then n else 0 | (n,lit) <- ts] + c +eval m (Expr ts) = sum [if and [m ! SAT.litVar lit == SAT.litPolarity lit | lit <- lits] then n else 0 | (n,lits) <- ts] diff --git a/src/SAT/MUS.hs b/src/SAT/MUS.hs new file mode 100644 --- /dev/null +++ b/src/SAT/MUS.hs @@ -0,0 +1,91 @@ +----------------------------------------------------------------------------- +-- | +-- Module : SAT.MUS +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : non-portable +-- +-- Minimal Unsatifiable Subset (MUS) Finder +-- +----------------------------------------------------------------------------- +module SAT.MUS + ( Options (..) + , defaultOptions + , findMUSAssumptions + ) where + +import Control.Monad +import Data.List +import qualified Data.IntSet as IS +import SAT + +-- | Options for 'findMUSAssumptions' function +data Options + = Options + { optLogger :: String -> IO () + , optUpdater :: [Lit] -> IO () + , optLitPrinter :: Lit -> String + } + +-- | default 'Options' value +defaultOptions :: Options +defaultOptions = + Options + { optLogger = \_ -> return () + , optUpdater = \_ -> return () + , optLitPrinter = show + } + +-- | Find a minimal set of assumptions that causes a conflict. +-- Initial set of assumptions is taken from 'SAT.failedAssumptions'. +findMUSAssumptions + :: SAT.Solver + -> Options + -> IO [Lit] +findMUSAssumptions solver opt = do + log "computing a minimal unsatisfiable core" + core <- liftM IS.fromList $ SAT.failedAssumptions solver + update $ IS.toList core + log $ "core = " ++ showLits core + mus <- loop core IS.empty + return $ IS.toList mus + + where + log :: String -> IO () + log = optLogger opt + + update :: [Lit] -> IO () + update = optUpdater opt + + showLit :: Lit -> String + showLit = optLitPrinter opt + + showLits :: IS.IntSet -> String + showLits ls = "{" ++ intercalate ", " (map showLit (IS.toList ls)) ++ "}" + + loop :: IS.IntSet -> IS.IntSet -> IO IS.IntSet + loop ls1 fixed = do + case IS.minView ls1 of + Nothing -> do + log $ "found a minimal unsatisfiable core" + return fixed + Just (l,ls) -> do + log $ "trying to remove " ++ showLit l + ret <- SAT.solveWith solver (IS.toList ls) + if not ret + then do + ls2 <- liftM IS.fromList $ SAT.failedAssumptions solver + let removed = ls1 `IS.difference` ls2 + log $ "successed to remove " ++ showLits removed + log $ "new core = " ++ showLits (ls2 `IS.union` fixed) + update $ IS.toList ls2 + forM_ (IS.toList removed) $ \l -> + SAT.addClause solver [-l] + loop ls2 fixed + else do + log $ "failed to remove " ++ showLit l + SAT.addClause solver [l] + loop ls (IS.insert l fixed) diff --git a/src/SAT/PBO.hs b/src/SAT/PBO.hs new file mode 100644 --- /dev/null +++ b/src/SAT/PBO.hs @@ -0,0 +1,128 @@ +{-# OPTIONS_GHC -Wall -fno-warn-unused-do-bind #-} +----------------------------------------------------------------------------- +-- | +-- Module : SAT.PBO +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : portable +-- +-- Pseudo-Boolean Optimization (PBO) Solver +-- +----------------------------------------------------------------------------- +module SAT.PBO where + +import Control.Monad +import Data.List +import Data.Ord +import Text.Printf +import SAT +import SAT.Types + +data SearchStrategy + = LinearSearch + | BinarySearch +-- 'nothaddock' is inserted not to confuse haddock + -- nothaddock | AdaptiveSearch + +data Options + = Options + { optLogger :: String -> IO () + , optUpdater :: Model -> Integer -> IO () + , optObjFunVarsHeuristics :: Bool + , optSearchStrategy :: SearchStrategy + } + +defaultOptions :: Options +defaultOptions + = Options + { optLogger = \_ -> return () + , optUpdater = \_ _ -> return () + , optObjFunVarsHeuristics = True + , optSearchStrategy = LinearSearch + } + +minimize :: Solver -> [(Integer, Lit)] -> Options -> IO (Maybe Model) +minimize solver obj opt = do + when (optObjFunVarsHeuristics opt) $ do + forM_ obj $ \(c,l) -> do + let p = if c > 0 then not (litPolarity l) else litPolarity l + setVarPolarity solver (litVar l) p + forM_ (zip [1..] (map snd (sortBy (comparing fst) [(abs c, l) | (c,l) <- obj]))) $ \(n,l) -> do + replicateM n $ varBumpActivity solver (litVar l) + + result <- solve solver + if not result then + return Nothing + else + case optSearchStrategy opt of + LinearSearch -> liftM Just linSearch + BinarySearch -> liftM Just binSearch + + where + logIO :: String -> IO () + logIO = optLogger opt + + update :: Model -> Integer -> IO () + update = optUpdater opt + + linSearch :: IO Model + linSearch = do + m <- model solver + let v = pbEval m obj + update m v + addPBAtMost solver obj (v - 1) + result <- solve solver + if result + then linSearch + else return m + + binSearch :: IO Model + binSearch = do +{- + logIO $ printf "Binary Search: minimizing %s \n" $ + intercalate " " + [c' ++ " " ++ l' + | (c,l) <- obj + , let c' = if c < 0 then show c else "+" ++ show c + , let l' = (if l < 0 then "~" else "") ++ "x" ++ show (litVar l) + ] +-} + m0 <- model solver + let v0 = pbEval m0 obj + update m0 v0 + let ub0 = v0 - 1 + lb0 = pbLowerBound obj + addPBAtMost solver obj ub0 + + let loop lb ub m | ub < lb = return m + loop lb ub m = do + let mid = (lb + ub) `div` 2 + logIO $ printf "Binary Search: %d <= obj <= %d; guessing obj <= %d" lb ub mid + sel <- newVar solver + addPBAtMostSoft solver sel obj mid + ret <- solveWith solver [sel] + if ret + then do + m2 <- model solver + let v = pbEval m2 obj + update m2 v + -- deactivating temporary constraint + -- FIXME: 本来は制約の削除をしたい + addClause solver [-sel] + let ub' = v - 1 + logIO $ printf "Binary Search: updating upper bound: %d -> %d" ub ub' + addPBAtMost solver obj ub' + loop lb ub' m2 + else do + -- deactivating temporary constraint + -- FIXME: 本来は制約の削除をしたい + addClause solver [-sel] + let lb' = mid + 1 + logIO $ printf "Binary Search: updating lower bound: %d -> %d" lb lb' + addPBAtLeast solver obj lb' + loop lb' ub m + + loop lb0 ub0 m0 diff --git a/src/SAT/Printer.hs b/src/SAT/Printer.hs --- a/src/SAT/Printer.hs +++ b/src/SAT/Printer.hs @@ -15,6 +15,7 @@ ( satPrintModel , maxsatPrintModel , pbPrintModel + , musPrintSol ) where import Control.Monad @@ -63,6 +64,15 @@ forM_ xs $ \(var,val) -> hPutStr h (" " ++ (if val then "" else "-") ++ "x" ++ show var) hPutStrLn h "" hFlush stdout + +musPrintSol :: Handle -> [Int] -> IO () +musPrintSol h is = do + forM_ (split 10 is) $ \xs -> do + hPutStr h "v" + forM_ xs $ \i -> hPutStr h (' ': show i) + hPutStrLn h "" + hPutStrLn h "v 0" + hFlush h -- ------------------------------------------------------------------------ diff --git a/src/SAT/TseitinEncoder.hs b/src/SAT/TseitinEncoder.hs --- a/src/SAT/TseitinEncoder.hs +++ b/src/SAT/TseitinEncoder.hs @@ -39,6 +39,7 @@ Encoder , newEncoder , setUsePB + , encSolver -- * Encoding of boolean formula , Formula (..) diff --git a/src/SAT/Types.hs b/src/SAT/Types.hs --- a/src/SAT/Types.hs +++ b/src/SAT/Types.hs @@ -3,6 +3,7 @@ ( -- * Variable Var + , VarSet , VarMap , validVar @@ -51,6 +52,7 @@ -- | Variable is represented as positive integers (DIMACS format). type Var = Int +type VarSet = IS.IntSet type VarMap = IM.IntMap {-# INLINE validVar #-} diff --git a/src/Simplex.hs b/src/Simplex.hs deleted file mode 100644 --- a/src/Simplex.hs +++ /dev/null @@ -1,307 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables #-} -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : Simplex --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (ScopedTypeVariables) --- --- Naïve implementation of Simplex method --- --- Reference: --- --- * --- ------------------------------------------------------------------------------ -module Simplex - ( module Data.OptDir - , Tableau - , RowIndex - , ColIndex - , Row - , PivotResult - , objRow - , pivot - , lookupRow - , setRow - , setObjFun - , currentObjValue - , simplex - , dualSimplex - , phaseI - , toCSV - ) where - -import Data.Ord -import Data.List (intersperse, minimumBy, foldl') -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS -import Data.OptDir -import Control.Exception - -import Data.Expr -import Data.Linear -import qualified Data.LA as LA - --- --------------------------------------------------------------------------- - -type Tableau r = VarMap (Row r) -{- -tbl ! v == (m, val) -==> -var v .+. m .==. constant val --} - -type RowIndex = Int -type ColIndex = Int -type Row r = (VarMap r, r) -data PivotResult r = PivotUnbounded | PivotFinished | PivotSuccess (Tableau r) - deriving (Show, Eq, Ord) - -objRow :: RowIndex -objRow = -1 - -pivot :: (Fractional r, Eq r) => RowIndex -> ColIndex -> Tableau r -> Tableau r -{-# INLINE pivot #-} -{-# SPECIALIZE pivot :: RowIndex -> ColIndex -> Tableau Rational -> Tableau Rational #-} -{-# SPECIALIZE pivot :: RowIndex -> ColIndex -> Tableau Double -> Tableau Double #-} -pivot r s tbl = - assert (validTableau tbl) $ -- precondition - assert (validTableau tbl') $ -- postcondition - tbl' - where - tbl' = IM.insert s row_s $ IM.map f $ IM.delete r $ tbl - f orig@(row_i, row_i_val) = - case IM.lookup s row_i of - Nothing -> orig - Just c -> - ( IM.filter (0/=) $ IM.unionWith (+) (IM.delete s row_i) (IM.map (negate c *) row_r') - , row_i_val - c*row_r_val' - ) - (row_r, row_r_val) = lookupRow r tbl - a_rs = row_r IM.! s - row_r' = IM.map (/ a_rs) $ IM.insert r 1 $ IM.delete s row_r - row_r_val' = row_r_val / a_rs - row_s = (row_r', row_r_val') - -lookupRow :: RowIndex -> Tableau r -> Row r -lookupRow r m = m IM.! r - --- 行の基底変数の列が0になるように変形 -normalizeRow :: (Num r, Eq r) => Tableau r -> Row r -> Row r -normalizeRow a (row0,val0) = obj' - where - obj' = g $ foldl' f (IM.empty, val0) $ - [ case IM.lookup j a of - Nothing -> (IM.singleton j x, 0) - Just (row,val) -> (IM.map ((-x)*) (IM.delete j row), -x*val) - | (j,x) <- IM.toList row0 ] - f (m1,v1) (m2,v2) = (IM.unionWith (+) m1 m2, v1+v2) - g (m,v) = (IM.filter (0/=) m, v) - -setRow :: (Num r, Eq r) => RowIndex -> Tableau r -> Row r -> Tableau r -setRow i tbl row = assert (validTableau tbl) $ assert (validTableau tbl') $ tbl' - where - tbl' = IM.insert i (normalizeRow tbl row) tbl - -setObjFun :: (Num r, Eq r) => Tableau r -> LA.Expr r -> Tableau r -setObjFun tbl e = setRow objRow tbl row - where - row = - case LA.extract LA.unitVar e of - (c, e') -> (LA.coeffMap (lnegate e'), c) - -copyObjRow :: (Num r, Eq r) => Tableau r -> Tableau r -> Tableau r -copyObjRow from to = - case IM.lookup objRow from of - Nothing -> IM.delete objRow to - Just row -> setRow objRow to row - -currentObjValue :: (Num r, Eq r) => Tableau r -> r -currentObjValue = snd . lookupRow objRow - -validTableau :: Tableau r -> Bool -validTableau tbl = - and [v `IM.notMember` m | (v, (m,_)) <- IM.toList tbl, v /= objRow] && - and [IS.null (IM.keysSet m `IS.intersection` vs) | (m,_) <- IM.elems tbl'] - where - tbl' = IM.delete objRow tbl - vs = IM.keysSet tbl' - -isFeasible :: Real r => Tableau r -> Bool -isFeasible tbl = - and [val >= 0 | (v, (_,val)) <- IM.toList tbl, v /= objRow] - -isOptimal :: Real r => OptDir -> Tableau r -> Bool -isOptimal optdir tbl = - and [not (cmp cj) | cj <- IM.elems (fst (lookupRow objRow tbl))] - where - cmp = case optdir of - OptMin -> (0<) - OptMax -> (0>) - -isImproving :: Real r => OptDir -> Tableau r -> Tableau r -> Bool -isImproving OptMin from to = currentObjValue to <= currentObjValue from -isImproving OptMax from to = currentObjValue to >= currentObjValue from - --- --------------------------------------------------------------------------- --- primal simplex - -simplex :: (Real r, Fractional r) => OptDir -> Tableau r -> (Bool, Tableau r) -{-# SPECIALIZE simplex :: OptDir -> Tableau Rational -> (Bool, Tableau Rational) #-} -{-# SPECIALIZE simplex :: OptDir -> Tableau Double -> (Bool, Tableau Double) #-} -simplex optdir = go - where - go tbl = assert (isFeasible tbl) $ - case primalPivot optdir tbl of - PivotFinished -> assert (isOptimal optdir tbl) (True, tbl) - PivotUnbounded -> (False, tbl) - PivotSuccess tbl' -> assert (isImproving optdir tbl tbl') $ go tbl' - -primalPivot :: (Real r, Fractional r) => OptDir -> Tableau r -> PivotResult r -{-# INLINE primalPivot #-} -primalPivot optdir tbl - | null cs = PivotFinished - | null rs = PivotUnbounded - | otherwise = PivotSuccess (pivot r s tbl) - where - cmp = case optdir of - OptMin -> (0<) - OptMax -> (0>) - cs = [(j,cj) | (j,cj) <- IM.toList (fst (lookupRow objRow tbl)), cmp cj] - -- smallest subscript rule - s = fst $ head cs - -- classical rule - --s = fst $ (if optdir==OptMin then maximumBy else minimumBy) (compare `on` snd) cs - rs = [ (i, y_i0 / y_is) - | (i, (row_i, y_i0)) <- IM.toList tbl, i /= objRow - , let y_is = IM.findWithDefault 0 s row_i, y_is > 0 - ] - r = fst $ minimumBy (comparing snd) rs - --- --------------------------------------------------------------------------- --- dual simplex - -dualSimplex :: (Real r, Fractional r) => OptDir -> Tableau r -> (Bool, Tableau r) -{-# SPECIALIZE dualSimplex :: OptDir -> Tableau Rational -> (Bool, Tableau Rational) #-} -{-# SPECIALIZE dualSimplex :: OptDir -> Tableau Double -> (Bool, Tableau Double) #-} -dualSimplex optdir = go - where - go tbl = assert (isOptimal optdir tbl) $ - case dualPivot optdir tbl of - PivotFinished -> assert (isFeasible tbl) $ (True, tbl) - PivotUnbounded -> (False, tbl) - PivotSuccess tbl' -> assert (isImproving optdir tbl' tbl) $ go tbl' - -dualPivot :: (Real r, Fractional r) => OptDir -> Tableau r -> PivotResult r -{-# INLINE dualPivot #-} -dualPivot optdir tbl - | null rs = PivotFinished - | null cs = PivotUnbounded - | otherwise = PivotSuccess (pivot r s tbl) - where - rs = [(i, row_i) | (i, (row_i, y_i0)) <- IM.toList tbl, i /= objRow, 0 > y_i0] - (r, row_r) = head rs - cs = [ (j, if optdir==OptMin then y_0j / y_rj else - y_0j / y_rj) - | (j, y_rj) <- IM.toList row_r - , y_rj < 0 - , let y_0j = IM.findWithDefault 0 j obj - ] - s = fst $ minimumBy (comparing snd) cs - (obj,_) = lookupRow objRow tbl - --- --------------------------------------------------------------------------- --- phase I of the two-phased method - -phaseI :: (Real r, Fractional r) => Tableau r -> VarSet -> (Bool, Tableau r) -{-# SPECIALIZE phaseI :: Tableau Rational -> VarSet -> (Bool, Tableau Rational) #-} -{-# SPECIALIZE phaseI :: Tableau Double -> VarSet -> (Bool, Tableau Double) #-} -phaseI tbl avs - | currentObjValue tbl1' /= 0 = (False, tbl1') - | otherwise = (True, copyObjRow tbl $ removeArtificialVariables avs $ tbl1') - where - optdir = OptMax - tbl1 = setObjFun tbl $ lnegate $ lsum [LA.var v | v <- IS.toList avs] - tbl1' = go tbl1 - go tbl2 - | currentObjValue tbl2 == 0 = tbl2 - | otherwise = - case primalPivot optdir tbl2 of - PivotSuccess tbl2' -> assert (isImproving optdir tbl2 tbl2') $ go tbl2' - PivotFinished -> assert (isOptimal optdir tbl2) tbl2 - PivotUnbounded -> error "phaseI: should not happen" - --- post-processing of phaseI --- pivotを使ってartificial variablesを基底から除いて、削除 -removeArtificialVariables :: (Real r, Fractional r) => VarSet -> Tableau r -> Tableau r -removeArtificialVariables avs tbl0 = tbl2 - where - tbl1 = foldl' f (IM.delete objRow tbl0) (IS.toList avs) - tbl2 = IM.map (\(row,val) -> (IM.filterWithKey (\j _ -> j `IS.notMember` avs) row, val)) tbl1 - f tbl i = - case IM.lookup i tbl of - Nothing -> tbl - Just row -> - case [j | (j,c) <- IM.toList (fst row), c /= 0, j `IS.notMember` avs] of - [] -> IM.delete i tbl - j:_ -> pivot i j tbl - - --- --------------------------------------------------------------------------- - -toCSV :: (Num r, Eq r, Show r) => (r -> String) -> Tableau r -> String -toCSV showCell tbl = unlines . map (concat . intersperse ",") $ header : body - where - header :: [String] - header = "" : map colName cols ++ [""] - - body :: [[String]] - body = [showRow i (Simplex.lookupRow i tbl) | i <- rows] - - rows :: [Simplex.RowIndex] - rows = IM.keys (IM.delete Simplex.objRow tbl) ++ [Simplex.objRow] - - cols :: [Simplex.ColIndex] - cols = [0..colMax] - where - colMax = maximum (-1 : [c | (row, _) <- IM.elems tbl, c <- IM.keys row]) - - rowName :: RowIndex -> String - rowName i = if i==Simplex.objRow then "obj" else "x" ++ show i - - colName :: ColIndex -> String - colName j = "x" ++ show j - - showRow i (row, row_val) = rowName i : [showCell (IM.findWithDefault 0 j row') | j <- cols] ++ [showCell row_val] - where row' = IM.insert i 1 row - --- --------------------------------------------------------------------------- - --- 退化して巡回の起こるKuhnの7変数3制約の例 - -kuhn_7_3 :: Tableau Rational -kuhn_7_3 = IM.fromList - [ (1, (IM.fromList [(4,-2), (5,-9), (6,1), (7,9)], 0)) - , (2, (IM.fromList [(4,1/3), (5,1), (6,-1/3), (7,-2)], 0)) - , (3, (IM.fromList [(4,2), (5,3), (6,-1), (7,-12)], 2)) - , (objRow, (IM.fromList [(4,2), (5,3), (6,-1), (7,-12)], 0)) - ] - -test_kuhn_7_3 = simplex OptMin kuhn_7_3 - --- from http://www.math.cuhk.edu.hk/~wei/lpch5.pdf -example_5_7 :: Tableau Rational -example_5_7 = IM.fromList - [ (4, (IM.fromList [(1,-1), (2,-2), (3,-3)], -5)) - , (5, (IM.fromList [(1,-2), (2,-2), (3,-1)], -6)) - , (objRow, (IM.fromList [(1,3),(2,4),(3,5)], 0)) - ] - -test_example_5_7 = dualSimplex OptMax example_5_7 --- optimal value should be -11 - --- --------------------------------------------------------------------------- diff --git a/src/Simplex2.hs b/src/Simplex2.hs deleted file mode 100644 --- a/src/Simplex2.hs +++ /dev/null @@ -1,1014 +0,0 @@ -{-# LANGUAGE DoAndIfThenElse, TypeSynonymInstances, FlexibleContexts, FlexibleInstances #-} ------------------------------------------------------------------------------ --- | --- Module : Simplex2 --- Copyright : (c) Masahiro Sakai 2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : provisional --- Portability : non-portable (DoAndIfThenElse, TypeSynonymInstances, FlexibleContexts, FlexibleInstances) --- --- Naïve implementation of Simplex method --- --- Reference: --- --- * --- --- * Bruno Dutertre and Leonardo de Moura. --- A Fast Linear-Arithmetic Solver for DPLL(T). --- Computer Aided Verification In Computer Aided Verification, Vol. 4144 (2006), pp. 81-94. --- --- --- * Bruno Dutertre and Leonardo de Moura. --- Integrating Simplex with DPLL(T). --- CSL Technical Report SRI-CSL-06-01. 2006. --- --- ------------------------------------------------------------------------------ -module Simplex2 - ( - -- * The @Solver@ type - Solver - , GenericSolver - , SolverValue (..) - , newSolver - , cloneSolver - - -- * Problem specification - , Var - , newVar - , RelOp (..) - , (.<=.), (.>=.), (.==.), (.<.), (.>.) - , Atom (..) - , assertAtom - , assertAtomEx - , assertLower - , assertUpper - , setObj - , OptDir (..) - , setOptDir - , getOptDir - - -- * Solving - , check - , Options (..) - , defaultOptions - , OptResult (..) - , optimize - , dualSimplex - - -- * Extract results - , Model - , model - , RawModel - , rawModel - , getValue - , getObjValue - - -- * Reading status - , getTableau - , getRow - , getCol - , getCoeff - , nVars - , isBasicVariable - , isNonBasicVariable - , isFeasible - , isOptimal - , getLB - , getUB - - -- * Configulation - , setLogger - , clearLogger - , PivotStrategy (..) - , setPivotStrategy - - -- * Debug - , dump - ) where - -import Prelude hiding (log) -import Control.Exception -import Control.Monad -import Data.Ord -import Data.IORef -import Data.List -import Data.Maybe -import Data.Ratio -import qualified Data.Map as Map -import qualified Data.IntMap as IM -import Text.Printf -import Data.OptDir -import System.CPUTime - -import qualified Data.LA as LA -import Data.LA (Atom (..)) -import qualified Data.Formula as F -import Data.Formula (RelOp (..), (.<=.), (.>=.), (.==.), (.<.), (.>.)) -import Data.Linear -import Data.Delta -import Util (showRational) - -{-------------------------------------------------------------------- - The @Solver@ type ---------------------------------------------------------------------} - -type Var = Int - -data GenericSolver v - = GenericSolver - { svTableau :: !(IORef (IM.IntMap (LA.Expr Rational))) - , svLB :: !(IORef (IM.IntMap v)) - , svUB :: !(IORef (IM.IntMap v)) - , svModel :: !(IORef (IM.IntMap v)) - , svVCnt :: !(IORef Int) - , svOk :: !(IORef Bool) - , svOptDir :: !(IORef OptDir) - - , svDefDB :: !(IORef (Map.Map (LA.Expr Rational) Var)) - - , svLogger :: !(IORef (Maybe (String -> IO ()))) - , svPivotStrategy :: !(IORef PivotStrategy) - , svNPivot :: !(IORef Int) - } - -type Solver = GenericSolver Rational - --- special basic variable -objVar :: Int -objVar = -1 - -newSolver :: SolverValue v => IO (GenericSolver v) -newSolver = do - t <- newIORef (IM.singleton objVar lzero) - l <- newIORef IM.empty - u <- newIORef IM.empty - m <- newIORef (IM.singleton objVar lzero) - v <- newIORef 0 - ok <- newIORef True - dir <- newIORef OptMin - defs <- newIORef Map.empty - logger <- newIORef Nothing - pivot <- newIORef PivotStrategyBlandRule - npivot <- newIORef 0 - return $ - GenericSolver - { svTableau = t - , svLB = l - , svUB = u - , svModel = m - , svVCnt = v - , svOk = ok - , svOptDir = dir - , svDefDB = defs - , svLogger = logger - , svNPivot = npivot - , svPivotStrategy = pivot - } - -cloneSolver :: GenericSolver v -> IO (GenericSolver v) -cloneSolver solver = do - t <- newIORef =<< readIORef (svTableau solver) - l <- newIORef =<< readIORef (svLB solver) - u <- newIORef =<< readIORef (svUB solver) - m <- newIORef =<< readIORef (svModel solver) - v <- newIORef =<< readIORef (svVCnt solver) - ok <- newIORef =<< readIORef (svOk solver) - dir <- newIORef =<< readIORef (svOptDir solver) - defs <- newIORef =<< readIORef (svDefDB solver) - logger <- newIORef =<< readIORef (svLogger solver) - pivot <- newIORef =<< readIORef (svPivotStrategy solver) - npivot <- newIORef =<< readIORef (svNPivot solver) - return $ - GenericSolver - { svTableau = t - , svLB = l - , svUB = u - , svModel = m - , svVCnt = v - , svOk = ok - , svOptDir = dir - , svDefDB = defs - , svLogger = logger - , svNPivot = npivot - , svPivotStrategy = pivot - } - -class (Linear Rational v, Ord v) => SolverValue v where - toValue :: Rational -> v - showValue :: Bool -> v -> String - model :: GenericSolver v -> IO Model - -instance SolverValue Rational where - toValue = id - showValue = showRational - model = rawModel - -instance SolverValue (Delta Rational) where - toValue = fromReal - showValue = showDelta - model solver = do - xs <- variables solver - ys <- liftM concat $ forM xs $ \x -> do - Delta p q <- getValue solver x - lb <- getLB solver x - ub <- getUB solver x - return $ - [(p - c) / (k - q) | Just (Delta c k) <- return lb, c < p, k > q] ++ - [(d - p) / (q - h) | Just (Delta d h) <- return ub, p < d, q > h] - let delta0 :: Rational - delta0 = if null ys then 0.1 else minimum ys - f :: Delta Rational -> Rational - f (Delta r k) = r + k * delta0 - liftM (IM.map f) $ readIORef (svModel solver) - -{- -Largest coefficient rule: original rule suggested by G. Dantzig. -Largest increase rule: computationally more expensive in comparison with Largest coefficient, but locally maximizes the progress. -Steepest edge rule: best pivot rule in practice, an efficient approximate implementation is "Devex". -Bland’s rule: avoids cycling but one of the slowest rules. -Random edge rule: Randomized have lead to the current best provable bounds for the number of pivot steps of the simplex method. -Lexicographic rule: used for avoiding cyclying. --} -data PivotStrategy - = PivotStrategyBlandRule - | PivotStrategyLargestCoefficient --- | PivotStrategySteepestEdge - deriving (Eq, Ord, Enum, Show, Read) - -setPivotStrategy :: GenericSolver v -> PivotStrategy -> IO () -setPivotStrategy solver ps = writeIORef (svPivotStrategy solver) ps - -{-------------------------------------------------------------------- - problem description ---------------------------------------------------------------------} - -newVar :: SolverValue v => GenericSolver v -> IO Var -newVar solver = do - v <- readIORef (svVCnt solver) - writeIORef (svVCnt solver) $! v+1 - modifyIORef (svModel solver) (IM.insert v lzero) - return v - -assertAtom :: Solver -> LA.Atom Rational -> IO () -assertAtom solver atom = do - (v,op,rhs') <- simplifyAtom solver atom - case op of - F.Le -> assertUpper solver v (toValue rhs') - F.Ge -> assertLower solver v (toValue rhs') - F.Eql -> do - assertLower solver v (toValue rhs') - assertUpper solver v (toValue rhs') - _ -> error "unsupported" - return () - -assertAtomEx :: GenericSolver (Delta Rational) -> LA.Atom Rational -> IO () -assertAtomEx solver atom = do - (v,op,rhs') <- simplifyAtom solver atom - case op of - F.Le -> assertUpper solver v (toValue rhs') - F.Ge -> assertLower solver v (toValue rhs') - F.Lt -> assertUpper solver v (toValue rhs' .-. delta) - F.Gt -> assertLower solver v (toValue rhs' .+. delta) - F.Eql -> do - assertLower solver v (toValue rhs') - assertUpper solver v (toValue rhs') - return () - -simplifyAtom :: SolverValue v => GenericSolver v -> LA.Atom Rational -> IO (Var, F.RelOp, Rational) -simplifyAtom solver (LA.Atom lhs op rhs) = do - let (lhs',rhs') = - case LA.extract LA.unitVar (lhs .-. rhs) of - (n,e) -> (e, -n) - case LA.terms lhs' of - [(1,v)] -> return (v, op, rhs') - [(-1,v)] -> return (v, F.flipOp op, -rhs') - _ -> do - defs <- readIORef (svDefDB solver) - let (c,lhs'') = scale lhs' -- lhs' = lhs'' / c = rhs' - rhs'' = c .*. rhs' - op'' = if c < 0 then F.flipOp op else op - case Map.lookup lhs'' defs of - Just v -> do - return (v,op'',rhs'') - Nothing -> do - v <- newVar solver - setRow solver v lhs'' - modifyIORef (svDefDB solver) $ Map.insert lhs'' v - return (v,op'',rhs'') - where - scale :: LA.Expr Rational -> (Rational, LA.Expr Rational) - scale e = (c, c .*. e) - where - c = c1 * c2 - c1 = fromIntegral $ foldl' lcm 1 [denominator c | (c, _) <- LA.terms e] - c2 = signum $ head ([c | (c,x) <- LA.terms e] ++ [1]) - -assertLower :: SolverValue v => GenericSolver v -> Var -> v -> IO () -assertLower solver x l = do - l0 <- getLB solver x - u0 <- getUB solver x - case (l0,u0) of - (Just l0', _) | l <= l0' -> return () - (_, Just u0') | u0' < l -> markBad solver - _ -> do - modifyIORef (svLB solver) (IM.insert x l) - b <- isNonBasicVariable solver x - v <- getValue solver x - when (b && not (l <= v)) $ update solver x l - checkNBFeasibility solver - -assertUpper :: SolverValue v => GenericSolver v -> Var -> v -> IO () -assertUpper solver x u = do - l0 <- getLB solver x - u0 <- getUB solver x - case (l0,u0) of - (_, Just u0') | u0' <= u -> return () - (Just l0', _) | u < l0' -> markBad solver - _ -> do - modifyIORef (svUB solver) (IM.insert x u) - b <- isNonBasicVariable solver x - v <- getValue solver x - when (b && not (v <= u)) $ update solver x u - checkNBFeasibility solver - --- FIXME: 式に定数項が含まれる可能性を考えるとこれじゃまずい? -setObj :: SolverValue v => GenericSolver v -> LA.Expr Rational -> IO () -setObj solver e = setRow solver objVar e - -setRow :: SolverValue v => GenericSolver v -> Var -> LA.Expr Rational -> IO () -setRow solver v e = do - modifyIORef (svTableau solver) $ \t -> - IM.insert v (LA.applySubst t e) t - modifyIORef (svModel solver) $ \m -> - IM.insert v (LA.evalLinear m (toValue 1) e) m - -setOptDir :: GenericSolver v -> OptDir -> IO () -setOptDir solver dir = writeIORef (svOptDir solver) dir - -getOptDir :: GenericSolver v -> IO OptDir -getOptDir solver = readIORef (svOptDir solver) - -{-------------------------------------------------------------------- - Status ---------------------------------------------------------------------} - -nVars :: GenericSolver v -> IO Int -nVars solver = readIORef (svVCnt solver) - -isBasicVariable :: GenericSolver v -> Var -> IO Bool -isBasicVariable solver v = do - t <- readIORef (svTableau solver) - return $ v `IM.member` t - -isNonBasicVariable :: GenericSolver v -> Var -> IO Bool -isNonBasicVariable solver x = liftM not (isBasicVariable solver x) - -isFeasible :: SolverValue v => GenericSolver v -> IO Bool -isFeasible solver = do - xs <- variables solver - liftM and $ forM xs $ \x -> do - v <- getValue solver x - l <- getLB solver x - u <- getUB solver x - return (testLB l v && testUB u v) - -isOptimal :: SolverValue v => GenericSolver v -> IO Bool -isOptimal solver = do - obj <- getRow solver objVar - ret <- selectEnteringVariable solver - return $! isNothing ret - -{-------------------------------------------------------------------- - Satisfiability solving ---------------------------------------------------------------------} - -check :: SolverValue v => GenericSolver v -> IO Bool -check solver = do - let - loop :: IO Bool - loop = do - m <- selectViolatingBasicVariable solver - - case m of - Nothing -> return True - Just xi -> do - li <- getLB solver xi - ui <- getUB solver xi - isLBViolated <- do - vi <- getValue solver xi - return $ not (testLB li vi) - let q = if isLBViolated - then -- select the smallest non-basic variable xj such that - -- (aij > 0 and β(xj) < uj) or (aij < 0 and β(xj) > lj) - canIncrease solver - else -- select the smallest non-basic variable xj such that - -- (aij < 0 and β(xj) < uj) or (aij > 0 and β(xj) > lj) - canDecrease solver - xi_def <- getRow solver xi - r <- liftM (fmap snd) $ findM q (LA.terms xi_def) - case r of - Nothing -> markBad solver >> return False - Just xj -> do - pivotAndUpdate solver xi xj (fromJust (if isLBViolated then li else ui)) - loop - - ok <- readIORef (svOk solver) - if not ok - then return False - else do - log solver "check" - result <- recordTime solver loop - when result $ checkFeasibility solver - return result - -selectViolatingBasicVariable :: SolverValue v => GenericSolver v -> IO (Maybe Var) -selectViolatingBasicVariable solver = do - let - p :: Var -> IO Bool - p x | x == objVar = return False - p xi = do - li <- getLB solver xi - ui <- getUB solver xi - vi <- getValue solver xi - return $ not (testLB li vi) || not (testUB ui vi) - vs <- basicVariables solver - - ps <- readIORef (svPivotStrategy solver) - case ps of - PivotStrategyBlandRule -> - findM p vs - PivotStrategyLargestCoefficient -> do - xs <- filterM p vs - case xs of - [] -> return Nothing - _ -> do - xs2 <- forM xs $ \xi -> do - vi <- getValue solver xi - li <- getLB solver xi - ui <- getUB solver xi - if not (testLB li vi) - then return (xi, fromJust li .-. vi) - else return (xi, vi .-. fromJust ui) - return $ Just $ fst $ maximumBy (comparing snd) xs2 - -{-------------------------------------------------------------------- - Optimization ---------------------------------------------------------------------} - --- | results of optimization -data OptResult = Optimum | Unsat | Unbounded | ObjLimit - deriving (Show, Eq, Ord) - -data Options - = Options - { objLimit :: Maybe Rational - } - deriving (Show, Eq, Ord) - -defaultOptions :: Options -defaultOptions - = Options - { objLimit = Nothing - } - -optimize :: Solver -> Options -> IO OptResult -optimize solver opt = do - ret <- do - is_fea <- isFeasible solver - if is_fea then return True else check solver - if not ret - then return Unsat -- unsat - else do - log solver "optimize" - result <- recordTime solver loop - when (result == Optimum) $ checkOptimality solver - return result - where - loop :: IO OptResult - loop = do - checkFeasibility solver - ret <- selectEnteringVariable solver - case ret of - Nothing -> return Optimum - Just (c,xj) -> do - dir <- getOptDir solver - r <- if dir==OptMin - then if c > 0 - then decreaseNB solver xj -- xj を小さくして目的関数を小さくする - else increaseNB solver xj -- xj を大きくして目的関数を小さくする - else if c > 0 - then increaseNB solver xj -- xj を大きくして目的関数を大きくする - else decreaseNB solver xj -- xj を小さくして目的関数を大きくする - if r - then loop - else return Unbounded - -selectEnteringVariable :: SolverValue v => GenericSolver v -> IO (Maybe (Rational, Var)) -selectEnteringVariable solver = do - ps <- readIORef (svPivotStrategy solver) - obj_def <- getRow solver objVar - case ps of - PivotStrategyBlandRule -> - findM canEnter (LA.terms obj_def) - PivotStrategyLargestCoefficient -> do - ts <- filterM canEnter (LA.terms obj_def) - case ts of - [] -> return Nothing - _ -> return $ Just $ snd $ maximumBy (comparing fst) [(abs c, (c,xj)) | (c,xj) <- ts] - where - canEnter :: (Rational, Var) -> IO Bool - canEnter (_,xj) | xj == LA.unitVar = return False - canEnter (c,xj) = do - dir <- getOptDir solver - if dir==OptMin - then canDecrease solver (c,xj) - else canIncrease solver (c,xj) - -canIncrease :: SolverValue v => GenericSolver v -> (Rational,Var) -> IO Bool -canIncrease solver (a,x) = - case compare a 0 of - EQ -> return False - GT -> canIncrease1 solver x - LT -> canDecrease1 solver x - -canDecrease :: SolverValue v => GenericSolver v -> (Rational,Var) -> IO Bool -canDecrease solver (a,x) = - case compare a 0 of - EQ -> return False - GT -> canDecrease1 solver x - LT -> canIncrease1 solver x - -canIncrease1 :: SolverValue v => GenericSolver v -> Var -> IO Bool -canIncrease1 solver x = do - u <- getUB solver x - v <- getValue solver x - case u of - Nothing -> return True - Just uv -> return $! (v < uv) - -canDecrease1 :: SolverValue v => GenericSolver v -> Var -> IO Bool -canDecrease1 solver x = do - l <- getLB solver x - v <- getValue solver x - case l of - Nothing -> return True - Just lv -> return $! (lv < v) - --- | feasibility を保ちつつ non-basic variable xj の値を大きくする -increaseNB :: Solver -> Var -> IO Bool -increaseNB solver xj = do - col <- getCol solver xj - - -- Upper bounds of θ - -- NOTE: xj 自体の上限も考慮するのに注意 - ubs <- liftM concat $ forM ((xj,1) : IM.toList col) $ \(xi,aij) -> do - v1 <- getValue solver xi - li <- getLB solver xi - ui <- getUB solver xi - return [ assert (theta >= lzero) ((xi,v2), theta) - | Just v2 <- [ui | aij > 0] ++ [li | aij < 0] - , let theta = (v2 .-. v1) ./. aij ] - - -- β(xj) := β(xj) + θ なので θ を大きく - case ubs of - [] -> return False -- unbounded - _ -> do - let (xi, v) = fst $ minimumBy (comparing snd) ubs - pivotAndUpdate solver xi xj v - return True - --- | feasibility を保ちつつ non-basic variable xj の値を小さくする -decreaseNB :: Solver -> Var -> IO Bool -decreaseNB solver xj = do - col <- getCol solver xj - - -- Lower bounds of θ - -- NOTE: xj 自体の下限も考慮するのに注意 - lbs <- liftM concat $ forM ((xj,1) : IM.toList col) $ \(xi,aij) -> do - v1 <- getValue solver xi - li <- getLB solver xi - ui <- getUB solver xi - return [ assert (theta <= lzero) ((xi,v2), theta) - | Just v2 <- [li | aij > 0] ++ [ui | aij < 0] - , let theta = (v2 .-. v1) ./. aij ] - - -- β(xj) := β(xj) + θ なので θ を小さく - case lbs of - [] -> return False -- unbounded - _ -> do - let (xi, v) = fst $ maximumBy (comparing snd) lbs - pivotAndUpdate solver xi xj v - return True - -dualSimplex :: Solver -> Options -> IO OptResult -dualSimplex solver opt = do - let - loop :: IO OptResult - loop = do - checkOptimality solver - - p <- prune solver opt - if p - then return ObjLimit - else do - m <- selectViolatingBasicVariable solver - case m of - Nothing -> return Optimum - Just xi -> do - xi_def <- getRow solver xi - li <- getLB solver xi - ui <- getUB solver xi - isLBViolated <- do - vi <- getValue solver xi - return $ not (testLB li vi) - r <- dualRTest solver xi_def isLBViolated - case r of - Nothing -> markBad solver >> return Unsat -- dual unbounded - Just xj -> do - pivotAndUpdate solver xi xj (fromJust (if isLBViolated then li else ui)) - loop - - ok <- readIORef (svOk solver) - if not ok - then return Unsat - else do - log solver "dual simplex" - result <- recordTime solver loop - when (result == Optimum) $ checkFeasibility solver - return result - -dualRTest :: Solver -> LA.Expr Rational -> Bool -> IO (Maybe Var) -dualRTest solver row isLBViolated = do - -- normalize to the cases of minimization - obj_def <- do - def <- getRow solver objVar - dir <- getOptDir solver - return $ - case dir of - OptMin -> def - OptMax -> lnegate def - -- normalize to the cases of lower bound violation - let xi_def = - if isLBViolated - then row - else lnegate row - ws <- do - -- select non-basic variable xj such that - -- (aij > 0 and β(xj) < uj) or (aij < 0 and β(xj) > lj) - liftM concat $ forM (LA.terms xi_def) $ \(aij, xj) -> do - b <- canIncrease solver (aij, xj) - if b - then do - let cj = LA.coeff xj obj_def - let ratio = cj / aij - return [(xj, ratio) | ratio >= 0] - else - return [] - case ws of - [] -> return Nothing - _ -> return $ Just $ fst $ minimumBy (comparing snd) ws - -prune :: Solver -> Options -> IO Bool -prune solver opt = - case objLimit opt of - Nothing -> return False - Just lim -> do - o <- getObjValue solver - dir <- getOptDir solver - case dir of - OptMin -> return $! (lim <= o) - OptMax -> return $! (lim >= o) - -{-------------------------------------------------------------------- - Extract results ---------------------------------------------------------------------} - -type RawModel v = IM.IntMap v - -rawModel :: GenericSolver v -> IO (RawModel v) -rawModel solver = do - xs <- variables solver - liftM IM.fromList $ forM xs $ \x -> do - val <- getValue solver x - return (x,val) - -getObjValue :: GenericSolver v -> IO v -getObjValue solver = getValue solver objVar - -type Model = IM.IntMap Rational - -{-------------------------------------------------------------------- - major function ---------------------------------------------------------------------} - -update :: SolverValue v => GenericSolver v -> Var -> v -> IO () -update solver xj v = do - -- log solver $ printf "before update x%d (%s)" xj (show v) - -- dump solver - - v0 <- getValue solver xj - let diff = v .-. v0 - - aj <- getCol solver xj - modifyIORef (svModel solver) $ \m -> - let m2 = IM.map (\aij -> aij .*. diff) aj - in IM.insert xj v $ IM.unionWith (.+.) m2 m - - -- log solver $ printf "after update x%d (%s)" xj (show v) - -- dump solver - -pivot :: SolverValue v => GenericSolver v -> Var -> Var -> IO () -pivot solver xi xj = do - modifyIORef' (svNPivot solver) (+1) - modifyIORef' (svTableau solver) $ \defs -> - case LA.solveFor (LA.Atom (LA.var xi) F.Eql (defs IM.! xi)) xj of - Just (F.Eql, xj_def) -> - IM.insert xj xj_def . IM.map (LA.applySubst1 xj xj_def) . IM.delete xi $ defs - _ -> error "pivot: should not happen" - -pivotAndUpdate :: SolverValue v => GenericSolver v -> Var -> Var -> v -> IO () -pivotAndUpdate solver xi xj v | xi == xj = update solver xi v -- xi = xj is non-basic variable -pivotAndUpdate solver xi xj v = do - -- xi is basic variable - -- xj is non-basic varaible - - -- log solver $ printf "before pivotAndUpdate x%d x%d (%s)" xi xj (show v) - -- dump solver - - m <- readIORef (svModel solver) - - aj <- getCol solver xj - let aij = aj IM.! xi - let theta = (v .-. (m IM.! xi)) ./. aij - - let m' = IM.fromList $ - [(xi, v), (xj, (m IM.! xj) .+. theta)] ++ - [(xk, (m IM.! xk) .+. (akj .*. theta)) | (xk, akj) <- IM.toList aj, xk /= xi] - writeIORef (svModel solver) (IM.union m' m) -- note that 'IM.union' is left biased. - - pivot solver xi xj - - -- log solver $ printf "after pivotAndUpdate x%d x%d (%s)" xi xj (show v) - -- dump solver - -getLB :: GenericSolver v -> Var -> IO (Maybe v) -getLB solver x = do - lb <- readIORef (svLB solver) - return $ IM.lookup x lb - -getUB :: GenericSolver v -> Var -> IO (Maybe v) -getUB solver x = do - ub <- readIORef (svUB solver) - return $ IM.lookup x ub - -getTableau :: GenericSolver v -> IO (IM.IntMap (LA.Expr Rational)) -getTableau solver = do - t <- readIORef (svTableau solver) - return $ IM.delete objVar t - -getValue :: GenericSolver v -> Var -> IO v -getValue solver x = do - m <- readIORef (svModel solver) - return $ m IM.! x - -getRow :: GenericSolver v -> Var -> IO (LA.Expr Rational) -getRow solver x = do - -- x should be basic variable or 'objVar' - t <- readIORef (svTableau solver) - return $! (t IM.! x) - --- aijが非ゼロの列も全部探しているのは効率が悪い -getCol :: SolverValue v => GenericSolver v -> Var -> IO (IM.IntMap Rational) -getCol solver xj = do - t <- readIORef (svTableau solver) - return $ IM.mapMaybe (LA.lookupCoeff xj) t - -getCoeff :: GenericSolver v -> Var -> Var -> IO Rational -getCoeff solver xi xj = do - xi_def <- getRow solver xi - return $! LA.coeff xj xi_def - -markBad :: GenericSolver v -> IO () -markBad solver = writeIORef (svOk solver) False - -{-------------------------------------------------------------------- - utility ---------------------------------------------------------------------} - -findM :: Monad m => (a -> m Bool) -> [a] -> m (Maybe a) -findM _ [] = return Nothing -findM p (x:xs) = do - r <- p x - if r - then return (Just x) - else findM p xs - -testLB :: SolverValue v => Maybe v -> v -> Bool -testLB Nothing _ = True -testLB (Just l) x = l <= x - -testUB :: SolverValue v => Maybe v -> v -> Bool -testUB Nothing _ = True -testUB (Just u) x = x <= u - -variables :: GenericSolver v -> IO [Var] -variables solver = do - vcnt <- nVars solver - return [0..vcnt-1] - -basicVariables :: GenericSolver v -> IO [Var] -basicVariables solver = do - t <- readIORef (svTableau solver) - return (IM.keys t) - -modifyIORef' :: IORef a -> (a -> a) -> IO () -modifyIORef' ref f = do - x <- readIORef ref - writeIORef ref $! f x - -recordTime :: SolverValue v => GenericSolver v -> IO a -> IO a -recordTime solver act = do - dumpSize solver - writeIORef (svNPivot solver) 0 - - start <- getCPUTime - result <- act - end <- getCPUTime - - (log solver . printf "time = %.3fs") (fromIntegral (end - start) / 10^(12::Int) :: Double) - (log solver . printf "#pivot = %d") =<< readIORef (svNPivot solver) - return result - -showDelta :: Bool -> Delta Rational -> String -showDelta asRatio v = - case v of - (Delta r k) -> - f r ++ - case compare k 0 of - EQ -> "" - GT -> " + " ++ f k ++ " delta" - LT -> " - " ++ f (abs k) ++ " delta" - where - f = showRational asRatio - -{-------------------------------------------------------------------- - Logging ---------------------------------------------------------------------} - --- | set callback function for receiving messages. -setLogger :: GenericSolver v -> (String -> IO ()) -> IO () -setLogger solver logger = do - writeIORef (svLogger solver) (Just logger) - -clearLogger :: GenericSolver v -> IO () -clearLogger solver = writeIORef (svLogger solver) Nothing - -log :: GenericSolver v -> String -> IO () -log solver msg = logIO solver (return msg) - -logIO :: GenericSolver v -> IO String -> IO () -logIO solver action = do - m <- readIORef (svLogger solver) - case m of - Nothing -> return () - Just logger -> action >>= logger - -{-------------------------------------------------------------------- - debug and tests ---------------------------------------------------------------------} - -test4 :: IO () -test4 = do - solver <- newSolver - setLogger solver putStrLn - x0 <- newVar solver - x1 <- newVar solver - - writeIORef (svTableau solver) (IM.fromList [(x1, LA.var x0)]) - writeIORef (svLB solver) (IM.fromList [(x0, toValue 0), (x1, toValue 0)]) - writeIORef (svUB solver) (IM.fromList [(x0, toValue 2), (x1, toValue 3)]) - setObj solver (LA.fromTerms [(-1, x0)]) - - ret <- optimize solver defaultOptions - print ret - dump solver - -test5 :: IO () -test5 = do - solver <- newSolver - setLogger solver putStrLn - x0 <- newVar solver - x1 <- newVar solver - - writeIORef (svTableau solver) (IM.fromList [(x1, LA.var x0)]) - writeIORef (svLB solver) (IM.fromList [(x0, toValue 0), (x1, toValue 0)]) - writeIORef (svUB solver) (IM.fromList [(x0, toValue 2), (x1, toValue 0)]) - setObj solver (LA.fromTerms [(-1, x0)]) - - checkFeasibility solver - - ret <- optimize solver defaultOptions - print ret - dump solver - -test6 :: IO () -test6 = do - solver <- newSolver - setLogger solver putStrLn - x0 <- newVar solver - - assertAtom solver (LA.constant 1 .<. LA.var x0) - assertAtom solver (LA.constant 2 .>. LA.var x0) - - ret <- check solver - print ret - dump solver - - m <- model solver - print m - -dumpSize :: SolverValue v => GenericSolver v -> IO () -dumpSize solver = do - t <- readIORef (svTableau solver) - let nrows = IM.size t - 1 -- -1 is objVar - xs <- variables solver - let ncols = length xs - nrows - let nnz = sum [IM.size $ LA.coeffMap xi_def | (xi,xi_def) <- IM.toList t, xi /= objVar] - log solver $ printf "%d rows, %d columns, %d non-zeros" nrows ncols nnz - -dump :: SolverValue v => GenericSolver v -> IO () -dump solver = do - log solver "=============" - - log solver "Tableau:" - t <- readIORef (svTableau solver) - log solver $ printf "obj = %s" (show (t IM.! objVar)) - forM_ (IM.toList t) $ \(xi, e) -> do - when (xi /= objVar) $ log solver $ printf "x%d = %s" xi (show e) - - log solver "" - - log solver "Assignments and Bounds:" - objVal <- getValue solver objVar - log solver $ printf "beta(obj) = %s" (showValue True objVal) - xs <- variables solver - forM_ xs $ \x -> do - l <- getLB solver x - u <- getUB solver x - v <- getValue solver x - let f Nothing = "Nothing" - f (Just x) = showValue True x - log solver $ printf "beta(x%d) = %s; %s <= x%d <= %s" x (showValue True v) (f l) x (f u) - - log solver "" - log solver "Status:" - is_fea <- isFeasible solver - is_opt <- isOptimal solver - log solver $ printf "Feasible: %s" (show is_fea) - log solver $ printf "Optimal: %s" (show is_opt) - - log solver "=============" - -checkFeasibility :: SolverValue v => GenericSolver v -> IO () -checkFeasibility _ | True = return () -checkFeasibility solver = do - xs <- variables solver - forM_ xs $ \x -> do - v <- getValue solver x - l <- getLB solver x - u <- getUB solver x - let f Nothing = "Nothing" - f (Just x) = showValue True x - unless (testLB l v) $ - error (printf "(%s) <= x%d is violated; x%d = (%s)" (f l) x x (showValue True v)) - unless (testUB u v) $ - error (printf "x%d <= (%s) is violated; x%d = (%s)" x (f u) x (showValue True v)) - return () - -checkNBFeasibility :: SolverValue v => GenericSolver v -> IO () -checkNBFeasibility _ | True = return () -checkNBFeasibility solver = do - xs <- variables solver - forM_ xs $ \x -> do - b <- isNonBasicVariable solver x - when b $ do - v <- getValue solver x - l <- getLB solver x - u <- getUB solver x - let f Nothing = "Nothing" - f (Just x) = showValue True x - unless (testLB l v) $ - error (printf "checkNBFeasibility: (%s) <= x%d is violated; x%d = (%s)" (f l) x x (showValue True v)) - unless (testUB u v) $ - error (printf "checkNBFeasibility: x%d <= (%s) is violated; x%d = (%s)" x (f u) x (showValue True v)) - -checkOptimality :: Solver -> IO () -checkOptimality _ | True = return () -checkOptimality solver = do - ret <- selectEnteringVariable solver - case ret of - Nothing -> return () -- optimal - Just (_,x) -> error (printf "checkOptimality: not optimal (x%d can be changed)" x) diff --git a/src/TestAReal.hs b/src/TestAReal.hs deleted file mode 100644 --- a/src/TestAReal.hs +++ /dev/null @@ -1,215 +0,0 @@ -{-# LANGUAGE TemplateHaskell, ScopedTypeVariables #-} - -import Data.Maybe -import Data.Ratio -import Test.HUnit hiding (Test) -import Test.QuickCheck -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Test.Framework.Providers.QuickCheck2 - -import Data.Polynomial hiding (deg) -import Data.AlgebraicNumber -import Data.AlgebraicNumber.Root -import Data.AlgebraicNumber.RealInstance - -import Control.Monad -import Control.Exception -import System.IO - -{-------------------------------------------------------------------- - sample values ---------------------------------------------------------------------} - --- ±√2 -sqrt2 :: AReal -[neg_sqrt2, sqrt2] = realRoots (x^2 - 2) - where - x = var () - --- ±√3 -sqrt3 :: AReal -[neg_sqrt3, sqrt3] = realRoots (x^2 - 3) - where - x = var () - -{-------------------------------------------------------------------- - root manipulation ---------------------------------------------------------------------} - -case__rootAdd_sqrt2_sqrt3 = assertBool "" $ abs valP <= 0.0001 - where - x = var () - - p :: UPolynomial Rational - p = rootAdd (x^2 - 2) (x^2 - 3) - - valP :: Double - valP = eval (\() -> sqrt 2 + sqrt 3) $ mapCoeff fromRational p - --- bug? -test_rootAdd = p - where - x = var () - p :: UPolynomial Rational - p = rootAdd (x^2 - 2) (x^6 + 6*x^3 - 2*x^2 + 9) - -case_rootSub_sqrt2_sqrt3 = assertBool "" $ abs valP <= 0.0001 - where - x = var () - - p :: UPolynomial Rational - p = rootSub (x^2 - 2) (x^2 - 3) - - valP :: Double - valP = eval (\() -> sqrt 2 - sqrt 3) $ mapCoeff fromRational p - -case_rootMul_sqrt2_sqrt3 = assertBool "" $ abs valP <= 0.0001 - where - x = var () - - p :: UPolynomial Rational - p = rootMul (x^2 - 2) (x^2 - 3) - - valP :: Double - valP = eval (\() -> sqrt 2 * sqrt 3) $ mapCoeff fromRational p - -case_rootNegate_test1 = assertBool "" $ abs valP <= 0.0001 - where - x = var () - - p :: UPolynomial Rational - p = rootNegate (x^3 - 3) - - valP :: Double - valP = eval (\() -> - (3 ** (1/3))) $ mapCoeff fromRational p - -case_rootNegate_test2 = rootNegate p @?= q - where - x :: UPolynomial Rational - x = var () - p = x^3 - 3 - q = x^3 + 3 - -case_rootNegate_test3 = rootNegate p @?= q - where - x :: UPolynomial Rational - x = var () - p = (x-2)*(x-3)*(x-4) - q = (x+2)*(x+3)*(x+4) - -case_rootScale = rootScale 2 p @?= q - where - x :: UPolynomial Rational - x = var () - p = (x-2)*(x-3)*(x-4) - q = (x-4)*(x-6)*(x-8) - -case_rootRecip = assertBool "" $ abs valP <= 0.0001 - where - x = var () - - p :: UPolynomial Rational - p = rootRecip (x^3 - 3) - - valP :: Double - valP = eval (\() -> 1 / (3 ** (1/3))) $ mapCoeff fromRational p - -{-------------------------------------------------------------------- - algebraic reals ---------------------------------------------------------------------} - -case_realRoots_zero = realRoots (0 :: UPolynomial Rational) @?= [] - -case_realRoots_nonminimal = - realRoots ((x^2 - 1) * (x - 3)) @?= [-1,1,3] - where - x = var () - -case_realRoots_minus_one = realRoots (x^2 + 1) @?= [] - where - x = var () - -case_realRoots_two = length (realRoots (x^2 - 2)) @?= 2 - where - x = var () - -case_eq = sqrt2*sqrt2 - 2 @?= 0 - -case_eq_refl = assertBool "" $ sqrt2 == sqrt2 - -case_diseq_1 = assertBool "" $ sqrt2 /= sqrt3 - -case_diseq_2 = assertBool "" $ sqrt2 /= neg_sqrt2 - -case_cmp_1 = assertBool "" $ 0 < sqrt2 - -case_cmp_2 = assertBool "" $ neg_sqrt2 < 0 - -case_cmp_3 = assertBool "" $ 0 < neg_sqrt2 * neg_sqrt2 - -case_cmp_4 = assertBool "" $ neg_sqrt2 * neg_sqrt2 * neg_sqrt2 < 0 - -case_floor_sqrt2 = floor' sqrt2 @?= 1 - -case_floor_neg_sqrt2 = floor' neg_sqrt2 @?= -2 - -case_floor_1 = floor' 1 @?= 1 - -case_floor_neg_1 = floor' (-1) @?= -1 - -case_ceiling_sqrt2 = ceiling' sqrt2 @?= 2 - -case_ceiling_neg_sqrt2 = ceiling' neg_sqrt2 @?= -1 - -case_ceiling_1 = ceiling' 1 @?= 1 - -case_ceiling_neg_1 = ceiling' (-1) @?= -1 - -case_round_sqrt2 = round' sqrt2 @?= 1 - -case_toRational = toRational r @?= 3/2 - where - x = var () - [r] = realRoots (2*x - 3) - -case_toRational_error = do - r <- try $ evaluate $ toRational sqrt2 - case r of - Left (e :: SomeException) -> return () - Right _ -> assertFailure "shuold be error" - --- 期待値は Wolfram Alpha で x^3 - Sqrt[2]*x + 3 を調べて Real root の exact form で得た -case_simpARealPoly = simpARealPoly p @?= q - where - x :: forall k. (Num k, Eq k) => UPolynomial k - x = var () - p = x^3 - constant sqrt2 * x + 3 - q = x^6 + 6*x^3 - 2*x^2 + 9 - -case_deg_sqrt2 = deg sqrt2 @?= 2 - -case_deg_neg_sqrt2 = deg neg_sqrt2 @?= 2 - -case_deg_sqrt2_minus_sqrt2 = deg (sqrt2 - sqrt2) @?= 1 - -case_deg_sqrt2_times_sqrt2 = deg (sqrt2 * sqrt2) @?= 1 - -case_isAlgebraicInteger_sqrt2 = isAlgebraicInteger sqrt2 @?= True - -case_isAlgebraicInteger_neg_sqrt2 = isAlgebraicInteger neg_sqrt2 @?= True - -case_isAlgebraicInteger_one_half = isAlgebraicInteger (1/2) @?= False - -case_isAlgebraicInteger_one_sqrt2 = isAlgebraicInteger (1 / sqrt2) @?= False - -case_height_sqrt2 = height sqrt2 @?= 2 - -case_height_10 = height 10 @?= 10 - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestAReal2.hs b/src/TestAReal2.hs deleted file mode 100644 --- a/src/TestAReal2.hs +++ /dev/null @@ -1,87 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} - -import Data.Maybe -import Data.Ratio -import Test.HUnit hiding (Test) -import Test.QuickCheck -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Test.Framework.Providers.QuickCheck2 - -import Data.Polynomial -import Data.AlgebraicNumber - -import Control.Monad -import System.IO - -{-------------------------------------------------------------------- - Num ---------------------------------------------------------------------} - -prop_add_comm = - forAll areals $ \a -> - forAll areals $ \b -> - a + b == b + a - -prop_add_assoc = - forAll areals $ \a -> - forAll areals $ \b -> - forAll areals $ \c -> - a + (b + c) == (a + b) + c - -prop_add_unitL = - forAll areals $ \a -> - 0 + a == a - -prop_add_unitR = - forAll areals $ \a -> - a + 0 == a - -prop_mult_comm = - forAll areals $ \a -> - forAll areals $ \b -> - a * b == b * a - -prop_mult_assoc = - forAll areals $ \a -> - forAll areals $ \b -> - forAll areals $ \c -> - a * (b * c) == (a * b) * c - -prop_mult_unitL = - forAll areals $ \a -> - 1 * a == a - -prop_mult_unitR = - forAll areals $ \a -> - a * 1 == a - -prop_mult_dist = - forAll areals $ \a -> - forAll areals $ \b -> - forAll areals $ \c -> - a * (b + c) == a * b + a * c - -prop_mult_zero = - forAll areals $ \a -> - 0 * a == 0 - -{-------------------------------------------------------------------- - Generators ---------------------------------------------------------------------} - -areals :: Gen AReal -areals = oneof $ map return $ samples - -samples :: [AReal] -samples = [0, 1, -1, 2, -2] ++ concatMap realRoots ps - where - x = var () - ps = [x^2 - 2, x^2 - 3 {- , x^3 - 2, x^6 + 6*x^3 - 2*x^2 + 9 -}] - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestInterval.hs b/src/TestInterval.hs deleted file mode 100644 --- a/src/TestInterval.hs +++ /dev/null @@ -1,469 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} - -import Data.Maybe -import Data.Ratio -import Test.HUnit hiding (Test) -import Test.QuickCheck -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Test.Framework.Providers.QuickCheck2 - -import Data.Linear -import Data.Interval (Interval, (=!), (>!), (=?), (>?)) -import qualified Data.Interval as Interval - -{-------------------------------------------------------------------- - empty ---------------------------------------------------------------------} - -prop_empty_is_bottom = - forAll intervals $ \a -> - Interval.isSubsetOf Interval.empty a - -prop_null_empty = - forAll intervals $ \a -> - Interval.null a == (a == Interval.empty) - -case_null_empty = - Interval.null (Interval.empty :: Interval Rational) @?= True - -{-------------------------------------------------------------------- - univ ---------------------------------------------------------------------} - -prop_univ_is_top = - forAll intervals $ \a -> - Interval.isSubsetOf a Interval.univ - -case_nonnull_top = - Interval.null (Interval.univ :: Interval Rational) @?= False - -{-------------------------------------------------------------------- - singleton ---------------------------------------------------------------------} - -prop_singleton_member = - forAll arbitrary $ \r -> - Interval.member (r::Rational) (Interval.singleton r) - -prop_singleton_member_intersection = - forAll intervals $ \a -> - forAll arbitrary $ \r -> - let b = Interval.singleton r - in Interval.member (r::Rational) a - ==> Interval.intersection a b == b - -prop_singleton_nonnull = - forAll arbitrary $ \r1 -> - not $ Interval.null $ Interval.singleton (r1::Rational) - -prop_distinct_singleton_intersection = - forAll arbitrary $ \r1 -> - forAll arbitrary $ \r2 -> - (r1::Rational) /= r2 ==> - Interval.intersection (Interval.singleton r1) (Interval.singleton r2) - == Interval.empty - -{-------------------------------------------------------------------- - Intersection ---------------------------------------------------------------------} - -prop_intersection_comm = - forAll intervals $ \a -> - forAll intervals $ \b -> - Interval.intersection a b == Interval.intersection b a - -prop_intersection_assoc = - forAll intervals $ \a -> - forAll intervals $ \b -> - forAll intervals $ \c -> - Interval.intersection a (Interval.intersection b c) == - Interval.intersection (Interval.intersection a b) c - -prop_intersection_unitL = - forAll intervals $ \a -> - Interval.intersection Interval.univ a == a - -prop_intersection_unitR = - forAll intervals $ \a -> - Interval.intersection a Interval.univ == a - -prop_intersection_empty = - forAll intervals $ \a -> - Interval.intersection a Interval.empty == Interval.empty - -prop_intersection_isSubsetOf = - forAll intervals $ \a -> - forAll intervals $ \b -> - Interval.isSubsetOf (Interval.intersection a b) a - -prop_intersection_isSubsetOf_equiv = - forAll intervals $ \a -> - forAll intervals $ \b -> - (Interval.intersection a b == a) - == Interval.isSubsetOf a b - -{-------------------------------------------------------------------- - Join ---------------------------------------------------------------------} - -prop_join_comm = - forAll intervals $ \a -> - forAll intervals $ \b -> - Interval.join a b == Interval.join b a - -prop_join_assoc = - forAll intervals $ \a -> - forAll intervals $ \b -> - forAll intervals $ \c -> - Interval.join a (Interval.join b c) == - Interval.join (Interval.join a b) c - -prop_join_unitL = - forAll intervals $ \a -> - Interval.join Interval.empty a == a - -prop_join_unitR = - forAll intervals $ \a -> - Interval.join a Interval.empty == a - -prop_join_univ = - forAll intervals $ \a -> - Interval.join a Interval.univ == Interval.univ - -prop_join_isSubsetOf = - forAll intervals $ \a -> - forAll intervals $ \b -> - Interval.isSubsetOf a (Interval.join a b) - -prop_join_isSubsetOf_equiv = - forAll intervals $ \a -> - forAll intervals $ \b -> - (Interval.join a b == b) - == Interval.isSubsetOf a b - -{-------------------------------------------------------------------- - member ---------------------------------------------------------------------} - -prop_member_isSubsetOf = - forAll arbitrary $ \r -> - forAll intervals $ \a -> - Interval.member r a == Interval.isSubsetOf (Interval.singleton r) a - -{-------------------------------------------------------------------- - isSubsetOf ---------------------------------------------------------------------} - -prop_isSubsetOf_refl = - forAll intervals $ \a -> - Interval.isSubsetOf a a - -prop_isSubsetOf_trans = - forAll intervals $ \a -> - forAll intervals $ \b -> - forAll intervals $ \c -> - Interval.isSubsetOf a b && Interval.isSubsetOf b c - ==> Interval.isSubsetOf a c - --- prop_isSubsetOf_antisym = --- forAll intervals $ \a -> --- forAll intervals $ \b -> --- Interval.isSubsetOf a b && Interval.isSubsetOf b a --- ==> a == b - -{-------------------------------------------------------------------- - pickup ---------------------------------------------------------------------} - -prop_pickup_member_null = - forAll intervals $ \a -> - case Interval.pickup a of - Nothing -> Interval.null a - Just x -> Interval.member x a - -case_pickup_empty = - Interval.pickup (Interval.empty :: Interval Rational) @?= Nothing - -case_pickup_univ = - isJust (Interval.pickup (Interval.univ :: Interval Rational)) @?= True - -{-------------------------------------------------------------------- - Comparison ---------------------------------------------------------------------} - -case_lt_all_1 = (a not (Interval.null a) ==> not (a not (Interval.null a) ==> a <=? a - -prop_lt_all_singleton = - forAll arbitrary $ \a -> - forAll arbitrary $ \b -> - (a::Rational) < b ==> Interval.singleton a - not $ Interval.singleton (a::Rational) - forAll arbitrary $ \b -> - (a::Rational) <= b ==> Interval.singleton a <=! Interval.singleton b - -prop_le_all_singleton_2 = - forAll arbitrary $ \a -> - Interval.singleton (a::Rational) <=! Interval.singleton a - -prop_lt_some_singleton = - forAll arbitrary $ \a -> - forAll arbitrary $ \b -> - (a::Rational) < b ==> Interval.singleton a - not $ Interval.singleton (a::Rational) - forAll arbitrary $ \b -> - (a::Rational) <= b ==> Interval.singleton a <=? Interval.singleton b - -prop_le_some_singleton_2 = - forAll arbitrary $ \a -> - Interval.singleton (a::Rational) <=? Interval.singleton a - -{-------------------------------------------------------------------- - Num ---------------------------------------------------------------------} - -prop_scale_empty = - forAll arbitrary $ \r -> - (r::Rational) .*. Interval.empty == Interval.empty - -prop_add_comm = - forAll intervals $ \a -> - forAll intervals $ \b -> - a + b == b + a - -prop_add_assoc = - forAll intervals $ \a -> - forAll intervals $ \b -> - forAll intervals $ \c -> - a + (b + c) == (a + b) + c - -prop_add_unitL = - forAll intervals $ \a -> - Interval.singleton 0 + a == a - -prop_add_unitR = - forAll intervals $ \a -> - a + Interval.singleton 0 == a - -prop_add_member = - forAll intervals $ \a -> - forAll intervals $ \b -> - and [ (x+y) `Interval.member` (a+b) - | x <- maybeToList $ Interval.pickup a - , y <- maybeToList $ Interval.pickup b - ] - -prop_mult_comm = - forAll intervals $ \a -> - forAll intervals $ \b -> - a * b == b * a - -prop_mult_assoc = - forAll intervals $ \a -> - forAll intervals $ \b -> - forAll intervals $ \c -> - a * (b * c) == (a * b) * c - -prop_mult_unitL = - forAll intervals $ \a -> - Interval.singleton 1 * a == a - -prop_mult_unitR = - forAll intervals $ \a -> - a * Interval.singleton 1 == a - -prop_mult_dist = - forAll intervals $ \a -> - forAll intervals $ \b -> - forAll intervals $ \c -> - (a * (b + c)) `Interval.isSubsetOf` (a * b + a * c) - -prop_mult_singleton = - forAll arbitrary $ \r -> - forAll intervals $ \a -> - Interval.singleton r * a == r .*. a - -prop_mult_empty = - forAll intervals $ \a -> - Interval.empty * a == Interval.empty - -prop_mult_zero = - forAll intervals $ \a -> - not (Interval.null a) ==> Interval.singleton 0 * a == Interval.singleton 0 - -prop_mult_member = - forAll intervals $ \a -> - forAll intervals $ \b -> - and [ (x*y) `Interval.member` (a*b) - | x <- maybeToList $ Interval.pickup a - , y <- maybeToList $ Interval.pickup b - ] - -case_mult_test1 = ival1 * ival2 @?= ival3 - where - ival1 = Interval.interval (Just (True,1)) (Just (True,2)) - ival2 = Interval.interval (Just (True,1)) (Just (True,2)) - ival3 = Interval.interval (Just (True,1)) (Just (True,4)) - -case_mult_test2 = ival1 * ival2 @?= ival3 - where - ival1 = Interval.interval (Just (True,1)) (Just (True,2)) - ival2 = Interval.interval (Just (False,1)) (Just (False,2)) - ival3 = Interval.interval (Just (False,1)) (Just (False,4)) - -case_mult_test3 = ival1 * ival2 @?= ival3 - where - ival1 = Interval.interval (Just (False,1)) (Just (False,2)) - ival2 = Interval.interval (Just (False,1)) (Just (False,2)) - ival3 = Interval.interval (Just (False,1)) (Just (False,4)) - -case_mult_test4 = ival1 * ival2 @?= ival3 - where - ival1 = Interval.interval (Just (False,2)) Nothing - ival2 = Interval.interval (Just (False,3)) Nothing - ival3 = Interval.interval (Just (False,6)) Nothing - -case_mult_test5 = ival1 * ival2 @?= ival3 - where - ival1 = Interval.interval Nothing (Just (False,-3)) - ival2 = Interval.interval Nothing (Just (False,-2)) - ival3 = Interval.interval (Just (False,6)) Nothing - -case_mult_test6 = ival1 * ival2 @?= ival3 - where - ival1 = Interval.interval (Just (False,2)) Nothing - ival2 = Interval.interval Nothing (Just (False,-2)) - ival3 = Interval.interval Nothing (Just (False,-4)) - -{-------------------------------------------------------------------- - Fractional ---------------------------------------------------------------------} - -prop_recip_singleton = - forAll arbitrary $ \r -> - let n = fromIntegral (numerator r) - d = fromIntegral (denominator r) - in Interval.singleton n / Interval.singleton d == Interval.singleton (r::Rational) - -case_recip_pos = - recip pos @?= pos - -case_recip_neg = - recip neg @?= neg - -case_recip_test1 = recip i1 @?= i2 - where - i1, i2 :: Interval Rational - i1 = Interval.interval (Just (True,2)) Nothing - i2 = Interval.interval (Just (False,0)) (Just (True,1/2)) - -{-------------------------------------------------------------------- - Generators ---------------------------------------------------------------------} - -intervals :: Gen (Interval Rational) -intervals = do - lb <- arbitrary - ub <- arbitrary - return $ Interval.interval lb ub - -pos :: Interval Rational -pos = Interval.interval (Just (False,0)) Nothing - -neg :: Interval Rational -neg = Interval.interval Nothing (Just (False,0)) - -nonpos :: Interval Rational -nonpos = Interval.interval Nothing (Just (True,0)) - -nonneg :: Interval Rational -nonneg = Interval.interval (Just (True,0)) Nothing - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestLPFile.hs b/src/TestLPFile.hs deleted file mode 100644 --- a/src/TestLPFile.hs +++ /dev/null @@ -1,66 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} -module Main (main) where - -import Control.Monad -import Data.List -import Data.Maybe -import Test.HUnit hiding (Test) -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Text.LPFile - -case_testdata = checkString "testdata" testdata -case_test_indicator = checkFile "samples/lp/test-indicator.lp" -case_test_qcp = checkFile "samples/lp/test-qcp.lp" -case_test_qcp2 = checkFile "samples/lp/test-qcp2.lp" -case_test_qp = checkFile "samples/lp/test-qp.lp" -case_empty_obj_1 = checkFile "samples/lp/empty_obj_1.lp" -case_empty_obj_2 = checkFile "samples/lp/empty_obj_2.lp" - ------------------------------------------------------------------------- --- Sample data - -testdata :: String -testdata = unlines - [ "Maximize" - , " obj: x1 + 2 x2 + 3 x3 + x4" - , "Subject To" - , " c1: - x1 + x2 + x3 + 10 x4 <= 20" - , " c2: x1 - 3 x2 + x3 <= 30" - , " c3: x2 - 3.5 x4 = 0" - , "Bounds" - , " 0 <= x1 <= 40" - , " 2 <= x4 <= 3" - , "General" - , " x4" - , "End" - ] - ------------------------------------------------------------------------- --- Utilities - -checkFile :: FilePath -> IO () -checkFile fname = do - r <- parseFile fname - case r of - Left err -> assertFailure $ show err - Right lp -> - case render lp of - Nothing -> assertFailure "render failure" - Just _ -> return () - -checkString :: String -> String -> IO () -checkString name str = do - case parseString name str of - Left err -> assertFailure $ show err - Right lp -> - case render lp of - Nothing -> assertFailure "render failure" - Just _ -> return () - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestMIPSolver2.hs b/src/TestMIPSolver2.hs deleted file mode 100644 --- a/src/TestMIPSolver2.hs +++ /dev/null @@ -1,125 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} -module Main (main) where - -import Control.Monad -import Data.List -import Data.Ratio -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS -import Test.HUnit hiding (Test) -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Text.Printf - -import Data.Linear -import Simplex2 -import MIPSolver2 -import qualified Data.LA as LA - ------------------------------------------------------------------------- - -example1 :: (OptDir, LA.Expr Rational, [Atom Rational], IS.IntSet) -example1 = (optdir, obj, cs, ivs) - where - optdir = OptMax - x1 = LA.var 1 - x2 = LA.var 2 - x3 = LA.var 3 - x4 = LA.var 4 - obj = x1 .+. 2 .*. x2 .+. 3 .*. x3 .+. x4 - cs = - [ LA.Atom ((-1) .*. x1 .+. x2 .+. x3 .+. 10.*.x4) Le (LA.constant 20) - , LA.Atom (x1 .-. 3 .*. x2 .+. x3) Le (LA.constant 30) - , LA.Atom (x2 .-. 3.5 .*. x4) Eql (LA.constant 0) - , LA.Atom (LA.constant 0) Le x1 - , LA.Atom x1 Le (LA.constant 40) - , LA.Atom (LA.constant 0) Le x2 - , LA.Atom (LA.constant 0) Le x3 - , LA.Atom (LA.constant 2) Le x4 - , LA.Atom x4 Le (LA.constant 3) - ] - ivs = IS.singleton 4 - -case_test1 = do - let (optdir, obj, cs, ivs) = example1 - lp <- Simplex2.newSolver - replicateM 5 (Simplex2.newVar lp) - setOptDir lp optdir - setObj lp obj - mapM_ (Simplex2.assertAtom lp) cs - mip <- MIPSolver2.newSolver lp ivs - ret <- MIPSolver2.optimize mip (\_ _ -> return ()) - - ret @?= Simplex2.Optimum - - m <- MIPSolver2.model mip - forM_ [(1,40 % 1),(2,21 % 2),(3,39 % 2),(4,3 % 1)] $ \(var, val) -> - m IM.! var @?= val - - v <- MIPSolver2.getObjValue mip - v @?= (245 % 2) - -case_test1' = do - let (optdir, obj, cs, ivs) = example1 - lp <- Simplex2.newSolver - replicateM 5 (Simplex2.newVar lp) - setOptDir lp (f optdir) - setObj lp (lnegate obj) - mapM_ (Simplex2.assertAtom lp) cs - mip <- MIPSolver2.newSolver lp ivs - ret <- MIPSolver2.optimize mip (\_ _ -> return ()) - - ret @?= Simplex2.Optimum - - m <- MIPSolver2.model mip - forM_ [(1,40 % 1),(2,21 % 2),(3,39 % 2),(4,3 % 1)] $ \(var, val) -> - m IM.! var @?= val - - v <- MIPSolver2.getObjValue mip - v @?= (- 245 % 2) - - where - f OptMin = OptMax - f OptMax = OptMin - --- 『数理計画法の基礎』(坂和 正敏) p.109 例 3.8 -example2 = (optdir, obj, cs, ivs) - where - optdir = OptMin - [x1,x2,x3] = map LA.var [1..3] - obj = (-1) .*. x1 .-. 3 .*. x2 .-. 5 .*. x3 - cs = - [ LA.Atom (3 .*. x1 .+. 4 .*. x2) Le (LA.constant 10) - , LA.Atom (2 .*. x1 .+. x2 .+. x3) Le (LA.constant 7) - , LA.Atom (3.*.x1 .+. x2 .+. 4 .*. x3) Eql (LA.constant 12) - , LA.Atom (LA.constant 0) Le x1 - , LA.Atom (LA.constant 0) Le x2 - , LA.Atom (LA.constant 0) Le x3 - ] - ivs = IS.fromList [1,2] - -case_test2 = do - let (optdir, obj, cs, ivs) = example2 - lp <- Simplex2.newSolver - replicateM 4 (Simplex2.newVar lp) - setOptDir lp optdir - setObj lp obj - mapM_ (Simplex2.assertAtom lp) cs - mip <- MIPSolver2.newSolver lp ivs - ret <- MIPSolver2.optimize mip (\_ _ -> return ()) - - ret @?= Simplex2.Optimum - - m <- MIPSolver2.model mip - forM_ [(1,0 % 1),(2,2 % 1),(3,5 % 2)] $ \(var, val) -> - m IM.! var @?= val - - v <- MIPSolver2.getObjValue mip - v @?= (- 37 % 2) - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestPBFile.hs b/src/TestPBFile.hs deleted file mode 100644 --- a/src/TestPBFile.hs +++ /dev/null @@ -1,146 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} -module Main (main) where - -import Control.Monad -import Data.List -import Data.Maybe -import Test.HUnit hiding (Test) -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Text.PBFile - -case_exampleLIN = checkOPBString "exampleLIN" exampleLIN -case_exampleNLC1 = checkOPBString "exampleNLC1" exampleNLC1 -case_exampleNLC2 = checkOPBString "exampleNLC2" exampleNLC2 -case_exampleWBO1 = checkWBOString "exampleWBO1" exampleWBO1 -case_exampleWBO2 = checkWBOString "exampleWBO2" exampleWBO2 -case_exampleWBO3 = checkWBOString "exampleWBO3" exampleWBO3 - ------------------------------------------------------------------------- --- Sample data - -exampleLIN :: String -exampleLIN = unlines - [ "* #variable= 5 #constraint= 4" - , "*" - , "* this is a dummy instance" - , "*" - , "min: 1 x2 -1 x3 ;" - , "1 x1 +4 x2 -2 x5 >= 2;" - , "-1 x1 +4 x2 -2 x5 >= +3;" - , "12345678901234567890 x4 +4 x3 >= 10;" - , "* an equality constraint" - , "2 x2 +3 x4 +2 x1 +3 x5 = 5;" - ] - -exampleNLC1 :: String -exampleNLC1 = unlines - [ "* #variable= 5 #constraint= 4 #product= 5 sizeproduct= 13" - , "*" - , "* this is a dummy instance" - , "*" - , "min: 1 x2 x3 -1 x3 ;" - , "1 x1 +4 x1 ~x2 -2 x5 >= 2;" - , "-1 x1 +4 x2 -2 x5 >= 3;" - , "12345678901234567890 x4 +4 x3 >= 10;" - , "2 x2 x3 +3 x4 ~x5 +2 ~x1 x2 +3 ~x1 x2 x3 ~x4 ~x5 = 5 ;" - ] - -exampleNLC2 :: String -exampleNLC2 = unlines - [ "* #variable= 6 #constraint= 3 #product= 9 sizeproduct= 18" - , "*" - , "* Factorization problem: find the smallest P such that P*Q=N" - , "* P is a 3 bits number (x3 x2 x1)" - , "* Q is a 3 bits number (x6 x5 x4)" - , "* N=35" - , "* " - , "* minimize the value of P" - , "min: +1 x1 +2 x2 +4 x3 ;" - , "* P>=2 (to avoid trivial factorization)" - , "+1 x1 +2 x2 +4 x3 >=2;" - , "* Q>=2 (to avoid trivial factorization)" - , "+1 x4 +2 x5 +4 x6 >=2;" - , "*" - , "* P*Q=N" - , "+1 x1 x4 +2 x1 x5 +4 x1 x6 +2 x2 x4 +4 x2 x5 +8 x2 x6 +4 x3 x4 +8 x3 x5 +16 x3 x6 = 35;" - ] - -exampleWBO1 :: String -exampleWBO1 = unlines $ - [ "* #variable= 1 #constraint= 2 #soft= 2 mincost= 2 maxcost= 3 sumcost= 5" - , "soft: 6 ;" - , "[2] +1 x1 >= 1 ;" - , "[3] -1 x1 >= 0 ;" - ] - -exampleWBO2 :: String -exampleWBO2 = unlines $ - [ "* #variable= 2 #constraint= 3 #soft= 2 mincost= 2 maxcost= 3 sumcost= 5" - , "soft: 6 ;" - , "[2] +1 x1 >= 1 ;" - , "[3] +1 x2 >= 1 ;" - , "-1 x1 -1 x2 >= -1 ;" - ] - -exampleWBO3 :: String -exampleWBO3 = unlines $ - [ "* #variable= 4 #constraint= 6 #soft= 4 mincost= 2 maxcost= 5 sumcost= 14" - , "soft: 6 ;" - , "[2] +1 x1 >= 1;" - , "[3] +1 x2 >= 1;" - , "[4] +1 x3 >= 1;" - , "[5] +1 x4 >= 1;" - , "-1 x1 -1 x2 >= -1 ;" - , "-1 x3 -1 x4 >= -1 ;" - ] - ------------------------------------------------------------------------- --- Utilities - -checkOPBFile :: FilePath -> IO () -checkOPBFile fname = do - r <- parseOPBFile fname - case r of - Left err -> assertFailure $ show err - Right _ -> return () - -checkOPBString :: String -> String -> IO () -checkOPBString name str = do - case parseOPBString name str of - Left err -> assertFailure $ show err - Right _ -> return () - -checkWBOFile :: FilePath -> IO () -checkWBOFile fname = do - r <- parseWBOFile fname - case r of - Left err -> assertFailure $ show err - Right _ -> return () - -checkWBOString :: String -> String -> IO () -checkWBOString name str = do - case parseWBOString name str of - Left err -> assertFailure $ show err - Right _ -> return () - -testOPB :: String -> Bool -testOPB s = sf == sf2 - where - Right sf = parseOPBString "-" s - s2 = showOPB sf "" - Right sf2 = parseOPBString "-" s2 - -testWBO :: String -> Bool -testWBO s = sf == sf2 - where - Right sf = parseWBOString "-" s - s2 = showWBO sf "" - Right sf2 = parseWBOString "-" s2 - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestPolynomial.hs b/src/TestPolynomial.hs deleted file mode 100644 --- a/src/TestPolynomial.hs +++ /dev/null @@ -1,543 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} - -import Prelude hiding (lex) -import Control.Monad -import Data.List -import Data.Ratio -import qualified Data.Set as Set -import qualified Data.Map as Map -import Test.HUnit hiding (Test) -import Test.QuickCheck -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Test.Framework.Providers.QuickCheck2 - -import Data.Polynomial -import Data.Polynomial.GBase -import Data.Polynomial.Sturm -import qualified Data.Polynomial.Lagrange as Lagrange -import qualified Data.Interval as Interval - -{-------------------------------------------------------------------- - Polynomial type ---------------------------------------------------------------------} - -prop_plus_comm = - forAll polynomials $ \a -> - forAll polynomials $ \b -> - a + b == b + a - -prop_plus_assoc = - forAll polynomials $ \a -> - forAll polynomials $ \b -> - forAll polynomials $ \c -> - a + (b + c) == (a + b) + c - -prop_plus_unitL = - forAll polynomials $ \a -> - constant 0 + a == a - -prop_plus_unitR = - forAll polynomials $ \a -> - a + constant 0 == a - -prop_prod_comm = - forAll polynomials $ \a -> - forAll polynomials $ \b -> - a * b == b * a - -prop_prod_assoc = - forAll polynomials $ \a -> - forAll polynomials $ \b -> - forAll polynomials $ \c -> - a * (b * c) == (a * b) * c - -prop_prod_unitL = - forAll polynomials $ \a -> - constant 1 * a == a - -prop_prod_unitR = - forAll polynomials $ \a -> - a * constant 1 == a - -prop_distL = - forAll polynomials $ \a -> - forAll polynomials $ \b -> - forAll polynomials $ \c -> - a * (b + c) == a * b + a * c - -prop_distR = - forAll polynomials $ \a -> - forAll polynomials $ \b -> - forAll polynomials $ \c -> - (b + c) * a == b * a + c * a - -prop_negate = - forAll polynomials $ \a -> - a + negate a == 0 - -prop_negate_involution = - forAll polynomials $ \a -> - negate (negate a) == a - -prop_polyMDivMod = - forAll polynomials $ \g -> - forAll (replicateM 3 polynomials) $ \fs -> - all (0/=) fs ==> - let (qs, r) = polyMDivMod lex g fs - in sum (zipWith (*) fs qs) + r == g - -{-------------------------------------------------------------------- - Univalent polynomials ---------------------------------------------------------------------} - -prop_polyDivMod = - forAll upolynomials $ \a -> - forAll upolynomials $ \b -> - b /= 0 ==> - let (q,r) = polyDivMod a b - in a == q*b + r && (r==0 || deg b > deg r) - -case_polyDivMod_1 = g*q + r @?= f - where - x :: UPolynomial Rational - x = var () - f = x^3 + x^2 + x - g = x^2 + 1 - (q,r) = f `polyDivMod` g - -prop_polyGCD_divisible = - forAll upolynomials $ \a -> - forAll upolynomials $ \b -> - let c = polyGCD a b - in a `polyMod` c == 0 && b `polyMod` c == 0 - -prop_polyGCD_comm = - forAll upolynomials $ \a -> - forAll upolynomials $ \b -> - polyGCD a b == polyGCD b a - -case_polyGCD_1 = polyGCD f1 f2 @?= 1 - where - x :: UPolynomial Rational - x = var () - f1 = x^3 + x^2 + x - f2 = x^2 + 1 - -prop_polyLCM_divisible = - forAll upolynomials $ \a -> - forAll upolynomials $ \b -> - (a /= 0 && b /= 0) ==> - let c = polyLCM a b - in c `polyMod` a == 0 && c `polyMod` b == 0 - -prop_polyLCM_comm = - forAll upolynomials $ \a -> - forAll upolynomials $ \b -> - polyLCM a b == polyLCM b a - -prop_deriv_integral = - forAll upolynomials $ \a -> - deriv (integral a x) x == a - where - x = () - -prop_integral_deriv = - forAll upolynomials $ \a -> - deg (integral (deriv a x) x - a) == 0 - where - x = () - -{-------------------------------------------------------------------- - Monomial ---------------------------------------------------------------------} - -{-------------------------------------------------------------------- - Monic Monomial ---------------------------------------------------------------------} - -prop_mmDegreeOfProduct = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - mmDegree (a `mmProd` b) == mmDegree a + mmDegree b - -prop_mmDegreeOfOne = - mmDegree mmOne == 0 - -prop_mmProd_unitL = - forAll monicMonomials $ \a -> - mmOne `mmProd` a == a - -prop_mmProd_unitR = - forAll monicMonomials $ \a -> - a `mmProd` mmOne == a - -prop_mmProd_comm = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - a `mmProd` b == b `mmProd` a - -prop_mmProd_assoc = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - forAll monicMonomials $ \c -> - a `mmProd` (b `mmProd` c) == (a `mmProd` b) `mmProd` c - -prop_mmProd_Divisible = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - let c = a `mmProd` b - in mmDivisible c a && mmDivisible c b - -prop_mmProd_Div = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - let c = a `mmProd` b - in c `mmDiv` a == b && c `mmDiv` b == a - -case_mmDeriv = mmDeriv p 1 @?= (2, q) - where - p = mmFromList [(1,2),(2,4)] - q = mmFromList [(1,1),(2,4)] - --- lcm (x1^2 * x2^4) (x1^3 * x2^1) = x1^3 * x2^4 -case_mmLCM = mmLCM p1 p2 @?= mmFromList [(1,3),(2,4)] - where - p1 = mmFromList [(1,2),(2,4)] - p2 = mmFromList [(1,3),(2,1)] - --- gcd (x1^2 * x2^4) (x2^1 * x3^2) = x2 -case_mmGCD = mmGCD p1 p2 @?= mmFromList [(2,1)] - where - p1 = mmFromList [(1,2),(2,4)] - p2 = mmFromList [(2,1),(3,2)] - -prop_mmLCM_divisible = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - let c = mmLCM a b - in c `mmDivisible` a && c `mmDivisible` b - -prop_mmGCD_divisible = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - let c = mmGCD a b - in a `mmDivisible` c && b `mmDivisible` c - -{-------------------------------------------------------------------- - Monomial Order ---------------------------------------------------------------------} - --- http://en.wikipedia.org/wiki/Monomial_order -case_lex = sortBy lex [a,b,c,d] @?= [b,a,d,c] - where - x = 1 - y = 2 - z = 3 - a = mmFromList [(x,1),(y,2),(z,1)] - b = mmFromList [(z,2)] - c = mmFromList [(x,3)] - d = mmFromList [(x,2),(z,2)] - --- http://en.wikipedia.org/wiki/Monomial_order -case_grlex = sortBy grlex [a,b,c,d] @?= [b,c,a,d] - where - x = 1 - y = 2 - z = 3 - a = mmFromList [(x,1),(y,2),(z,1)] - b = mmFromList [(z,2)] - c = mmFromList [(x,3)] - d = mmFromList [(x,2),(z,2)] - --- http://en.wikipedia.org/wiki/Monomial_order -case_grevlex = sortBy grevlex [a,b,c,d] @?= [b,c,d,a] - where - x = 1 - y = 2 - z = 3 - a = mmFromList [(x,1),(y,2),(z,1)] - b = mmFromList [(z,2)] - c = mmFromList [(x,3)] - d = mmFromList [(x,2),(z,2)] - -prop_refl_lex = propRefl lex -prop_refl_grlex = propRefl grlex -prop_refl_grevlex = propRefl grevlex - -prop_trans_lex = propTrans lex -prop_trans_grlex = propTrans grlex -prop_trans_grevlex = propTrans grevlex - -prop_sym_lex = propSym lex -prop_sym_grlex = propSym grlex -prop_sym_grevlex = propSym grevlex - -prop_monomial_order_property1_lex = monomialOrderProp1 lex -prop_monomial_order_property1_grlex = monomialOrderProp1 grlex -prop_monomial_order_property1_grevlex = monomialOrderProp1 grevlex - -prop_monomial_order_property2_lex = monomialOrderProp2 lex -prop_monomial_order_property2_grlex = monomialOrderProp2 grlex -prop_monomial_order_property2_grevlex = monomialOrderProp2 grevlex - -propRefl cmp = - forAll monicMonomials $ \a -> cmp a a == EQ - -propTrans cmp = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - cmp a b == LT ==> - forAll monicMonomials $ \c -> - cmp b c == LT ==> cmp a c == LT - -propSym cmp = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - cmp a b == flipOrdering (cmp b a) - where - flipOrdering EQ = EQ - flipOrdering LT = GT - flipOrdering GT = LT - -monomialOrderProp1 cmp = - forAll monicMonomials $ \a -> - forAll monicMonomials $ \b -> - let r = cmp a b - in cmp a b /= EQ ==> - forAll monicMonomials $ \c -> - cmp (a `mmProd` c) (b `mmProd` c) == r - -monomialOrderProp2 cmp = - forAll monicMonomials $ \a -> - a /= mmOne ==> cmp mmOne a == LT - -{-------------------------------------------------------------------- - Gröbner basis ---------------------------------------------------------------------} - --- http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf --- Example 1 -case_spolynomial = spolynomial grlex f g @?= - x^3*y^3 - constant (1/3) * y^3 + x^2 - where - x = var 1 - y = var 2 - f, g :: Polynomial Rational Int - f = x^3*y^2 - x^2*y^3 + x - g = 3*x^4*y + y^2 - - --- http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf --- Exercise 1 -case_buchberger1 = Set.fromList gbase @?= Set.fromList expected - where - gbase = buchberger lex [x^2-y, x^3-z] - expected = [y^3 - z^2, x^2 - y, x*z - y^2, x*y - z] - - x :: Polynomial Rational Int - x = var 1 - y = var 2 - z = var 3 - --- http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf --- Exercise 2 -case_buchberger2 = Set.fromList gbase @?= Set.fromList expected - where - gbase = buchberger grlex [x^3-2*x*y, x^2*y-2*y^2+x] - expected = [x^2, x*y, y^2 - constant (1/2) * x] - - x :: Polynomial Rational Int - x = var 1 - y = var 2 - --- http://www.iisdavinci.it/jeometry/buchberger.html -case_buchberger3 = Set.fromList gbase @?= Set.fromList expected - where - gbase = buchberger lex [x^2+2*x*y^2, x*y+2*y^3-1] - expected = [x, y^3 - constant (1/2)] - x :: Polynomial Rational Int - x = var 1 - y = var 2 - --- http://www.orcca.on.ca/~reid/NewWeb/DetResDes/node4.html --- 時間がかかるので自動実行されるテストケースには含めていない -test_buchberger4 = Set.fromList gbase @?= Set.fromList expected - where - x :: Polynomial Rational Int - x = var 1 - y = var 2 - z = var 3 - - gbase = buchberger lex [x^2+y*z-2, x*z+y^2-3, x*y+z^2-5] - - expected = reduceGBase lex $ - [ 8*z^8-100*z^6+438*z^4-760*z^2+361 - , 361*y+8*z^7+52*z^5-740*z^3+1425*z - , 361*x-88*z^7+872*z^5-2690*z^3+2375*z - ] -{- -Risa/Asir での結果 - -load("gr"); -gr([x^2+y*z-2, x*z+y^2-3, x*y+z^2-5],[x,y,z], 2); - -[8*z^8-100*z^6+438*z^4-760*z^2+361, -361*y+8*z^7+52*z^5-740*z^3+1425*z, -361*x-88*z^7+872*z^5-2690*z^3+2375*z] --} - --- Seven Trees in One --- http://arxiv.org/abs/math/9405205 -case_Seven_Trees_in_One = reduce lex (x^7 - x) gbase @?= 0 - where - x :: Polynomial Rational Int - x = var 1 - gbase = buchberger lex [x-(x^2 + 1)] - --- Non-linear loop invariant generation using Gröbner bases --- http://portal.acm.org/citation.cfm?id=964028 --- http://www-step.stanford.edu/papers/popl04.pdf --- Example 3 --- Consider again the ideal from Example 2; I = {f : x^2-y, g : y-z, h --- : x+z}. The Gröbner basis for I is G = {f' : z^2-z, g : y-z, h : --- x+z}. With this basis, every reduction of p : x^2 - y^2 will yield --- a normal form 0. -case_sankaranarayanan04nonlinear = do - Set.fromList gbase @?= Set.fromList [f', g, h] - reduce lex (x^2 - y^2) gbase @?= 0 - where - x :: Polynomial Rational Int - x = var 1 - y = var 2 - z = var 3 - f = x^2 - y - g = y - z - h = x + z - f' = z^2 - z - gbase = buchberger lex [f, g, h] - -{-------------------------------------------------------------------- - Generators ---------------------------------------------------------------------} - -monicMonomials :: Gen (MonicMonomial Int) -monicMonomials = do - size <- choose (0, 3) - xs <- replicateM size $ do - v <- choose (-5, 5) - e <- liftM ((+1) . abs) arbitrary - return $ mmFromList [(v,e)] - return $ foldl mmProd mmOne xs - -monomials :: Gen (Monomial Rational Int) -monomials = do - m <- monicMonomials - c <- arbitrary - return (c,m) - -polynomials :: Gen (Polynomial Rational Int) -polynomials = do - size <- choose (0, 5) - xs <- replicateM size monomials - return $ sum $ map fromMonomial xs - -umonicMonomials :: Gen (MonicMonomial ()) -umonicMonomials = do - size <- choose (0, 3) - xs <- replicateM size $ do - e <- choose (1, 4) - return $ mmFromList [((),e)] - return $ foldl mmProd mmOne xs - -umonomials :: Gen (Monomial Rational ()) -umonomials = do - m <- umonicMonomials - c <- arbitrary - return (c,m) - -upolynomials :: Gen (UPolynomial Rational) -upolynomials = do - size <- choose (0, 5) - xs <- replicateM size umonomials - return $ sum $ map fromMonomial xs - ------------------------------------------------------------------------- - --- http://mathworld.wolfram.com/SturmFunction.html -case_sturmChain = sturmChain p0 @?= chain - where - x = var () - p0 = x^5 - 3*x - 1 - p1 = 5*x^4 - 3 - p2 = constant (1/5) * (12*x + 5) - p3 = constant (59083 / 20736) - chain = [p0, p1, p2, p3] - --- http://mathworld.wolfram.com/SturmFunction.html -case_numRoots_1 = - sequence_ - [ numRoots p (Interval.closedInterval (-2) 0) @?= 2 - , numRoots p (Interval.closedInterval 0 2) @?= 1 - , numRoots p (Interval.closedInterval (-1.5) (-1.0)) @?= 1 - , numRoots p (Interval.closedInterval (-0.5) 0) @?= 1 - , numRoots p (Interval.closedInterval 1 (1.5)) @?= 1 - ] - where - x = var () - p = x^5 - 3*x - 1 - --- check interpretation of intervals -case_numRoots_2 = - sequence_ - [ numRoots p (Interval.interval (Just (False,2)) (Just (True,3))) @?= 0 - , numRoots p (Interval.interval (Just (True,2)) (Just (True,3))) @?= 1 - , numRoots p (Interval.interval (Just (False,1)) (Just (False,2))) @?= 0 - , numRoots p (Interval.interval (Just (False,1)) (Just (True,2))) @?= 1 - ] - where - x = var () - p = x^2 - 4 - -case_separate = do - forM_ (zip vals intervals) $ \(v,ival) -> do - Interval.member v ival @?= True - forM_ (filter (v/=) vals) $ \v2 -> do - Interval.member v2 ival @?= False - where - x = var () - p = x^5 - 3*x - 1 - intervals = separate p - vals = [-1.21465, -0.334734, 1.38879] - ------------------------------------------------------------------------- - --- http://en.wikipedia.org/wiki/Lagrange_polynomial -case_Lagrange_interpolation_1 = p @?= q - where - x :: UPolynomial Rational - x = var () - p = Lagrange.interpolation - [ (1, 1) - , (2, 4) - , (3, 9) - ] - q = x^2 - --- http://en.wikipedia.org/wiki/Lagrange_polynomial -case_Lagrange_interpolation_2 = p @?= q - where - x :: UPolynomial Rational - x = var () - p = Lagrange.interpolation - [ (1, 1) - , (2, 8) - , (3, 27) - ] - q = 6*x^2 - 11*x + 6 - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestSAT.hs b/src/TestSAT.hs deleted file mode 100644 --- a/src/TestSAT.hs +++ /dev/null @@ -1,475 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} -module Main (main) where - -import Control.Monad -import Data.List -import Test.HUnit hiding (Test) -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import SAT -import SAT.Types -import qualified SAT.TseitinEncoder as Tseitin -import SAT.TseitinEncoder (Formula (..)) - --- should be SAT -case_solve_SAT :: IO () -case_solve_SAT = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addClause solver [literal x1 True, literal x2 True] -- x1 or x2 - addClause solver [literal x1 True, literal x2 False] -- x1 or not x2 - addClause solver [literal x1 False, literal x2 False] -- not x1 or not x2 - ret <- solve solver - ret @?= True - --- shuld be UNSAT -case_solve_UNSAT :: IO () -case_solve_UNSAT = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addClause solver [literal x1 True, literal x2 True] -- x1 or x2 - addClause solver [literal x1 False, literal x2 True] -- not x1 or x2 - addClause solver [literal x1 True, literal x2 False] -- x1 or not x2 - addClause solver [literal x1 False, literal x2 False] -- not x2 or not x2 - ret <- solve solver - ret @?= False - --- top level でいきなり矛盾 -case_root_inconsistent :: IO () -case_root_inconsistent = do - solver <- newSolver - x1 <- newVar solver - addClause solver [literal x1 True] - addClause solver [literal x1 False] - ret <- solve solver -- unsat - ret @?= False - --- incremental に制約を追加 -case_incremental_solving :: IO () -case_incremental_solving = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addClause solver [literal x1 True, literal x2 True] -- x1 or x2 - addClause solver [literal x1 True, literal x2 False] -- x1 or not x2 - addClause solver [literal x1 False, literal x2 False] -- not x1 or not x2 - ret <- solve solver -- sat - ret @?= True - - addClause solver [literal x1 False, literal x2 True] -- not x1 or x2 - ret <- solve solver -- unsat - ret @?= False - --- 制約なし -case_empty_constraint :: IO () -case_empty_constraint = do - solver <- newSolver - ret <- solve solver - ret @?= True - --- 空の節 -case_empty_claue :: IO () -case_empty_claue = do - solver <- newSolver - addClause solver [] - ret <- solve solver - ret @?= False - --- 自明に真な節 -case_excluded_middle_claue :: IO () -case_excluded_middle_claue = do - solver <- newSolver - x1 <- newVar solver - addClause solver [x1, -x1] -- x1 or not x1 - ret <- solve solver - ret @?= True - --- 冗長な節 -case_redundant_clause :: IO () -case_redundant_clause = do - solver <- newSolver - x1 <- newVar solver - addClause solver [x1,x1] -- x1 or x1 - ret <- solve solver - ret @?= True - -case_instantiateClause :: IO () -case_instantiateClause = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addClause solver [x1] - addClause solver [x1,x2] - addClause solver [-x1,x2] - ret <- solve solver - ret @?= True - -case_instantiateAtLeast :: IO () -case_instantiateAtLeast = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - x4 <- newVar solver - addClause solver [x1] - - addAtLeast solver [x1,x2,x3,x4] 2 - ret <- solve solver - ret @?= True - - addAtLeast solver [-x1,-x2,-x3,-x4] 2 - ret <- solve solver - ret @?= True - -case_inconsistent_AtLeast :: IO () -case_inconsistent_AtLeast = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addAtLeast solver [x1,x2] 3 - ret <- solve solver -- unsat - ret @?= False - -case_trivial_AtLeast :: IO () -case_trivial_AtLeast = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addAtLeast solver [x1,x2] 0 - ret <- solve solver - ret @?= True - - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addAtLeast solver [x1,x2] (-1) - ret <- solve solver - ret @?= True - -case_AtLeast_1 :: IO () -case_AtLeast_1 = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - addAtLeast solver [x1,x2,x3] 2 - addAtLeast solver [-x1,-x2,-x3] 2 - ret <- solve solver -- unsat - ret @?= False - -case_AtLeast_2 :: IO () -case_AtLeast_2 = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - x4 <- newVar solver - addAtLeast solver [x1,x2,x3,x4] 2 - addClause solver [-x1,-x2] - addClause solver [-x1,-x3] - ret <- solve solver - ret @?= True - -case_AtLeast_3 :: IO () -case_AtLeast_3 = do - forM_ [(-1) .. 3] $ \n -> do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addAtLeast solver [x1,x2] n - ret <- solve solver - assertEqual ("case_AtLeast3_" ++ show n) (n <= 2) ret - --- from http://www.cril.univ-artois.fr/PB11/format.pdf -case_PB_sample1 :: IO () -case_PB_sample1 = do - solver <- newSolver - - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - x4 <- newVar solver - x5 <- newVar solver - - addPBAtLeast solver [(1,x1),(4,x2),(-2,x5)] 2 - addPBAtLeast solver [(-1,x1),(4,x2),(-2,x5)] 3 - addPBAtLeast solver [(12345678901234567890,x4),(4,x3)] 10 - addPBExactly solver [(2,x2),(3,x4),(2,x1),(3,x5)] 5 - - ret <- solve solver - ret @?= True - --- 一部の変数を否定に置き換えたもの -case_PB_sample1' :: IO () -case_PB_sample1' = do - solver <- newSolver - - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - x4 <- newVar solver - x5 <- newVar solver - - addPBAtLeast solver [(1,x1),(4,-x2),(-2,x5)] 2 - addPBAtLeast solver [(-1,x1),(4,-x2),(-2,x5)] 3 - addPBAtLeast solver [(12345678901234567890,-x4),(4,x3)] 10 - addPBExactly solver [(2,-x2),(3,-x4),(2,x1),(3,x5)] 5 - - ret <- solve solver - ret @?= True - --- いきなり矛盾したPB制約 -case_root_inconsistent_PB :: IO () -case_root_inconsistent_PB = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addPBAtLeast solver [(2,x1),(3,x2)] 6 - ret <- solve solver - ret @?= False - -case_pb_propagate :: IO () -case_pb_propagate = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addPBAtLeast solver [(1,x1),(3,x2)] 3 - addClause solver [-x1] - ret <- solve solver - ret @?= True - -case_solveWith_1 :: IO () -case_solveWith_1 = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - addClause solver [x1, x2] -- x1 or x2 - addClause solver [x1, -x2] -- x1 or not x2 - addClause solver [-x1, -x2] -- not x1 or not x2 - addClause solver [-x3, -x1, x2] -- not x3 or not x1 or x2 - - ret <- solve solver -- sat - ret @?= True - - ret <- solveWith solver [x3] -- unsat - ret @?= False - - ret <- solve solver -- sat - ret @?= True - -case_solveWith_2 :: IO () -case_solveWith_2 = do - solver <- newSolver - x1 <- newVar solver - x2 <- newVar solver - addClause solver [-x1, x2] -- -x1 or x2 - addClause solver [x1] -- x1 - - ret <- solveWith solver [x2] - ret @?= True - - ret <- solveWith solver [-x2] - ret @?= False - ------------------------------------------------------------------------- - --- -4*(not x1) + 3*x1 + 10*(not x2) >= 3 --- ⇔ -4*(1 - x1) + 3*x1 + 10*(not x2) >= 3 --- ⇔ -4 + 4*x1 + 3*x1 + 10*(not x2) >= 3 --- ⇔ 7*x1 + 10*(not x2) >= 7 --- ⇔ 7*x1 + 7*(not x2) >= 7 --- ⇔ x1 + (not x2) >= 1 -case_normalizePBAtLeast :: Assertion -case_normalizePBAtLeast = (sort lhs, rhs) @?= (sort [(1,x1),(1,-x2)], 1) - where - x1 = 1 - x2 = 2 - (lhs,rhs) = normalizePBAtLeast ([(-4,-x1),(3,x1),(10,-x2)], 3) - -case_normalizePBExactly_1 :: Assertion -case_normalizePBExactly_1 = (sort lhs, rhs) @?= (sort [(3,x1),(2,x2)], 1) - where - x1 = 1 - x2 = 2 - (lhs,rhs) = normalizePBExactly ([(6,x1),(4,x2)], 2) - -case_normalizePBExactly_2 :: Assertion -case_normalizePBExactly_2 = (sort lhs, rhs) @?= ([], 1) - where - x1 = 1 - x2 = 2 - x3 = 3 - (lhs,rhs) = normalizePBExactly ([(2,x1),(2,x2),(2,x3)], 3) - -case_cutResolve_1 :: Assertion -case_cutResolve_1 = (sort lhs, rhs) @?= (sort [(1,x3),(1,x4)], 1) - where - x1 = 1 - x2 = 2 - x3 = 3 - x4 = 4 - pb1 = ([(1,x1), (1,x2), (1,x3)], 1) - pb2 = ([(2,-x1), (2,-x2), (1,x4)], 3) - (lhs,rhs) = cutResolve pb1 pb2 x1 - -case_cutResolve_2 :: Assertion -case_cutResolve_2 = (sort lhs, rhs) @?= (sort [(3,x1),(2,-x2),(2,x4)], 3) - where - x1 = 1 - x2 = 2 - x3 = 3 - x4 = 4 - pb1 = ([(3,x1), (2,-x2), (1,x3), (1,x4)], 3) - pb2 = ([(1,-x3), (1,x4)], 1) - (lhs,rhs) = cutResolve pb1 pb2 x3 - -case_cardinalityReduction :: Assertion -case_cardinalityReduction = (sort lhs, rhs) @?= ([1,2,3,4,5],4) - where - (lhs, rhs) = cardinalityReduction ([(6,1),(5,2),(4,3),(3,4),(2,5),(1,6)], 17) - --- from "Pueblo: A Hybrid Pseudo-Boolean SAT Solver" --- clauseがunitになるレベルで、PB制約が違反状態のままという例。 -case_hybridLearning_1 :: IO () -case_hybridLearning_1 = do - solver <- newSolver - [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11] <- replicateM 11 (newVar solver) - - addClause solver [x11, x10, x9] -- C1 - addClause solver [x8, x7, x6] -- C2 - addClause solver [x5, x4, x3] -- C3 - addAtLeast solver [-x2, -x5, -x8, -x11] 3 -- C4 - addAtLeast solver [-x1, -x4, -x7, -x10] 3 -- C5 - - replicateM 3 (varBumpActivity solver x3) - setVarPolarity solver x3 False - - replicateM 2 (varBumpActivity solver x6) - setVarPolarity solver x6 False - - replicateM 1 (varBumpActivity solver x9) - setVarPolarity solver x9 False - - setVarPolarity solver x1 True - - setLearningStrategy solver LearningHybrid - ret <- solve solver - ret @?= True - --- from "Pueblo: A Hybrid Pseudo-Boolean SAT Solver" --- clauseがunitになるレベルで、PB制約が違反状態のままという例。 --- さらに、学習したPB制約はunitにはならない。 -case_hybridLearning_2 :: IO () -case_hybridLearning_2 = do - solver <- newSolver - [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12] <- replicateM 12 (newVar solver) - - addClause solver [x11, x10, x9] -- C1 - addClause solver [x8, x7, x6] -- C2 - addClause solver [x5, x4, x3] -- C3 - addAtLeast solver [-x2, -x5, -x8, -x11] 3 -- C4 - addAtLeast solver [-x1, -x4, -x7, -x10] 3 -- C5 - - addClause solver [x12, -x3] - addClause solver [x12, -x6] - addClause solver [x12, -x9] - - varBumpActivity solver x12 - setVarPolarity solver x12 False - - setLearningStrategy solver LearningHybrid - ret <- solve solver - ret @?= True - --- regression test for the bug triggered by normalized-blast-floppy1-8.ucl.opb.bz2 -case_addPBAtLeast_regression :: IO () -case_addPBAtLeast_regression = do - solver <- newSolver - [x1,x2,x3,x4] <- replicateM 4 (newVar solver) - addClause solver [-x1] - addClause solver [-x2, -x3] - addClause solver [-x2, -x4] - addPBAtLeast solver [(1,x1),(2,x2),(1,x3),(1,x4)] 3 - ret <- solve solver - ret @?= False - ------------------------------------------------------------------------- - -case_addFormula = do - solver <- newSolver - enc <- Tseitin.newEncoder solver - - [x1,x2,x3,x4,x5] <- replicateM 5 $ liftM Var $ newVar solver - Tseitin.addFormula enc $ Or [Imply x1 (And [x3,x4]), Imply x2 (And [x3,x5])] - -- x6 = x3 ∧ x4 - -- x7 = x3 ∧ x5 - Tseitin.addFormula enc $ Or [x1, x2] - Tseitin.addFormula enc $ Imply x4 (Not x5) - ret <- solve solver - ret @?= True - - Tseitin.addFormula enc $ Equiv x2 x4 - ret <- solve solver - ret @?= True - - Tseitin.addFormula enc $ Equiv x1 x5 - ret <- solve solver - ret @?= True - - Tseitin.addFormula enc $ Imply (Not x1) (And [x3,x5]) - ret <- solve solver - ret @?= True - - Tseitin.addFormula enc $ Imply (Not x2) (And [x3,x4]) - ret <- solve solver - ret @?= False - -case_encodeConj = do - solver <- newSolver - enc <- Tseitin.newEncoder solver - x1 <- newVar solver - x2 <- newVar solver - x3 <- Tseitin.encodeConj enc [x1,x2] - - ret <- solveWith solver [x3] - ret @?= True - m <- model solver - evalLit m x1 @?= True - evalLit m x2 @?= True - evalLit m x3 @?= True - - ret <- solveWith solver [-x3] - ret @?= True - m <- model solver - (evalLit m x1 && evalLit m x2) @?= False - evalLit m x3 @?= False - -case_encodeDisj = do - solver <- newSolver - enc <- Tseitin.newEncoder solver - x1 <- newVar solver - x2 <- newVar solver - x3 <- Tseitin.encodeDisj enc [x1,x2] - - ret <- solveWith solver [x3] - ret @?= True - m <- model solver - (evalLit m x1 || evalLit m x2) @?= True - evalLit m x3 @?= True - - ret <- solveWith solver [-x3] - ret @?= True - m <- model solver - evalLit m x1 @?= False - evalLit m x2 @?= False - evalLit m x3 @?= False - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/TestSimplex2.hs b/src/TestSimplex2.hs deleted file mode 100644 --- a/src/TestSimplex2.hs +++ /dev/null @@ -1,409 +0,0 @@ -{-# LANGUAGE TemplateHaskell #-} -module Main (main) where - -import Control.Monad -import Data.List -import Data.Ratio -import Test.HUnit hiding (Test) -import Test.Framework (Test, defaultMain, testGroup) -import Test.Framework.TH -import Test.Framework.Providers.HUnit -import Text.Printf - -import Data.Linear -import Simplex2 -import qualified Data.LA as LA - -case_test1 :: IO () -case_test1 = do - solver <- newSolver - x <- newVar solver - y <- newVar solver - z <- newVar solver - assertAtom solver (LA.fromTerms [(7,x), (12,y), (31,z)] .==. LA.constant 17) - assertAtom solver (LA.fromTerms [(3,x), (5,y), (14,z)] .==. LA.constant 7) - assertAtom solver (LA.var x .>=. LA.constant 1) - assertAtom solver (LA.var x .<=. LA.constant 40) - assertAtom solver (LA.var y .>=. LA.constant (-50)) - assertAtom solver (LA.var y .<=. LA.constant 50) - - ret <- check solver - ret @?= True - - vx <- getValue solver x - vy <- getValue solver y - vz <- getValue solver z - 7*vx + 12*vy + 31*vz @?= 17 - 3*vx + 5*vy + 14*vz @?= 7 - assertBool (printf "vx should be >=1 but %s" (show vx)) $ vx >= 1 - assertBool (printf "vx should be <=40 but %s" (show vx)) $ vx <= 40 - assertBool (printf "vx should be >=-50 but %s" (show vy)) $ vy >= -50 - assertBool (printf "vx should be <=50 but %s" (show vy)) $ vy <= 50 - -case_test2 :: IO () -case_test2 = do - solver <- newSolver - x <- newVar solver - y <- newVar solver - assertAtom solver (LA.fromTerms [(11,x), (13,y)] .>=. LA.constant 27) - assertAtom solver (LA.fromTerms [(11,x), (13,y)] .<=. LA.constant 45) - assertAtom solver (LA.fromTerms [(7,x), (-9,y)] .>=. LA.constant (-10)) - assertAtom solver (LA.fromTerms [(7,x), (-9,y)] .<=. LA.constant 4) - - ret <- check solver - ret @?= True - - vx <- getValue solver x - vy <- getValue solver y - let v1 = 11*vx + 13*vy - v2 = 7*vx - 9*vy - assertBool (printf "11*vx + 13*vy should be >=27 but %s" (show v1)) $ 27 <= v1 - assertBool (printf "11*vx + 13*vy should be <=45 but %s" (show v1)) $ v1 <= 45 - assertBool (printf "7*vx - 9*vy should be >=-10 but %s" (show v2)) $ -10 <= v2 - assertBool (printf "7*vx - 9*vy should be >=-10 but %s" (show v2)) $ v2 <= 4 - - -{- -Minimize - obj: - x1 - 2 x2 - 3 x3 - x4 -Subject To - c1: - x1 + x2 + x3 + 10 x4 <= 20 - c2: x1 - 3 x2 + x3 <= 30 - c3: x2 - 3.5 x4 = 0 -Bounds - 0 <= x1 <= 40 - 2 <= x4 <= 3 -End --} -case_test3 :: IO () -case_test3 = do - solver <- newSolver - - _ <- newVar solver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - x4 <- newVar solver - - setObj solver (LA.fromTerms [(-1,x1), (-2,x2), (-3,x3), (-1,x4)]) - - assertAtom solver (LA.fromTerms [(-1,x1), (1,x2), (1,x3), (10,x4)] .<=. LA.constant 20) - assertAtom solver (LA.fromTerms [(1,x1), (-3,x2), (1,x3)] .<=. LA.constant 30) - assertAtom solver (LA.fromTerms [(1,x2), (-3.5,x4)] .==. LA.constant 0) - - assertAtom solver (LA.fromTerms [(1,x1)] .>=. LA.constant 0) - assertAtom solver (LA.fromTerms [(1,x1)] .<=. LA.constant 40) - assertAtom solver (LA.fromTerms [(1,x2)] .>=. LA.constant 0) - assertAtom solver (LA.fromTerms [(1,x3)] .>=. LA.constant 0) - assertAtom solver (LA.fromTerms [(1,x4)] .>=. LA.constant 2) - assertAtom solver (LA.fromTerms [(1,x4)] .<=. LA.constant 3) - - ret1 <- check solver - ret1 @?= True - - ret2 <- optimize solver defaultOptions - ret2 @?= Optimum - -{- -http://www.math.cuhk.edu.hk/~wei/lpch5.pdf -example 5.7 - -minimize 3 x1 + 4 x2 + 5 x3 -subject to -1 x1 + 2 x2 + 3 x3 >= 5 -2 x1 + 2 x2 + 1 x3 >= 6 - -optimal value is 11 --} -case_test6 :: IO () -case_test6 = do - solver <- newSolver - - _ <- newVar solver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - - assertLower solver x1 0 - assertLower solver x2 0 - assertLower solver x3 0 - assertAtom solver (LA.fromTerms [(1,x1),(2,x2),(3,x3)] .>=. LA.constant 5) - assertAtom solver (LA.fromTerms [(2,x1),(2,x2),(1,x3)] .>=. LA.constant 6) - - setObj solver (LA.fromTerms [(3,x1),(4,x2),(5,x3)]) - setOptDir solver OptMin - b <- isOptimal solver - assertBool "should be optimal" $ b - - ret <- dualSimplex solver defaultOptions - ret @?= Optimum - - val <- getObjValue solver - val @?= 11 - -{- -http://www.math.cuhk.edu.hk/~wei/lpch5.pdf -example 5.7 - -maximize -3 x1 -4 x2 -5 x3 -subject to --1 x1 -2 x2 -3 x3 <= -5 --2 x1 -2 x2 -1 x3 <= -6 - -optimal value should be -11 --} -case_test7 :: IO () -case_test7 = do - solver <- newSolver - - _ <- newVar solver - x1 <- newVar solver - x2 <- newVar solver - x3 <- newVar solver - - assertLower solver x1 0 - assertLower solver x2 0 - assertLower solver x3 0 - assertAtom solver (LA.fromTerms [(-1,x1),(-2,x2),(-3,x3)] .<=. LA.constant (-5)) - assertAtom solver (LA.fromTerms [(-2,x1),(-2,x2),(-1,x3)] .<=. LA.constant (-6)) - - setObj solver (LA.fromTerms [(-3,x1),(-4,x2),(-5,x3)]) - setOptDir solver OptMax - b <- isOptimal solver - assertBool "should be optimal" $ b - - ret <- dualSimplex solver defaultOptions - ret @?= Optimum - - val <- getObjValue solver - val @?= -11 - -case_AssertAtom :: IO () -case_AssertAtom = do - solver <- newSolver - x0 <- newVar solver - assertAtom solver (LA.constant 1 .<=. LA.var x0) - ret <- getLB solver x0 - ret @?= Just 1 - - solver <- newSolver - x0 <- newVar solver - assertAtom solver (LA.var x0 .>=. LA.constant 1) - ret <- getLB solver x0 - ret @?= Just 1 - - solver <- newSolver - x0 <- newVar solver - assertAtom solver (LA.constant 1 .>=. LA.var x0) - ret <- getUB solver x0 - ret @?= Just 1 - - solver <- newSolver - x0 <- newVar solver - assertAtom solver (LA.var x0 .<=. LA.constant 1) - ret <- getUB solver x0 - ret @?= Just 1 - ------------------------------------------------------------------------- - -case_example_3_2 = do - solver <- newSolver - [x1,x2,x3] <- replicateM 3 (newVar solver) - setOptDir solver OptMax - setObj solver $ LA.fromTerms [(3,x1), (2,x2), (3,x3)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(2,x1), (1,x2), (1,x3)] .<=. LA.constant 2 - , LA.fromTerms [(1,x1), (2,x2), (3,x3)] .<=. LA.constant 5 - , LA.fromTerms [(2,x1), (2,x2), (1,x3)] .<=. LA.constant 6 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - , LA.var x3 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= 27/5 - - forM_ [(x1,1/5),(x2,0),(x3,8/5)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - -case_example_3_5 = do - solver <- newSolver - [x1,x2,x3,x4,x5] <- replicateM 5 (newVar solver) - setOptDir solver OptMin - setObj solver $ LA.fromTerms [(-2,x1), (4,x2), (7,x3), (1,x4), (5,x5)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(-1,x1), (1,x2), (2,x3), (1,x4), (2,x5)] .==. LA.constant 7 - , LA.fromTerms [(-1,x1), (2,x2), (3,x3), (1,x4), (1,x5)] .==. LA.constant 6 - , LA.fromTerms [(-1,x1), (1,x2), (1,x3), (2,x4), (1,x5)] .==. LA.constant 4 - , LA.var x2 .>=. LA.constant 0 - , LA.var x3 .>=. LA.constant 0 - , LA.var x4 .>=. LA.constant 0 - , LA.var x5 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= 19 - - forM_ [(x1,-1),(x2,0),(x3,1),(x4,0),(x5,2)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - -case_example_4_1 = do - solver <- newSolver - [x1,x2] <- replicateM 2 (newVar solver) - setOptDir solver OptMin - setObj solver $ LA.fromTerms [(2,x1), (1,x2)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(-1,x1), (1,x2)] .>=. LA.constant 2 - , LA.fromTerms [( 1,x1), (1,x2)] .<=. LA.constant 1 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - ] - ret <- optimize solver defaultOptions - ret @?= Unsat - -case_example_4_2 = do - solver <- newSolver - [x1,x2] <- replicateM 2 (newVar solver) - setOptDir solver OptMax - setObj solver $ LA.fromTerms [(2,x1), (1,x2)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(-1,x1), (-1,x2)] .<=. LA.constant 10 - , LA.fromTerms [( 2,x1), (-1,x2)] .<=. LA.constant 40 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - ] - ret <- optimize solver defaultOptions - ret @?= Unbounded - -case_example_4_3 = do - solver <- newSolver - [x1,x2] <- replicateM 2 (newVar solver) - setOptDir solver OptMax - setObj solver $ LA.fromTerms [(6,x1), (-2,x2)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(2,x1), (-1,x2)] .<=. LA.constant 2 - , LA.var x1 .<=. LA.constant 4 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= 12 - - forM_ [(x1,4),(x2,6)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - -case_example_4_5 = do - solver <- newSolver - [x1,x2] <- replicateM 2 (newVar solver) - setOptDir solver OptMax - setObj solver $ LA.fromTerms [(2,x1), (1,x2)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(4,x1), ( 3,x2)] .<=. LA.constant 12 - , LA.fromTerms [(4,x1), ( 1,x2)] .<=. LA.constant 8 - , LA.fromTerms [(4,x1), (-1,x2)] .<=. LA.constant 8 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= 5 - - forM_ [(x1,3/2),(x2,2)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - -case_example_4_6 = do - solver <- newSolver - [x1,x2,x3,x4] <- replicateM 4 (newVar solver) - setOptDir solver OptMax - setObj solver $ LA.fromTerms [(20,x1), (1/2,x2), (-6,x3), (3/4,x4)] - mapM_ (assertAtom solver) $ - [ LA.var x1 .<=. LA.constant 2 - , LA.fromTerms [( 8,x1), ( -1,x2), (9,x3), (1/4, x4)] .<=. LA.constant 16 - , LA.fromTerms [(12,x1), (-1/2,x2), (3,x3), (1/2, x4)] .<=. LA.constant 24 - , LA.var x2 .<=. LA.constant 1 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - , LA.var x3 .>=. LA.constant 0 - , LA.var x4 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= 165/4 - - forM_ [(x1,2),(x2,1),(x3,0),(x4,1)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - -case_example_4_7 = do - solver <- newSolver - [x1,x2,x3,x4] <- replicateM 4 (newVar solver) - setOptDir solver OptMax - setObj solver $ LA.fromTerms [(1,x1), (1.5,x2), (5,x3), (2,x4)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(3,x1), (2,x2), ( 1,x3), (4,x4)] .<=. LA.constant 6 - , LA.fromTerms [(2,x1), (1,x2), ( 5,x3), (1,x4)] .<=. LA.constant 4 - , LA.fromTerms [(2,x1), (6,x2), (-4,x3), (8,x4)] .==. LA.constant 0 - , LA.fromTerms [(1,x1), (3,x2), (-2,x3), (4,x4)] .==. LA.constant 0 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - , LA.var x3 .>=. LA.constant 0 - , LA.var x4 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= 48/11 - - forM_ [(x1,0),(x2,0),(x3,8/11),(x4,4/11)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - --- 退化して巡回の起こるKuhnの7変数3制約の例 -case_kuhn_7_3 = do - solver <- newSolver - [x1,x2,x3,x4,x5,x6,x7] <- replicateM 7 (newVar solver) - setOptDir solver OptMin - setObj solver $ LA.fromTerms [(-2,x4),(-3,x5),(1,x6),(12,x7)] - mapM_ (assertAtom solver) $ - [ LA.fromTerms [(1,x1), ( -2,x4), (-9,x5), ( 1,x6), ( 9,x7)] .==. LA.constant 0 - , LA.fromTerms [(1,x2), (1/3,x4), ( 1,x5), (-1/3,x6), ( -2,x7)] .==. LA.constant 0 - , LA.fromTerms [(1,x3), ( 2,x4), ( 3,x5), ( -1,x6), (-12,x7)] .==. LA.constant 2 - , LA.var x1 .>=. LA.constant 0 - , LA.var x2 .>=. LA.constant 0 - , LA.var x3 .>=. LA.constant 0 - , LA.var x4 .>=. LA.constant 0 - , LA.var x5 .>=. LA.constant 0 - , LA.var x6 .>=. LA.constant 0 - , LA.var x7 .>=. LA.constant 0 - ] - - ret <- optimize solver defaultOptions - ret @?= Optimum - val <- getObjValue solver - val @?= -2 - - forM_ [(x1,2),(x2,0),(x3,0),(x4,2),(x5,0),(x6,2),(x7,0)] $ \(var,expected) -> do - val <- getValue solver var - val @?= expected - ------------------------------------------------------------------------- --- Test harness - -main :: IO () -main = $(defaultMainGenerator) diff --git a/src/Text/GCNF.hs b/src/Text/GCNF.hs new file mode 100644 --- /dev/null +++ b/src/Text/GCNF.hs @@ -0,0 +1,92 @@ +{-# OPTIONS_GHC -Wall #-} +----------------------------------------------------------------------------- +-- | +-- Module : Text.GCNF +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : portable +-- +-- References: +-- +-- * +-- +-- +----------------------------------------------------------------------------- +module Text.GCNF + ( + GCNF (..) + , GroupIndex + , GClause + + -- * Parsing .gcnf files + , parseString + , parseFile + ) where + +import qualified SAT.Types as SAT + +data GCNF + = GCNF + { numVars :: !Int + , numClauses :: !Int + , lastGroupIndex :: !GroupIndex + , clauses :: [GClause] + } + +type GroupIndex = Int + +type GClause = (GroupIndex, SAT.Clause) + +parseString :: String -> Either String GCNF +parseString s = + case words l of + (["p","gcnf", nbvar', nbclauses', lastGroupIndex']) -> + Right $ + GCNF + { numVars = read nbvar' + , numClauses = read nbclauses' + , lastGroupIndex = read lastGroupIndex' + , clauses = map parseLine ls + } + (["p","cnf", nbvar', nbclause']) -> + Right $ + GCNF + { numVars = read nbvar' + , numClauses = read nbclause' + , lastGroupIndex = read nbclause' + , clauses = zip [1..] $ map parseCNFLine ls + } + _ -> + Left "cannot find gcnf header" + where + (l:ls) = filter (not . isComment) (lines s) + +parseFile :: FilePath -> IO (Either String GCNF) +parseFile filename = do + s <- readFile filename + return $ parseString s + +isComment :: String -> Bool +isComment ('c':_) = True +isComment _ = False + +parseLine :: String -> GClause +parseLine s = + case words s of + (('{':w):xs) -> + let ys = map read $ init xs + idx = read $ init w + in seq idx $ seqList ys $ (idx, ys) + _ -> error "parse error" + +parseCNFLine :: String -> SAT.Clause +parseCNFLine s = seq xs $ seqList xs $ xs + where + xs = init (map read (words s)) + +seqList :: [a] -> b -> b +seqList [] b = b +seqList (x:xs) b = seq x $ seqList xs b diff --git a/src/Text/GurobiSol.hs b/src/Text/GurobiSol.hs new file mode 100644 --- /dev/null +++ b/src/Text/GurobiSol.hs @@ -0,0 +1,17 @@ +module Text.GurobiSol + ( Model + , render + ) where + +import qualified Data.Map as Map +import Data.Ratio + +type Model = Map.Map String Double + +render :: Model -> Maybe Double -> String +render m obj = unlines $ ls1 ++ ls2 + where + ls1 = case obj of + Nothing -> [] + Just val -> ["# Objective value = " ++ show val] + ls2 = [name ++ " " ++ show val | (name,val) <- Map.toList m] diff --git a/src/Text/LPFile.hs b/src/Text/LPFile.hs --- a/src/Text/LPFile.hs +++ b/src/Text/LPFile.hs @@ -31,6 +31,8 @@ , Bounds , Label , Var + , VarType (..) + , VarInfo (..) , BoundExpr (..) , RelOp (..) , SOSType (..) @@ -38,7 +40,11 @@ , defaultBounds , defaultLB , defaultUB + , getVarInfo + , getVarType , getBounds + , integerVariables + , semiContinuousVariables , parseString , parseFile , render @@ -66,10 +72,7 @@ , dir :: OptDir , objectiveFunction :: ObjectiveFunction , constraints :: [Constraint] - , bounds :: Map.Map Var Bounds - , integerVariables :: Set.Set Var - , binaryVariables :: Set.Set Var - , semiContinuousVariables :: Set.Set Var + , varInfo :: Map.Map Var VarInfo , sos :: [SOS] } deriving (Show, Eq, Ord) @@ -100,6 +103,31 @@ } deriving (Eq, Ord, Show) +data VarType + = ContinuousVariable + | IntegerVariable +-- 'nothaddock' is inserted not to confuse haddock + -- nothaddock | BinaryVariable + | SemiContinuousVariable + -- nothaddock | SemiIntegerVariable + deriving (Eq, Ord, Show) + +data VarInfo + = VarInfo + { varName :: Var + , varType :: VarType + , varBounds :: Bounds + } + deriving (Eq, Ord, Show) + +defaultVarInfo :: VarInfo +defaultVarInfo + = VarInfo + { varName = "" + , varType = ContinuousVariable + , varBounds = defaultBounds + } + -- | type for representing lower/upper bound of variables type Bounds = (BoundExpr, BoundExpr) @@ -156,13 +184,31 @@ defaultUB :: BoundExpr defaultUB = PosInf --- | lookuping bounds for a variable +-- | looking up attributes for a variable +getVarInfo :: LP -> Var -> VarInfo +getVarInfo lp v = Map.findWithDefault defaultVarInfo v (varInfo lp) + +-- | looking up bounds for a variable +getVarType :: LP -> Var -> VarType +getVarType lp v = varType $ getVarInfo lp v + +-- | looking up bounds for a variable getBounds :: LP -> Var -> Bounds -getBounds lp v = Map.findWithDefault defaultBounds v (bounds lp) +getBounds lp v = varBounds $ getVarInfo lp v intersectBounds :: Bounds -> Bounds -> Bounds intersectBounds (lb1,ub1) (lb2,ub2) = (max lb1 lb2, min ub1 ub2) +integerVariables :: LP -> Set.Set Var +integerVariables lp = Map.keysSet $ Map.filter p (varInfo lp) + where + p VarInfo{ varType = vt } = vt == IntegerVariable + +semiContinuousVariables :: LP -> Set.Set Var +semiContinuousVariables lp = Map.keysSet $ Map.filter p (varInfo lp) + where + p VarInfo{ varType = vt } = vt == SemiContinuousVariable + -- --------------------------------------------------------------------------- -- | Parse a string containing LP file data. @@ -238,24 +284,45 @@ ] bnds <- option Map.empty (try boundsSection) - xs <- many (liftM Left generalSection <|> liftM Right binarySection) - let ints = Set.fromList $ concat [x | Left x <- xs] - bins = Set.fromList $ concat [x | Right x <- xs] - bnds <- return $ Map.unionWith intersectBounds + exvs <- many (liftM Left generalSection <|> liftM Right binarySection) + let ints = Set.fromList $ concat [x | Left x <- exvs] + bins = Set.fromList $ concat [x | Right x <- exvs] + bnds2 <- return $ Map.unionWith intersectBounds bnds (Map.fromAscList [(v, (Finite 0, Finite 1)) | v <- Set.toAscList bins]) scs <- liftM Set.fromList $ option [] (try semiSection) ss <- option [] (try sosSection) end let vs = Set.unions $ map vars cs ++ - [ Map.keysSet bnds + [ Map.keysSet bnds2 , ints , bins , scs , vars (snd obj) ] ++ [Set.fromList (map fst xs) | (_,_,xs) <- ss] - return $ LP vs flag obj cs bnds ints bins scs ss + return $ + LP + { variables = vs + , dir = flag + , objectiveFunction = obj + , constraints = cs + , sos = ss + , varInfo = + Map.fromAscList + [ ( v + , VarInfo + { varName = v + , varBounds = Map.findWithDefault defaultBounds v bnds2 + , varType = + if v `Set.member` ints || v `Set.member` bins then IntegerVariable + else if v `Set.member` scs then SemiContinuousVariable + else ContinuousVariable + } + ) + | v <- Set.toAscList vs + ] + } problem :: Parser (OptDir, ObjectiveFunction) problem = do @@ -440,10 +507,10 @@ term flag = do s <- if flag then optionMaybe sign else liftM Just sign c <- optionMaybe number - e <- liftM (\s -> [Term 1 [s]]) ident <|> qexpr + e <- liftM (\s' -> [Term 1 [s']]) ident <|> qexpr return $ case combineMaybe (*) s c of Nothing -> e - Just d -> [Term (d*c) vs | Term c vs <- e] + Just d -> [Term (d*c') vs | Term c' vs <- e] qexpr :: Parser Expr qexpr = do @@ -513,10 +580,11 @@ OptMax -> "MAXIMIZE" tell $ showChar '\n' - let (l, obj) = objectiveFunction lp - renderLabel l - renderExpr True obj - tell $ showChar '\n' + do + let (l, obj) = objectiveFunction lp + renderLabel l + renderExpr True obj + tell $ showChar '\n' tell $ showString "SUBJECT TO\n" forM_ (constraints lp) $ \c -> do @@ -538,26 +606,31 @@ renderConstraint c tell $ showChar '\n' + let ivs = integerVariables lp + (bins,gens) = Set.partition (\v -> getBounds lp v == (Finite 0, Finite 1)) ivs + scs = semiContinuousVariables lp + tell $ showString "BOUNDS\n" - forM_ (Map.toAscList (bounds lp)) $ \(v, b@(lb,ub)) -> do - renderBoundExpr lb - tell $ showString " <= " - tell $ showString v - tell $ showString " <= " - renderBoundExpr ub - tell $ showChar '\n' + forM_ (Map.toAscList (varInfo lp)) $ \(v, VarInfo{ varBounds = (lb,ub) }) -> do + unless (v `Set.member` bins) $ do + renderBoundExpr lb + tell $ showString " <= " + tell $ showString v + tell $ showString " <= " + renderBoundExpr ub + tell $ showChar '\n' - unless (Set.null (integerVariables lp)) $ do + unless (Set.null gens) $ do tell $ showString "GENERALS\n" - renderVariableList $ Set.toList $ integerVariables lp + renderVariableList $ Set.toList gens - unless (Set.null (binaryVariables lp)) $ do + unless (Set.null bins) $ do tell $ showString "BINARIES\n" - renderVariableList $ Set.toList $ binaryVariables lp + renderVariableList $ Set.toList bins - unless (Set.null (semiContinuousVariables lp)) $ do + unless (Set.null scs) $ do tell $ showString "SEMI-CONTINUOUS\n" - renderVariableList $ Set.toList $ semiContinuousVariables lp + renderVariableList $ Set.toList scs unless (null (sos lp)) $ do tell $ showString "SOS\n" @@ -635,9 +708,9 @@ renderLabel (constrLabel c) case constrIndicator c of Nothing -> return () - Just (v,val) -> do + Just (v,vval) -> do tell $ showString v . showString " = " - tell $ showValue val + tell $ showValue vval tell $ showString " -> " renderExpr False e @@ -655,7 +728,7 @@ renderVariableList vs = fill 80 vs >> tell (showChar '\n') fill :: Int -> [String] -> WriterT ShowS Maybe () -fill width xs = go xs 0 +fill width str = go str 0 where go [] _ = return () go (x:xs) 0 = tell (showString x) >> go xs (length x) @@ -666,6 +739,7 @@ -- --------------------------------------------------------------------------- +{- compileExpr :: Expr -> Maybe (Map.Map Var Rational) compileExpr e = do xs <- forM e $ \(Term c vs) -> @@ -673,5 +747,6 @@ [v] -> return (v, c) _ -> mzero return (Map.fromList xs) +-} -- --------------------------------------------------------------------------- diff --git a/src/Text/MPSFile.hs b/src/Text/MPSFile.hs new file mode 100644 --- /dev/null +++ b/src/Text/MPSFile.hs @@ -0,0 +1,535 @@ +{-# OPTIONS_GHC -Wall -fno-warn-unused-do-bind #-} +----------------------------------------------------------------------------- +-- | +-- Module : Text.MPSFile +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : provisional +-- Portability : portable +-- +-- A .mps format parser library. +-- +-- References: +-- +-- * +-- +-- * +-- +-- * +-- +-- * +-- +----------------------------------------------------------------------------- +module Text.MPSFile + ( parseString + , parseFile + ) where + +import Control.Monad +import Data.Maybe +import qualified Data.Set as Set +import qualified Data.Map as Map +import Data.Ratio + +import qualified Text.ParserCombinators.Parsec as P +import Text.ParserCombinators.Parsec hiding (spaces, newline, Column) + +import Data.OptDir +import qualified Text.LPFile as LPFile + +type Column = String +type Row = String + +data BoundType + = LO -- lower bound + | UP -- upper bound + | FX -- variable is fixed at the specified value + | FR -- free variable (no lower or upper bound) + | MI -- infinite lower bound + | PL -- infinite upper bound + | BV -- variable is binary (equal 0 or 1) + | LI -- lower bound for integer variable + | UI -- upper bound for integer variable + | SC -- upper bound for semi-continuous variable + deriving (Eq, Ord, Show, Read) + +-- --------------------------------------------------------------------------- + +-- | Parse a string containing LP file data. +-- The source name is only | used in error messages and may be the empty string. +parseString :: SourceName -> String -> Either ParseError LPFile.LP +parseString = parse mpsfile + +-- | Parse a file containing LP file data. +parseFile :: FilePath -> IO (Either ParseError LPFile.LP) +parseFile = parseFromFile mpsfile + +-- --------------------------------------------------------------------------- + +space' :: Parser Char +space' = oneOf [' ', '\t'] + +spaces' :: Parser () +spaces' = skipMany space' >> return () + +spaces1' :: Parser () +spaces1' = skipMany1 space' >> return () + +commentline :: Parser () +commentline = do + _ <- char '*' + _ <- manyTill anyChar P.newline + return () + +newline' :: Parser () +newline' = do + spaces' + _ <- P.newline + skipMany commentline + return () + +tok :: Parser a -> Parser a +tok p = do + x <- p + msum [spaces1', lookAhead (try (char '\n' >> return ())), eof] + return x + +ident :: Parser String +ident = tok $ many1 $ noneOf [' ', '\t', '\n'] + +stringLn :: String -> Parser () +stringLn s = string s >> newline' + +sign :: Num a => Parser a +sign = (char '+' >> return 1) <|> (char '-' >> return (-1)) + +number :: Parser Rational +number = tok $ do + b <- (do{ s <- option 1 sign; x <- nat; y <- option 0 frac; return (s * (fromInteger x + y)) }) + <|> frac + c <- option 0 e + return (b*10^^c) + where + digits = many1 digit + + nat :: Parser Integer + nat = liftM read digits + + frac :: Parser Rational + frac = do + char '.' + s <- digits + return (read s % 10^(length s)) + + e :: Parser Integer + e = do + oneOf "eE" + f <- msum [ char '+' >> return id + , char '-' >> return negate + , return id + ] + liftM f nat + +-- --------------------------------------------------------------------------- + +mpsfile :: Parser LPFile.LP +mpsfile = do + many commentline + + _name <- nameSection + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_objsen.html + -- CPLEX extends the MPS standard by allowing two additional sections: OBJSEN and OBJNAME. + -- If these options are used, they must appear in order and as the first and second sections after the NAME section. + objsense <- optionMaybe $ objSenseSection + objname <- optionMaybe $ objNameSection + + rows <- rowsSection + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_usercuts.html + -- The order of sections must be ROWS USERCUTS. + usercuts <- option [] userCutsSection + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_lazycons.html + -- The order of sections must be ROWS USERCUTS LAZYCONS. + lazycons <- option [] lazyConsSection + + (cols, intvs1) <- colsSection + rhss <- rhsSection + rngs <- option Map.empty rangesSection + bnds <- option [] boundsSection + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_quadobj.html + -- Following the BOUNDS section, a QMATRIX section may be specified. + qobj <- msum [quadObjSection, qMatrixSection, return []] + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_sos.html + -- Note that in an MPS file, the SOS section must follow the BOUNDS section. + sos <- option [] sosSection + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_qcmatrix.html + -- QCMATRIX sections appear after the optional SOS section. + qterms <- liftM Map.fromList $ many qcMatrixSection + + -- http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_ext_indicators.html + -- The INDICATORS section follows any quadratic constraint section and any quadratic objective section. + inds <- option Map.empty indicatorsSection + + string "ENDATA" + + let objrow = + case objname of + Nothing -> head [row | (Nothing, row) <- rows] -- XXX + Just r -> r + objdir = + case objsense of + Nothing -> OptMin + Just d -> d + vs = Map.keysSet cols + intvs2 = Set.fromList [col | (t,col,_) <- bnds, t `elem` [BV,LI,UI]] + scvs = Set.fromList [col | (SC,col,_) <- bnds] + + let explicitBounds = Map.fromListWith f + [ case typ of + LO -> (col, (Just (LPFile.Finite val), Nothing)) + UP -> (col, (Nothing, Just (LPFile.Finite val))) + FX -> (col, (Just (LPFile.Finite val), Just (LPFile.Finite val))) + FR -> (col, (Just LPFile.NegInf, Just LPFile.PosInf)) + MI -> (col, (Just LPFile.NegInf, Nothing)) + PL -> (col, (Nothing, Just LPFile.PosInf)) + BV -> (col, (Just (LPFile.Finite 0), Just (LPFile.Finite 1))) + LI -> (col, (Just (LPFile.Finite val), Nothing)) + UI -> (col, (Nothing, Just (LPFile.Finite val))) + SC -> (col, (Nothing, Just (LPFile.Finite val))) + | (typ,col,val) <- bnds ] + where + f (a1,b1) (a2,b2) = (g a1 a2, g b1 b2) + g _ (Just x) = Just x + g x Nothing = x + + let bounds = Map.fromList + [ case Map.lookup v explicitBounds of + Nothing -> + if v `Set.member` intvs1 + then + -- http://eaton.math.rpi.edu/cplex90html/reffileformatscplex/reffileformatscplex9.html + -- If no bounds are specified for the variables within markers, bounds of 0 (zero) and 1 (one) are assumed. + (v, (LPFile.Finite 0, LPFile.Finite 1)) + else + (v, (LPFile.Finite 0, LPFile.PosInf)) + Just (Nothing, Just (LPFile.Finite ub)) | ub < 0 -> + {- + http://pic.dhe.ibm.com/infocenter/cosinfoc/v12r4/topic/ilog.odms.cplex.help/CPLEX/File_formats_reference/topics/MPS_records.html + If no bounds are specified, CPLEX assumes a lower + bound of 0 (zero) and an upper bound of +∞. If only a + single bound is specified, the unspecified bound + remains at 0 or +∞, whichever applies, with one + exception. If an upper bound of less than 0 is + specified and no other bound is specified, the lower + bound is automatically set to -∞. CPLEX deviates + slightly from a convention used by some MPS readers + when it encounters an upper bound of 0 (zero). Rather + than automatically set this variable’s lower bound to + -∞, CPLEX accepts both a lower and upper bound of 0, + effectively fixing that variable at 0. CPLEX resets + the lower bound to -∞ only if the upper bound is less + than 0. A warning message is issued when this + exception is encountered. + -} + (v, (LPFile.NegInf, LPFile.Finite ub)) + {- + lp_solve uses 1 as default lower bound for semi-continuous variable. + + But Gurobi Optimizer uses 0 as default lower bound for semi-continuous variable. + Here we adopt Gurobi's way. + -} +{- + Just (Nothing, ub) | v `Set.member` scvs -> + (v, (LPFile.Finite 1, fromMaybe LPFile.PosInf ub)) +-} + Just (lb,ub) -> + (v, (fromMaybe (LPFile.Finite 0) lb, fromMaybe LPFile.PosInf ub)) + | v <- Set.toList vs ] + + let lp = + LPFile.LP + { LPFile.variables = vs + , LPFile.dir = objdir + , LPFile.objectiveFunction = + ( Just objrow + , [LPFile.Term c [col] | (col,m) <- Map.toList cols, c <- maybeToList (Map.lookup objrow m)] ++ qobj + ) + , LPFile.constraints = + [ LPFile.Constraint + { LPFile.constrType = typ + , LPFile.constrLabel = Just row + , LPFile.constrIndicator = Map.lookup row inds + , LPFile.constrBody = (lhs, op2, rhs2) + } + | (typ, (Just op, row)) <- zip (repeat LPFile.NormalConstraint) rows ++ + zip (repeat LPFile.UserDefinedCut) usercuts ++ + zip (repeat LPFile.LazyConstraint) lazycons + , let lhs = [LPFile.Term c　[col] | (col,m) <- Map.toList cols, c <- maybeToList (Map.lookup row m)] + ++ Map.findWithDefault [] row qterms + , let rhs = Map.findWithDefault 0 row rhss + , (op2,rhs2) <- + case Map.lookup row rngs of + Nothing -> return (op, rhs) + Just rng -> + case op of + LPFile.Ge -> [(LPFile.Ge, rhs), (LPFile.Le, rhs + abs rng)] + LPFile.Le -> [(LPFile.Ge, rhs - abs rng), (LPFile.Le, rhs)] + LPFile.Eql -> + if rng < 0 + then [(LPFile.Ge, rhs + rng), (LPFile.Le, rhs)] + else [(LPFile.Ge, rhs), (LPFile.Le, rhs + rng)] + ] + , LPFile.varInfo = + Map.fromAscList + [ ( v + , LPFile.VarInfo + { LPFile.varName = v + , LPFile.varBounds = Map.findWithDefault LPFile.defaultBounds v bounds + , LPFile.varType = + if v `Set.member` intvs1 || v `Set.member` intvs2 then LPFile.IntegerVariable + else if v `Set.member` scvs then LPFile.SemiContinuousVariable + else LPFile.ContinuousVariable + } + ) + | v <- Set.toAscList vs + ] + , LPFile.sos = sos + } + + return lp + +nameSection :: Parser (Maybe String) +nameSection = do + string "NAME" + n <- optionMaybe $ do + spaces1' + ident + newline' + return n + +objSenseSection :: Parser OptDir +objSenseSection = do + try $ stringLn "OBJSENSE" + spaces1' + d <- (try (stringLn "MAX") >> return OptMax) + <|> (stringLn "MIN" >> return OptMin) + return d + +objNameSection :: Parser String +objNameSection = do + try $ stringLn "OBJNAME" + spaces1' + name <- ident + newline' + return name + +rowsSection :: Parser [(Maybe LPFile.RelOp, Row)] +rowsSection = do + try $ stringLn "ROWS" + rowsBody + +userCutsSection :: Parser [(Maybe LPFile.RelOp, Row)] +userCutsSection = do + try $ stringLn "USERCUTS" + rowsBody + +lazyConsSection :: Parser [(Maybe LPFile.RelOp, Row)] +lazyConsSection = do + try $ stringLn "LAZYCONS" + rowsBody + +rowsBody :: Parser [(Maybe LPFile.RelOp, Row)] +rowsBody = many $ do + spaces1' + op <- msum + [ char 'N' >> return Nothing + , char 'G' >> return (Just LPFile.Ge) + , char 'L' >> return (Just LPFile.Le) + , char 'E' >> return (Just LPFile.Eql) + ] + spaces1' + name <- ident + newline' + return (op, name) + +colsSection :: Parser (Map.Map Column (Map.Map Row Rational), Set.Set Column) +colsSection = do + try $ stringLn "COLUMNS" + body False Map.empty Set.empty + where + body :: Bool -> Map.Map Column (Map.Map Row Rational) -> Set.Set Column -> Parser (Map.Map Column (Map.Map Row Rational), Set.Set Column) + body isInt rs ivs = msum + [ do isInt' <- try intMarker + body isInt' rs ivs + , do (k,v) <- entry + let rs' = Map.insertWith Map.union k v rs + ivs' = if isInt then Set.insert k ivs else ivs + seq rs' $ seq ivs' $ body isInt rs' ivs' + , return (rs, ivs) + ] + + intMarker :: Parser Bool + intMarker = do + spaces1' + _marker <- ident + string "'MARKER'" + spaces1' + b <- (try (string "'INTORG'") >> return True) + <|> (string "'INTEND'" >> return False) + newline' + return b + + entry :: Parser (Column, Map.Map Row Rational) + entry = do + spaces1' + col <- ident + rv1 <- rowAndVal + opt <- optionMaybe rowAndVal + newline' + case opt of + Nothing -> return (col, rv1) + Just rv2 -> return (col, Map.union rv1 rv2) + +rowAndVal :: Parser (Map.Map Row Rational) +rowAndVal = do + row <- ident + val <- number + return $ Map.singleton row val + +rhsSection :: Parser (Map.Map Row Rational) +rhsSection = do + try $ stringLn "RHS" + liftM Map.unions $ many entry + where + entry = do + spaces1' + _name <- ident + rv1 <- rowAndVal + opt <- optionMaybe rowAndVal + newline' + case opt of + Nothing -> return rv1 + Just rv2 -> return $ Map.union rv1 rv2 + +rangesSection :: Parser (Map.Map Row Rational) +rangesSection = do + try $ stringLn "RANGES" + liftM Map.unions $ many entry + where + entry = do + spaces1' + _name <- ident + rv1 <- rowAndVal + opt <- optionMaybe rowAndVal + newline' + case opt of + Nothing -> return rv1 + Just rv2 -> return $ Map.union rv1 rv2 + +boundsSection :: Parser [(BoundType, Column, Rational)] +boundsSection = do + try $ stringLn "BOUNDS" + many entry + where + entry = do + spaces1' + typ <- boundType + _name <- ident + col <- ident + val <- if typ `elem` [FR, BV, MI, PL] + then return 0 + else number + newline' + return (typ, col, val) + +boundType :: Parser BoundType +boundType = tok $ do + let ks = ["LO", "UP", "FX", "FR", "MI", "PL", "BV", "LI", "UI", "SC"] + msum [try (string k) >> return (read k) | k <- ks] + +sosSection :: Parser [(Maybe String, LPFile.SOSType, [(Column, Rational)])] +sosSection = do + try $ stringLn "SOS" + many entry + where + entry = do + spaces1' + typ <- (try (string "S1") >> return LPFile.S1) + <|> (string "S2" >> return LPFile.S2) + spaces1' + name <- ident + newline' + xs <- many (try identAndVal) + return (Just name, typ, xs) + + identAndVal :: Parser (Row, Rational) + identAndVal = do + spaces1' + row <- ident + val <- number + newline' + return (row, val) + +quadObjSection :: Parser [LPFile.Term] +quadObjSection = do + try $ stringLn "QUADOBJ" + many entry + where + entry = do + spaces1' + col1 <- ident + col2 <- ident + val <- number + newline' + return $ LPFile.Term (if col1 /= col2 then val else val / 2) [col1, col2] + +qMatrixSection :: Parser [LPFile.Term] +qMatrixSection = do + try $ stringLn "QMATRIX" + many entry + where + entry = do + spaces1' + col1 <- ident + col2 <- ident + val <- number + newline' + return $ LPFile.Term (val / 2) [col1, col2] + +qcMatrixSection :: Parser (Row, [LPFile.Term]) +qcMatrixSection = do + try $ stringLn "QCMATRIX" + spaces1' + row <- ident + xs <- many entry + return (row, xs) + where + entry = do + spaces1' + col1 <- ident + col2 <- ident + val <- number + newline' + return $ LPFile.Term val [col1, col2] + +indicatorsSection :: Parser (Map.Map Row (Column, Rational)) +indicatorsSection = do + try $ stringLn "INDICATORS" + liftM Map.fromList $ many entry + where + entry = do + spaces1' + string "IF" + spaces1' + row <- ident + var <- ident + val <- number + newline' + return (row, (var, val)) diff --git a/src/Text/MaxSAT.hs b/src/Text/MaxSAT.hs --- a/src/Text/MaxSAT.hs +++ b/src/Text/MaxSAT.hs @@ -13,14 +13,10 @@ -- -- * -- --- TODO: --- --- * Error handling --- ----------------------------------------------------------------------------- module Text.MaxSAT ( - WCNF + WCNF (..) , WeightedClause , Weight @@ -31,30 +27,55 @@ import qualified SAT.Types as SAT -type WCNF = (Int, Weight, [WeightedClause]) +data WCNF + = WCNF + { numVars :: !Int + , numClauses :: !Int + , topCost :: !Weight + , clauses :: [WeightedClause] + } type WeightedClause = (Weight, SAT.Clause) -- | should be able to represent 2^63 type Weight = Integer -parseWCNFString :: String -> WCNF +parseWCNFString :: String -> Either String WCNF parseWCNFString s = case words l of - (["p","wcnf", nvar, _nclause, top]) -> - (read nvar, read top, map parseWCNFLine ls) - (["p","wcnf", nvar, _nclause]) -> - (read nvar, 2^(63::Int), map parseWCNFLine ls) - (["p","cnf", nvar, _nclause]) -> - (read nvar, 2, map parseCNFLine ls) - _ -> error "parse error" + (["p","wcnf", nvar, nclause, top]) -> + Right $ + WCNF + { numVars = read nvar + , numClauses = read nclause + , topCost = read top + , clauses = map parseWCNFLine ls + } + (["p","wcnf", nvar, nclause]) -> + Right $ + WCNF + { numVars = read nvar + , numClauses = read nclause + , topCost = 2^(63::Int) + , clauses = map parseWCNFLine ls + } + (["p","cnf", nvar, nclause]) -> + Right $ + WCNF + { numVars = read nvar + , numClauses = read nclause + , topCost = 2 + , clauses = map parseCNFLine ls + } + _ -> + Left "cannot find wcnf/cnf header" where (l:ls) = filter (not . isComment) (lines s) -parseWCNFFile :: FilePath -> IO WCNF +parseWCNFFile :: FilePath -> IO (Either String WCNF) parseWCNFFile filename = do s <- readFile filename - return $! parseWCNFString s + return $ parseWCNFString s isComment :: String -> Bool isComment ('c':_) = True diff --git a/src/Util.hs b/src/Util.hs --- a/src/Util.hs +++ b/src/Util.hs @@ -15,7 +15,9 @@ module Util where +import Control.Monad import Data.Ratio +import qualified Data.Set as Set -- | Combining two @Maybe@ values using given function. combineMaybe :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a @@ -45,6 +47,26 @@ | asRatio = show (numerator v) ++ "/" ++ show (denominator v) | otherwise = show (fromRational v :: Double) +showRationalAsFiniteDecimal :: Rational -> Maybe String +showRationalAsFiniteDecimal x = do + let a :: Integer + (a,b) = properFraction (abs x) + s1 = if x < 0 then "-" else "" + s2 = show a + s3 <- if b == 0 + then return ".0" + else liftM ("." ++ ) $ loop Set.empty b + return $ s1 ++ s2 ++ s3 + where + loop :: Set.Set Rational -> Rational -> Maybe String + loop _ 0 = return "" + loop rs r + | r `Set.member` rs = mzero + | otherwise = do + let a :: Integer + (a,b) = properFraction (r * 10) + s <- loop (Set.insert r rs) b + return $ show a ++ s {-# INLINE revSequence #-} revSequence :: Monad m => [m a] -> m [a] diff --git a/src/Version.hs b/src/Version.hs --- a/src/Version.hs +++ b/src/Version.hs @@ -1,15 +1,12 @@ {-# LANGUAGE CPP #-} -module Version where +module Version + ( version + , packageVersions + ) where import Data.List import Data.Version - -version :: Version -version - = Version - { versionBranch = [0,0,1] - , versionTags = [] - } +import Paths_toysolver packageVersions :: [(String, String)] packageVersions = sort $ tail @@ -32,6 +29,12 @@ #ifdef VERSION_deepseq , ("deepseq", VERSION_deepseq ) #endif +#ifdef VERSION_filepath + , ("filepath", VERSION_filepath ) +#endif +#ifdef VERSION_heaps + , ("heaps", VERSION_heaps ) +#endif #ifdef VERSION_mtl , ("mtl", VERSION_mtl ) #endif @@ -44,13 +47,25 @@ #ifdef VERSION_parsec , ("parsec", VERSION_parsec ) #endif +#ifdef VERSION_primes + , ("primes", VERSION_primes ) +#endif #ifdef VERSION_queue , ("queue", VERSION_queue ) #endif +#ifdef VERSION_random + , ("random", VERSION_random ) +#endif #ifdef VERSION_stm - , ("stm", VERSION_stm ) + , ("stm", VERSION_stm ) #endif #ifdef VERSION_time , ("time", VERSION_time ) +#endif +#ifdef VERSION_unbounded_delays + , ("unbounded-delays", VERSION_unbounded_delays) +#endif +#ifdef VERSION_logic_TPTP + , ("logic-TPTP", VERSION_logic_TPTP ) #endif ] diff --git a/src/Wang.hs b/src/Wang.hs deleted file mode 100644 --- a/src/Wang.hs +++ /dev/null @@ -1,46 +0,0 @@ -import Control.Monad (guard,msum) -import Data.List (intersect) -import Data.Maybe (isJust, listToMaybe) - -data Formula x - = Atom x - | Not !(Formula x) - | Imply !(Formula x) !(Formula x) - | And !(Formula x) !(Formula x) - | Or !(Formula x) !(Formula x) - deriving Eq - -type Sequent x = ([Formula x], [Formula x]) - -isValid :: Eq x => Sequent x -> Bool -isValid = isJust . isValid' - -isValid' :: Eq x => Sequent x -> Maybe () -isValid' (l,r) = - do xs <- listToMaybe $ msum $ - [ do let i = intersect l r - guard $ not $ null i - return [] - , do (Not p, r) <- pick r - return [(p:l,r)] - , do (Not p, l) <- pick l - return [(l,p:r)] - , do (Imply p q, r) <- pick r - return [(p:l,q:r)] - , do (Or p q, r) <- pick r - return [(l,p:q:r)] - , do (And p q, l) <- pick l - return [(p:q:l,r)] - , do (Or p q, l) <- pick l - return [(p:l,r), (q:l,r)] - , do (And p q, r) <- pick r - return [(l,p:r), (l,q:r)] - , do (Imply p q, l) <- pick l - return [(q:l,r), (l,p:r)] - ] - mapM_ isValid' xs - return () - -pick :: [x] -> [(x,[x])] -pick [] = [] -pick (x:xs) = (x,xs) : [(y,x:ys) | (y,ys) <- pick xs] diff --git a/src/cnf2lp.hs b/src/cnf2lp.hs deleted file mode 100644 --- a/src/cnf2lp.hs +++ /dev/null @@ -1,68 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : cnf2lp --- Copyright : (c) Masahiro Sakai 2011-2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : experimental --- Portability : portable --- ------------------------------------------------------------------------------ -module Main where - -import qualified Data.ByteString.Lazy as BS -import Data.Char -import System.IO -import System.Environment -import System.Exit -import System.Console.GetOpt - -import qualified Text.LPFile as LPFile -import qualified Language.CNF.Parse.ParseDIMACS as DIMACS - -import Converter.CNF2LP - -data Flag - = Help - | ObjType ObjType - deriving Eq - -options :: [OptDescr Flag] -options = - [ Option ['h'] ["help"] (NoArg Help) "show help" - , Option [] ["obj"] (ReqArg (ObjType . parseObjType) "STRING") "none (default), max-one, max-zero" - ] - where - parseObjType s = - case map toLower s of - "none" -> ObjNone - "max-one" -> ObjMaxOne - "max-zero" -> ObjMaxZero - _ -> error ("unknown obj: " ++ s) - -main :: IO () -main = do - args <- getArgs - case getOpt Permute options args of - (o,_,[]) - | Help `elem` o -> putStrLn (usageInfo header options) - (o,[fname],[]) -> do - ret <- case fname of - "-" -> fmap (DIMACS.parseByteString "-") $ BS.hGetContents stdin - _ -> DIMACS.parseFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right cnf -> do - let objType = last (ObjNone : [t | ObjType t <- o]) - (lp, _) = convert objType cnf - case LPFile.render lp of - Nothing -> hPutStrLn stderr "conversion failure" >> exitFailure - Just s2 -> putStr s2 - (_,_,errs) -> do - hPutStrLn stderr $ concat errs ++ usageInfo header options - exitFailure - -header :: String -header = "Usage: cnf2lp [OPTION]... [file.cnf|-]" diff --git a/src/lp2yices.hs b/src/lp2yices.hs deleted file mode 100644 --- a/src/lp2yices.hs +++ /dev/null @@ -1,235 +0,0 @@ -{-# OPTIONS_GHC -Wall -fno-warn-unused-do-bind #-} ------------------------------------------------------------------------------ --- | --- Module : lp2yices --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : experimental --- Portability : portable --- ------------------------------------------------------------------------------ -module Main where - -import Data.Ord -import Data.List -import Data.Ratio -import qualified Data.Set as Set -import qualified Data.Map as Map -import System.Console.GetOpt -import System.Environment -import System.Exit -import System.IO -import Text.Printf -import qualified Text.LPFile as LP - -type Var = String -type Env = Map.Map LP.Var Var - -concatS :: [ShowS] -> ShowS -concatS = foldr (.) id - -unlinesS :: [ShowS] -> ShowS -unlinesS = concatS . map (. showChar '\n') - -list :: [ShowS] -> ShowS -list xs = showParen True $ concatS (intersperse (showChar ' ') xs) - -and' :: [ShowS] -> ShowS -and' [] = showString "true" -and' [x] = x -and' xs = list (showString "and" : xs) - -or' :: [ShowS] -> ShowS -or' [] = showString "false" -or' [x] = x -or' xs = list (showString "or" : xs) - -not' :: ShowS -> ShowS -not' x = list [showString "not", x] - -expr :: Env -> LP.Expr -> ShowS -expr env e = - case e of - [] -> showChar '0' - _ -> list (showChar '+' : map f e) - where - f (LP.Term c []) = num c - f (LP.Term c vs) = - case xs of - [] -> showChar '1' - [x] -> x - _ -> list (showChar '*' : xs) - where - xs = [num c | c /= 1] ++ [showString (env Map.! v) | v <- vs] - -num :: Rational -> ShowS -num r - | denominator r == 1 = shows (numerator r) - | otherwise = shows (numerator r) . showChar '/' . shows (denominator r) - -rel :: Bool -> LP.RelOp -> ShowS -> ShowS -> ShowS -rel True LP.Eql x y = and' [rel False LP.Le x y, rel False LP.Ge x y] -rel _ LP.Eql x y = list [showString "=", x, y] -rel _ LP.Le x y = list [showString "<=", x, y] -rel _ LP.Ge x y = list [showString ">=", x, y] - -assert :: ShowS -> ShowS -assert x = list [showString "assert", x] - -constraint :: Bool -> Env -> LP.Constraint -> ShowS -constraint q env LP.Constraint{ LP.constrIndicator = g, LP.constrBody = (e, op, b) } = - case g of - Nothing -> c - Just (var,val) -> - list [ showString "=>" - , rel q LP.Eql (expr env [LP.Term 1 [var]]) (num val) - , c - ] - where - c = rel q op (expr env e) (num b) - -conditions :: Bool -> Env -> LP.LP -> [ShowS] -conditions q env lp = bnds ++ bins ++ cs ++ ss - where - vs = LP.variables lp - bins = do - v <- Set.toList (LP.binaryVariables lp) - let v2 = env Map.! v - return $ list [showString "or", rel q LP.Eql (showString v2) (showChar '0'), rel q LP.Eql (showString v2) (showChar '1')] - bnds = map bnd (Set.toList vs) - bnd v = - if v `Set.member` (LP.semiContinuousVariables lp) - then or' [list [showString "=", showString v2, num 0], and' (s1 ++ s2)] - else and' (s1 ++ s2) - where - v2 = env Map.! v - (lb,ub) = LP.getBounds lp v - s1 = case lb of - LP.NegInf -> [] - LP.PosInf -> [showString "false"] - LP.Finite x -> [list [showString "<=", num x, showString v2]] - s2 = case ub of - LP.NegInf -> [showString "false"] - LP.PosInf -> [] - LP.Finite x -> [list [showString "<=", showString v2, num x]] - cs = map (constraint q env) (LP.constraints lp) - ss = concatMap sos (LP.sos lp) - sos (_, typ, xs) = do - (x1,x2) <- case typ of - LP.S1 -> pairs $ map fst xs - LP.S2 -> nonAdjacentPairs $ map fst $ sortBy (comparing snd) $ xs - return $ not' $ and' [list [showString "/=", showString (env Map.! v), showChar '0'] | v<-[x1,x2]] - -pairs :: [a] -> [(a,a)] -pairs [] = [] -pairs (x:xs) = [(x,x2) | x2 <- xs] ++ pairs xs - -nonAdjacentPairs :: [a] -> [(a,a)] -nonAdjacentPairs (x1:x2:xs) = [(x1,x3) | x3 <- xs] ++ nonAdjacentPairs (x2:xs) -nonAdjacentPairs _ = [] - -lp2ys :: LP.LP -> Bool -> Bool -> ShowS -lp2ys lp optimize check = - unlinesS $ defs ++ map assert (conditions False env lp) - ++ [ optimalityDef ] - ++ [ assert (showString "optimality") | optimize ] - ++ [ list [showString "set-evidence!", showString "true"] | check ] - ++ [ list [showString "check"] | check ] - where - vs = LP.variables lp - real_vs = vs `Set.difference` int_vs - int_vs = LP.integerVariables lp `Set.union` LP.binaryVariables lp - ts = [(v, "real")| v <- Set.toList real_vs] ++ [(v, "int") | v <- Set.toList int_vs] - obj = snd (LP.objectiveFunction lp) - env = Map.fromList [(v, encode v) | v <- Set.toList vs] - -- Note that identifiers of LPFile does not contain '-'. - -- So that there are no name crash. - env2 = Map.fromList [(v, encode v ++ "-2") | v <- Set.toList vs] - - defs = do - (v,t) <- ts - let v2 = env Map.! v - return $ showString $ printf "(define %s::%s) ; %s" v2 t v - - optimalityDef = list [showString "define", showString "optimality::bool", optimality] - - optimality = list [showString "forall", decl, body] - where - decl = list [showString $ printf "%s::%s" (env2 Map.! v) t | (v,t) <- ts] - body = list [showString "=>" - , and' (conditions True env2 lp) - , list [ showString $ if LP.dir lp == LP.OptMin then "<=" else ">=" - , expr env obj, expr env2 obj - ] - ] - -encode :: String -> String -encode s = concatMap f s - where - -- Note that '[', ']', '\\' does not appear in identifiers of LP file. - f '(' = "[" - f ')' = "]" - f c | c `elem` "/\";" = printf "\\x%02d" (fromEnum c :: Int) - f c = [c] - -data Flag - = Help - | Optimize - | NoCheck - deriving Eq - -options :: [OptDescr Flag] -options = - [ Option ['h'] ["help"] (NoArg Help) "show help" - , Option [] ["optimize"] (NoArg Optimize) "output optimiality condition which uses quantifiers" - , Option [] ["no-check"] (NoArg NoCheck) "do not output \"(check)\"" - ] - - -main :: IO () -main = do - args <- getArgs - case getOpt Permute options args of - (o,_,[]) - | Help `elem` o -> putStrLn (usageInfo header options) - (o,[fname],[]) -> do - ret <- if fname == "-" - then fmap (LP.parseString "-") getContents - else LP.parseFile fname - case ret of - Right lp -> putStrLn $ lp2ys lp (Optimize `elem` o) (not (NoCheck `elem` o)) "" - Left err -> hPrint stderr err >> exitFailure - (_,_,errs) -> do - hPutStrLn stderr $ concat errs ++ usageInfo header options - exitFailure - -header :: String -header = "Usage: lp2yice [OPTION]... [file.lp|-]" - -testFile :: FilePath -> IO () -testFile fname = do - result <- LP.parseFile fname - case result of - Right lp -> putStrLn $ lp2ys lp True True "" - Left err -> hPrint stderr err - -test :: IO () -test = putStrLn $ lp2ys testdata True True "" - -testdata :: LP.LP -Right testdata = LP.parseString "test" $ unlines - [ "Maximize" - , " obj: x1 + 2 x2 + 3 x3 + x4" - , "Subject To" - , " c1: - x1 + x2 + x3 + 10 x4 <= 20" - , " c2: x1 - 3 x2 + x3 <= 30" - , " c3: x2 - 3.5 x4 = 0" - , "Bounds" - , " 0 <= x1 <= 40" - , " 2 <= x4 <= 3" - , "General" - , " x4" - , "End" - ] diff --git a/src/maxsat2lp.hs b/src/maxsat2lp.hs deleted file mode 100644 --- a/src/maxsat2lp.hs +++ /dev/null @@ -1,37 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : maxsat2lp --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : experimental --- Portability : portable --- ------------------------------------------------------------------------------ - -module Main where - -import Control.Monad -import System.Environment -import System.Exit -import System.IO -import qualified Text.MaxSAT as MaxSAT -import qualified Text.LPFile as LPFile -import qualified Converter.MaxSAT2LP as MaxSAT2LP - -header :: String -header = "Usage: maxsat2lp [file.cnf|file.wcnf|-]" - -main :: IO () -main = do - args <- getArgs - wcnf <- case args of - ["-"] -> liftM MaxSAT.parseWCNFString getContents - [fname] -> MaxSAT.parseWCNFFile fname - _ -> hPutStrLn stderr header >> exitFailure - let (lp, _) = MaxSAT2LP.convert wcnf - case LPFile.render lp of - Nothing -> hPutStrLn stderr "conversion failure" >> exitFailure - Just s -> putStr s diff --git a/src/pb2lp.hs b/src/pb2lp.hs deleted file mode 100644 --- a/src/pb2lp.hs +++ /dev/null @@ -1,79 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} ------------------------------------------------------------------------------ --- | --- Module : pb2lp --- Copyright : (c) Masahiro Sakai 2011-2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : experimental --- Portability : portable --- ------------------------------------------------------------------------------ -module Main where - -import Control.Monad -import Data.Char -import System.Environment -import System.IO -import System.Exit -import System.Console.GetOpt -import qualified Text.PBFile as PBFile -import qualified Text.LPFile as LPFile -import Converter.PB2LP - -data Flag - = Help - | WBO - | ObjType ObjType - | IndicatorConstraint - deriving Eq - -options :: [OptDescr Flag] -options = - [ Option ['h'] ["help"] (NoArg Help) "show help" - , Option [] ["wbo"] (NoArg WBO) "input is .wbo file" - , Option [] ["obj"] (ReqArg (ObjType . parseObjType) "STRING") "objective function for PBS: none (default), max-one, max-zero" - , Option [] ["indicator"] (NoArg IndicatorConstraint) "use indicator constraints in output LP file" - ] - where - parseObjType s = - case map toLower s of - "none" -> ObjNone - "max-one" -> ObjMaxOne - "max-zero" -> ObjMaxZero - _ -> error ("unknown obj: " ++ s) - -main :: IO () -main = do - args <- getArgs - case getOpt Permute options args of - (o,_,[]) - | Help `elem` o -> putStrLn (usageInfo header options) - (o,[fname],[]) -> do - let objType = last (ObjNone : [t | ObjType t <- o]) - (lp, _) <- - if WBO `elem` o - then do - ret <- if fname == "-" - then liftM (PBFile.parseWBOString "-") getContents - else PBFile.parseWBOFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right formula -> return (convertWBO (IndicatorConstraint `elem` o) formula) - else do - ret <- if fname == "-" - then liftM (PBFile.parseOPBString "-") getContents - else PBFile.parseOPBFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right formula -> return (convert objType formula) - case LPFile.render lp of - Nothing -> hPutStrLn stderr "conversion failure" >> exitFailure - Just s -> putStr s - (_,_,errs) -> do - hPutStrLn stderr $ concat errs ++ usageInfo header options - exitFailure - -header :: String -header = "Usage: pb2lp [OPTION]... [file.opb|file.wbo|-]" diff --git a/src/toysat.hs b/src/toysat.hs deleted file mode 100644 --- a/src/toysat.hs +++ /dev/null @@ -1,689 +0,0 @@ -{-# LANGUAGE ScopedTypeVariables, DoAndIfThenElse, CPP #-} -{-# OPTIONS_GHC -Wall -fno-warn-unused-do-bind #-} ------------------------------------------------------------------------------ --- | --- Module : toysat --- Copyright : (c) Masahiro Sakai 2012 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : experimental --- Portability : non-portable (ScopedTypeVariables) --- --- A toy-level SAT solver based on CDCL. --- ------------------------------------------------------------------------------ - -module Main where - -import Control.Monad -import Control.Exception -import Data.Array.IArray -import qualified Data.ByteString.Lazy as BS -import qualified Data.Set as Set -import qualified Data.Map as Map -import Data.Char -import Data.IORef -import Data.List -import Data.Maybe -import Data.Ord -import Data.Ratio -import Data.Version -import Data.Time.LocalTime -import Data.Time.Format -import System.IO -import System.Environment -import System.Exit -import System.Locale -import System.Console.GetOpt -import System.CPUTime -import System.FilePath -import System.Timeout -import qualified System.Info as SysInfo -import qualified Language.CNF.Parse.ParseDIMACS as DIMACS -import Text.Printf -#ifdef __GLASGOW_HASKELL__ -import GHC.Environment (getFullArgs) -#endif -#ifdef FORCE_CHAR8 -import GHC.IO.Encoding -#endif - -import Data.Linear -import qualified SAT -import qualified SAT.Integer -import qualified SAT.TseitinEncoder as Tseitin -import SAT.Types (pbEval, pbLowerBound) -import SAT.Printer -import qualified Text.PBFile as PBFile -import qualified Text.LPFile as LPFile -import qualified Text.MaxSAT as MaxSAT -import Version -import Util (showRational, revMapM, revForM) - --- ------------------------------------------------------------------------ - -data Mode = ModeHelp | ModeVersion | ModeSAT | ModePB | ModeWBO | ModeMaxSAT | ModeLP - -data Options - = Options - { optMode :: Maybe Mode - , optRestartStrategy :: SAT.RestartStrategy - , optRestartFirst :: Int - , optRestartInc :: Double - , optLearningStrategy :: SAT.LearningStrategy - , optLearntSizeInc :: Double - , optCCMin :: Int - , optRandomFreq :: Double - , optRandomSeed :: Int - , optLinearizerPB :: Bool - , optBinarySearch :: Bool - , optObjFunVarsHeuristics :: Bool - , optPrintRational :: Bool - , optCheckModel :: Bool - , optTimeout :: Integer - } - -defaultOptions :: Options -defaultOptions - = Options - { optMode = Nothing - , optRestartStrategy = SAT.defaultRestartStrategy - , optRestartFirst = SAT.defaultRestartFirst - , optRestartInc = SAT.defaultRestartInc - , optLearningStrategy = SAT.defaultLearningStrategy - , optLearntSizeInc = SAT.defaultLearntSizeInc - , optCCMin = SAT.defaultCCMin - , optRandomFreq = SAT.defaultRandomFreq - , optRandomSeed = 0 - , optLinearizerPB = False - , optBinarySearch = False - , optObjFunVarsHeuristics = True - , optPrintRational = False - , optCheckModel = False - , optTimeout = 0 - } - -options :: [OptDescr (Options -> Options)] -options = - [ Option ['h'] ["help"] (NoArg (\opt -> opt{ optMode = Just ModeHelp })) "show help" - , Option [] ["version"] (NoArg (\opt -> opt{ optMode = Just ModeVersion})) "show version" - - , Option [] ["sat"] (NoArg (\opt -> opt{ optMode = Just ModeSAT })) "solve pseudo boolean problems in .cnf file (default)" - , Option [] ["pb"] (NoArg (\opt -> opt{ optMode = Just ModePB })) "solve pseudo boolean problems in .pb file" - , Option [] ["wbo"] (NoArg (\opt -> opt{ optMode = Just ModeWBO })) "solve weighted boolean optimization problem in .opb file" - , Option [] ["maxsat"] (NoArg (\opt -> opt{ optMode = Just ModeMaxSAT })) "solve MaxSAT problem in .cnf or .wcnf file" - , Option [] ["lp"] (NoArg (\opt -> opt{ optMode = Just ModeLP })) "solve binary integer programming problem in .lp file" - - , Option [] ["restart"] - (ReqArg (\val opt -> opt{ optRestartStrategy = parseRestartStrategy val }) "") - "Restart startegy: MiniSAT (default), Armin, Luby." - , Option [] ["restart-first"] - (ReqArg (\val opt -> opt{ optRestartFirst = read val }) "") - (printf "The initial restart limit. (default %d)" SAT.defaultRestartFirst) - , Option [] ["restart-inc"] - (ReqArg (\val opt -> opt{ optRestartInc = read val }) "") - (printf "The factor with which the restart limit is multiplied in each restart. (default %f)" SAT.defaultRestartInc) - , Option [] ["learning"] - (ReqArg (\val opt -> opt{ optLearningStrategy = parseLS val }) "") - "Leaning scheme: clause (default)" - , Option [] ["learnt-size-inc"] - (ReqArg (\val opt -> opt{ optLearntSizeInc = read val }) "") - (printf "The limit for learnt clauses is multiplied with this factor periodically. (default %f)" SAT.defaultLearntSizeInc) - , Option [] ["ccmin"] - (ReqArg (\val opt -> opt{ optCCMin = read val }) "") - (printf "Conflict clause minimization (0=none, 1=local, 2=recursive; default %d)" SAT.defaultCCMin) - - , Option [] ["random-freq"] - (ReqArg (\val opt -> opt{ optRandomFreq = read val }) "<0..1>") - (printf "The frequency with which the decision heuristic tries to choose a random variable (default %f)" SAT.defaultRandomFreq) - , Option [] ["random-seed"] - (ReqArg (\val opt -> opt{ optRandomSeed = read val }) "") - "Used by the random variable selection" - - , Option [] ["linearizer-pb"] - (NoArg (\opt -> opt{ optLinearizerPB = True })) - "Use PB constraint in linearization." - - , Option [] ["search"] - (ReqArg (\val opt -> opt{ optBinarySearch = parseSearch val }) "") - "Search algorithm used in optimization; linear (default), binary" - , Option [] ["objfun-heuristics"] - (NoArg (\opt -> opt{ optObjFunVarsHeuristics = True })) - "Enable heuristics for polarity/activity of variables in objective function (default)" - , Option [] ["no-objfun-heuristics"] - (NoArg (\opt -> opt{ optObjFunVarsHeuristics = False })) - "Disable heuristics for polarity/activity of variables in objective function" - - , Option [] ["print-rational"] - (NoArg (\opt -> opt{ optPrintRational = True })) - "print rational numbers instead of decimals" - - , Option [] ["check-model"] - (NoArg (\opt -> opt{ optCheckModel = True })) - "check model for debug" - - , Option [] ["timeout"] - (ReqArg (\val opt -> opt{ optTimeout = read val }) "") - "Kill toysat after given number of seconds (default 0 (no limit))" - ] - where - parseRestartStrategy s = - case map toLower s of - "minisat" -> SAT.MiniSATRestarts - "armin" -> SAT.ArminRestarts - "luby" -> SAT.LubyRestarts - _ -> undefined - - parseSearch s = - case map toLower s of - "linear" -> False - "binary" -> True - _ -> undefined - - parseLS "clause" = SAT.LearningClause - parseLS "hybrid" = SAT.LearningHybrid - parseLS s = error (printf "unknown learning strategy %s" s) - -main :: IO () -main = do -#ifdef FORCE_CHAR8 - setLocaleEncoding char8 - setForeignEncoding char8 - setFileSystemEncoding char8 -#endif - - start <- getCPUTime - args <- getArgs - case getOpt Permute options args of - (o,args2,[]) -> do - printSysInfo -#ifdef __GLASGOW_HASKELL__ - fullArgs <- getFullArgs -#else - let fullArgs = args -#endif - printf "c command line = %s\n" (show fullArgs) - let opt = foldl (flip id) defaultOptions o - timelim = optTimeout opt * 10^(6::Int) - - if (timelim > fromIntegral (maxBound :: Int)) - then do - printf "c TIMEOUT is too long" - printf "s UNKNOWN" - exitFailure - else do - ret <- timeout (if timelim > 0 then fromIntegral timelim else (-1)) $ do - solver <- newSolver opt - let mode = - case optMode opt of - Just m -> m - Nothing -> - case args2 of - [] -> ModeHelp - fname : _ -> - case map toLower (takeExtension fname) of - ".cnf" -> ModeSAT - ".opb" -> ModePB - ".wbo" -> ModeWBO - ".wcnf" -> ModeMaxSAT - ".lp" -> ModeLP - _ -> ModeSAT - case mode of - ModeHelp -> showHelp stdout - ModeVersion -> hPutStrLn stdout (showVersion version) - ModeSAT -> mainSAT opt solver args2 - ModePB -> mainPB opt solver args2 - ModeWBO -> mainWBO opt solver args2 - ModeMaxSAT -> mainMaxSAT opt solver args2 - ModeLP -> mainLP opt solver args2 - - when (isNothing ret) $ do - putStrLn "c TIMEOUT" - putStrLn "s UNKNOWN" - end <- getCPUTime - printf "c total time = %.3fs\n" (fromIntegral (end - start) / 10^(12::Int) :: Double) - when (isNothing ret) exitFailure - - (_,_,errs) -> do - mapM_ putStrLn errs - exitFailure - -showHelp :: Handle -> IO () -showHelp h = hPutStrLn h (usageInfo header options) - -header :: String -header = unlines - [ "Usage:" - , " toysat [OPTION]... [file.cnf||-]" - , " toysat [OPTION]... --pb [file.opb|-]" - , " toysat [OPTION]... --wbo [file.wbo|-]" - , " toysat [OPTION]... --maxsat [file.cnf|file.wcnf|-]" - , " toysat [OPTION]... --lp [file.lp|-]" - , "" - , "Options:" - ] - -printSysInfo :: IO () -printSysInfo = do - tm <- getZonedTime - hPrintf stdout "c %s\n" (formatTime defaultTimeLocale "%FT%X%z" tm) - hPrintf stdout "c arch = %s\n" SysInfo.arch - hPrintf stdout "c os = %s\n" SysInfo.os - hPrintf stdout "c compiler = %s %s\n" SysInfo.compilerName (showVersion SysInfo.compilerVersion) - hPutStrLn stdout "c packages:" - forM_ packageVersions $ \(package, ver) -> do - hPrintf stdout "c %s-%s\n" package ver - -newSolver :: Options -> IO SAT.Solver -newSolver opts = do - solver <- SAT.newSolver - SAT.setRestartStrategy solver (optRestartStrategy opts) - SAT.setRestartFirst solver (optRestartFirst opts) - SAT.setRestartInc solver (optRestartInc opts) - SAT.setLearntSizeInc solver (optLearntSizeInc opts) - SAT.setCCMin solver (optCCMin opts) - SAT.setRandomFreq solver (optRandomFreq opts) - when (optRandomSeed opts /= 0) $ - SAT.setRandomSeed solver (optRandomSeed opts) - SAT.setLearningStrategy solver (optLearningStrategy opts) - SAT.setLogger solver $ \str -> do - putStr "c " - putStrLn str - hFlush stdout - SAT.setCheckModel solver (optCheckModel opts) - return solver - --- ------------------------------------------------------------------------ - -mainSAT :: Options -> SAT.Solver -> [String] -> IO () -mainSAT opt solver args = do - ret <- case args of - ["-"] -> fmap (DIMACS.parseByteString "-") $ BS.hGetContents stdin - [fname] -> DIMACS.parseFile fname - _ -> showHelp stderr >> exitFailure - case ret of - Left err -> hPrint stderr err >> exitFailure - Right cnf -> solveSAT opt solver cnf - -solveSAT :: Options -> SAT.Solver -> DIMACS.CNF -> IO () -solveSAT _ solver cnf = do - printf "c #vars %d\n" (DIMACS.numVars cnf) - printf "c #constraints %d\n" (length (DIMACS.clauses cnf)) - _ <- replicateM (DIMACS.numVars cnf) (SAT.newVar solver) - forM_ (DIMACS.clauses cnf) $ \clause -> - SAT.addClause solver (elems clause) - result <- SAT.solve solver - putStrLn $ "s " ++ (if result then "SATISFIABLE" else "UNSATISFIABLE") - hFlush stdout - when result $ do - m <- SAT.model solver - satPrintModel stdout m (DIMACS.numVars cnf) - --- ------------------------------------------------------------------------ - -mainPB :: Options -> SAT.Solver -> [String] -> IO () -mainPB opt solver args = do - ret <- case args of - ["-"] -> fmap (PBFile.parseOPBString "-") $ hGetContents stdin - [fname] -> PBFile.parseOPBFile fname - _ -> showHelp stderr >> exitFailure - case ret of - Left err -> hPrint stderr err >> exitFailure - Right formula -> solvePB opt solver formula - -solvePB :: Options -> SAT.Solver -> PBFile.Formula -> IO () -solvePB opt solver formula@(obj, cs) = do - let n = PBFile.pbNumVars formula - - printf "c #vars %d\n" n - printf "c #constraints %d\n" (length cs) - - _ <- replicateM n (SAT.newVar solver) - enc <- Tseitin.newEncoder solver - Tseitin.setUsePB enc (optLinearizerPB opt) - - forM_ cs $ \(lhs, op, rhs) -> do - lhs' <- pbConvSum enc lhs - case op of - PBFile.Ge -> SAT.addPBAtLeast solver lhs' rhs - PBFile.Eq -> SAT.addPBExactly solver lhs' rhs - - case obj of - Nothing -> do - result <- SAT.solve solver - putStrLn $ "s " ++ (if result then "SATISFIABLE" else "UNSATISFIABLE") - hFlush stdout - when result $ do - m <- SAT.model solver - pbPrintModel stdout m n - - Just obj' -> do - obj'' <- pbConvSum enc obj' - - modelRef <- newIORef Nothing - - result <- try $ minimize opt solver obj'' $ \m val -> do - writeIORef modelRef (Just m) - putStrLn $ "o " ++ show val - hFlush stdout - - case result of - Right Nothing -> do - putStrLn $ "s " ++ "UNSATISFIABLE" - hFlush stdout - Right (Just m) -> do - putStrLn $ "s " ++ "OPTIMUM FOUND" - hFlush stdout - pbPrintModel stdout m n - Left (e :: AsyncException) -> do - r <- readIORef modelRef - case r of - Nothing -> do - putStrLn $ "s " ++ "UNKNOWN" - hFlush stdout - Just m -> do - putStrLn $ "s " ++ "SATISFIABLE" - pbPrintModel stdout m n - throwIO e - -pbConvSum :: Tseitin.Encoder -> PBFile.Sum -> IO [(Integer, SAT.Lit)] -pbConvSum enc = revMapM f - where - f (w,ls) = do - l <- Tseitin.encodeConj enc ls - return (w,l) - -minimize :: Options -> SAT.Solver -> [(Integer, SAT.Lit)] -> (SAT.Model -> Integer -> IO ()) -> IO (Maybe SAT.Model) -minimize opt solver obj update = do - when (optObjFunVarsHeuristics opt) $ do - forM_ obj $ \(c,l) -> do - let p = if c > 0 then not (SAT.litPolarity l) else SAT.litPolarity l - SAT.setVarPolarity solver (SAT.litVar l) p - forM_ (zip [1..] (map snd (sortBy (comparing fst) [(abs c, l) | (c,l) <- obj]))) $ \(n,l) -> do - replicateM n $ SAT.varBumpActivity solver (SAT.litVar l) - - result <- SAT.solve solver - if not result then - return Nothing - else if optBinarySearch opt then - liftM Just binSearch - else - liftM Just linSearch - - where - linSearch :: IO SAT.Model - linSearch = do - m <- SAT.model solver - let v = pbEval m obj - update m v - SAT.addPBAtMost solver obj (v - 1) - result <- SAT.solve solver - if result - then linSearch - else return m - - binSearch :: IO SAT.Model - binSearch = do -{- - printf "c Binary Search: minimizing %s \n" $ - intercalate " " - [c' ++ " " ++ l' - | (c,l) <- obj - , let c' = if c < 0 then show c else "+" ++ show c - , let l' = (if l < 0 then "~" else "") ++ "x" ++ show (SAT.litVar l) - ] --} - m0 <- SAT.model solver - let v0 = pbEval m0 obj - update m0 v0 - let ub0 = v0 - 1 - lb0 = pbLowerBound obj - SAT.addPBAtMost solver obj ub0 - - let loop lb ub m | ub < lb = return m - loop lb ub m = do - let mid = (lb + ub) `div` 2 - printf "c Binary Search: %d <= obj <= %d; guessing obj <= %d\n" lb ub mid - sel <- SAT.newVar solver - SAT.addPBAtMostSoft solver sel obj mid - ret <- SAT.solveWith solver [sel] - if ret - then do - m2 <- SAT.model solver - let v = pbEval m2 obj - update m2 v - -- deactivating temporary constraint - -- FIXME: –{—ˆ‚͐§–ñ‚̍폜‚ð‚µ‚½‚¢ - SAT.addClause solver [-sel] - let ub' = v - 1 - printf "c Binary Search: updating upper bound: %d -> %d\n" ub ub' - SAT.addPBAtMost solver obj ub' - loop lb ub' m2 - else do - -- deactivating temporary constraint - -- FIXME: –{—ˆ‚͐§–ñ‚̍폜‚ð‚µ‚½‚¢ - SAT.addClause solver [-sel] - let lb' = mid + 1 - printf "c Binary Search: updating lower bound: %d -> %d\n" lb lb' - SAT.addPBAtLeast solver obj lb' - loop lb' ub m - - loop lb0 ub0 m0 - --- ------------------------------------------------------------------------ - -mainWBO :: Options -> SAT.Solver -> [String] -> IO () -mainWBO opt solver args = do - ret <- case args of - ["-"] -> fmap (PBFile.parseWBOString "-") $ hGetContents stdin - [fname] -> PBFile.parseWBOFile fname - _ -> showHelp stderr >> exitFailure - case ret of - Left err -> hPrint stderr err >> exitFailure - Right formula -> solveWBO opt solver False formula - -solveWBO :: Options -> SAT.Solver -> Bool -> PBFile.SoftFormula -> IO () -solveWBO opt solver isMaxSat formula@(tco, cs) = do - let nvar = PBFile.wboNumVars formula - printf "c #vars %d\n" nvar - printf "c #constraints %d\n" (length cs) - - _ <- replicateM nvar (SAT.newVar solver) - enc <- Tseitin.newEncoder solver - Tseitin.setUsePB enc (optLinearizerPB opt) - - obj <- liftM concat $ revForM cs $ \(cost, (lhs, op, rhs)) -> do - lhs' <- pbConvSum enc lhs - case cost of - Nothing -> do - case op of - PBFile.Ge -> SAT.addPBAtLeast solver lhs' rhs - PBFile.Eq -> SAT.addPBExactly solver lhs' rhs - return [] - Just cval -> do - sel <- SAT.newVar solver - case op of - PBFile.Ge -> SAT.addPBAtLeastSoft solver sel lhs' rhs - PBFile.Eq -> SAT.addPBExactlySoft solver sel lhs' rhs - return [(cval, SAT.litNot sel)] - - case tco of - Nothing -> return () - Just c -> SAT.addPBAtMost solver obj (c-1) - - modelRef <- newIORef Nothing - result <- try $ minimize opt solver obj $ \m val -> do - writeIORef modelRef (Just m) - putStrLn $ "o " ++ show val - hFlush stdout - - case result of - Right Nothing -> do - putStrLn $ "s " ++ "UNSATISFIABLE" - hFlush stdout - Right (Just m) -> do - putStrLn $ "s " ++ "OPTIMUM FOUND" - hFlush stdout - if isMaxSat - then maxsatPrintModel stdout m nvar - else pbPrintModel stdout m nvar - Left (e :: AsyncException) -> do - r <- readIORef modelRef - case r of - Just m | not isMaxSat -> do - putStrLn $ "s " ++ "SATISFIABLE" - pbPrintModel stdout m nvar - _ -> do - putStrLn $ "s " ++ "UNKNOWN" - hFlush stdout - throwIO e - --- ------------------------------------------------------------------------ - -mainMaxSAT :: Options -> SAT.Solver -> [String] -> IO () -mainMaxSAT opt solver args = do - s <- case args of - ["-"] -> getContents - [fname] -> readFile fname - _ -> showHelp stderr >> exitFailure - let wcnf = MaxSAT.parseWCNFString s - solveMaxSAT opt solver wcnf - -solveMaxSAT :: Options -> SAT.Solver -> MaxSAT.WCNF -> IO () -solveMaxSAT opt solver (_, top, cs) = do - solveWBO opt solver True - ( Nothing - , [ (if w >= top then Nothing else Just w - , ([(1,[lit]) | lit<-lits], PBFile.Ge, 1)) - | (w,lits) <- cs - ] - ) - --- ------------------------------------------------------------------------ - -mainLP :: Options -> SAT.Solver -> [String] -> IO () -mainLP opt solver args = do - ret <- case args of - ["-"] -> fmap (LPFile.parseString "-") $ hGetContents stdin - [fname] -> LPFile.parseFile fname - _ -> showHelp stderr >> exitFailure - case ret of - Left err -> hPrint stderr err >> exitFailure - Right lp -> solveLP opt solver lp - -solveLP :: Options -> SAT.Solver -> LPFile.LP -> IO () -solveLP opt solver lp = do - if not (Set.null nivs) - then do - putStrLn $ "c cannot handle non-integer variables: " ++ intercalate ", " (Set.toList nivs) - putStrLn "s UNKNOWN" - exitFailure - else do - putStrLn "c Loading variables and bounds" - vmap <- liftM Map.fromList $ revForM (Set.toList ivs) $ \v -> do - let (lb,ub) = LPFile.getBounds lp v - case (lb,ub) of - (LPFile.Finite lb', LPFile.Finite ub') -> do - v2 <- SAT.Integer.newVar solver (ceiling lb') (floor ub') - return (v,v2) - _ -> do - putStrLn $ "c cannot handle unbounded variable: " ++ v - putStrLn "s UNKNOWN" - exitFailure - - putStrLn "c Loading constraints" - forM_ (LPFile.constraints lp) $ \c -> do - let indicator = LPFile.constrIndicator c - (lhs, op, rhs) = LPFile.constrBody c - let d = foldl' lcm 1 (map denominator (rhs:[r | LPFile.Term r _ <- lhs])) - lhs' = lsum [asInteger (r * fromIntegral d) .*. (vmap Map.! asSingleton vs) | LPFile.Term r vs <- lhs] - rhs' = asInteger (rhs * fromIntegral d) - case indicator of - Nothing -> - case op of - LPFile.Le -> SAT.Integer.addLe solver lhs' (SAT.Integer.constant rhs') - LPFile.Ge -> SAT.Integer.addGe solver lhs' (SAT.Integer.constant rhs') - LPFile.Eql -> SAT.Integer.addEq solver lhs' (SAT.Integer.constant rhs') - Just (var, val) -> do - let var' = asBin (vmap Map.! var) - f sel = do - case op of - LPFile.Le -> SAT.Integer.addLeSoft solver sel lhs' (SAT.Integer.constant rhs') - LPFile.Ge -> SAT.Integer.addGeSoft solver sel lhs' (SAT.Integer.constant rhs') - LPFile.Eql -> SAT.Integer.addEqSoft solver sel lhs' (SAT.Integer.constant rhs') - case val of - 1 -> f var' - 0 -> f (SAT.litNot var') - _ -> return () - - putStrLn "c Loading SOS constraints" - forM_ (LPFile.sos lp) $ \(_label, typ, xs) -> do - case typ of - LPFile.S1 -> SAT.addAtMost solver (map (asBin . (vmap Map.!) . fst) xs) 1 - LPFile.S2 -> do - let ps = nonAdjacentPairs $ map fst $ sortBy (comparing snd) $ xs - forM_ ps $ \(x1,x2) -> do - SAT.addClause solver [SAT.litNot $ asBin $ vmap Map.! v | v <- [x1,x2]] - - let (_label,obj) = LPFile.objectiveFunction lp - d = foldl' lcm 1 [denominator r | LPFile.Term r _ <- obj] * - (if LPFile.dir lp == LPFile.OptMin then 1 else -1) - obj2 = lsum [asInteger (r * fromIntegral d) .*. (vmap Map.! (asSingleton vs)) | LPFile.Term r vs <- obj] - SAT.Integer.Expr obj3 obj3_c = obj2 - - modelRef <- newIORef Nothing - - result <- try $ minimize opt solver obj3 $ \m val -> do - writeIORef modelRef (Just m) - putStrLn $ "o " ++ showRational (optPrintRational opt) (fromIntegral (val + obj3_c) / fromIntegral d) - hFlush stdout - - let printModel :: SAT.Model -> IO () - printModel m = do - forM_ (Set.toList ivs) $ \v -> do - let val = SAT.Integer.eval m (vmap Map.! v) - printf "v %s = %d\n" v val - hFlush stdout - - case result of - Right Nothing -> do - putStrLn $ "s " ++ "UNSATISFIABLE" - hFlush stdout - Right (Just m) -> do - putStrLn $ "s " ++ "OPTIMUM FOUND" - hFlush stdout - printModel m - Left (e :: AsyncException) -> do - r <- readIORef modelRef - case r of - Nothing -> do - putStrLn $ "s " ++ "UNKNOWN" - hFlush stdout - Just m -> do - putStrLn $ "s " ++ "SATISFIABLE" - printModel m - throwIO e - where - ivs = LPFile.binaryVariables lp `Set.union` LPFile.integerVariables lp - nivs = LPFile.variables lp `Set.difference` ivs - - asSingleton :: [a] -> a - asSingleton [v] = v - asSingleton _ = error "not a singleton" - - asInteger :: Rational -> Integer - asInteger r - | denominator r /= 1 = error (show r ++ " is not integer") - | otherwise = numerator r - - nonAdjacentPairs :: [a] -> [(a,a)] - nonAdjacentPairs (x1:x2:xs) = [(x1,x3) | x3 <- xs] ++ nonAdjacentPairs (x2:xs) - nonAdjacentPairs _ = [] - - asBin :: SAT.Integer.Expr -> SAT.Lit - asBin (SAT.Integer.Expr [(1,lit)] _) = lit - asBin _ = error "asBin: failure" - --- ------------------------------------------------------------------------ - diff --git a/src/toysolver.hs b/src/toysolver.hs deleted file mode 100644 --- a/src/toysolver.hs +++ /dev/null @@ -1,300 +0,0 @@ ------------------------------------------------------------------------------ --- | --- Module : toysolver --- Copyright : (c) Masahiro Sakai 2011 --- License : BSD-style --- --- Maintainer : masahiro.sakai@gmail.com --- Stability : experimental --- Portability : portable --- ------------------------------------------------------------------------------ - - -module Main where - -import Control.Monad -import Data.Char -import Data.List -import Data.Maybe -import Data.Ratio -import qualified Data.Version as V -import qualified Data.Set as Set -import qualified Data.Map as Map -import qualified Data.IntMap as IM -import qualified Data.IntSet as IS -import System.Exit -import System.Environment -import System.FilePath -import System.Console.GetOpt -import System.IO -import Text.Printf -import qualified Language.CNF.Parse.ParseDIMACS as DIMACS - -import Data.Expr -import Data.Formula -import qualified Data.LA as LA -import qualified OmegaTest -import qualified Cooper -import qualified MIPSolverHL -import qualified Text.LPFile as LP -import qualified Text.PBFile as PBFile -import qualified Text.MaxSAT as MaxSAT -import qualified Converter.CNF2LP as CNF2LP -import qualified Converter.PB2LP as PB2LP -import qualified Converter.MaxSAT2LP as MaxSAT2LP -import qualified Simplex2 -import qualified MIPSolver2 -import SAT.Printer -import Version -import Util - --- --------------------------------------------------------------------------- - -data Mode = ModeSAT | ModePB | ModeWBO | ModeMaxSAT | ModeLP - deriving (Eq, Ord) - -data Flag - = Help - | Version - | Solver String - | PrintRational - | PivotStrategy String - | NThread !Int - | Mode !Mode - deriving Eq - -options :: [OptDescr Flag] -options = - [ Option ['h'] ["help"] (NoArg Help) "show help" - , Option ['v'] ["version"] (NoArg Version) "show version number" - , Option [] ["solver"] (ReqArg Solver "SOLVER") "mip (default), omega-test, cooper, old-mip" - , Option [] ["print-rational"] (NoArg PrintRational) "print rational numbers instead of decimals" - , Option [] ["pivot-strategy"] (ReqArg PivotStrategy "[bland-rule|largest-coefficient]") "pivot strategy for simplex (default: bland-rule)" - , Option [] ["threads"] (ReqArg (NThread . read) "INTEGER") "number of threads to use" - - , Option [] ["sat"] (NoArg (Mode ModeSAT)) "solve pseudo boolean problems in .cnf file" - , Option [] ["pb"] (NoArg (Mode ModePB)) "solve pseudo boolean problems in .pb file" - , Option [] ["wbo"] (NoArg (Mode ModeWBO)) "solve weighted boolean optimization problem in .opb file" - , Option [] ["maxsat"] (NoArg (Mode ModeMaxSAT)) "solve MaxSAT problem in .cnf or .wcnf file" - , Option [] ["lp"] (NoArg (Mode ModeLP)) "solve binary integer programming problem in .lp file (default)" - ] - -header :: String -header = "Usage: toysolver [OPTION]... file.lp" - --- --------------------------------------------------------------------------- - -run - :: String - -> [Flag] - -> LP.LP - -> (Map.Map String Rational -> IO ()) - -> IO () -run solver opt lp printModel = do - unless (Set.null (LP.semiContinuousVariables lp)) $ do - hPutStrLn stderr "semi-continuous variables are not supported." - exitFailure - case map toLower solver of - s | s `elem` ["omega-test", "cooper"] -> solveByQE - s | s `elem` ["old-mip"] -> solveByMIP - _ -> solveByMIP2 - where - vs = LP.variables lp - vsAssoc = zip (Set.toList vs) [0..] - nameToVar = Map.fromList vsAssoc - varToName = IM.fromList [(v,name) | (name,v) <- vsAssoc] - - compileE :: LP.Expr -> Expr Rational - compileE = foldr (+) (Const 0) . map compileT - - compileT :: LP.Term -> Expr Rational - compileT (LP.Term c vs) = - foldr (*) (Const c) [Var (nameToVar Map.! v) | v <- vs] - - obj = compileE $ snd $ LP.objectiveFunction lp - - cs1 = do - v <- Set.toList vs - let v2 = Var (nameToVar Map.! v) - let (l,u) = LP.getBounds lp v - [Const x .<=. v2 | LP.Finite x <- return l] ++ - [v2 .<=. Const x | LP.Finite x <- return u] - cs2 = do - LP.Constraint - { LP.constrIndicator = ind - , LP.constrBody = (lhs, rel, rhs) - } <- LP.constraints lp - let rel2 = case rel of - LP.Ge -> Ge - LP.Le -> Le - LP.Eql -> Eql - case ind of - Nothing -> return (Rel (compileE lhs) rel2 (Const rhs)) - Just _ -> error "indicator constraint is not supported yet" - cs3 = do - v <- Set.toList (LP.binaryVariables lp) - let v' = nameToVar Map.! v - [ Const 0 .<=. Var v', Var v' .<=. Const 1 ] - - ivs = f (LP.integerVariables lp) `IS.union` f (LP.binaryVariables lp) - where - f = IS.fromList . map (nameToVar Map.!) . Set.toList - - solveByQE = - case mapM LA.compileAtom (cs1 ++ cs2 ++ cs3) of - Nothing -> do - putStrLn "s UNKNOWN" - exitFailure - Just cs -> - case f cs ivs of - Nothing -> do - putStrLn "s UNSATISFIABLE" - exitFailure - Just m -> do - putStrLn $ "o " ++ showValue (Data.Expr.eval m obj) - putStrLn "s SATISFIABLE" - let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] - printModel m2 - where - f = case solver of - "omega-test" -> OmegaTest.solveQFLA - "cooper" -> Cooper.solveQFLA - _ -> error "unknown solver" - - solveByMIP = - case MIPSolverHL.optimize (LP.dir lp) obj (cs1 ++ cs2 ++ cs3) ivs of - OptUnknown -> do - putStrLn "s UNKNOWN" - exitFailure - OptUnsat -> do - putStrLn "s UNSATISFIABLE" - exitFailure - Unbounded -> do - putStrLn "s UNBOUNDED" - exitFailure - Optimum r m -> do - putStrLn $ "o " ++ showValue r - putStrLn "s OPTIMUM FOUND" - let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] - printModel m2 - - solveByMIP2 = do - solver <- Simplex2.newSolver - - let ps = last ("bland-rule" : [s | PivotStrategy s <- opt]) - case ps of - "bland-rule" -> Simplex2.setPivotStrategy solver Simplex2.PivotStrategyBlandRule - "largest-coefficient" -> Simplex2.setPivotStrategy solver Simplex2.PivotStrategyLargestCoefficient - _ -> error ("unknown pivot strategy \"" ++ ps ++ "\"") - - let nthreads = last (0 : [n | NThread n <- opt]) - - let logger s = putStr "c " >> putStrLn s >> hFlush stdout - - Simplex2.setLogger solver logger - replicateM (length vsAssoc) (Simplex2.newVar solver) -- XXX - Simplex2.setOptDir solver (LP.dir lp) - Simplex2.setObj solver $ fromJust (LA.compileExpr obj) - logger "Loading constraints... " - forM_ (cs1 ++ cs2 ++ cs3) $ \c -> do - Simplex2.assertAtom solver $ fromJust (LA.compileAtom c) - logger "Loading constraints finished" - - mip <- MIPSolver2.newSolver solver ivs - MIPSolver2.setShowRational mip printRat - MIPSolver2.setLogger mip logger - MIPSolver2.setNThread mip nthreads - let update m val = do - putStrLn $ "o " ++ showValue val - ret <- MIPSolver2.optimize mip update - case ret of - Simplex2.Unsat -> do - putStrLn "s UNSATISFIABLE" - exitFailure - Simplex2.Unbounded -> do - putStrLn "s UNBOUNDED" - exitFailure - Simplex2.Optimum -> do - m <- MIPSolver2.model mip - r <- MIPSolver2.getObjValue mip - putStrLn "s OPTIMUM FOUND" - let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] - printModel m2 - - printRat :: Bool - printRat = PrintRational `elem` opt - - showValue :: Rational -> String - showValue = showRational printRat - -lpPrintModel :: Handle -> Bool -> Map.Map String Rational -> IO () -lpPrintModel h asRat m = do - forM_ (Map.toList m) $ \(v, val) -> do - printf "v %s = %s\n" v (showRational asRat val) - --- --------------------------------------------------------------------------- - -getSolver :: [Flag] -> String -getSolver xs = last $ "mip" : [s | Solver s <- xs] - -main :: IO () -main = do - args <- getArgs - case getOpt Permute options args of - (o,_,[]) - | Help `elem` o -> putStrLn (usageInfo header options) - | Version `elem` o -> putStrLn (V.showVersion version) - (o,[fname],[]) -> do - - let mode = - case reverse [m | Mode m <- o] of - m:_ -> m - [] -> - case map toLower (takeExtension fname) of - ".cnf" -> ModeSAT - ".opb" -> ModePB - ".wbo" -> ModeWBO - ".wcnf" -> ModeMaxSAT - ".lp" -> ModeLP - _ -> ModeLP - - case mode of - ModeSAT -> do - ret <- DIMACS.parseFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right cnf -> do - let (lp,mtrans) = CNF2LP.convert CNF2LP.ObjNone cnf - run (getSolver o) o lp $ \m -> do - satPrintModel stdout (mtrans m) 0 - ModePB -> do - ret <- PBFile.parseOPBFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right pb -> do - let (lp,mtrans) = PB2LP.convert PB2LP.ObjNone pb - run (getSolver o) o lp $ \m -> do - pbPrintModel stdout (mtrans m) 0 - ModeWBO -> do - ret <- PBFile.parseWBOFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right wbo -> do - let (lp,mtrans) = PB2LP.convertWBO False wbo - run (getSolver o) o lp $ \m -> do - pbPrintModel stdout (mtrans m) 0 - ModeMaxSAT -> do - wcnf <- MaxSAT.parseWCNFFile fname - let (lp,mtrans) = MaxSAT2LP.convert wcnf - run (getSolver o) o lp $ \m -> do - maxsatPrintModel stdout (mtrans m) 0 - ModeLP -> do - ret <- LP.parseFile fname - case ret of - Left err -> hPrint stderr err >> exitFailure - Right lp -> do - run (getSolver o) o lp $ \m -> do - lpPrintModel stdout (PrintRational `elem` o) m - (_,_,errs) -> - hPutStrLn stderr $ concat errs ++ usageInfo header options diff --git a/test/TestAReal.hs b/test/TestAReal.hs new file mode 100644 --- /dev/null +++ b/test/TestAReal.hs @@ -0,0 +1,214 @@ +{-# LANGUAGE TemplateHaskell, ScopedTypeVariables #-} + +import Data.Maybe +import Data.Ratio +import Test.HUnit hiding (Test) +import Test.QuickCheck +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Test.Framework.Providers.QuickCheck2 + +import Data.Polynomial hiding (deg) +import Data.AlgebraicNumber +import Data.AlgebraicNumber.Root + +import Control.Monad +import Control.Exception +import System.IO + +{-------------------------------------------------------------------- + sample values +--------------------------------------------------------------------} + +-- ±√2 +sqrt2 :: AReal +[neg_sqrt2, sqrt2] = realRoots (x^2 - 2) + where + x = var () + +-- ±√3 +sqrt3 :: AReal +[neg_sqrt3, sqrt3] = realRoots (x^2 - 3) + where + x = var () + +{-------------------------------------------------------------------- + root manipulation +--------------------------------------------------------------------} + +case_rootAdd_sqrt2_sqrt3 = assertBool "" $ abs valP <= 0.0001 + where + x = var () + + p :: UPolynomial Rational + p = rootAdd (x^2 - 2) (x^2 - 3) + + valP :: Double + valP = eval (\() -> sqrt 2 + sqrt 3) $ mapCoeff fromRational p + +-- bug? +sample_rootAdd = p + where + x = var () + p :: UPolynomial Rational + p = rootAdd (x^2 - 2) (x^6 + 6*x^3 - 2*x^2 + 9) + +case_rootSub_sqrt2_sqrt3 = assertBool "" $ abs valP <= 0.0001 + where + x = var () + + p :: UPolynomial Rational + p = rootSub (x^2 - 2) (x^2 - 3) + + valP :: Double + valP = eval (\() -> sqrt 2 - sqrt 3) $ mapCoeff fromRational p + +case_rootMul_sqrt2_sqrt3 = assertBool "" $ abs valP <= 0.0001 + where + x = var () + + p :: UPolynomial Rational + p = rootMul (x^2 - 2) (x^2 - 3) + + valP :: Double + valP = eval (\() -> sqrt 2 * sqrt 3) $ mapCoeff fromRational p + +case_rootNegate_test1 = assertBool "" $ abs valP <= 0.0001 + where + x = var () + + p :: UPolynomial Rational + p = rootNegate (x^3 - 3) + + valP :: Double + valP = eval (\() -> - (3 ** (1/3))) $ mapCoeff fromRational p + +case_rootNegate_test2 = rootNegate p @?= q + where + x :: UPolynomial Rational + x = var () + p = x^3 - 3 + q = x^3 + 3 + +case_rootNegate_test3 = rootNegate p @?= q + where + x :: UPolynomial Rational + x = var () + p = (x-2)*(x-3)*(x-4) + q = (x+2)*(x+3)*(x+4) + +case_rootScale = rootScale 2 p @?= q + where + x :: UPolynomial Rational + x = var () + p = (x-2)*(x-3)*(x-4) + q = (x-4)*(x-6)*(x-8) + +case_rootRecip = assertBool "" $ abs valP <= 0.0001 + where + x = var () + + p :: UPolynomial Rational + p = rootRecip (x^3 - 3) + + valP :: Double + valP = eval (\() -> 1 / (3 ** (1/3))) $ mapCoeff fromRational p + +{-------------------------------------------------------------------- + algebraic reals +--------------------------------------------------------------------} + +case_realRoots_zero = realRoots (0 :: UPolynomial Rational) @?= [] + +case_realRoots_nonminimal = + realRoots ((x^2 - 1) * (x - 3)) @?= [-1,1,3] + where + x = var () + +case_realRoots_minus_one = realRoots (x^2 + 1) @?= [] + where + x = var () + +case_realRoots_two = length (realRoots (x^2 - 2)) @?= 2 + where + x = var () + +case_eq = sqrt2*sqrt2 - 2 @?= 0 + +case_eq_refl = assertBool "" $ sqrt2 == sqrt2 + +case_diseq_1 = assertBool "" $ sqrt2 /= sqrt3 + +case_diseq_2 = assertBool "" $ sqrt2 /= neg_sqrt2 + +case_cmp_1 = assertBool "" $ 0 < sqrt2 + +case_cmp_2 = assertBool "" $ neg_sqrt2 < 0 + +case_cmp_3 = assertBool "" $ 0 < neg_sqrt2 * neg_sqrt2 + +case_cmp_4 = assertBool "" $ neg_sqrt2 * neg_sqrt2 * neg_sqrt2 < 0 + +case_floor_sqrt2 = floor sqrt2 @?= 1 + +case_floor_neg_sqrt2 = floor neg_sqrt2 @?= -2 + +case_floor_1 = floor 1 @?= 1 + +case_floor_neg_1 = floor (-1) @?= -1 + +case_ceiling_sqrt2 = ceiling sqrt2 @?= 2 + +case_ceiling_neg_sqrt2 = ceiling neg_sqrt2 @?= -1 + +case_ceiling_1 = ceiling 1 @?= 1 + +case_ceiling_neg_1 = ceiling (-1) @?= -1 + +case_round_sqrt2 = round sqrt2 @?= 1 + +case_toRational = toRational r @?= 3/2 + where + x = var () + [r] = realRoots (2*x - 3) + +case_toRational_error = do + r <- try $ evaluate $ toRational sqrt2 + case r of + Left (e :: SomeException) -> return () + Right _ -> assertFailure "shuold be error" + +-- 期待値は Wolfram Alpha で x^3 - Sqrt[2]*x + 3 を調べて Real root の exact form で得た +case_simpARealPoly = simpARealPoly p @?= q + where + x :: forall k. (Num k, Eq k) => UPolynomial k + x = var () + p = x^3 - constant sqrt2 * x + 3 + q = x^6 + 6*x^3 - 2*x^2 + 9 + +case_deg_sqrt2 = deg sqrt2 @?= 2 + +case_deg_neg_sqrt2 = deg neg_sqrt2 @?= 2 + +case_deg_sqrt2_minus_sqrt2 = deg (sqrt2 - sqrt2) @?= 1 + +case_deg_sqrt2_times_sqrt2 = deg (sqrt2 * sqrt2) @?= 1 + +case_isAlgebraicInteger_sqrt2 = isAlgebraicInteger sqrt2 @?= True + +case_isAlgebraicInteger_neg_sqrt2 = isAlgebraicInteger neg_sqrt2 @?= True + +case_isAlgebraicInteger_one_half = isAlgebraicInteger (1/2) @?= False + +case_isAlgebraicInteger_one_sqrt2 = isAlgebraicInteger (1 / sqrt2) @?= False + +case_height_sqrt2 = height sqrt2 @?= 2 + +case_height_10 = height 10 @?= 10 + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestAReal2.hs b/test/TestAReal2.hs new file mode 100644 --- /dev/null +++ b/test/TestAReal2.hs @@ -0,0 +1,87 @@ +{-# LANGUAGE TemplateHaskell #-} + +import Data.Maybe +import Data.Ratio +import Test.HUnit hiding (Test) +import Test.QuickCheck +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Test.Framework.Providers.QuickCheck2 + +import Data.Polynomial +import Data.AlgebraicNumber + +import Control.Monad +import System.IO + +{-------------------------------------------------------------------- + Num +--------------------------------------------------------------------} + +prop_add_comm = + forAll areals $ \a -> + forAll areals $ \b -> + a + b == b + a + +prop_add_assoc = + forAll areals $ \a -> + forAll areals $ \b -> + forAll areals $ \c -> + a + (b + c) == (a + b) + c + +prop_add_unitL = + forAll areals $ \a -> + 0 + a == a + +prop_add_unitR = + forAll areals $ \a -> + a + 0 == a + +prop_mult_comm = + forAll areals $ \a -> + forAll areals $ \b -> + a * b == b * a + +prop_mult_assoc = + forAll areals $ \a -> + forAll areals $ \b -> + forAll areals $ \c -> + a * (b * c) == (a * b) * c + +prop_mult_unitL = + forAll areals $ \a -> + 1 * a == a + +prop_mult_unitR = + forAll areals $ \a -> + a * 1 == a + +prop_mult_dist = + forAll areals $ \a -> + forAll areals $ \b -> + forAll areals $ \c -> + a * (b + c) == a * b + a * c + +prop_mult_zero = + forAll areals $ \a -> + 0 * a == 0 + +{-------------------------------------------------------------------- + Generators +--------------------------------------------------------------------} + +areals :: Gen AReal +areals = oneof $ map return $ samples + +samples :: [AReal] +samples = [0, 1, -1, 2, -2] ++ concatMap realRoots ps + where + x = var () + ps = [x^2 - 2, x^2 - 3 {- , x^3 - 2, x^6 + 6*x^3 - 2*x^2 + 9 -}] + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestContiTraverso.hs b/test/TestContiTraverso.hs new file mode 100644 --- /dev/null +++ b/test/TestContiTraverso.hs @@ -0,0 +1,96 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import qualified Data.IntMap as IM +import qualified Data.Map as Map +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit + +import Algorithm.ContiTraverso + +import Data.ArithRel +import Data.Linear +import qualified Data.LA as LA +import Data.OptDir +import Data.Polynomial + +-- http://madscientist.jp/~ikegami/articles/IntroSequencePolynomial.html +-- optimum is (3,2,0) +case_ikegami = solve grlex OptMin obj cs @?= Just (IM.fromList [(1,3),(2,2),(3,0)]) + where + [x,y,z] = map LA.var [1..3] + cs = [ 2.*.x .+. 2.*.y .+. 2.*.z .==. LA.constant 10 + , 3.*.x .+. y .+. z .==. LA.constant 11 + , x .>=. LA.constant 0 + , y .>=. LA.constant 0 + , z .>=. LA.constant 0 + ] + obj = x .+. 2.*.y .+. 3.*.z + +case_ikegami' = solve' grlex obj cs @?= Just (IM.fromList [(1,3),(2,2),(3,0)]) + where + [x,y,z] = [1..3] + cs = [ (LA.fromTerms [(2,x),(2,y),(2,z)], 10) + , (LA.fromTerms [(3,x),(1,y),(1,z)], 11) + ] + obj = LA.fromTerms [(1,x),(2,y),(3,z)] + +-- http://posso.dm.unipi.it/users/traverso/conti-traverso-ip.ps +-- optimum is (39, 75, 1, 8, 122) +disabled_case_test1 = solve grlex OptMin obj cs @?= Just (IM.fromList [(1,39), (2,75), (3,1), (4,8), (5,122)]) + where + vs@[x1,x2,x3,x4,x5] = map LA.var [1..5] + cs = [ 2.*.x1 .+. 5.*.x2 .-. 3.*.x3 .+. x4 .-. 2.*.x5 .==. LA.constant 214 + , x1 .+. 7.*.x2 .+. 2.*.x3 .+. 3.*.x4 .+. x5 .==. LA.constant 712 + , 4.*.x1 .-. 2.*.x2 .-. x3 .-. 5.*.x4 .+. 3.*.x5 .==. LA.constant 331 + ] ++ + [ v .>=. LA.constant 0 | v <- vs ] + obj = x1 .+. x2 .+. x3 .+. x4 .+. x5 + +disabled_case_test1' = solve' grlex obj cs @?= Just (IM.fromList [(1,39), (2,75), (3,1), (4,8), (5,122)]) + where + [x1,x2,x3,x4,x5] = [1..5] + cs = [ (LA.fromTerms [(2, x1), ( 5, x2), (-3, x3), ( 1,x4), (-2, x5)], 214) + , (LA.fromTerms [(1, x1), ( 7, x2), ( 2, x3), ( 3,x4), ( 1, x5)], 712) + , (LA.fromTerms [(4, x1), (-2, x2), (-1, x3), (-5,x4), ( 3, x5)], 331) + ] + obj = LA.fromTerms [(1,x1),(1,x2),(1,x3),(1,x4),(1,x5)] + +-- optimum is (0,2,2) +case_test2 = solve grlex OptMin obj cs @?= Just (IM.fromList [(1,0),(2,2),(3,2)]) + where + vs@[x1,x2,x3] = map LA.var [1..3] + cs = [ 2.*.x1 .+. 3.*.x2 .-. x3 .==. LA.constant 4 ] ++ + [ v .>=. LA.constant 0 | v <- vs ] + obj = 2.*.x1 .+. x2 + +case_test2' = solve' grlex obj cs @?= Just (IM.fromList [(1,0),(2,2),(3,2)]) + where + [x1,x2,x3] = [1..3] + cs = [ (LA.fromTerms [(2, x1), (3, x2), (-1, x3)], 4) ] + obj = LA.fromTerms [(2,x1),(1,x2)] + +-- infeasible +case_test3 = solve grlex OptMin obj cs @?= Nothing + where + vs@[x1,x2,x3] = map LA.var [1..3] + cs = [ 2.*.x1 .+. 2.*.x2 .+. 2.*.x3 .==. LA.constant 3 ] ++ + [ v .>=. LA.constant 0 | v <- vs ] + obj = x1 + +case_test3' = solve' grlex obj cs @?= Nothing + where + [x1,x2,x3] = [1..3] + cs = [ (LA.fromTerms [(2, x1), (2, x2), (2, x3)], 3) ] + obj = LA.fromTerms [(1,x1)] + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) + diff --git a/test/TestInterval.hs b/test/TestInterval.hs new file mode 100644 --- /dev/null +++ b/test/TestInterval.hs @@ -0,0 +1,469 @@ +{-# LANGUAGE TemplateHaskell #-} + +import Data.Maybe +import Data.Ratio +import Test.HUnit hiding (Test) +import Test.QuickCheck +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Test.Framework.Providers.QuickCheck2 + +import Data.Linear +import Data.Interval (Interval, (=!), (>!), (=?), (>?)) +import qualified Data.Interval as Interval + +{-------------------------------------------------------------------- + empty +--------------------------------------------------------------------} + +prop_empty_is_bottom = + forAll intervals $ \a -> + Interval.isSubsetOf Interval.empty a + +prop_null_empty = + forAll intervals $ \a -> + Interval.null a == (a == Interval.empty) + +case_null_empty = + Interval.null (Interval.empty :: Interval Rational) @?= True + +{-------------------------------------------------------------------- + univ +--------------------------------------------------------------------} + +prop_univ_is_top = + forAll intervals $ \a -> + Interval.isSubsetOf a Interval.univ + +case_nonnull_top = + Interval.null (Interval.univ :: Interval Rational) @?= False + +{-------------------------------------------------------------------- + singleton +--------------------------------------------------------------------} + +prop_singleton_member = + forAll arbitrary $ \r -> + Interval.member (r::Rational) (Interval.singleton r) + +prop_singleton_member_intersection = + forAll intervals $ \a -> + forAll arbitrary $ \r -> + let b = Interval.singleton r + in Interval.member (r::Rational) a + ==> Interval.intersection a b == b + +prop_singleton_nonnull = + forAll arbitrary $ \r1 -> + not $ Interval.null $ Interval.singleton (r1::Rational) + +prop_distinct_singleton_intersection = + forAll arbitrary $ \r1 -> + forAll arbitrary $ \r2 -> + (r1::Rational) /= r2 ==> + Interval.intersection (Interval.singleton r1) (Interval.singleton r2) + == Interval.empty + +{-------------------------------------------------------------------- + Intersection +--------------------------------------------------------------------} + +prop_intersection_comm = + forAll intervals $ \a -> + forAll intervals $ \b -> + Interval.intersection a b == Interval.intersection b a + +prop_intersection_assoc = + forAll intervals $ \a -> + forAll intervals $ \b -> + forAll intervals $ \c -> + Interval.intersection a (Interval.intersection b c) == + Interval.intersection (Interval.intersection a b) c + +prop_intersection_unitL = + forAll intervals $ \a -> + Interval.intersection Interval.univ a == a + +prop_intersection_unitR = + forAll intervals $ \a -> + Interval.intersection a Interval.univ == a + +prop_intersection_empty = + forAll intervals $ \a -> + Interval.intersection a Interval.empty == Interval.empty + +prop_intersection_isSubsetOf = + forAll intervals $ \a -> + forAll intervals $ \b -> + Interval.isSubsetOf (Interval.intersection a b) a + +prop_intersection_isSubsetOf_equiv = + forAll intervals $ \a -> + forAll intervals $ \b -> + (Interval.intersection a b == a) + == Interval.isSubsetOf a b + +{-------------------------------------------------------------------- + Join +--------------------------------------------------------------------} + +prop_join_comm = + forAll intervals $ \a -> + forAll intervals $ \b -> + Interval.join a b == Interval.join b a + +prop_join_assoc = + forAll intervals $ \a -> + forAll intervals $ \b -> + forAll intervals $ \c -> + Interval.join a (Interval.join b c) == + Interval.join (Interval.join a b) c + +prop_join_unitL = + forAll intervals $ \a -> + Interval.join Interval.empty a == a + +prop_join_unitR = + forAll intervals $ \a -> + Interval.join a Interval.empty == a + +prop_join_univ = + forAll intervals $ \a -> + Interval.join a Interval.univ == Interval.univ + +prop_join_isSubsetOf = + forAll intervals $ \a -> + forAll intervals $ \b -> + Interval.isSubsetOf a (Interval.join a b) + +prop_join_isSubsetOf_equiv = + forAll intervals $ \a -> + forAll intervals $ \b -> + (Interval.join a b == b) + == Interval.isSubsetOf a b + +{-------------------------------------------------------------------- + member +--------------------------------------------------------------------} + +prop_member_isSubsetOf = + forAll arbitrary $ \r -> + forAll intervals $ \a -> + Interval.member r a == Interval.isSubsetOf (Interval.singleton r) a + +{-------------------------------------------------------------------- + isSubsetOf +--------------------------------------------------------------------} + +prop_isSubsetOf_refl = + forAll intervals $ \a -> + Interval.isSubsetOf a a + +prop_isSubsetOf_trans = + forAll intervals $ \a -> + forAll intervals $ \b -> + forAll intervals $ \c -> + Interval.isSubsetOf a b && Interval.isSubsetOf b c + ==> Interval.isSubsetOf a c + +-- prop_isSubsetOf_antisym = +-- forAll intervals $ \a -> +-- forAll intervals $ \b -> +-- Interval.isSubsetOf a b && Interval.isSubsetOf b a +-- ==> a == b + +{-------------------------------------------------------------------- + pickup +--------------------------------------------------------------------} + +prop_pickup_member_null = + forAll intervals $ \a -> + case Interval.pickup a of + Nothing -> Interval.null a + Just x -> Interval.member x a + +case_pickup_empty = + Interval.pickup (Interval.empty :: Interval Rational) @?= Nothing + +case_pickup_univ = + isJust (Interval.pickup (Interval.univ :: Interval Rational)) @?= True + +{-------------------------------------------------------------------- + Comparison +--------------------------------------------------------------------} + +case_lt_all_1 = (a not (Interval.null a) ==> not (a not (Interval.null a) ==> a <=? a + +prop_lt_all_singleton = + forAll arbitrary $ \a -> + forAll arbitrary $ \b -> + (a::Rational) < b ==> Interval.singleton a + not $ Interval.singleton (a::Rational) + forAll arbitrary $ \b -> + (a::Rational) <= b ==> Interval.singleton a <=! Interval.singleton b + +prop_le_all_singleton_2 = + forAll arbitrary $ \a -> + Interval.singleton (a::Rational) <=! Interval.singleton a + +prop_lt_some_singleton = + forAll arbitrary $ \a -> + forAll arbitrary $ \b -> + (a::Rational) < b ==> Interval.singleton a + not $ Interval.singleton (a::Rational) + forAll arbitrary $ \b -> + (a::Rational) <= b ==> Interval.singleton a <=? Interval.singleton b + +prop_le_some_singleton_2 = + forAll arbitrary $ \a -> + Interval.singleton (a::Rational) <=? Interval.singleton a + +{-------------------------------------------------------------------- + Num +--------------------------------------------------------------------} + +prop_scale_empty = + forAll arbitrary $ \r -> + (r::Rational) .*. Interval.empty == Interval.empty + +prop_add_comm = + forAll intervals $ \a -> + forAll intervals $ \b -> + a + b == b + a + +prop_add_assoc = + forAll intervals $ \a -> + forAll intervals $ \b -> + forAll intervals $ \c -> + a + (b + c) == (a + b) + c + +prop_add_unitL = + forAll intervals $ \a -> + Interval.singleton 0 + a == a + +prop_add_unitR = + forAll intervals $ \a -> + a + Interval.singleton 0 == a + +prop_add_member = + forAll intervals $ \a -> + forAll intervals $ \b -> + and [ (x+y) `Interval.member` (a+b) + | x <- maybeToList $ Interval.pickup a + , y <- maybeToList $ Interval.pickup b + ] + +prop_mult_comm = + forAll intervals $ \a -> + forAll intervals $ \b -> + a * b == b * a + +prop_mult_assoc = + forAll intervals $ \a -> + forAll intervals $ \b -> + forAll intervals $ \c -> + a * (b * c) == (a * b) * c + +prop_mult_unitL = + forAll intervals $ \a -> + Interval.singleton 1 * a == a + +prop_mult_unitR = + forAll intervals $ \a -> + a * Interval.singleton 1 == a + +prop_mult_dist = + forAll intervals $ \a -> + forAll intervals $ \b -> + forAll intervals $ \c -> + (a * (b + c)) `Interval.isSubsetOf` (a * b + a * c) + +prop_mult_singleton = + forAll arbitrary $ \r -> + forAll intervals $ \a -> + Interval.singleton r * a == r .*. a + +prop_mult_empty = + forAll intervals $ \a -> + Interval.empty * a == Interval.empty + +prop_mult_zero = + forAll intervals $ \a -> + not (Interval.null a) ==> Interval.singleton 0 * a == Interval.singleton 0 + +prop_mult_member = + forAll intervals $ \a -> + forAll intervals $ \b -> + and [ (x*y) `Interval.member` (a*b) + | x <- maybeToList $ Interval.pickup a + , y <- maybeToList $ Interval.pickup b + ] + +case_mult_test1 = ival1 * ival2 @?= ival3 + where + ival1 = Interval.interval (Just (True,1)) (Just (True,2)) + ival2 = Interval.interval (Just (True,1)) (Just (True,2)) + ival3 = Interval.interval (Just (True,1)) (Just (True,4)) + +case_mult_test2 = ival1 * ival2 @?= ival3 + where + ival1 = Interval.interval (Just (True,1)) (Just (True,2)) + ival2 = Interval.interval (Just (False,1)) (Just (False,2)) + ival3 = Interval.interval (Just (False,1)) (Just (False,4)) + +case_mult_test3 = ival1 * ival2 @?= ival3 + where + ival1 = Interval.interval (Just (False,1)) (Just (False,2)) + ival2 = Interval.interval (Just (False,1)) (Just (False,2)) + ival3 = Interval.interval (Just (False,1)) (Just (False,4)) + +case_mult_test4 = ival1 * ival2 @?= ival3 + where + ival1 = Interval.interval (Just (False,2)) Nothing + ival2 = Interval.interval (Just (False,3)) Nothing + ival3 = Interval.interval (Just (False,6)) Nothing + +case_mult_test5 = ival1 * ival2 @?= ival3 + where + ival1 = Interval.interval Nothing (Just (False,-3)) + ival2 = Interval.interval Nothing (Just (False,-2)) + ival3 = Interval.interval (Just (False,6)) Nothing + +case_mult_test6 = ival1 * ival2 @?= ival3 + where + ival1 = Interval.interval (Just (False,2)) Nothing + ival2 = Interval.interval Nothing (Just (False,-2)) + ival3 = Interval.interval Nothing (Just (False,-4)) + +{-------------------------------------------------------------------- + Fractional +--------------------------------------------------------------------} + +prop_recip_singleton = + forAll arbitrary $ \r -> + let n = fromIntegral (numerator r) + d = fromIntegral (denominator r) + in Interval.singleton n / Interval.singleton d == Interval.singleton (r::Rational) + +case_recip_pos = + recip pos @?= pos + +case_recip_neg = + recip neg @?= neg + +case_recip_test1 = recip i1 @?= i2 + where + i1, i2 :: Interval Rational + i1 = Interval.interval (Just (True,2)) Nothing + i2 = Interval.interval (Just (False,0)) (Just (True,1/2)) + +{-------------------------------------------------------------------- + Generators +--------------------------------------------------------------------} + +intervals :: Gen (Interval Rational) +intervals = do + lb <- arbitrary + ub <- arbitrary + return $ Interval.interval lb ub + +pos :: Interval Rational +pos = Interval.interval (Just (False,0)) Nothing + +neg :: Interval Rational +neg = Interval.interval Nothing (Just (False,0)) + +nonpos :: Interval Rational +nonpos = Interval.interval Nothing (Just (True,0)) + +nonneg :: Interval Rational +nonneg = Interval.interval (Just (True,0)) Nothing + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestLPFile.hs b/test/TestLPFile.hs new file mode 100644 --- /dev/null +++ b/test/TestLPFile.hs @@ -0,0 +1,66 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import Data.Maybe +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Text.LPFile + +case_testdata = checkString "testdata" testdata +case_test_indicator = checkFile "samples/lp/test-indicator.lp" +case_test_qcp = checkFile "samples/lp/test-qcp.lp" +case_test_qcp2 = checkFile "samples/lp/test-qcp2.lp" +case_test_qp = checkFile "samples/lp/test-qp.lp" +case_empty_obj_1 = checkFile "samples/lp/empty_obj_1.lp" +case_empty_obj_2 = checkFile "samples/lp/empty_obj_2.lp" + +------------------------------------------------------------------------ +-- Sample data + +testdata :: String +testdata = unlines + [ "Maximize" + , " obj: x1 + 2 x2 + 3 x3 + x4" + , "Subject To" + , " c1: - x1 + x2 + x3 + 10 x4 <= 20" + , " c2: x1 - 3 x2 + x3 <= 30" + , " c3: x2 - 3.5 x4 = 0" + , "Bounds" + , " 0 <= x1 <= 40" + , " 2 <= x4 <= 3" + , "General" + , " x4" + , "End" + ] + +------------------------------------------------------------------------ +-- Utilities + +checkFile :: FilePath -> IO () +checkFile fname = do + r <- parseFile fname + case r of + Left err -> assertFailure $ show err + Right lp -> + case render lp of + Nothing -> assertFailure "render failure" + Just _ -> return () + +checkString :: String -> String -> IO () +checkString name str = do + case parseString name str of + Left err -> assertFailure $ show err + Right lp -> + case render lp of + Nothing -> assertFailure "render failure" + Just _ -> return () + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestMIPSolver2.hs b/test/TestMIPSolver2.hs new file mode 100644 --- /dev/null +++ b/test/TestMIPSolver2.hs @@ -0,0 +1,127 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import Data.Ratio +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Text.Printf + +import Data.Linear +import qualified Data.LA as LA +import qualified Algorithm.Simplex2 as Simplex2 +import Algorithm.Simplex2 +import qualified Algorithm.MIPSolver2 as MIPSolver2 +--import Algorithm.MIPSolver2 + +------------------------------------------------------------------------ + +example1 :: (OptDir, LA.Expr Rational, [Atom Rational], IS.IntSet) +example1 = (optdir, obj, cs, ivs) + where + optdir = OptMax + x1 = LA.var 1 + x2 = LA.var 2 + x3 = LA.var 3 + x4 = LA.var 4 + obj = x1 .+. 2 .*. x2 .+. 3 .*. x3 .+. x4 + cs = + [ (-1) .*. x1 .+. x2 .+. x3 .+. 10.*.x4 .<=. LA.constant 20 + , x1 .-. 3 .*. x2 .+. x3 .<=. LA.constant 30 + , x2 .-. 3.5 .*. x4 .==. LA.constant 0 + , LA.constant 0 .<=. x1 + , x1 .<=. LA.constant 40 + , LA.constant 0 .<=. x2 + , LA.constant 0 .<=. x3 + , LA.constant 2 .<=. x4 + , x4 .<=. LA.constant 3 + ] + ivs = IS.singleton 4 + +case_test1 = do + let (optdir, obj, cs, ivs) = example1 + lp <- Simplex2.newSolver + replicateM 5 (Simplex2.newVar lp) + setOptDir lp optdir + setObj lp obj + mapM_ (Simplex2.assertAtom lp) cs + mip <- MIPSolver2.newSolver lp ivs + ret <- MIPSolver2.optimize mip (\_ _ -> return ()) + + ret @?= Simplex2.Optimum + + m <- MIPSolver2.model mip + forM_ [(1,40),(2,21/2),(3,39/2),(4,3)] $ \(var, val) -> + m IM.! var @?= val + + v <- MIPSolver2.getObjValue mip + v @?= 245/2 + +case_test1' = do + let (optdir, obj, cs, ivs) = example1 + lp <- Simplex2.newSolver + replicateM 5 (Simplex2.newVar lp) + setOptDir lp (f optdir) + setObj lp (lnegate obj) + mapM_ (Simplex2.assertAtom lp) cs + mip <- MIPSolver2.newSolver lp ivs + ret <- MIPSolver2.optimize mip (\_ _ -> return ()) + + ret @?= Simplex2.Optimum + + m <- MIPSolver2.model mip + forM_ [(1,40),(2,21/2),(3,39/2),(4,3)] $ \(var, val) -> + m IM.! var @?= val + + v <- MIPSolver2.getObjValue mip + v @?= -245/2 + + where + f OptMin = OptMax + f OptMax = OptMin + +-- 『数理計画法の基礎』(坂和 正敏) p.109 例 3.8 +example2 = (optdir, obj, cs, ivs) + where + optdir = OptMin + [x1,x2,x3] = map LA.var [1..3] + obj = (-1) .*. x1 .-. 3 .*. x2 .-. 5 .*. x3 + cs = + [ 3 .*. x1 .+. 4 .*. x2 .<=. LA.constant 10 + , 2 .*. x1 .+. x2 .+. x3 .<=. LA.constant 7 + , 3.*.x1 .+. x2 .+. 4 .*. x3 .==. LA.constant 12 + , LA.constant 0 .<=. x1 + , LA.constant 0 .<=. x2 + , LA.constant 0 .<=. x3 + ] + ivs = IS.fromList [1,2] + +case_test2 = do + let (optdir, obj, cs, ivs) = example2 + lp <- Simplex2.newSolver + replicateM 4 (Simplex2.newVar lp) + setOptDir lp optdir + setObj lp obj + mapM_ (Simplex2.assertAtom lp) cs + mip <- MIPSolver2.newSolver lp ivs + ret <- MIPSolver2.optimize mip (\_ _ -> return ()) + + ret @?= Simplex2.Optimum + + m <- MIPSolver2.model mip + forM_ [(1,0),(2,2),(3,5/2)] $ \(var, val) -> + m IM.! var @?= val + + v <- MIPSolver2.getObjValue mip + v @?= -37/2 + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestMPSFile.hs b/test/TestMPSFile.hs new file mode 100644 --- /dev/null +++ b/test/TestMPSFile.hs @@ -0,0 +1,68 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import Data.Maybe +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Text.MPSFile + +case_testdata = checkString "testdata" testdata +case_example2 = checkFile "samples/mps/example2.mps" +case_ind1 = checkFile "samples/mps/ind1.mps" +case_intvar1 = checkFile "samples/mps/intvar1.mps" +case_intvar2 = checkFile "samples/mps/intvar2.mps" +case_quadobj1 = checkFile "samples/mps/quadobj1.mps" +case_quadobj2 = checkFile "samples/mps/quadobj2.mps" +case_ranges = checkFile "samples/mps/ranges.mps" +case_sos = checkFile "samples/mps/sos.mps" +case_sc = checkFile "samples/mps/sc.mps" + +------------------------------------------------------------------------ +-- Sample data + +testdata :: String +testdata = unlines + [ "NAME example2.mps" + , "ROWS" + , " N obj " + , " L c1 " + , " L c2 " + , "COLUMNS" + , " x1 obj -1 c1 -1" + , " x1 c2 1" + , " x2 obj -2 c1 1" + , " x2 c2 -3" + , " x3 obj -3 c1 1" + , " x3 c2 1" + , "RHS" + , " rhs c1 20 c2 30" + , "BOUNDS" + , " UP BOUND x1 40" + , "ENDATA" + ] + +------------------------------------------------------------------------ +-- Utilities + +checkFile :: FilePath -> IO () +checkFile fname = do + r <- parseFile fname + case r of + Left err -> assertFailure (show err) + Right lp -> return () + +checkString :: String -> String -> IO () +checkString name str = do + case parseString name str of + Left err -> assertFailure (show err) + Right lp -> return () + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestPBFile.hs b/test/TestPBFile.hs new file mode 100644 --- /dev/null +++ b/test/TestPBFile.hs @@ -0,0 +1,146 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import Data.Maybe +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Text.PBFile + +case_exampleLIN = checkOPBString "exampleLIN" exampleLIN +case_exampleNLC1 = checkOPBString "exampleNLC1" exampleNLC1 +case_exampleNLC2 = checkOPBString "exampleNLC2" exampleNLC2 +case_exampleWBO1 = checkWBOString "exampleWBO1" exampleWBO1 +case_exampleWBO2 = checkWBOString "exampleWBO2" exampleWBO2 +case_exampleWBO3 = checkWBOString "exampleWBO3" exampleWBO3 + +------------------------------------------------------------------------ +-- Sample data + +exampleLIN :: String +exampleLIN = unlines + [ "* #variable= 5 #constraint= 4" + , "*" + , "* this is a dummy instance" + , "*" + , "min: 1 x2 -1 x3 ;" + , "1 x1 +4 x2 -2 x5 >= 2;" + , "-1 x1 +4 x2 -2 x5 >= +3;" + , "12345678901234567890 x4 +4 x3 >= 10;" + , "* an equality constraint" + , "2 x2 +3 x4 +2 x1 +3 x5 = 5;" + ] + +exampleNLC1 :: String +exampleNLC1 = unlines + [ "* #variable= 5 #constraint= 4 #product= 5 sizeproduct= 13" + , "*" + , "* this is a dummy instance" + , "*" + , "min: 1 x2 x3 -1 x3 ;" + , "1 x1 +4 x1 ~x2 -2 x5 >= 2;" + , "-1 x1 +4 x2 -2 x5 >= 3;" + , "12345678901234567890 x4 +4 x3 >= 10;" + , "2 x2 x3 +3 x4 ~x5 +2 ~x1 x2 +3 ~x1 x2 x3 ~x4 ~x5 = 5 ;" + ] + +exampleNLC2 :: String +exampleNLC2 = unlines + [ "* #variable= 6 #constraint= 3 #product= 9 sizeproduct= 18" + , "*" + , "* Factorization problem: find the smallest P such that P*Q=N" + , "* P is a 3 bits number (x3 x2 x1)" + , "* Q is a 3 bits number (x6 x5 x4)" + , "* N=35" + , "* " + , "* minimize the value of P" + , "min: +1 x1 +2 x2 +4 x3 ;" + , "* P>=2 (to avoid trivial factorization)" + , "+1 x1 +2 x2 +4 x3 >=2;" + , "* Q>=2 (to avoid trivial factorization)" + , "+1 x4 +2 x5 +4 x6 >=2;" + , "*" + , "* P*Q=N" + , "+1 x1 x4 +2 x1 x5 +4 x1 x6 +2 x2 x4 +4 x2 x5 +8 x2 x6 +4 x3 x4 +8 x3 x5 +16 x3 x6 = 35;" + ] + +exampleWBO1 :: String +exampleWBO1 = unlines $ + [ "* #variable= 1 #constraint= 2 #soft= 2 mincost= 2 maxcost= 3 sumcost= 5" + , "soft: 6 ;" + , "[2] +1 x1 >= 1 ;" + , "[3] -1 x1 >= 0 ;" + ] + +exampleWBO2 :: String +exampleWBO2 = unlines $ + [ "* #variable= 2 #constraint= 3 #soft= 2 mincost= 2 maxcost= 3 sumcost= 5" + , "soft: 6 ;" + , "[2] +1 x1 >= 1 ;" + , "[3] +1 x2 >= 1 ;" + , "-1 x1 -1 x2 >= -1 ;" + ] + +exampleWBO3 :: String +exampleWBO3 = unlines $ + [ "* #variable= 4 #constraint= 6 #soft= 4 mincost= 2 maxcost= 5 sumcost= 14" + , "soft: 6 ;" + , "[2] +1 x1 >= 1;" + , "[3] +1 x2 >= 1;" + , "[4] +1 x3 >= 1;" + , "[5] +1 x4 >= 1;" + , "-1 x1 -1 x2 >= -1 ;" + , "-1 x3 -1 x4 >= -1 ;" + ] + +------------------------------------------------------------------------ +-- Utilities + +checkOPBFile :: FilePath -> IO () +checkOPBFile fname = do + r <- parseOPBFile fname + case r of + Left err -> assertFailure $ show err + Right _ -> return () + +checkOPBString :: String -> String -> IO () +checkOPBString name str = do + case parseOPBString name str of + Left err -> assertFailure $ show err + Right _ -> return () + +checkWBOFile :: FilePath -> IO () +checkWBOFile fname = do + r <- parseWBOFile fname + case r of + Left err -> assertFailure $ show err + Right _ -> return () + +checkWBOString :: String -> String -> IO () +checkWBOString name str = do + case parseWBOString name str of + Left err -> assertFailure $ show err + Right _ -> return () + +testOPB :: String -> Bool +testOPB s = sf == sf2 + where + Right sf = parseOPBString "-" s + s2 = showOPB sf "" + Right sf2 = parseOPBString "-" s2 + +testWBO :: String -> Bool +testWBO s = sf == sf2 + where + Right sf = parseWBOString "-" s + s2 = showWBO sf "" + Right sf2 = parseWBOString "-" s2 + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestPolynomial.hs b/test/TestPolynomial.hs new file mode 100644 --- /dev/null +++ b/test/TestPolynomial.hs @@ -0,0 +1,543 @@ +{-# LANGUAGE TemplateHaskell #-} + +import Prelude hiding (lex) +import Control.Monad +import Data.List +import Data.Ratio +import qualified Data.Set as Set +import qualified Data.Map as Map +import Test.HUnit hiding (Test) +import Test.QuickCheck +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Test.Framework.Providers.QuickCheck2 + +import Data.Polynomial +import Data.Polynomial.GBase +import Data.Polynomial.Sturm +import qualified Data.Polynomial.Lagrange as Lagrange +import qualified Data.Interval as Interval + +{-------------------------------------------------------------------- + Polynomial type +--------------------------------------------------------------------} + +prop_plus_comm = + forAll polynomials $ \a -> + forAll polynomials $ \b -> + a + b == b + a + +prop_plus_assoc = + forAll polynomials $ \a -> + forAll polynomials $ \b -> + forAll polynomials $ \c -> + a + (b + c) == (a + b) + c + +prop_plus_unitL = + forAll polynomials $ \a -> + constant 0 + a == a + +prop_plus_unitR = + forAll polynomials $ \a -> + a + constant 0 == a + +prop_prod_comm = + forAll polynomials $ \a -> + forAll polynomials $ \b -> + a * b == b * a + +prop_prod_assoc = + forAll polynomials $ \a -> + forAll polynomials $ \b -> + forAll polynomials $ \c -> + a * (b * c) == (a * b) * c + +prop_prod_unitL = + forAll polynomials $ \a -> + constant 1 * a == a + +prop_prod_unitR = + forAll polynomials $ \a -> + a * constant 1 == a + +prop_distL = + forAll polynomials $ \a -> + forAll polynomials $ \b -> + forAll polynomials $ \c -> + a * (b + c) == a * b + a * c + +prop_distR = + forAll polynomials $ \a -> + forAll polynomials $ \b -> + forAll polynomials $ \c -> + (b + c) * a == b * a + c * a + +prop_negate = + forAll polynomials $ \a -> + a + negate a == 0 + +prop_negate_involution = + forAll polynomials $ \a -> + negate (negate a) == a + +prop_polyMDivMod = + forAll polynomials $ \g -> + forAll (replicateM 3 polynomials) $ \fs -> + all (0/=) fs ==> + let (qs, r) = polyMDivMod lex g fs + in sum (zipWith (*) fs qs) + r == g + +{-------------------------------------------------------------------- + Univalent polynomials +--------------------------------------------------------------------} + +prop_polyDivMod = + forAll upolynomials $ \a -> + forAll upolynomials $ \b -> + b /= 0 ==> + let (q,r) = polyDivMod a b + in a == q*b + r && (r==0 || deg b > deg r) + +case_polyDivMod_1 = g*q + r @?= f + where + x :: UPolynomial Rational + x = var () + f = x^3 + x^2 + x + g = x^2 + 1 + (q,r) = f `polyDivMod` g + +prop_polyGCD_divisible = + forAll upolynomials $ \a -> + forAll upolynomials $ \b -> + let c = polyGCD a b + in a `polyMod` c == 0 && b `polyMod` c == 0 + +prop_polyGCD_comm = + forAll upolynomials $ \a -> + forAll upolynomials $ \b -> + polyGCD a b == polyGCD b a + +case_polyGCD_1 = polyGCD f1 f2 @?= 1 + where + x :: UPolynomial Rational + x = var () + f1 = x^3 + x^2 + x + f2 = x^2 + 1 + +prop_polyLCM_divisible = + forAll upolynomials $ \a -> + forAll upolynomials $ \b -> + (a /= 0 && b /= 0) ==> + let c = polyLCM a b + in c `polyMod` a == 0 && c `polyMod` b == 0 + +prop_polyLCM_comm = + forAll upolynomials $ \a -> + forAll upolynomials $ \b -> + polyLCM a b == polyLCM b a + +prop_deriv_integral = + forAll upolynomials $ \a -> + deriv (integral a x) x == a + where + x = () + +prop_integral_deriv = + forAll upolynomials $ \a -> + deg (integral (deriv a x) x - a) == 0 + where + x = () + +{-------------------------------------------------------------------- + Monomial +--------------------------------------------------------------------} + +{-------------------------------------------------------------------- + Monic Monomial +--------------------------------------------------------------------} + +prop_mmDegreeOfProduct = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + mmDegree (a `mmProd` b) == mmDegree a + mmDegree b + +prop_mmDegreeOfOne = + mmDegree mmOne == 0 + +prop_mmProd_unitL = + forAll monicMonomials $ \a -> + mmOne `mmProd` a == a + +prop_mmProd_unitR = + forAll monicMonomials $ \a -> + a `mmProd` mmOne == a + +prop_mmProd_comm = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + a `mmProd` b == b `mmProd` a + +prop_mmProd_assoc = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + forAll monicMonomials $ \c -> + a `mmProd` (b `mmProd` c) == (a `mmProd` b) `mmProd` c + +prop_mmProd_Divisible = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + let c = a `mmProd` b + in mmDivisible c a && mmDivisible c b + +prop_mmProd_Div = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + let c = a `mmProd` b + in c `mmDiv` a == b && c `mmDiv` b == a + +case_mmDeriv = mmDeriv p 1 @?= (2, q) + where + p = mmFromList [(1,2),(2,4)] + q = mmFromList [(1,1),(2,4)] + +-- lcm (x1^2 * x2^4) (x1^3 * x2^1) = x1^3 * x2^4 +case_mmLCM = mmLCM p1 p2 @?= mmFromList [(1,3),(2,4)] + where + p1 = mmFromList [(1,2),(2,4)] + p2 = mmFromList [(1,3),(2,1)] + +-- gcd (x1^2 * x2^4) (x2^1 * x3^2) = x2 +case_mmGCD = mmGCD p1 p2 @?= mmFromList [(2,1)] + where + p1 = mmFromList [(1,2),(2,4)] + p2 = mmFromList [(2,1),(3,2)] + +prop_mmLCM_divisible = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + let c = mmLCM a b + in c `mmDivisible` a && c `mmDivisible` b + +prop_mmGCD_divisible = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + let c = mmGCD a b + in a `mmDivisible` c && b `mmDivisible` c + +{-------------------------------------------------------------------- + Monomial Order +--------------------------------------------------------------------} + +-- http://en.wikipedia.org/wiki/Monomial_order +case_lex = sortBy lex [a,b,c,d] @?= [b,a,d,c] + where + x = 1 + y = 2 + z = 3 + a = mmFromList [(x,1),(y,2),(z,1)] + b = mmFromList [(z,2)] + c = mmFromList [(x,3)] + d = mmFromList [(x,2),(z,2)] + +-- http://en.wikipedia.org/wiki/Monomial_order +case_grlex = sortBy grlex [a,b,c,d] @?= [b,c,a,d] + where + x = 1 + y = 2 + z = 3 + a = mmFromList [(x,1),(y,2),(z,1)] + b = mmFromList [(z,2)] + c = mmFromList [(x,3)] + d = mmFromList [(x,2),(z,2)] + +-- http://en.wikipedia.org/wiki/Monomial_order +case_grevlex = sortBy grevlex [a,b,c,d] @?= [b,c,d,a] + where + x = 1 + y = 2 + z = 3 + a = mmFromList [(x,1),(y,2),(z,1)] + b = mmFromList [(z,2)] + c = mmFromList [(x,3)] + d = mmFromList [(x,2),(z,2)] + +prop_refl_lex = propRefl lex +prop_refl_grlex = propRefl grlex +prop_refl_grevlex = propRefl grevlex + +prop_trans_lex = propTrans lex +prop_trans_grlex = propTrans grlex +prop_trans_grevlex = propTrans grevlex + +prop_sym_lex = propSym lex +prop_sym_grlex = propSym grlex +prop_sym_grevlex = propSym grevlex + +prop_monomial_order_property1_lex = monomialOrderProp1 lex +prop_monomial_order_property1_grlex = monomialOrderProp1 grlex +prop_monomial_order_property1_grevlex = monomialOrderProp1 grevlex + +prop_monomial_order_property2_lex = monomialOrderProp2 lex +prop_monomial_order_property2_grlex = monomialOrderProp2 grlex +prop_monomial_order_property2_grevlex = monomialOrderProp2 grevlex + +propRefl cmp = + forAll monicMonomials $ \a -> cmp a a == EQ + +propTrans cmp = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + cmp a b == LT ==> + forAll monicMonomials $ \c -> + cmp b c == LT ==> cmp a c == LT + +propSym cmp = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + cmp a b == flipOrdering (cmp b a) + where + flipOrdering EQ = EQ + flipOrdering LT = GT + flipOrdering GT = LT + +monomialOrderProp1 cmp = + forAll monicMonomials $ \a -> + forAll monicMonomials $ \b -> + let r = cmp a b + in cmp a b /= EQ ==> + forAll monicMonomials $ \c -> + cmp (a `mmProd` c) (b `mmProd` c) == r + +monomialOrderProp2 cmp = + forAll monicMonomials $ \a -> + a /= mmOne ==> cmp mmOne a == LT + +{-------------------------------------------------------------------- + Gröbner basis +--------------------------------------------------------------------} + +-- http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf +-- Example 1 +case_spolynomial = spolynomial grlex f g @?= - x^3*y^3 - constant (1/3) * y^3 + x^2 + where + x = var 1 + y = var 2 + f, g :: Polynomial Rational Int + f = x^3*y^2 - x^2*y^3 + x + g = 3*x^4*y + y^2 + + +-- http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf +-- Exercise 1 +case_buchberger1 = Set.fromList gbase @?= Set.fromList expected + where + gbase = buchberger lex [x^2-y, x^3-z] + expected = [y^3 - z^2, x^2 - y, x*z - y^2, x*y - z] + + x :: Polynomial Rational Int + x = var 1 + y = var 2 + z = var 3 + +-- http://math.rice.edu/~cbruun/vigre/vigreHW6.pdf +-- Exercise 2 +case_buchberger2 = Set.fromList gbase @?= Set.fromList expected + where + gbase = buchberger grlex [x^3-2*x*y, x^2*y-2*y^2+x] + expected = [x^2, x*y, y^2 - constant (1/2) * x] + + x :: Polynomial Rational Int + x = var 1 + y = var 2 + +-- http://www.iisdavinci.it/jeometry/buchberger.html +case_buchberger3 = Set.fromList gbase @?= Set.fromList expected + where + gbase = buchberger lex [x^2+2*x*y^2, x*y+2*y^3-1] + expected = [x, y^3 - constant (1/2)] + x :: Polynomial Rational Int + x = var 1 + y = var 2 + +-- http://www.orcca.on.ca/~reid/NewWeb/DetResDes/node4.html +-- 時間がかかるので自動実行されるテストケースには含めていない +disabled_case_buchberger4 = Set.fromList gbase @?= Set.fromList expected + where + x :: Polynomial Rational Int + x = var 1 + y = var 2 + z = var 3 + + gbase = buchberger lex [x^2+y*z-2, x*z+y^2-3, x*y+z^2-5] + + expected = reduceGBase lex $ + [ 8*z^8-100*z^6+438*z^4-760*z^2+361 + , 361*y+8*z^7+52*z^5-740*z^3+1425*z + , 361*x-88*z^7+872*z^5-2690*z^3+2375*z + ] +{- +Risa/Asir での結果 + +load("gr"); +gr([x^2+y*z-2, x*z+y^2-3, x*y+z^2-5],[x,y,z], 2); + +[8*z^8-100*z^6+438*z^4-760*z^2+361, +361*y+8*z^7+52*z^5-740*z^3+1425*z, +361*x-88*z^7+872*z^5-2690*z^3+2375*z] +-} + +-- Seven Trees in One +-- http://arxiv.org/abs/math/9405205 +case_Seven_Trees_in_One = reduce lex (x^7 - x) gbase @?= 0 + where + x :: Polynomial Rational Int + x = var 1 + gbase = buchberger lex [x-(x^2 + 1)] + +-- Non-linear loop invariant generation using Gröbner bases +-- http://portal.acm.org/citation.cfm?id=964028 +-- http://www-step.stanford.edu/papers/popl04.pdf +-- Example 3 +-- Consider again the ideal from Example 2; I = {f : x^2-y, g : y-z, h +-- : x+z}. The Gröbner basis for I is G = {f' : z^2-z, g : y-z, h : +-- x+z}. With this basis, every reduction of p : x^2 - y^2 will yield +-- a normal form 0. +case_sankaranarayanan04nonlinear = do + Set.fromList gbase @?= Set.fromList [f', g, h] + reduce lex (x^2 - y^2) gbase @?= 0 + where + x :: Polynomial Rational Int + x = var 1 + y = var 2 + z = var 3 + f = x^2 - y + g = y - z + h = x + z + f' = z^2 - z + gbase = buchberger lex [f, g, h] + +{-------------------------------------------------------------------- + Generators +--------------------------------------------------------------------} + +monicMonomials :: Gen (MonicMonomial Int) +monicMonomials = do + size <- choose (0, 3) + xs <- replicateM size $ do + v <- choose (-5, 5) + e <- liftM ((+1) . abs) arbitrary + return $ mmFromList [(v,e)] + return $ foldl mmProd mmOne xs + +monomials :: Gen (Monomial Rational Int) +monomials = do + m <- monicMonomials + c <- arbitrary + return (c,m) + +polynomials :: Gen (Polynomial Rational Int) +polynomials = do + size <- choose (0, 5) + xs <- replicateM size monomials + return $ sum $ map fromMonomial xs + +umonicMonomials :: Gen (MonicMonomial ()) +umonicMonomials = do + size <- choose (0, 3) + xs <- replicateM size $ do + e <- choose (1, 4) + return $ mmFromList [((),e)] + return $ foldl mmProd mmOne xs + +umonomials :: Gen (Monomial Rational ()) +umonomials = do + m <- umonicMonomials + c <- arbitrary + return (c,m) + +upolynomials :: Gen (UPolynomial Rational) +upolynomials = do + size <- choose (0, 5) + xs <- replicateM size umonomials + return $ sum $ map fromMonomial xs + +------------------------------------------------------------------------ + +-- http://mathworld.wolfram.com/SturmFunction.html +case_sturmChain = sturmChain p0 @?= chain + where + x = var () + p0 = x^5 - 3*x - 1 + p1 = 5*x^4 - 3 + p2 = constant (1/5) * (12*x + 5) + p3 = constant (59083 / 20736) + chain = [p0, p1, p2, p3] + +-- http://mathworld.wolfram.com/SturmFunction.html +case_numRoots_1 = + sequence_ + [ numRoots p (Interval.closedInterval (-2) 0) @?= 2 + , numRoots p (Interval.closedInterval 0 2) @?= 1 + , numRoots p (Interval.closedInterval (-1.5) (-1.0)) @?= 1 + , numRoots p (Interval.closedInterval (-0.5) 0) @?= 1 + , numRoots p (Interval.closedInterval 1 (1.5)) @?= 1 + ] + where + x = var () + p = x^5 - 3*x - 1 + +-- check interpretation of intervals +case_numRoots_2 = + sequence_ + [ numRoots p (Interval.interval (Just (False,2)) (Just (True,3))) @?= 0 + , numRoots p (Interval.interval (Just (True,2)) (Just (True,3))) @?= 1 + , numRoots p (Interval.interval (Just (False,1)) (Just (False,2))) @?= 0 + , numRoots p (Interval.interval (Just (False,1)) (Just (True,2))) @?= 1 + ] + where + x = var () + p = x^2 - 4 + +case_separate = do + forM_ (zip vals intervals) $ \(v,ival) -> do + Interval.member v ival @?= True + forM_ (filter (v/=) vals) $ \v2 -> do + Interval.member v2 ival @?= False + where + x = var () + p = x^5 - 3*x - 1 + intervals = separate p + vals = [-1.21465, -0.334734, 1.38879] + +------------------------------------------------------------------------ + +-- http://en.wikipedia.org/wiki/Lagrange_polynomial +case_Lagrange_interpolation_1 = p @?= q + where + x :: UPolynomial Rational + x = var () + p = Lagrange.interpolation + [ (1, 1) + , (2, 4) + , (3, 9) + ] + q = x^2 + +-- http://en.wikipedia.org/wiki/Lagrange_polynomial +case_Lagrange_interpolation_2 = p @?= q + where + x :: UPolynomial Rational + x = var () + p = Lagrange.interpolation + [ (1, 1) + , (2, 8) + , (3, 27) + ] + q = 6*x^2 - 11*x + 6 + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestQE.hs b/test/TestQE.hs new file mode 100644 --- /dev/null +++ b/test/TestQE.hs @@ -0,0 +1,255 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import qualified Data.IntMap as IM +import qualified Data.Map as Map +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit + +import Data.AlgebraicNumber +import Data.ArithRel +import Data.Expr +import Data.Formula +import Data.Linear +import qualified Data.LA as LA +import qualified Data.Polynomial as P +import Data.OptDir + +import qualified Algorithm.FourierMotzkin as FourierMotzkin +import qualified Algorithm.OmegaTest as OmegaTest +import qualified Algorithm.Cooper as Cooper +import qualified Algorithm.CAD as CAD +import qualified Algorithm.Simplex2 as Simplex2 +import qualified Algorithm.ContiTraverso as ContiTraverso + +------------------------------------------------------------------------ + +{- +Example from the OmegaTest paper + +7x + 12y + 31z = 17 +3x + 5y + 14z = 7 +1 ≤ x ≤ 40 +-50 ≤ y ≤ 50 + +satisfiable in R +satisfiable in Z + +(declare-fun x () Int) +(declare-fun y () Int) +(declare-fun z () Int) +(assert (= (+ (* 7 x) (* 12 y) (* 31 z)) 17)) +(assert (= (+ (* 3 x) (* 5 y) (* 14 z)) 7)) +(assert (<= 1 x)) +(assert (<= x 40)) +(assert (<= (- 50) y)) +(assert (<= y 50)) +(check-sat) ; => sat +(get-model) + +Just (DNF {unDNF = [[Nonneg (fromTerms [(-17,-1),(7,0),(12,1),(31,2)]),Nonneg (fromTerms [(17,-1),(-7,0),(-12,1),(-31,2)]),Nonneg (fromTerms [(-7,-1),(3,0),(5,1),(14,2)]),Nonneg (fromTerms [(7,-1),(-3,0),(-5,1),(-14,2)]),Nonneg (fromTerms [(-1,-1),(1,0)]),Nonneg (fromTerms [(40,-1),(-1,0)]),Nonneg (fromTerms [(50,-1),(1,1)]),Nonneg (fromTerms [(50,-1),(-1,1)])]]}) + +7x+12y+31z - 17 >= 0 +-7x-12y-31z + 17 >= 0 +3x+5y+14z - 7 >= 0 +-3x-5y-14z + 7 >= 0 +x - 1 >= 0 +-x + 40 >= 0 +y + 50 >= 0 +-y + 50 >= 0 +-} +test1 :: Formula (Atom Rational) +test1 = c1 .&&. c2 .&&. c3 .&&. c4 + where + x = Var 0 + y = Var 1 + z = Var 2 + c1 = 7*x + 12*y + 31*z .==. 17 + c2 = 3*x + 5*y + 14*z .==. 7 + c3 = 1 .<=. x .&&. x .<=. 40 + c4 = (-50) .<=. y .&&. y .<=. 50 + +test1' :: [LA.Atom Rational] +test1' = [c1, c2] ++ c3 ++ c4 + where + x = LA.var 0 + y = LA.var 1 + z = LA.var 2 + c1 = 7.*.x .+. 12.*.y .+. 31.*.z .==. LA.constant 17 + c2 = 3.*.x .+. 5.*.y .+. 14.*.z .==. LA.constant 7 + c3 = [LA.constant 1 .<=. x, x .<=. LA.constant 40] + c4 = [LA.constant (-50) .<=. y, y .<=. LA.constant 50] + + +{- +Example from the OmegaTest paper + +27 ≤ 11x+13y ≤ 45 +-10 ≤ 7x-9y ≤ 4 + +satisfiable in R +but unsatisfiable in Z + +(declare-fun x () Int) +(declare-fun y () Int) +(define-fun t1 () Int (+ (* 11 x) (* 13 y))) +(define-fun t2 () Int (- (* 7 x) (* 9 y))) +(assert (<= 27 t1)) +(assert (<= t1 45)) +(assert (<= (- 10) t2)) +(assert (<= t2 4)) +(check-sat) ; unsat +(get-model) +-} +test2 :: Formula (Atom Rational) +test2 = c1 .&&. c2 + where + x = Var 0 + y = Var 1 + t1 = 11*x + 13*y + t2 = 7*x - 9*y + c1 = 27 .<=. t1 .&&. t1 .<=. 45 + c2 = (-10) .<=. t2 .&&. t2 .<=. 4 + +test2' :: [LA.Atom Rational] +test2' = + [ LA.constant 27 .<=. t1 + , t1 .<=. LA.constant 45 + , LA.constant (-10) .<=. t2 + , t2 .<=. LA.constant 4 + ] + where + x = LA.var 0 + y = LA.var 1 + t1 = 11.*.x .+. 13.*.y + t2 = 7.*.x .-. 9.*.y + +------------------------------------------------------------------------ + +case_FourierMotzkin_test1 :: IO () +case_FourierMotzkin_test1 = + case FourierMotzkin.solveConj test1' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> + forM_ test1' $ \a -> do + LA.evalAtom m a @?= True + +case_FourierMotzkin_test2 :: IO () +case_FourierMotzkin_test2 = + case FourierMotzkin.solveConj test2' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> + forM_ test2' $ \a -> do + LA.evalAtom m a @?= True + +------------------------------------------------------------------------ + +case_CAD_test1 :: IO () +case_CAD_test1 = + case CAD.solve test1'' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> + forM_ test1'' $ \a -> do + evalPAtom m a @?= True + where + test1'' = map toPRel test1' + +case_CAD_test2 :: IO () +case_CAD_test2 = + case CAD.solve test2'' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> + forM_ test2'' $ \a -> do + evalPAtom m a @?= True + where + test2'' = map toPRel test2' + +toP :: LA.Expr Rational -> P.Polynomial Rational Int +toP e = P.fromTerms [(c, if x == LA.unitVar then P.mmOne else P.mmVar x) | (c,x) <- LA.terms e] + +toPRel :: LA.Atom Rational -> Rel (P.Polynomial Rational Int) +toPRel (Rel lhs op rhs) = Rel (toP lhs) op (toP rhs) + +evalP :: Map.Map Int AReal -> P.Polynomial Rational Int -> AReal +evalP m p = P.eval (m Map.!) $ P.mapCoeff fromRational p + +evalPAtom :: Map.Map Int AReal -> Rel (P.Polynomial Rational Int) -> Bool +evalPAtom m (Rel lhs op rhs) =　evalOp op (evalP m lhs) (evalP m rhs) + +------------------------------------------------------------------------ + +case_OmegaTest_test1 :: IO () +case_OmegaTest_test1 = + case OmegaTest.solve test1' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> do + forM_ test1' $ \a -> do + LA.evalAtom (IM.map fromInteger m) a @?= True + +case_OmegaTest_test2 :: IO () +case_OmegaTest_test2 = + case OmegaTest.solve test2' of + Just _ -> assertFailure "expected: Nothing\n but got: Just" + Nothing -> return () + +------------------------------------------------------------------------ + +case_Cooper_test1 :: IO () +case_Cooper_test1 = + case Cooper.solveConj test1' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> do + forM_ test1' $ \a -> do + LA.evalAtom (IM.map fromInteger m) a @?= True + +case_Cooper_test2 :: IO () +case_Cooper_test2 = + case Cooper.solveConj test2' of + Just _ -> assertFailure "expected: Nothing\n but got: Just" + Nothing -> return () + +------------------------------------------------------------------------ + +case_Simplex2_test1 :: IO () +case_Simplex2_test1 = do + solver <- Simplex2.newSolver + replicateM 3 (Simplex2.newVar solver) -- XXX + mapM_ (Simplex2.assertAtomEx solver) test1' + ret <- Simplex2.check solver + ret @?= True + +case_Simplex2_test2 :: IO () +case_Simplex2_test2 = do + solver <- Simplex2.newSolver + replicateM 2 (Simplex2.newVar solver) -- XXX + mapM_ (Simplex2.assertAtomEx solver) test2' + ret <- Simplex2.check solver + ret @?= True + +------------------------------------------------------------------------ + +-- Too slow + +disabled_case_ContiTraverso_test1 :: IO () +disabled_case_ContiTraverso_test1 = + case ContiTraverso.solve P.grlex OptMin (LA.constant 0) test1' of + Nothing -> assertFailure "expected: Just\n but got: Nothing" + Just m -> do + forM_ test1' $ \a -> do + LA.evalAtom (IM.map fromInteger m) a @?= True + +disabled_case_ContiTraverso_test2 :: IO () +disabled_case_ContiTraverso_test2 = + case ContiTraverso.solve P.grlex OptMin (LA.constant 0) test2' of + Just _ -> assertFailure "expected: Nothing\n but got: Just" + Nothing -> return () + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestSAT.hs b/test/TestSAT.hs new file mode 100644 --- /dev/null +++ b/test/TestSAT.hs @@ -0,0 +1,555 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import qualified Data.Set as Set +import qualified Data.IntSet as IS +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import SAT +import SAT.Types +import qualified SAT.TseitinEncoder as Tseitin +import SAT.TseitinEncoder (Formula (..)) +import qualified SAT.MUS as MUS +import qualified SAT.CAMUS as CAMUS + +-- should be SAT +case_solve_SAT :: IO () +case_solve_SAT = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addClause solver [literal x1 True, literal x2 True] -- x1 or x2 + addClause solver [literal x1 True, literal x2 False] -- x1 or not x2 + addClause solver [literal x1 False, literal x2 False] -- not x1 or not x2 + ret <- solve solver + ret @?= True + +-- shuld be UNSAT +case_solve_UNSAT :: IO () +case_solve_UNSAT = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addClause solver [literal x1 True, literal x2 True] -- x1 or x2 + addClause solver [literal x1 False, literal x2 True] -- not x1 or x2 + addClause solver [literal x1 True, literal x2 False] -- x1 or not x2 + addClause solver [literal x1 False, literal x2 False] -- not x2 or not x2 + ret <- solve solver + ret @?= False + +-- top level でいきなり矛盾 +case_root_inconsistent :: IO () +case_root_inconsistent = do + solver <- newSolver + x1 <- newVar solver + addClause solver [literal x1 True] + addClause solver [literal x1 False] + ret <- solve solver -- unsat + ret @?= False + +-- incremental に制約を追加 +case_incremental_solving :: IO () +case_incremental_solving = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addClause solver [literal x1 True, literal x2 True] -- x1 or x2 + addClause solver [literal x1 True, literal x2 False] -- x1 or not x2 + addClause solver [literal x1 False, literal x2 False] -- not x1 or not x2 + ret <- solve solver -- sat + ret @?= True + + addClause solver [literal x1 False, literal x2 True] -- not x1 or x2 + ret <- solve solver -- unsat + ret @?= False + +-- 制約なし +case_empty_constraint :: IO () +case_empty_constraint = do + solver <- newSolver + ret <- solve solver + ret @?= True + +-- 空の節 +case_empty_claue :: IO () +case_empty_claue = do + solver <- newSolver + addClause solver [] + ret <- solve solver + ret @?= False + +-- 自明に真な節 +case_excluded_middle_claue :: IO () +case_excluded_middle_claue = do + solver <- newSolver + x1 <- newVar solver + addClause solver [x1, -x1] -- x1 or not x1 + ret <- solve solver + ret @?= True + +-- 冗長な節 +case_redundant_clause :: IO () +case_redundant_clause = do + solver <- newSolver + x1 <- newVar solver + addClause solver [x1,x1] -- x1 or x1 + ret <- solve solver + ret @?= True + +case_instantiateClause :: IO () +case_instantiateClause = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addClause solver [x1] + addClause solver [x1,x2] + addClause solver [-x1,x2] + ret <- solve solver + ret @?= True + +case_instantiateAtLeast :: IO () +case_instantiateAtLeast = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + x4 <- newVar solver + addClause solver [x1] + + addAtLeast solver [x1,x2,x3,x4] 2 + ret <- solve solver + ret @?= True + + addAtLeast solver [-x1,-x2,-x3,-x4] 2 + ret <- solve solver + ret @?= True + +case_inconsistent_AtLeast :: IO () +case_inconsistent_AtLeast = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addAtLeast solver [x1,x2] 3 + ret <- solve solver -- unsat + ret @?= False + +case_trivial_AtLeast :: IO () +case_trivial_AtLeast = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addAtLeast solver [x1,x2] 0 + ret <- solve solver + ret @?= True + + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addAtLeast solver [x1,x2] (-1) + ret <- solve solver + ret @?= True + +case_AtLeast_1 :: IO () +case_AtLeast_1 = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + addAtLeast solver [x1,x2,x3] 2 + addAtLeast solver [-x1,-x2,-x3] 2 + ret <- solve solver -- unsat + ret @?= False + +case_AtLeast_2 :: IO () +case_AtLeast_2 = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + x4 <- newVar solver + addAtLeast solver [x1,x2,x3,x4] 2 + addClause solver [-x1,-x2] + addClause solver [-x1,-x3] + ret <- solve solver + ret @?= True + +case_AtLeast_3 :: IO () +case_AtLeast_3 = do + forM_ [(-1) .. 3] $ \n -> do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addAtLeast solver [x1,x2] n + ret <- solve solver + assertEqual ("case_AtLeast3_" ++ show n) (n <= 2) ret + +-- from http://www.cril.univ-artois.fr/PB11/format.pdf +case_PB_sample1 :: IO () +case_PB_sample1 = do + solver <- newSolver + + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + x4 <- newVar solver + x5 <- newVar solver + + addPBAtLeast solver [(1,x1),(4,x2),(-2,x5)] 2 + addPBAtLeast solver [(-1,x1),(4,x2),(-2,x5)] 3 + addPBAtLeast solver [(12345678901234567890,x4),(4,x3)] 10 + addPBExactly solver [(2,x2),(3,x4),(2,x1),(3,x5)] 5 + + ret <- solve solver + ret @?= True + +-- 一部の変数を否定に置き換えたもの +case_PB_sample1' :: IO () +case_PB_sample1' = do + solver <- newSolver + + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + x4 <- newVar solver + x5 <- newVar solver + + addPBAtLeast solver [(1,x1),(4,-x2),(-2,x5)] 2 + addPBAtLeast solver [(-1,x1),(4,-x2),(-2,x5)] 3 + addPBAtLeast solver [(12345678901234567890,-x4),(4,x3)] 10 + addPBExactly solver [(2,-x2),(3,-x4),(2,x1),(3,x5)] 5 + + ret <- solve solver + ret @?= True + +-- いきなり矛盾したPB制約 +case_root_inconsistent_PB :: IO () +case_root_inconsistent_PB = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addPBAtLeast solver [(2,x1),(3,x2)] 6 + ret <- solve solver + ret @?= False + +case_pb_propagate :: IO () +case_pb_propagate = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addPBAtLeast solver [(1,x1),(3,x2)] 3 + addClause solver [-x1] + ret <- solve solver + ret @?= True + +case_solveWith_1 :: IO () +case_solveWith_1 = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + addClause solver [x1, x2] -- x1 or x2 + addClause solver [x1, -x2] -- x1 or not x2 + addClause solver [-x1, -x2] -- not x1 or not x2 + addClause solver [-x3, -x1, x2] -- not x3 or not x1 or x2 + + ret <- solve solver -- sat + ret @?= True + + ret <- solveWith solver [x3] -- unsat + ret @?= False + + ret <- solve solver -- sat + ret @?= True + +case_solveWith_2 :: IO () +case_solveWith_2 = do + solver <- newSolver + x1 <- newVar solver + x2 <- newVar solver + addClause solver [-x1, x2] -- -x1 or x2 + addClause solver [x1] -- x1 + + ret <- solveWith solver [x2] + ret @?= True + + ret <- solveWith solver [-x2] + ret @?= False + +------------------------------------------------------------------------ + +-- -4*(not x1) + 3*x1 + 10*(not x2) >= 3 +-- ⇔ -4*(1 - x1) + 3*x1 + 10*(not x2) >= 3 +-- ⇔ -4 + 4*x1 + 3*x1 + 10*(not x2) >= 3 +-- ⇔ 7*x1 + 10*(not x2) >= 7 +-- ⇔ 7*x1 + 7*(not x2) >= 7 +-- ⇔ x1 + (not x2) >= 1 +case_normalizePBAtLeast :: Assertion +case_normalizePBAtLeast = (sort lhs, rhs) @?= (sort [(1,x1),(1,-x2)], 1) + where + x1 = 1 + x2 = 2 + (lhs,rhs) = normalizePBAtLeast ([(-4,-x1),(3,x1),(10,-x2)], 3) + +case_normalizePBExactly_1 :: Assertion +case_normalizePBExactly_1 = (sort lhs, rhs) @?= (sort [(3,x1),(2,x2)], 1) + where + x1 = 1 + x2 = 2 + (lhs,rhs) = normalizePBExactly ([(6,x1),(4,x2)], 2) + +case_normalizePBExactly_2 :: Assertion +case_normalizePBExactly_2 = (sort lhs, rhs) @?= ([], 1) + where + x1 = 1 + x2 = 2 + x3 = 3 + (lhs,rhs) = normalizePBExactly ([(2,x1),(2,x2),(2,x3)], 3) + +case_cutResolve_1 :: Assertion +case_cutResolve_1 = (sort lhs, rhs) @?= (sort [(1,x3),(1,x4)], 1) + where + x1 = 1 + x2 = 2 + x3 = 3 + x4 = 4 + pb1 = ([(1,x1), (1,x2), (1,x3)], 1) + pb2 = ([(2,-x1), (2,-x2), (1,x4)], 3) + (lhs,rhs) = cutResolve pb1 pb2 x1 + +case_cutResolve_2 :: Assertion +case_cutResolve_2 = (sort lhs, rhs) @?= (sort [(3,x1),(2,-x2),(2,x4)], 3) + where + x1 = 1 + x2 = 2 + x3 = 3 + x4 = 4 + pb1 = ([(3,x1), (2,-x2), (1,x3), (1,x4)], 3) + pb2 = ([(1,-x3), (1,x4)], 1) + (lhs,rhs) = cutResolve pb1 pb2 x3 + +case_cardinalityReduction :: Assertion +case_cardinalityReduction = (sort lhs, rhs) @?= ([1,2,3,4,5],4) + where + (lhs, rhs) = cardinalityReduction ([(6,1),(5,2),(4,3),(3,4),(2,5),(1,6)], 17) + +-- from "Pueblo: A Hybrid Pseudo-Boolean SAT Solver" +-- clauseがunitになるレベルで、PB制約が違反状態のままという例。 +case_hybridLearning_1 :: IO () +case_hybridLearning_1 = do + solver <- newSolver + [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11] <- replicateM 11 (newVar solver) + + addClause solver [x11, x10, x9] -- C1 + addClause solver [x8, x7, x6] -- C2 + addClause solver [x5, x4, x3] -- C3 + addAtLeast solver [-x2, -x5, -x8, -x11] 3 -- C4 + addAtLeast solver [-x1, -x4, -x7, -x10] 3 -- C5 + + replicateM 3 (varBumpActivity solver x3) + setVarPolarity solver x3 False + + replicateM 2 (varBumpActivity solver x6) + setVarPolarity solver x6 False + + replicateM 1 (varBumpActivity solver x9) + setVarPolarity solver x9 False + + setVarPolarity solver x1 True + + setLearningStrategy solver LearningHybrid + ret <- solve solver + ret @?= True + +-- from "Pueblo: A Hybrid Pseudo-Boolean SAT Solver" +-- clauseがunitになるレベルで、PB制約が違反状態のままという例。 +-- さらに、学習したPB制約はunitにはならない。 +case_hybridLearning_2 :: IO () +case_hybridLearning_2 = do + solver <- newSolver + [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12] <- replicateM 12 (newVar solver) + + addClause solver [x11, x10, x9] -- C1 + addClause solver [x8, x7, x6] -- C2 + addClause solver [x5, x4, x3] -- C3 + addAtLeast solver [-x2, -x5, -x8, -x11] 3 -- C4 + addAtLeast solver [-x1, -x4, -x7, -x10] 3 -- C5 + + addClause solver [x12, -x3] + addClause solver [x12, -x6] + addClause solver [x12, -x9] + + varBumpActivity solver x12 + setVarPolarity solver x12 False + + setLearningStrategy solver LearningHybrid + ret <- solve solver + ret @?= True + +-- regression test for the bug triggered by normalized-blast-floppy1-8.ucl.opb.bz2 +case_addPBAtLeast_regression :: IO () +case_addPBAtLeast_regression = do + solver <- newSolver + [x1,x2,x3,x4] <- replicateM 4 (newVar solver) + addClause solver [-x1] + addClause solver [-x2, -x3] + addClause solver [-x2, -x4] + addPBAtLeast solver [(1,x1),(2,x2),(1,x3),(1,x4)] 3 + ret <- solve solver + ret @?= False + +------------------------------------------------------------------------ + +case_addFormula = do + solver <- newSolver + enc <- Tseitin.newEncoder solver + + [x1,x2,x3,x4,x5] <- replicateM 5 $ liftM Var $ newVar solver + Tseitin.addFormula enc $ Or [Imply x1 (And [x3,x4]), Imply x2 (And [x3,x5])] + -- x6 = x3 ∧ x4 + -- x7 = x3 ∧ x5 + Tseitin.addFormula enc $ Or [x1, x2] + Tseitin.addFormula enc $ Imply x4 (Not x5) + ret <- solve solver + ret @?= True + + Tseitin.addFormula enc $ Equiv x2 x4 + ret <- solve solver + ret @?= True + + Tseitin.addFormula enc $ Equiv x1 x5 + ret <- solve solver + ret @?= True + + Tseitin.addFormula enc $ Imply (Not x1) (And [x3,x5]) + ret <- solve solver + ret @?= True + + Tseitin.addFormula enc $ Imply (Not x2) (And [x3,x4]) + ret <- solve solver + ret @?= False + +case_encodeConj = do + solver <- newSolver + enc <- Tseitin.newEncoder solver + x1 <- newVar solver + x2 <- newVar solver + x3 <- Tseitin.encodeConj enc [x1,x2] + + ret <- solveWith solver [x3] + ret @?= True + m <- model solver + evalLit m x1 @?= True + evalLit m x2 @?= True + evalLit m x3 @?= True + + ret <- solveWith solver [-x3] + ret @?= True + m <- model solver + (evalLit m x1 && evalLit m x2) @?= False + evalLit m x3 @?= False + +case_encodeDisj = do + solver <- newSolver + enc <- Tseitin.newEncoder solver + x1 <- newVar solver + x2 <- newVar solver + x3 <- Tseitin.encodeDisj enc [x1,x2] + + ret <- solveWith solver [x3] + ret @?= True + m <- model solver + (evalLit m x1 || evalLit m x2) @?= True + evalLit m x3 @?= True + + ret <- solveWith solver [-x3] + ret @?= True + m <- model solver + evalLit m x1 @?= False + evalLit m x2 @?= False + evalLit m x3 @?= False + +------------------------------------------------------------------------ + +case_MUS = do + solver <- newSolver + [x1,x2,x3] <- newVars solver 3 + sels@[y1,y2,y3,y4,y5,y6] <- newVars solver 6 + addClause solver [-y1, x1] + addClause solver [-y2, -x1] + addClause solver [-y3, -x1, x2] + addClause solver [-y4, -x2] + addClause solver [-y5, -x1, x3] + addClause solver [-y6, -x3] + + ret <- solveWith solver sels + ret @?= False + + actual <- MUS.findMUSAssumptions solver MUS.defaultOptions + let actual' = IS.fromList $ map (\x -> x-3) actual + expected = map IS.fromList [[1, 2], [1, 3, 4], [1, 5, 6]] + actual' `elem` expected @?= True + +------------------------------------------------------------------------ + +{- +c http://sun.iwu.edu/~mliffito/publications/jar_liffiton_CAMUS.pdf +c φ= (x1) ∧ (¬x1) ∧ (¬x1∨x2) ∧ (¬x2) ∧ (¬x1∨x3) ∧ (¬x3) +c MUSes(φ) = {{C1, C2}, {C1, C3, C4}, {C1, C5, C6}} +c MCSes(φ) = {{C1}, {C2, C3, C5}, {C2, C3, C6}, {C2, C4, C5}, {C2, C4, C6}} +p cnf 3 6 +1 0 +-1 0 +-1 2 0 +-2 0 +-1 3 0 +-3 0 +-} + +case_camus_allMCSAssumptions = do + solver <- newSolver + [x1,x2,x3] <- newVars solver 3 + sels@[y1,y2,y3,y4,y5,y6] <- newVars solver 6 + addClause solver [-y1, x1] + addClause solver [-y2, -x1] + addClause solver [-y3, -x1, x2] + addClause solver [-y4, -x2] + addClause solver [-y5, -x1, x3] + addClause solver [-y6, -x3] + actual <- CAMUS.allMCSAssumptions solver sels CAMUS.defaultOptions + let actual' = Set.fromList $ map IS.fromList actual + expected = [[1], [2,3,5], [2,3,6], [2,4,5], [2,4,6]] + expected' = Set.fromList $ map (IS.fromList . map (+3)) expected + actual' @?= expected' + +case_camus_allMUSAssumptions = do + solver <- newSolver + [x1,x2,x3] <- newVars solver 3 + sels@[y1,y2,y3,y4,y5,y6] <- newVars solver 6 + addClause solver [-y1, x1] + addClause solver [-y2, -x1] + addClause solver [-y3, -x1, x2] + addClause solver [-y4, -x2] + addClause solver [-y5, -x1, x3] + addClause solver [-y6, -x3] + actual <- CAMUS.allMUSAssumptions solver sels CAMUS.defaultOptions + let actual' = Set.fromList $ map IS.fromList actual + expected = [[1,2], [1,3,4], [1,5,6]] + expected' = Set.fromList $ map (IS.fromList . map (+3)) expected + actual' @?= expected' + +case_camus_hittingSetDual = actual' @?= expected' + where + actual = CAMUS.hittingSetDual [[1], [2,3,5], [2,3,6], [2,4,5], [2,4,6]] + actual' = Set.fromList $ map IS.fromList actual + expected = [[1,2], [1,3,4], [1,5,6]] + expected' = Set.fromList $ map IS.fromList expected + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestSimplex2.hs b/test/TestSimplex2.hs new file mode 100644 --- /dev/null +++ b/test/TestSimplex2.hs @@ -0,0 +1,409 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Control.Monad +import Data.List +import Data.Ratio +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Text.Printf + +import Data.Linear +import qualified Data.LA as LA +import Algorithm.Simplex2 + +case_test1 :: IO () +case_test1 = do + solver <- newSolver + x <- newVar solver + y <- newVar solver + z <- newVar solver + assertAtom solver (LA.fromTerms [(7,x), (12,y), (31,z)] .==. LA.constant 17) + assertAtom solver (LA.fromTerms [(3,x), (5,y), (14,z)] .==. LA.constant 7) + assertAtom solver (LA.var x .>=. LA.constant 1) + assertAtom solver (LA.var x .<=. LA.constant 40) + assertAtom solver (LA.var y .>=. LA.constant (-50)) + assertAtom solver (LA.var y .<=. LA.constant 50) + + ret <- check solver + ret @?= True + + vx <- getValue solver x + vy <- getValue solver y + vz <- getValue solver z + 7*vx + 12*vy + 31*vz @?= 17 + 3*vx + 5*vy + 14*vz @?= 7 + assertBool (printf "vx should be >=1 but %s" (show vx)) $ vx >= 1 + assertBool (printf "vx should be <=40 but %s" (show vx)) $ vx <= 40 + assertBool (printf "vx should be >=-50 but %s" (show vy)) $ vy >= -50 + assertBool (printf "vx should be <=50 but %s" (show vy)) $ vy <= 50 + +case_test2 :: IO () +case_test2 = do + solver <- newSolver + x <- newVar solver + y <- newVar solver + assertAtom solver (LA.fromTerms [(11,x), (13,y)] .>=. LA.constant 27) + assertAtom solver (LA.fromTerms [(11,x), (13,y)] .<=. LA.constant 45) + assertAtom solver (LA.fromTerms [(7,x), (-9,y)] .>=. LA.constant (-10)) + assertAtom solver (LA.fromTerms [(7,x), (-9,y)] .<=. LA.constant 4) + + ret <- check solver + ret @?= True + + vx <- getValue solver x + vy <- getValue solver y + let v1 = 11*vx + 13*vy + v2 = 7*vx - 9*vy + assertBool (printf "11*vx + 13*vy should be >=27 but %s" (show v1)) $ 27 <= v1 + assertBool (printf "11*vx + 13*vy should be <=45 but %s" (show v1)) $ v1 <= 45 + assertBool (printf "7*vx - 9*vy should be >=-10 but %s" (show v2)) $ -10 <= v2 + assertBool (printf "7*vx - 9*vy should be >=-10 but %s" (show v2)) $ v2 <= 4 + + +{- +Minimize + obj: - x1 - 2 x2 - 3 x3 - x4 +Subject To + c1: - x1 + x2 + x3 + 10 x4 <= 20 + c2: x1 - 3 x2 + x3 <= 30 + c3: x2 - 3.5 x4 = 0 +Bounds + 0 <= x1 <= 40 + 2 <= x4 <= 3 +End +-} +case_test3 :: IO () +case_test3 = do + solver <- newSolver + + _ <- newVar solver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + x4 <- newVar solver + + setObj solver (LA.fromTerms [(-1,x1), (-2,x2), (-3,x3), (-1,x4)]) + + assertAtom solver (LA.fromTerms [(-1,x1), (1,x2), (1,x3), (10,x4)] .<=. LA.constant 20) + assertAtom solver (LA.fromTerms [(1,x1), (-3,x2), (1,x3)] .<=. LA.constant 30) + assertAtom solver (LA.fromTerms [(1,x2), (-3.5,x4)] .==. LA.constant 0) + + assertAtom solver (LA.fromTerms [(1,x1)] .>=. LA.constant 0) + assertAtom solver (LA.fromTerms [(1,x1)] .<=. LA.constant 40) + assertAtom solver (LA.fromTerms [(1,x2)] .>=. LA.constant 0) + assertAtom solver (LA.fromTerms [(1,x3)] .>=. LA.constant 0) + assertAtom solver (LA.fromTerms [(1,x4)] .>=. LA.constant 2) + assertAtom solver (LA.fromTerms [(1,x4)] .<=. LA.constant 3) + + ret1 <- check solver + ret1 @?= True + + ret2 <- optimize solver defaultOptions + ret2 @?= Optimum + +{- +http://www.math.cuhk.edu.hk/~wei/lpch5.pdf +example 5.7 + +minimize 3 x1 + 4 x2 + 5 x3 +subject to +1 x1 + 2 x2 + 3 x3 >= 5 +2 x1 + 2 x2 + 1 x3 >= 6 + +optimal value is 11 +-} +case_test6 :: IO () +case_test6 = do + solver <- newSolver + + _ <- newVar solver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + + assertLower solver x1 0 + assertLower solver x2 0 + assertLower solver x3 0 + assertAtom solver (LA.fromTerms [(1,x1),(2,x2),(3,x3)] .>=. LA.constant 5) + assertAtom solver (LA.fromTerms [(2,x1),(2,x2),(1,x3)] .>=. LA.constant 6) + + setObj solver (LA.fromTerms [(3,x1),(4,x2),(5,x3)]) + setOptDir solver OptMin + b <- isOptimal solver + assertBool "should be optimal" $ b + + ret <- dualSimplex solver defaultOptions + ret @?= Optimum + + val <- getObjValue solver + val @?= 11 + +{- +http://www.math.cuhk.edu.hk/~wei/lpch5.pdf +example 5.7 + +maximize -3 x1 -4 x2 -5 x3 +subject to +-1 x1 -2 x2 -3 x3 <= -5 +-2 x1 -2 x2 -1 x3 <= -6 + +optimal value should be -11 +-} +case_test7 :: IO () +case_test7 = do + solver <- newSolver + + _ <- newVar solver + x1 <- newVar solver + x2 <- newVar solver + x3 <- newVar solver + + assertLower solver x1 0 + assertLower solver x2 0 + assertLower solver x3 0 + assertAtom solver (LA.fromTerms [(-1,x1),(-2,x2),(-3,x3)] .<=. LA.constant (-5)) + assertAtom solver (LA.fromTerms [(-2,x1),(-2,x2),(-1,x3)] .<=. LA.constant (-6)) + + setObj solver (LA.fromTerms [(-3,x1),(-4,x2),(-5,x3)]) + setOptDir solver OptMax + b <- isOptimal solver + assertBool "should be optimal" $ b + + ret <- dualSimplex solver defaultOptions + ret @?= Optimum + + val <- getObjValue solver + val @?= -11 + +case_AssertAtom :: IO () +case_AssertAtom = do + solver <- newSolver + x0 <- newVar solver + assertAtom solver (LA.constant 1 .<=. LA.var x0) + ret <- getLB solver x0 + ret @?= Just 1 + + solver <- newSolver + x0 <- newVar solver + assertAtom solver (LA.var x0 .>=. LA.constant 1) + ret <- getLB solver x0 + ret @?= Just 1 + + solver <- newSolver + x0 <- newVar solver + assertAtom solver (LA.constant 1 .>=. LA.var x0) + ret <- getUB solver x0 + ret @?= Just 1 + + solver <- newSolver + x0 <- newVar solver + assertAtom solver (LA.var x0 .<=. LA.constant 1) + ret <- getUB solver x0 + ret @?= Just 1 + +------------------------------------------------------------------------ + +case_example_3_2 = do + solver <- newSolver + [x1,x2,x3] <- replicateM 3 (newVar solver) + setOptDir solver OptMax + setObj solver $ LA.fromTerms [(3,x1), (2,x2), (3,x3)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(2,x1), (1,x2), (1,x3)] .<=. LA.constant 2 + , LA.fromTerms [(1,x1), (2,x2), (3,x3)] .<=. LA.constant 5 + , LA.fromTerms [(2,x1), (2,x2), (1,x3)] .<=. LA.constant 6 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + , LA.var x3 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= 27/5 + + forM_ [(x1,1/5),(x2,0),(x3,8/5)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +case_example_3_5 = do + solver <- newSolver + [x1,x2,x3,x4,x5] <- replicateM 5 (newVar solver) + setOptDir solver OptMin + setObj solver $ LA.fromTerms [(-2,x1), (4,x2), (7,x3), (1,x4), (5,x5)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(-1,x1), (1,x2), (2,x3), (1,x4), (2,x5)] .==. LA.constant 7 + , LA.fromTerms [(-1,x1), (2,x2), (3,x3), (1,x4), (1,x5)] .==. LA.constant 6 + , LA.fromTerms [(-1,x1), (1,x2), (1,x3), (2,x4), (1,x5)] .==. LA.constant 4 + , LA.var x2 .>=. LA.constant 0 + , LA.var x3 .>=. LA.constant 0 + , LA.var x4 .>=. LA.constant 0 + , LA.var x5 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= 19 + + forM_ [(x1,-1),(x2,0),(x3,1),(x4,0),(x5,2)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +case_example_4_1 = do + solver <- newSolver + [x1,x2] <- replicateM 2 (newVar solver) + setOptDir solver OptMin + setObj solver $ LA.fromTerms [(2,x1), (1,x2)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(-1,x1), (1,x2)] .>=. LA.constant 2 + , LA.fromTerms [( 1,x1), (1,x2)] .<=. LA.constant 1 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + ] + ret <- optimize solver defaultOptions + ret @?= Unsat + +case_example_4_2 = do + solver <- newSolver + [x1,x2] <- replicateM 2 (newVar solver) + setOptDir solver OptMax + setObj solver $ LA.fromTerms [(2,x1), (1,x2)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(-1,x1), (-1,x2)] .<=. LA.constant 10 + , LA.fromTerms [( 2,x1), (-1,x2)] .<=. LA.constant 40 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + ] + ret <- optimize solver defaultOptions + ret @?= Unbounded + +case_example_4_3 = do + solver <- newSolver + [x1,x2] <- replicateM 2 (newVar solver) + setOptDir solver OptMax + setObj solver $ LA.fromTerms [(6,x1), (-2,x2)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(2,x1), (-1,x2)] .<=. LA.constant 2 + , LA.var x1 .<=. LA.constant 4 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= 12 + + forM_ [(x1,4),(x2,6)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +case_example_4_5 = do + solver <- newSolver + [x1,x2] <- replicateM 2 (newVar solver) + setOptDir solver OptMax + setObj solver $ LA.fromTerms [(2,x1), (1,x2)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(4,x1), ( 3,x2)] .<=. LA.constant 12 + , LA.fromTerms [(4,x1), ( 1,x2)] .<=. LA.constant 8 + , LA.fromTerms [(4,x1), (-1,x2)] .<=. LA.constant 8 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= 5 + + forM_ [(x1,3/2),(x2,2)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +case_example_4_6 = do + solver <- newSolver + [x1,x2,x3,x4] <- replicateM 4 (newVar solver) + setOptDir solver OptMax + setObj solver $ LA.fromTerms [(20,x1), (1/2,x2), (-6,x3), (3/4,x4)] + mapM_ (assertAtom solver) $ + [ LA.var x1 .<=. LA.constant 2 + , LA.fromTerms [( 8,x1), ( -1,x2), (9,x3), (1/4, x4)] .<=. LA.constant 16 + , LA.fromTerms [(12,x1), (-1/2,x2), (3,x3), (1/2, x4)] .<=. LA.constant 24 + , LA.var x2 .<=. LA.constant 1 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + , LA.var x3 .>=. LA.constant 0 + , LA.var x4 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= 165/4 + + forM_ [(x1,2),(x2,1),(x3,0),(x4,1)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +case_example_4_7 = do + solver <- newSolver + [x1,x2,x3,x4] <- replicateM 4 (newVar solver) + setOptDir solver OptMax + setObj solver $ LA.fromTerms [(1,x1), (1.5,x2), (5,x3), (2,x4)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(3,x1), (2,x2), ( 1,x3), (4,x4)] .<=. LA.constant 6 + , LA.fromTerms [(2,x1), (1,x2), ( 5,x3), (1,x4)] .<=. LA.constant 4 + , LA.fromTerms [(2,x1), (6,x2), (-4,x3), (8,x4)] .==. LA.constant 0 + , LA.fromTerms [(1,x1), (3,x2), (-2,x3), (4,x4)] .==. LA.constant 0 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + , LA.var x3 .>=. LA.constant 0 + , LA.var x4 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= 48/11 + + forM_ [(x1,0),(x2,0),(x3,8/11),(x4,4/11)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +-- 退化して巡回の起こるKuhnの7変数3制約の例 +case_kuhn_7_3 = do + solver <- newSolver + [x1,x2,x3,x4,x5,x6,x7] <- replicateM 7 (newVar solver) + setOptDir solver OptMin + setObj solver $ LA.fromTerms [(-2,x4),(-3,x5),(1,x6),(12,x7)] + mapM_ (assertAtom solver) $ + [ LA.fromTerms [(1,x1), ( -2,x4), (-9,x5), ( 1,x6), ( 9,x7)] .==. LA.constant 0 + , LA.fromTerms [(1,x2), (1/3,x4), ( 1,x5), (-1/3,x6), ( -2,x7)] .==. LA.constant 0 + , LA.fromTerms [(1,x3), ( 2,x4), ( 3,x5), ( -1,x6), (-12,x7)] .==. LA.constant 2 + , LA.var x1 .>=. LA.constant 0 + , LA.var x2 .>=. LA.constant 0 + , LA.var x3 .>=. LA.constant 0 + , LA.var x4 .>=. LA.constant 0 + , LA.var x5 .>=. LA.constant 0 + , LA.var x6 .>=. LA.constant 0 + , LA.var x7 .>=. LA.constant 0 + ] + + ret <- optimize solver defaultOptions + ret @?= Optimum + val <- getObjValue solver + val @?= -2 + + forM_ [(x1,2),(x2,0),(x3,0),(x4,2),(x5,0),(x6,2),(x7,0)] $ \(var,expected) -> do + val <- getValue solver var + val @?= expected + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/test/TestUtil.hs b/test/TestUtil.hs new file mode 100644 --- /dev/null +++ b/test/TestUtil.hs @@ -0,0 +1,29 @@ +{-# LANGUAGE TemplateHaskell #-} +module Main (main) where + +import Test.HUnit hiding (Test) +import Test.Framework (Test, defaultMain, testGroup) +import Test.Framework.TH +import Test.Framework.Providers.HUnit +import Util + +-- should be SAT +case_showRationalAsDecimal :: IO () +case_showRationalAsDecimal = do + showRationalAsFiniteDecimal 0 @?= Just "0.0" + showRationalAsFiniteDecimal 1 @?= Just "1.0" + showRationalAsFiniteDecimal (-1) @?= Just "-1.0" + showRationalAsFiniteDecimal 0.1 @?= Just "0.1" + showRationalAsFiniteDecimal (-0.1) @?= Just "-0.1" + showRationalAsFiniteDecimal 1.1 @?= Just "1.1" + showRationalAsFiniteDecimal (-1.1) @?= Just "-1.1" + showRationalAsFiniteDecimal (5/4) @?= Just "1.25" + showRationalAsFiniteDecimal (-5/4) @?= Just "-1.25" + showRationalAsFiniteDecimal (4/3) @?= Nothing + showRationalAsFiniteDecimal (-4/3) @?= Nothing + +------------------------------------------------------------------------ +-- Test harness + +main :: IO () +main = $(defaultMainGenerator) diff --git a/toyfmf/toyfmf.hs b/toyfmf/toyfmf.hs new file mode 100644 --- /dev/null +++ b/toyfmf/toyfmf.hs @@ -0,0 +1,120 @@ +----------------------------------------------------------------------------- +-- | +-- Module : toyfmf +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : experimental +-- Portability : portable +-- +-- A toy-level model finder +-- +----------------------------------------------------------------------------- +module Main where + +import Control.Monad +import Data.IORef +import qualified Data.Map as Map +import Data.Ratio +import System.Environment +import System.IO +import qualified Codec.TPTP as TPTP +import qualified Algorithm.FOLModelFinder as MF + +main :: IO () +main = do + args <- getArgs + case args of + [fpath, size] -> solve fpath (read size) + _ -> hPutStrLn stderr "Usage: toyfmf " + +solve :: FilePath -> Int -> IO () +solve _ size | size <= 0 = error " should be >=1" +solve fpath size = do + inputs <- TPTP.parseFile fpath + let fs = translateProblem inputs + + ref <- newIORef 0 + let skolem name _ = do + n <- readIORef ref + let fsym = name ++ "#" ++ show n + writeIORef ref (n+1) + return fsym + cs <- liftM concat $ mapM (MF.toSkolemNF skolem) fs + + ret <- MF.findModel size cs + case ret of + Nothing -> do + putStrLn "s NO MODEL FOUND" + Just m -> do + putStrLn "s SATISFIABLE" + let isSkolem k = '#' `elem` k + let m' = m{ MF.mFunctions = Map.filterWithKey (\k _ -> not (isSkolem k)) (MF.mFunctions m) } + forM_ (MF.showModel m') $ \s -> + putStrLn $ "v " ++ s + + return () + +-- --------------------------------------------------------------------------- + +translateProblem :: [TPTP.TPTP_Input] -> [MF.Formula] +translateProblem inputs = do + i <- inputs + case i of + TPTP.Comment _ -> [] + TPTP.Include _ _ -> error "\"include\" is not supported yet " + TPTP.AFormula{ TPTP.name = _, TPTP.role = role, TPTP.formula = formula, TPTP.annotations = _ } -> + return $ translateFormula formula + +translateFormula :: TPTP.Formula -> MF.Formula +translateFormula = TPTP.foldF neg quant binop eq rel + where + neg phi = MF.Not $ translateFormula phi + quant q vs phi = foldr q' (translateFormula phi) [v | TPTP.V v <- vs] + where + q' = + case q of + TPTP.All -> MF.Forall + TPTP.Exists -> MF.Exists + binop phi op psi = op' phi' psi' + where + phi' = translateFormula phi + psi' = translateFormula psi + op' = + case op of + (TPTP.:<=>:) -> MF.Equiv + (TPTP.:=>:) -> MF.Imply + (TPTP.:<=:) -> flip MF.Imply + (TPTP.:&:) -> MF.And + (TPTP.:|:) -> MF.Or + (TPTP.:~&:) -> \a b -> MF.Not (a `MF.And` b) + (TPTP.:~|:) -> \a b -> MF.Not (a `MF.Or` b) + (TPTP.:<~>:) -> \a b -> MF.Not (a `MF.Equiv` b) + eq lhs op rhs = + case op of + (TPTP.:=:) -> MF.Atom $ MF.PApp "=" [lhs', rhs'] + (TPTP.:!=:) -> MF.Not $ MF.Atom $ MF.PApp "=" [lhs', rhs'] + where + lhs' = translateTerm lhs + rhs' = translateTerm rhs + rel (TPTP.AtomicWord p) ts = MF.Atom $ MF.PApp p ts' + where + ts' = map translateTerm ts + +translateTerm :: TPTP.Term -> MF.Term +translateTerm = TPTP.foldT str num var app + where + str s = MF.TmApp (show s) [] + num r = MF.TmApp (showRational r) [] + var (TPTP.V v) = MF.TmVar v + app (TPTP.AtomicWord f) ts = MF.TmApp f ts' + where + ts' = map translateTerm ts + + showRational r = + if denominator r == 1 + then show (numerator r) + else show (numerator r) ++ "/" ++ show (denominator r) + +-- --------------------------------------------------------------------------- diff --git a/toysat/toysat.hs b/toysat/toysat.hs new file mode 100644 --- /dev/null +++ b/toysat/toysat.hs @@ -0,0 +1,798 @@ +{-# LANGUAGE ScopedTypeVariables, DoAndIfThenElse, CPP #-} +{-# OPTIONS_GHC -Wall -fno-warn-unused-do-bind #-} +----------------------------------------------------------------------------- +-- | +-- Module : toysat +-- Copyright : (c) Masahiro Sakai 2012 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : experimental +-- Portability : non-portable (ScopedTypeVariables) +-- +-- A toy-level SAT solver based on CDCL. +-- +----------------------------------------------------------------------------- + +module Main where + +import Control.Concurrent.Timeout +import Control.Monad +import Control.Exception +import Data.Array.IArray +import qualified Data.ByteString.Lazy as BS +import qualified Data.Set as Set +import qualified Data.Map as Map +import Data.Char +import Data.IORef +import Data.List +import Data.Maybe +import Data.Ord +import Data.Ratio +import Data.Version +import Data.Time +import System.IO +import System.Environment +import System.Exit +import System.Locale +import System.Console.GetOpt +import System.CPUTime +import System.FilePath +import qualified System.Info as SysInfo +import qualified Language.CNF.Parse.ParseDIMACS as DIMACS +import Text.Printf +#ifdef __GLASGOW_HASKELL__ +import GHC.Environment (getFullArgs) +#endif +#ifdef FORCE_CHAR8 +import GHC.IO.Encoding +#endif +#if defined(__GLASGOW_HASKELL__) && MIN_VERSION_base(4,5,0) +import qualified GHC.Stats as Stats +#endif + +import Data.ArithRel +import Data.Linear +import qualified SAT +import qualified SAT.PBO as PBO +import qualified SAT.Integer +import qualified SAT.TseitinEncoder as Tseitin +import qualified SAT.MUS as MUS +import qualified SAT.CAMUS as CAMUS +import SAT.Types (pbEval) +import SAT.Printer +import qualified Text.PBFile as PBFile +import qualified Text.LPFile as LPFile +import qualified Text.MPSFile as MPSFile +import qualified Text.MaxSAT as MaxSAT +import qualified Text.GCNF as GCNF +import qualified Text.GurobiSol as GurobiSol +import Version +import Util (showRational, revMapM, revForM) + +-- ------------------------------------------------------------------------ + +data Mode = ModeHelp | ModeVersion | ModeSAT | ModeMUS | ModePB | ModeWBO | ModeMaxSAT | ModeLP + +data Options + = Options + { optMode :: Maybe Mode + , optRestartStrategy :: SAT.RestartStrategy + , optRestartFirst :: Int + , optRestartInc :: Double + , optLearningStrategy :: SAT.LearningStrategy + , optLearntSizeFirst :: Int + , optLearntSizeInc :: Double + , optCCMin :: Int + , optRandomFreq :: Double + , optRandomSeed :: Int + , optLinearizerPB :: Bool + , optSearchStrategy :: PBO.SearchStrategy + , optObjFunVarsHeuristics :: Bool + , optAllMUSes :: Bool + , optPrintRational :: Bool + , optCheckModel :: Bool + , optTimeout :: Integer + , optWriteFile :: Maybe FilePath + } + +defaultOptions :: Options +defaultOptions + = Options + { optMode = Nothing + , optRestartStrategy = SAT.defaultRestartStrategy + , optRestartFirst = SAT.defaultRestartFirst + , optRestartInc = SAT.defaultRestartInc + , optLearningStrategy = SAT.defaultLearningStrategy + , optLearntSizeFirst = SAT.defaultLearntSizeFirst + , optLearntSizeInc = SAT.defaultLearntSizeInc + , optCCMin = SAT.defaultCCMin + , optRandomFreq = SAT.defaultRandomFreq + , optRandomSeed = 0 + , optLinearizerPB = False + , optSearchStrategy = PBO.optSearchStrategy PBO.defaultOptions + , optObjFunVarsHeuristics = PBO.optObjFunVarsHeuristics PBO.defaultOptions + , optAllMUSes = False + , optPrintRational = False + , optCheckModel = False + , optTimeout = 0 + , optWriteFile = Nothing + } + +options :: [OptDescr (Options -> Options)] +options = + [ Option ['h'] ["help"] (NoArg (\opt -> opt{ optMode = Just ModeHelp })) "show help" + , Option [] ["version"] (NoArg (\opt -> opt{ optMode = Just ModeVersion})) "show version" + + , Option [] ["sat"] (NoArg (\opt -> opt{ optMode = Just ModeSAT })) "solve pseudo boolean problems in .cnf file (default)" + , Option [] ["mus"] (NoArg (\opt -> opt{ optMode = Just ModeMUS })) "solve minimally unsatisfiable subset problems in .gcnf or .cnf file" + , Option [] ["pb"] (NoArg (\opt -> opt{ optMode = Just ModePB })) "solve pseudo boolean problems in .pb file" + , Option [] ["wbo"] (NoArg (\opt -> opt{ optMode = Just ModeWBO })) "solve weighted boolean optimization problem in .opb file" + , Option [] ["maxsat"] (NoArg (\opt -> opt{ optMode = Just ModeMaxSAT })) "solve MaxSAT problem in .cnf or .wcnf file" + , Option [] ["lp"] (NoArg (\opt -> opt{ optMode = Just ModeLP })) "solve binary integer programming problem in .lp or .mps file" + + , Option [] ["restart"] + (ReqArg (\val opt -> opt{ optRestartStrategy = parseRestartStrategy val }) "") + "Restart startegy: MiniSAT (default), Armin, Luby." + , Option [] ["restart-first"] + (ReqArg (\val opt -> opt{ optRestartFirst = read val }) "") + (printf "The initial restart limit. (default %d)" SAT.defaultRestartFirst) + , Option [] ["restart-inc"] + (ReqArg (\val opt -> opt{ optRestartInc = read val }) "") + (printf "The factor with which the restart limit is multiplied in each restart. (default %f)" SAT.defaultRestartInc) + , Option [] ["learning"] + (ReqArg (\val opt -> opt{ optLearningStrategy = parseLS val }) "") + "Leaning scheme: clause (default)" + , Option [] ["learnt-size-first"] + (ReqArg (\val opt -> opt{ optLearntSizeFirst = read val }) "") + "The initial limit for learnt clauses." + , Option [] ["learnt-size-inc"] + (ReqArg (\val opt -> opt{ optLearntSizeInc = read val }) "") + (printf "The limit for learnt clauses is multiplied with this factor periodically. (default %f)" SAT.defaultLearntSizeInc) + , Option [] ["ccmin"] + (ReqArg (\val opt -> opt{ optCCMin = read val }) "") + (printf "Conflict clause minimization (0=none, 1=local, 2=recursive; default %d)" SAT.defaultCCMin) + + , Option [] ["random-freq"] + (ReqArg (\val opt -> opt{ optRandomFreq = read val }) "<0..1>") + (printf "The frequency with which the decision heuristic tries to choose a random variable (default %f)" SAT.defaultRandomFreq) + , Option [] ["random-seed"] + (ReqArg (\val opt -> opt{ optRandomSeed = read val }) "") + "Used by the random variable selection" + + , Option [] ["linearizer-pb"] + (NoArg (\opt -> opt{ optLinearizerPB = True })) + "Use PB constraint in linearization." + + , Option [] ["search"] + (ReqArg (\val opt -> opt{ optSearchStrategy = parseSearch val }) "") + "Search algorithm used in optimization; linear (default), binary" + , Option [] ["objfun-heuristics"] + (NoArg (\opt -> opt{ optObjFunVarsHeuristics = True })) + "Enable heuristics for polarity/activity of variables in objective function (default)" + , Option [] ["no-objfun-heuristics"] + (NoArg (\opt -> opt{ optObjFunVarsHeuristics = False })) + "Disable heuristics for polarity/activity of variables in objective function" + + , Option [] ["all-mus"] + (NoArg (\opt -> opt{ optAllMUSes = True })) + "enumerate all MUSes" + + , Option [] ["print-rational"] + (NoArg (\opt -> opt{ optPrintRational = True })) + "print rational numbers instead of decimals" + , Option ['w'] [] + (ReqArg (\val opt -> opt{ optWriteFile = Just val }) "") + "write model to filename in Gurobi .sol format" + + , Option [] ["check-model"] + (NoArg (\opt -> opt{ optCheckModel = True })) + "check model for debug" + + , Option [] ["timeout"] + (ReqArg (\val opt -> opt{ optTimeout = read val }) "") + "Kill toysat after given number of seconds (default 0 (no limit))" + ] + where + parseRestartStrategy s = + case map toLower s of + "minisat" -> SAT.MiniSATRestarts + "armin" -> SAT.ArminRestarts + "luby" -> SAT.LubyRestarts + _ -> undefined + + parseSearch s = + case map toLower s of + "linear" -> PBO.LinearSearch + "binary" -> PBO.BinarySearch + _ -> error (printf "unknown search strategy %s" s) + + parseLS "clause" = SAT.LearningClause + parseLS "hybrid" = SAT.LearningHybrid + parseLS s = error (printf "unknown learning strategy %s" s) + +main :: IO () +main = do +#ifdef FORCE_CHAR8 + setLocaleEncoding char8 + setForeignEncoding char8 + setFileSystemEncoding char8 +#endif + + startCPU <- getCPUTime + startWC <- getCurrentTime + args <- getArgs + case getOpt Permute options args of + (_,_,errs@(_:_)) -> do + mapM_ putStrLn errs + exitFailure + + (o,args2,[]) -> do + let opt = foldl (flip id) defaultOptions o + mode = + case optMode opt of + Just m -> m + Nothing -> + case args2 of + [] -> ModeHelp + fname : _ -> + case map toLower (takeExtension fname) of + ".cnf" -> ModeSAT + ".gcnf" -> ModeMUS + ".opb" -> ModePB + ".wbo" -> ModeWBO + ".wcnf" -> ModeMaxSAT + ".lp" -> ModeLP + ".mps" -> ModeLP + _ -> ModeSAT + + case mode of + ModeHelp -> showHelp stdout + ModeVersion -> hPutStrLn stdout (showVersion version) + _ -> do + printSysInfo +#ifdef __GLASGOW_HASKELL__ + fullArgs <- getFullArgs +#else + let fullArgs = args +#endif + putCommentLine $ printf "command line = %s" (show fullArgs) + + let timelim = optTimeout opt * 10^(6::Int) + + ret <- timeout (if timelim > 0 then timelim else (-1)) $ do + solver <- newSolver opt + case mode of + ModeHelp -> showHelp stdout + ModeVersion -> hPutStrLn stdout (showVersion version) + ModeSAT -> mainSAT opt solver args2 + ModeMUS -> mainMUS opt solver args2 + ModePB -> mainPB opt solver args2 + ModeWBO -> mainWBO opt solver args2 + ModeMaxSAT -> mainMaxSAT opt solver args2 + ModeLP -> mainLP opt solver args2 + + when (isNothing ret) $ do + putCommentLine "TIMEOUT" + endCPU <- getCPUTime + endWC <- getCurrentTime + putCommentLine $ printf "total CPU time = %.3fs" (fromIntegral (endCPU - startCPU) / 10^(12::Int) :: Double) + putCommentLine $ printf "total wall clock time = %.3fs" (realToFrac (endWC `diffUTCTime` startWC) :: Double) + +#if defined(__GLASGOW_HASKELL__) && MIN_VERSION_base(4,5,0) + stat <- Stats.getGCStats + putCommentLine "GCStats:" + putCommentLine $ printf " bytesAllocated = %d" $ Stats.bytesAllocated stat + putCommentLine $ printf " numGcs = %d" $ Stats.numGcs stat + putCommentLine $ printf " maxBytesUsed = %d" $ Stats.maxBytesUsed stat + putCommentLine $ printf " numByteUsageSamples = %d" $ Stats.numByteUsageSamples stat + putCommentLine $ printf " cumulativeBytesUsed = %d" $ Stats.cumulativeBytesUsed stat + putCommentLine $ printf " bytesCopied = %d" $ Stats.bytesCopied stat + putCommentLine $ printf " currentBytesUsed = %d" $ Stats.currentBytesUsed stat + putCommentLine $ printf " currentBytesSlop = %d" $ Stats.currentBytesSlop stat + putCommentLine $ printf " maxBytesSlop = %d" $ Stats.maxBytesSlop stat + putCommentLine $ printf " peakMegabytesAllocated = %d" $ Stats.peakMegabytesAllocated stat + putCommentLine $ printf " mutatorCpuSeconds = %5.2f" $ Stats.mutatorCpuSeconds stat + putCommentLine $ printf " mutatorWallSeconds = %5.2f" $ Stats.mutatorWallSeconds stat + putCommentLine $ printf " gcCpuSeconds = %5.2f" $ Stats.gcCpuSeconds stat + putCommentLine $ printf " gcWallSeconds = %5.2f" $ Stats.gcWallSeconds stat + putCommentLine $ printf " cpuSeconds = %5.2f" $ Stats.cpuSeconds stat + putCommentLine $ printf " wallSeconds = %5.2f" $ Stats.wallSeconds stat + putCommentLine $ printf " parAvgBytesCopied = %d" $ Stats.parAvgBytesCopied stat + putCommentLine $ printf " parMaxBytesCopied = %d" $ Stats.parMaxBytesCopied stat +#endif + +showHelp :: Handle -> IO () +showHelp h = hPutStrLn h (usageInfo header options) + +header :: String +header = unlines + [ "Usage:" + , " toysat [OPTION]... [file.cnf||-]" + , " toysat [OPTION]... --mus [file.gcnf|-]" + , " toysat [OPTION]... --pb [file.opb|-]" + , " toysat [OPTION]... --wbo [file.wbo|-]" + , " toysat [OPTION]... --maxsat [file.cnf|file.wcnf|-]" + , " toysat [OPTION]... --lp [file.lp|file.mps|-]" + , "" + , "Options:" + ] + +printSysInfo :: IO () +printSysInfo = do + tm <- getZonedTime + putCommentLine $ printf "%s" (formatTime defaultTimeLocale "%FT%X%z" tm) + putCommentLine $ printf "arch = %s" SysInfo.arch + putCommentLine $ printf "os = %s" SysInfo.os + putCommentLine $ printf "compiler = %s %s" SysInfo.compilerName (showVersion SysInfo.compilerVersion) + putCommentLine "packages:" + forM_ packageVersions $ \(package, ver) -> do + putCommentLine $ printf " %s-%s" package ver + +putCommentLine :: String -> IO () +putCommentLine s = do + putStr "c " + putStrLn s + hFlush stdout + +newSolver :: Options -> IO SAT.Solver +newSolver opts = do + solver <- SAT.newSolver + SAT.setRestartStrategy solver (optRestartStrategy opts) + SAT.setRestartFirst solver (optRestartFirst opts) + SAT.setRestartInc solver (optRestartInc opts) + SAT.setLearntSizeFirst solver (optLearntSizeFirst opts) + SAT.setLearntSizeInc solver (optLearntSizeInc opts) + SAT.setCCMin solver (optCCMin opts) + SAT.setRandomFreq solver (optRandomFreq opts) + when (optRandomSeed opts /= 0) $ + SAT.setRandomSeed solver (optRandomSeed opts) + SAT.setLearningStrategy solver (optLearningStrategy opts) + SAT.setLogger solver putCommentLine + SAT.setCheckModel solver (optCheckModel opts) + return solver + +-- ------------------------------------------------------------------------ + +mainSAT :: Options -> SAT.Solver -> [String] -> IO () +mainSAT opt solver args = do + ret <- case args of + ["-"] -> fmap (DIMACS.parseByteString "-") $ BS.hGetContents stdin + [fname] -> DIMACS.parseFile fname + _ -> showHelp stderr >> exitFailure + case ret of + Left err -> hPrint stderr err >> exitFailure + Right cnf -> solveSAT opt solver cnf + +solveSAT :: Options -> SAT.Solver -> DIMACS.CNF -> IO () +solveSAT opt solver cnf = do + putCommentLine $ printf "#vars %d" (DIMACS.numVars cnf) + putCommentLine $ printf "#constraints %d" (length (DIMACS.clauses cnf)) + SAT.newVars_ solver (DIMACS.numVars cnf) + forM_ (DIMACS.clauses cnf) $ \clause -> + SAT.addClause solver (elems clause) + result <- SAT.solve solver + putStrLn $ "s " ++ (if result then "SATISFIABLE" else "UNSATISFIABLE") + hFlush stdout + when result $ do + m <- SAT.model solver + satPrintModel stdout m (DIMACS.numVars cnf) + writeSOLFile opt m Nothing (DIMACS.numVars cnf) + +-- ------------------------------------------------------------------------ + +mainMUS :: Options -> SAT.Solver -> [String] -> IO () +mainMUS opt solver args = do + gcnf <- case args of + ["-"] -> do + s <- hGetContents stdin + case GCNF.parseString s of + Left err -> hPutStrLn stderr err >> exitFailure + Right gcnf -> return gcnf + [fname] -> do + ret <- GCNF.parseFile fname + case ret of + Left err -> hPutStrLn stderr err >> exitFailure + Right gcnf -> return gcnf + _ -> showHelp stderr >> exitFailure + solveMUS opt solver gcnf + +solveMUS :: Options -> SAT.Solver -> GCNF.GCNF -> IO () +solveMUS opt solver gcnf = do + putCommentLine $ printf "#vars %d" (GCNF.numVars gcnf) + putCommentLine $ printf "#constraints %d" (length (GCNF.clauses gcnf)) + putCommentLine $ printf "#groups %d" (GCNF.lastGroupIndex gcnf) + + SAT.newVars_ solver (GCNF.numVars gcnf) + + tbl <- forM [1 .. GCNF.lastGroupIndex gcnf] $ \i -> do + sel <- SAT.newVar solver + return (i, sel) + let idx2sel :: Array Int SAT.Var + idx2sel = array (1, GCNF.lastGroupIndex gcnf) tbl + selrng = if null tbl then (0,-1) else (snd $ head tbl, snd $ last tbl) + sel2idx :: Array SAT.Lit Int + sel2idx = array selrng [(sel, idx) | (idx, sel) <- tbl] + + forM_ (GCNF.clauses gcnf) $ \(idx, clause) -> + if idx==0 + then SAT.addClause solver clause + else SAT.addClause solver (- (idx2sel ! idx) : clause) + + result <- SAT.solveWith solver (map (idx2sel !) [1..GCNF.lastGroupIndex gcnf]) + putStrLn $ "s " ++ (if result then "SATISFIABLE" else "UNSATISFIABLE") + hFlush stdout + if result + then do + m <- SAT.model solver + satPrintModel stdout m (GCNF.numVars gcnf) + writeSOLFile opt m Nothing (GCNF.numVars gcnf) + else do + if not (optAllMUSes opt) + then do + let opt2 = MUS.defaultOptions + { MUS.optLogger = putCommentLine + , MUS.optLitPrinter = \lit -> + show (sel2idx ! lit) + } + mus <- MUS.findMUSAssumptions solver opt2 + musPrintSol stdout (map (sel2idx !) mus) + else do + let opt2 = CAMUS.defaultOptions + { CAMUS.optLogger = putCommentLine + , CAMUS.optCallback = \mcs -> do + let mcs2 = sort $ map (sel2idx !) mcs + putCommentLine $ "MCS found: " ++ show mcs2 + } + muses <- CAMUS.allMUSAssumptions solver (map snd tbl) opt2 + forM_ (zip [(1::Int)..] muses) $ \(i, mus) -> do + putCommentLine $ "MUS #" ++ show i + musPrintSol stdout (sort (map (sel2idx !) mus)) + +-- ------------------------------------------------------------------------ + +mainPB :: Options -> SAT.Solver -> [String] -> IO () +mainPB opt solver args = do + ret <- case args of + ["-"] -> fmap (PBFile.parseOPBString "-") $ hGetContents stdin + [fname] -> PBFile.parseOPBFile fname + _ -> showHelp stderr >> exitFailure + case ret of + Left err -> hPrint stderr err >> exitFailure + Right formula -> solvePB opt solver formula + +solvePB :: Options -> SAT.Solver -> PBFile.Formula -> IO () +solvePB opt solver formula@(obj, cs) = do + let n = PBFile.pbNumVars formula + + putCommentLine $ printf "#vars %d" n + putCommentLine $ printf "#constraints %d" (length cs) + + SAT.newVars_ solver n + enc <- Tseitin.newEncoder solver + Tseitin.setUsePB enc (optLinearizerPB opt) + + forM_ cs $ \(lhs, op, rhs) -> do + lhs' <- pbConvSum enc lhs + case op of + PBFile.Ge -> SAT.addPBAtLeast solver lhs' rhs + PBFile.Eq -> SAT.addPBExactly solver lhs' rhs + + case obj of + Nothing -> do + result <- SAT.solve solver + putStrLn $ "s " ++ (if result then "SATISFIABLE" else "UNSATISFIABLE") + hFlush stdout + when result $ do + m <- SAT.model solver + pbPrintModel stdout m n + writeSOLFile opt m Nothing n + + Just obj' -> do + obj'' <- pbConvSum enc obj' + + modelRef <- newIORef Nothing + + result <- try $ minimize opt solver obj'' $ \m val -> do + writeIORef modelRef (Just m) + putStrLn $ "o " ++ show val + hFlush stdout + + case result of + Right Nothing -> do + putStrLn $ "s " ++ "UNSATISFIABLE" + hFlush stdout + Right (Just m) -> do + putStrLn $ "s " ++ "OPTIMUM FOUND" + hFlush stdout + pbPrintModel stdout m n + let objval = pbEval m obj'' + writeSOLFile opt m (Just objval) n + Left (e :: SomeException) -> do + r <- readIORef modelRef + case r of + Nothing -> do + putStrLn $ "s " ++ "UNKNOWN" + hFlush stdout + Just m -> do + putStrLn $ "s " ++ "SATISFIABLE" + pbPrintModel stdout m n + let objval = pbEval m obj'' + writeSOLFile opt m (Just objval) n + throwIO e + +pbConvSum :: Tseitin.Encoder -> PBFile.Sum -> IO [(Integer, SAT.Lit)] +pbConvSum enc = revMapM f + where + f (w,ls) = do + l <- Tseitin.encodeConj enc ls + return (w,l) + +minimize :: Options -> SAT.Solver -> [(Integer, SAT.Lit)] -> (SAT.Model -> Integer -> IO ()) -> IO (Maybe SAT.Model) +minimize opt solver obj update = do + let opt2 = + PBO.defaultOptions + { PBO.optObjFunVarsHeuristics = optObjFunVarsHeuristics opt + , PBO.optSearchStrategy = optSearchStrategy opt + , PBO.optLogger = putCommentLine + , PBO.optUpdater = update + } + PBO.minimize solver obj opt2 + +-- ------------------------------------------------------------------------ + +mainWBO :: Options -> SAT.Solver -> [String] -> IO () +mainWBO opt solver args = do + ret <- case args of + ["-"] -> fmap (PBFile.parseWBOString "-") $ hGetContents stdin + [fname] -> PBFile.parseWBOFile fname + _ -> showHelp stderr >> exitFailure + case ret of + Left err -> hPrint stderr err >> exitFailure + Right formula -> solveWBO opt solver False formula + +solveWBO :: Options -> SAT.Solver -> Bool -> PBFile.SoftFormula -> IO () +solveWBO opt solver isMaxSat formula@(tco, cs) = do + let nvar = PBFile.wboNumVars formula + putCommentLine $ printf "#vars %d" nvar + putCommentLine $ printf "#constraints %d" (length cs) + + SAT.newVars_ solver nvar + enc <- Tseitin.newEncoder solver + Tseitin.setUsePB enc (optLinearizerPB opt) + + obj <- liftM concat $ revForM cs $ \(cost, (lhs, op, rhs)) -> do + lhs' <- pbConvSum enc lhs + case cost of + Nothing -> do + case op of + PBFile.Ge -> SAT.addPBAtLeast solver lhs' rhs + PBFile.Eq -> SAT.addPBExactly solver lhs' rhs + return [] + Just cval -> do + sel <- SAT.newVar solver + case op of + PBFile.Ge -> SAT.addPBAtLeastSoft solver sel lhs' rhs + PBFile.Eq -> SAT.addPBExactlySoft solver sel lhs' rhs + return [(cval, SAT.litNot sel)] + + case tco of + Nothing -> return () + Just c -> SAT.addPBAtMost solver obj (c-1) + + modelRef <- newIORef Nothing + result <- try $ minimize opt solver obj $ \m val -> do + writeIORef modelRef (Just m) + putStrLn $ "o " ++ show val + hFlush stdout + + case result of + Right Nothing -> do + putStrLn $ "s " ++ "UNSATISFIABLE" + hFlush stdout + Right (Just m) -> do + putStrLn $ "s " ++ "OPTIMUM FOUND" + hFlush stdout + if isMaxSat + then maxsatPrintModel stdout m nvar + else pbPrintModel stdout m nvar + let objval = pbEval m obj + writeSOLFile opt m (Just objval) nvar + Left (e :: SomeException) -> do + r <- readIORef modelRef + case r of + Just m | not isMaxSat -> do + putStrLn $ "s " ++ "SATISFIABLE" + pbPrintModel stdout m nvar + let objval = pbEval m obj + writeSOLFile opt m (Just objval) nvar + _ -> do + putStrLn $ "s " ++ "UNKNOWN" + hFlush stdout + throwIO e + +-- ------------------------------------------------------------------------ + +mainMaxSAT :: Options -> SAT.Solver -> [String] -> IO () +mainMaxSAT opt solver args = do + s <- case args of + ["-"] -> getContents + [fname] -> readFile fname + _ -> showHelp stderr >> exitFailure + let ret = MaxSAT.parseWCNFString s + case ret of + Left err -> hPutStrLn stderr err >> exitFailure + Right wcnf -> solveMaxSAT opt solver wcnf + +solveMaxSAT :: Options -> SAT.Solver -> MaxSAT.WCNF -> IO () +solveMaxSAT opt solver + MaxSAT.WCNF + { MaxSAT.topCost = top + , MaxSAT.clauses = cs + } = do + solveWBO opt solver True + ( Nothing + , [ (if w >= top then Nothing else Just w + , ([(1,[lit]) | lit<-lits], PBFile.Ge, 1)) + | (w,lits) <- cs + ] + ) + +-- ------------------------------------------------------------------------ + +mainLP :: Options -> SAT.Solver -> [String] -> IO () +mainLP opt solver args = do + (fname,s) <- + case args of + ["-"] -> do + s <- hGetContents stdin + return ("-", s) + [fname] -> do + s <- readFile fname + return (fname, s) + _ -> showHelp stderr >> exitFailure + lp <- + case LPFile.parseString fname s of + Right lp -> return lp + Left err -> + case MPSFile.parseString fname s of + Right lp -> return lp + Left err2 -> do + hPrint stderr err + hPrint stderr err2 + exitFailure + solveLP opt solver lp + +solveLP :: Options -> SAT.Solver -> LPFile.LP -> IO () +solveLP opt solver lp = do + if not (Set.null nivs) + then do + putCommentLine $ "cannot handle non-integer variables: " ++ intercalate ", " (Set.toList nivs) + putStrLn "s UNKNOWN" + exitFailure + else do + enc <- Tseitin.newEncoder solver + Tseitin.setUsePB enc (optLinearizerPB opt) + + putCommentLine $ "Loading variables and bounds" + vmap <- liftM Map.fromList $ revForM (Set.toList ivs) $ \v -> do + let (lb,ub) = LPFile.getBounds lp v + case (lb,ub) of + (LPFile.Finite lb', LPFile.Finite ub') -> do + v2 <- SAT.Integer.newVar solver (ceiling lb') (floor ub') + return (v,v2) + _ -> do + putCommentLine $ "cannot handle unbounded variable: " ++ v + putStrLn "s UNKNOWN" + exitFailure + + putCommentLine "Loading constraints" + forM_ (LPFile.constraints lp) $ \c -> do + let indicator = LPFile.constrIndicator c + (lhs, op, rhs) = LPFile.constrBody c + let d = foldl' lcm 1 (map denominator (rhs:[r | LPFile.Term r _ <- lhs])) + lhs' = lsum [asInteger (r * fromIntegral d) .*. product [vmap Map.! v | v <- vs] | LPFile.Term r vs <- lhs] + rhs' = asInteger (rhs * fromIntegral d) + case indicator of + Nothing -> + case op of + LPFile.Le -> SAT.Integer.addConstraint enc $ lhs' .<=. fromInteger rhs' + LPFile.Ge -> SAT.Integer.addConstraint enc $ lhs' .>=. fromInteger rhs' + LPFile.Eql -> SAT.Integer.addConstraint enc $ lhs' .==. fromInteger rhs' + Just (var, val) -> do + let var' = asBin (vmap Map.! var) + f sel = do + case op of + LPFile.Le -> SAT.Integer.addConstraintSoft enc sel $ lhs' .<=. fromInteger rhs' + LPFile.Ge -> SAT.Integer.addConstraintSoft enc sel $ lhs' .>=. fromInteger rhs' + LPFile.Eql -> SAT.Integer.addConstraintSoft enc sel $ lhs' .==. fromInteger rhs' + case val of + 1 -> f var' + 0 -> f (SAT.litNot var') + _ -> return () + + putCommentLine "Loading SOS constraints" + forM_ (LPFile.sos lp) $ \(_label, typ, xs) -> do + case typ of + LPFile.S1 -> SAT.addAtMost solver (map (asBin . (vmap Map.!) . fst) xs) 1 + LPFile.S2 -> do + let ps = nonAdjacentPairs $ map fst $ sortBy (comparing snd) $ xs + forM_ ps $ \(x1,x2) -> do + SAT.addClause solver [SAT.litNot $ asBin $ vmap Map.! v | v <- [x1,x2]] + + let (_label,obj) = LPFile.objectiveFunction lp + d = foldl' lcm 1 [denominator r | LPFile.Term r _ <- obj] * + (if LPFile.dir lp == LPFile.OptMin then 1 else -1) + obj2 = lsum [asInteger (r * fromIntegral d) .*. product [vmap Map.! v | v <- vs] | LPFile.Term r vs <- obj] + (obj3,obj3_c) <- SAT.Integer.linearize enc obj2 + + modelRef <- newIORef Nothing + + result <- try $ minimize opt solver obj3 $ \m val -> do + writeIORef modelRef (Just m) + putStrLn $ "o " ++ showRational (optPrintRational opt) (fromIntegral (val + obj3_c) / fromIntegral d) + hFlush stdout + + let printModel :: SAT.Model -> IO () + printModel m = do + forM_ (Set.toList ivs) $ \v -> do + let val = SAT.Integer.eval m (vmap Map.! v) + printf "v %s = %d\n" v val + hFlush stdout + writeSol m + + writeSol :: SAT.Model -> IO () + writeSol m = do + case optWriteFile opt of + Nothing -> return () + Just fname -> do + let m2 = Map.fromList [ (v, fromInteger val) + | v <- Set.toList ivs + , let val = SAT.Integer.eval m (vmap Map.! v) ] + o = fromInteger $ SAT.Integer.eval m obj2 + writeFile fname (GurobiSol.render m2 (Just o)) + + case result of + Right Nothing -> do + putStrLn $ "s " ++ "UNSATISFIABLE" + hFlush stdout + Right (Just m) -> do + putStrLn $ "s " ++ "OPTIMUM FOUND" + hFlush stdout + printModel m + Left (e :: SomeException) -> do + r <- readIORef modelRef + case r of + Nothing -> do + putStrLn $ "s " ++ "UNKNOWN" + hFlush stdout + Just m -> do + putStrLn $ "s " ++ "SATISFIABLE" + printModel m + throwIO e + where + ivs = LPFile.integerVariables lp + nivs = LPFile.variables lp `Set.difference` ivs + + asInteger :: Rational -> Integer + asInteger r + | denominator r /= 1 = error (show r ++ " is not integer") + | otherwise = numerator r + + nonAdjacentPairs :: [a] -> [(a,a)] + nonAdjacentPairs (x1:x2:xs) = [(x1,x3) | x3 <- xs] ++ nonAdjacentPairs (x2:xs) + nonAdjacentPairs _ = [] + + asBin :: SAT.Integer.Expr -> SAT.Lit + asBin (SAT.Integer.Expr [(1,[lit])]) = lit + asBin _ = error "asBin: failure" + +-- ------------------------------------------------------------------------ + +writeSOLFile :: Options -> SAT.Model -> Maybe Integer -> Int -> IO () +writeSOLFile opt m obj nbvar = do + case optWriteFile opt of + Nothing -> return () + Just fname -> do + let m2 = Map.fromList [("x" ++ show x, if b then 1 else 0) | (x,b) <- assocs m, x <= nbvar] + writeFile fname (GurobiSol.render (Map.map fromInteger m2) (fmap fromInteger obj)) diff --git a/toysolver.cabal b/toysolver.cabal --- a/toysolver.cabal +++ b/toysolver.cabal @@ -1,5 +1,5 @@ Name: toysolver -Version: 0.0.2 +Version: 0.0.3 License: BSD3 License-File: COPYING Author: Masahiro Sakai (masahiro.sakai@gmail.com) @@ -12,24 +12,12 @@ Extra-Source-Files: README.md COPYING + .travis.yml src/TseitinEncode.hs - src/CongruenceClosure.hs - src/ContiTraverso.hs - src/Data/Polynomial.hs - src/Data/Polynomial/GBase.hs - src/Data/Polynomial/FactorZ.hs - src/Data/Polynomial/Graeffe.hs - src/Data/Polynomial/Lagrange.hs - src/Data/Polynomial/Sturm.hs - src/Data/AlgebraicNumber.hs - src/Data/AlgebraicNumber/Root.hs - src/Data/AlgebraicNumber/RealInstance.hs src/Data/Polyhedron.hs - src/Text/SDPFile.hs - src/TestAReal2.hs src/pbverify.hs src/pigeonhole.hs - src/Wang.hs + src/Algorithm/Wang.hs samples/gcnf/*.gcnf samples/lp/*.lp samples/lp/error/*.lp @@ -43,6 +31,9 @@ samples/sdp/*.dat-s samples/smt/*.smt2 samples/qbf/*.qdimacs + test/TestAReal2.hs + benchmarks/UF250.1065.100/*.cnf + benchmarks/UUF250.1065.100/*.cnf Build-Type: Simple Flag ForceChar8 @@ -53,45 +44,85 @@ type: git location: git://github.com/msakai/toysolver.git -Executable toysolver - Main-is: toysolver.hs - HS-Source-Dirs: src - Other-Modules: +Library + Exposed: False + Hs-source-dirs: src + Build-Depends: + base >=4 && <5, + containers >= 0.4.2, mtl, array, random, stm >=2.3, parsec, bytestring, filepath, deepseq, time, old-locale, primes, + parse-dimacs, queue, heaps, unbounded-delays, + OptDir + Extensions: + MultiParamTypeClasses + FlexibleInstances + BangPatterns + DoAndIfThenElse + CPP + Exposed-Modules: + Algorithm.BoundsInference + Algorithm.CAD + Algorithm.CongruenceClosure + Algorithm.ContiTraverso + Algorithm.Cooper + Algorithm.FOLModelFinder + Algorithm.FourierMotzkin + Algorithm.LPSolver + Algorithm.LPSolverHL + Algorithm.LPUtil + Algorithm.MIPSolverHL + Algorithm.MIPSolver2 + Algorithm.OmegaTest + Algorithm.Simplex + Algorithm.Simplex2 Converter.CNF2LP Converter.ObjType Converter.PB2LP + Converter.LP2SMT + Converter.MaxSAT2LP + Data.AlgebraicNumber + Data.AlgebraicNumber.Root + Data.ArithRel Data.Delta Data.Expr - Data.Lattice Data.Formula Data.LA + Data.Lattice + Data.LBool Data.Linear Data.Interval + Data.Polynomial + Data.Polynomial.FactorZ + Data.Polynomial.GBase + Data.Polynomial.Lagrange + Data.Polynomial.Sturm + SAT + SAT.Integer + SAT.MUS + SAT.CAMUS + SAT.PBO + SAT.TheorySolver + SAT.TseitinEncoder + SAT.Types SAT.Printer + Text.GCNF + Text.GurobiSol Text.LPFile - Text.PBFile + Text.MPSFile Text.MaxSAT - BoundsInference - Cooper - FourierMotzkin - LPSolver - LPSolverHL - MIPSolverHL - OmegaTest - Simplex - Simplex2 - MIPSolver2 + Text.PBFile + Text.SDPFile Util Version - Build-Depends: base >=4 && <5, mtl, containers, array, filepath, parsec, OptDir, deepseq, stm >=2.3, parse-dimacs - Extensions: - BangPatterns - ScopedTypeVariables - FlexibleInstances - MultiParamTypeClasses - FunctionalDependencies - GeneralizedNewtypeDeriving - DoAndIfThenElse + Other-Modules: + Data.IndexedPriorityQueue + Data.SeqQueue + Paths_toysolver + GHC-Prof-Options: -auto-all + +Executable toysolver + Main-is: toysolver.hs + HS-Source-Dirs: toysolver + Build-Depends: base >=4.4 && <5, containers, array, filepath, parsec, OptDir, parse-dimacs, toysolver if impl(ghc) GHC-Options: -threaded if impl(ghc >= 7) @@ -100,28 +131,8 @@ Executable toysat Main-is: toysat.hs - HS-Source-Dirs: src - Other-Modules: - Data.LBool - Data.IndexedPriorityQueue - Data.SeqQueue - Text.LPFile - Text.PBFile - Text.MaxSAT - SAT - SAT.Integer - SAT.TseitinEncoder - SAT.Types - SAT.TheorySolver - SAT.Printer - Version - Build-Depends: base >=4 && <5, mtl, containers >= 0.4.2, array, random, parsec, bytestring, filepath, parse-dimacs, queue, OptDir, time, old-locale - Extensions: - MultiParamTypeClasses - FlexibleInstances - BangPatterns - DoAndIfThenElse - CPP + HS-Source-Dirs: toysat + Build-Depends: base >=4 && <5, containers >= 0.4.2, array, parsec, bytestring, filepath, parse-dimacs, time, old-locale, unbounded-delays, toysolver if impl(ghc >= 7) GHC-Options: -rtsopts GHC-Prof-Options: -auto-all @@ -129,116 +140,105 @@ Build-Depends: base >=4.5 CPP-OPtions: "-DFORCE_CHAR8" -Executable lp2yices - Main-is: lp2yices.hs - HS-Source-Dirs: src - Other-Modules: - Text.LPFile - Util - Build-Depends: base >=4 && <5, mtl, containers, parsec, OptDir - Extensions: - BangPatterns - ScopedTypeVariables - FlexibleInstances - MultiParamTypeClasses - FunctionalDependencies - GeneralizedNewtypeDeriving - -Executable cnf2lp - Main-is: cnf2lp.hs - HS-Source-Dirs: src - Other-Modules: - Text.LPFile - Converter.CNF2LP - Converter.ObjType - Util - Build-Depends: base >=4 && <5, mtl, containers, array, parsec, bytestring, parse-dimacs, OptDir - Extensions: - BangPatterns - ScopedTypeVariables - FlexibleInstances - MultiParamTypeClasses - FunctionalDependencies - GeneralizedNewtypeDeriving - -Executable maxsat2lp - Main-is: maxsat2lp.hs - HS-Source-Dirs: src - Other-Modules: - SAT.Types - Text.MaxSAT - Converter.MaxSAT2LP - Build-Depends: base >=4 && <5, mtl, containers, array, parsec, OptDir +Executable toyfmf + Main-is: toyfmf.hs + HS-Source-Dirs: toyfmf + Build-Depends: base >=4 && <5, containers >= 0.4.2, toysolver, logic-TPTP + if impl(ghc >= 7) + GHC-Options: -rtsopts + GHC-Prof-Options: -auto-all -Executable pb2lp - Main-is: pb2lp.hs - HS-Source-Dirs: src - Other-Modules: - Text.LPFile - Text.PBFile - Converter.PB2LP - Converter.ObjType - Build-Depends: base >=4 && <5, mtl, containers, array, parsec, OptDir +Executable lpconvert + Main-is: lpconvert.hs + HS-Source-Dirs: lpconvert + Build-Depends: base >=4 && <5, containers, filepath, parse-dimacs, toysolver Test-suite TestSAT Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestSAT.hs - Build-depends: base >=4 && <5, array, containers, random, queue, test-framework,test-framework-th,test-framework-hunit,HUnit,OptDir + Build-depends: base >=4 && <5, array, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,HUnit Extensions: TemplateHaskell, DoAndIfThenElse Test-suite TestSimplex2 Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestSimplex2.hs - Build-depends: base >=4 && <5, containers, deepseq, queue, test-framework,test-framework-th,test-framework-hunit,HUnit,OptDir + Build-depends: base >=4 && <5, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,HUnit Extensions: TemplateHaskell, DoAndIfThenElse Test-suite TestMIPSolver2 Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestMIPSolver2.hs - Build-depends: base >=4 && <5, containers, deepseq, queue, test-framework, test-framework-th, test-framework-hunit, HUnit, OptDir, stm + Build-depends: base >=4 && <5, containers, toysolver, test-framework, test-framework-th, test-framework-hunit, HUnit, OptDir, stm Extensions: TemplateHaskell, DoAndIfThenElse Test-suite TestPolynomial Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestPolynomial.hs - Build-depends: base >=4 && <5, containers, heaps, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Build-depends: base >=4 && <5, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 Extensions: TemplateHaskell, DoAndIfThenElse Test-suite TestInterval Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestInterval.hs - Build-depends: base >=4 && <5, containers, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Build-depends: base >=4 && <5, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 Extensions: TemplateHaskell, DoAndIfThenElse Test-suite TestAReal Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestAReal.hs - Build-depends: base >=4 && <5, containers, heaps, primes, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Build-depends: base >=4 && <5, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 Extensions: TemplateHaskell, DoAndIfThenElse +Test-suite TestQE + Type: exitcode-stdio-1.0 + HS-Source-Dirs: test + Main-is: TestQE.hs + Build-depends: base >=4 && <5, containers, toysolver, OptDir, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Extensions: TemplateHaskell, DoAndIfThenElse + +Test-suite TestContiTraverso + Type: exitcode-stdio-1.0 + HS-Source-Dirs: test + Main-is: TestContiTraverso.hs + Build-depends: base >=4 && <5, containers, toysolver, OptDir, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Extensions: TemplateHaskell, DoAndIfThenElse + Test-suite TestLPFile Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestLPFile.hs - Build-depends: base >=4 && <5, mtl, containers, parsec, OptDir, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Build-depends: base >=4 && <5, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 Extensions: TemplateHaskell, DoAndIfThenElse +Test-suite TestMPSFile + Type: exitcode-stdio-1.0 + HS-Source-Dirs: test + Main-is: TestMPSFile.hs + Build-depends: base >=4 && <5, containers, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Extensions: TemplateHaskell, DoAndIfThenElse + Test-suite TestPBFile Type: exitcode-stdio-1.0 - HS-Source-Dirs: src + HS-Source-Dirs: test Main-is: TestPBFile.hs - Build-depends: base >=4 && <5, mtl, containers, parsec, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Build-depends: base >=4 && <5, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 Extensions: TemplateHaskell, DoAndIfThenElse +Test-suite TestUtil + Type: exitcode-stdio-1.0 + HS-Source-Dirs: test + Main-is: TestUtil.hs + Build-depends: base >=4 && <5, toysolver, test-framework,test-framework-th,test-framework-hunit,test-framework-quickcheck2,HUnit,QuickCheck >=2 && <3 + Extensions: TemplateHaskell, DoAndIfThenElse + Benchmark BenchmarkSATLIB type: exitcode-stdio-1.0 - hs-source-dirs: src + hs-source-dirs: benchmarks main-is: BenchmarkSATLIB.hs - build-depends: base >=4 && <5, array, containers, random, queue, parse-dimacs, criterion - Extensions: TemplateHaskell, DoAndIfThenElse + build-depends: base >=4 && <5, array, containers, random, parse-dimacs, toysolver, criterion diff --git a/toysolver/toysolver.hs b/toysolver/toysolver.hs new file mode 100644 --- /dev/null +++ b/toysolver/toysolver.hs @@ -0,0 +1,424 @@ +----------------------------------------------------------------------------- +-- | +-- Module : toysolver +-- Copyright : (c) Masahiro Sakai 2011 +-- License : BSD-style +-- +-- Maintainer : masahiro.sakai@gmail.com +-- Stability : experimental +-- Portability : portable +-- +----------------------------------------------------------------------------- + + +module Main where + +import Control.Monad +import Control.Concurrent +import Data.Array.IArray +import Data.Char +import Data.List +import Data.Maybe +import Data.Ratio +import qualified Data.Version as V +import qualified Data.Set as Set +import qualified Data.Map as Map +import qualified Data.IntMap as IM +import qualified Data.IntSet as IS +import System.Exit +import System.Environment +import System.FilePath +import System.Console.GetOpt +import System.IO +import Text.Printf +import qualified Language.CNF.Parse.ParseDIMACS as DIMACS + +import Data.Expr +import Data.ArithRel +import Data.Formula (Atom (..)) +import Data.OptDir +import qualified Data.LA as LA +import qualified Data.Polynomial as P +import qualified Data.AlgebraicNumber as AReal +import qualified Algorithm.OmegaTest as OmegaTest +import qualified Algorithm.Cooper as Cooper +import qualified Algorithm.MIPSolverHL as MIPSolverHL +import qualified Algorithm.Simplex2 as Simplex2 +import qualified Algorithm.MIPSolver2 as MIPSolver2 +import qualified Algorithm.CAD as CAD +import qualified Algorithm.ContiTraverso as ContiTraverso +import qualified Text.LPFile as LP +import qualified Text.MPSFile as MPS +import qualified Text.PBFile as PBFile +import qualified Text.MaxSAT as MaxSAT +import qualified Text.GurobiSol as GurobiSol +import qualified Converter.CNF2LP as CNF2LP +import qualified Converter.PB2LP as PB2LP +import qualified Converter.MaxSAT2LP as MaxSAT2LP +import SAT.Printer +import qualified SAT.Types as SAT +import Version +import Util + +-- --------------------------------------------------------------------------- + +data Mode = ModeSAT | ModePB | ModeWBO | ModeMaxSAT | ModeLP + deriving (Eq, Ord) + +data Flag + = Help + | Version + | Solver String + | PrintRational + | WriteFile !FilePath + | NoMIP + | PivotStrategy String + | NThread !Int + | Mode !Mode + deriving Eq + +options :: [OptDescr Flag] +options = + [ Option ['h'] ["help"] (NoArg Help) "show help" + , Option ['v'] ["version"] (NoArg Version) "show version number" + , Option [] ["solver"] (ReqArg Solver "SOLVER") "mip (default), omega-test, cooper, cad, old-mip, ct" + , Option [] ["print-rational"] (NoArg PrintRational) "print rational numbers instead of decimals" + , Option ['w'] [] (ReqArg WriteFile "") "write solution to filename in Gurobi .sol format" + + , Option [] ["print-rational"] (NoArg PrintRational) "print rational numbers instead of decimals" + + , Option [] ["pivot-strategy"] (ReqArg PivotStrategy "[bland-rule|largest-coefficient]") "pivot strategy for simplex (default: bland-rule)" + , Option [] ["threads"] (ReqArg (NThread . read) "INTEGER") "number of threads to use" + + , Option [] ["sat"] (NoArg (Mode ModeSAT)) "solve boolean satisfiability problems in .cnf file" + , Option [] ["pb"] (NoArg (Mode ModePB)) "solve pseudo boolean problems in .pb file" + , Option [] ["wbo"] (NoArg (Mode ModeWBO)) "solve weighted boolean optimization problem in .opb file" + , Option [] ["maxsat"] (NoArg (Mode ModeMaxSAT)) "solve MaxSAT problem in .cnf or .wcnf file" + , Option [] ["lp"] (NoArg (Mode ModeLP)) "solve binary integer programming problem in .lp or .mps file (default)" + + , Option [] ["nomip"] (NoArg NoMIP) "consider all integer variables as continuous" + ] + +header :: String +header = "Usage: toysolver [OPTION]... file" + +-- --------------------------------------------------------------------------- + +run + :: String + -> [Flag] + -> LP.LP + -> (Map.Map String Rational -> IO ()) + -> IO () +run solver opt lp printModel = do + unless (Set.null (LP.semiContinuousVariables lp)) $ do + hPutStrLn stderr "semi-continuous variables are not supported." + exitFailure + case map toLower solver of + s | s `elem` ["omega", "omega-test", "cooper"] -> solveByQE + s | s `elem` ["old-mip"] -> solveByMIP + s | s `elem` ["cad"] -> solveByCAD + s | s `elem` ["ct", "conti-traverso"] -> solveByContiTraverso + _ -> solveByMIP2 + where + vs = LP.variables lp + vsAssoc = zip (Set.toList vs) [0..] + nameToVar = Map.fromList vsAssoc + varToName = IM.fromList [(v,name) | (name,v) <- vsAssoc] + + compileE :: LP.Expr -> Expr Rational + compileE = foldr (+) (Const 0) . map compileT + + compileT :: LP.Term -> Expr Rational + compileT (LP.Term c vs) = + foldr (*) (Const c) [Var (nameToVar Map.! v) | v <- vs] + + obj = compileE $ snd $ LP.objectiveFunction lp + + cs1 = do + v <- Set.toList vs + let v2 = Var (nameToVar Map.! v) + let (l,u) = LP.getBounds lp v + [Const x .<=. v2 | LP.Finite x <- return l] ++ + [v2 .<=. Const x | LP.Finite x <- return u] + cs2 = do + LP.Constraint + { LP.constrIndicator = ind + , LP.constrBody = (lhs, rel, rhs) + } <- LP.constraints lp + let rel2 = case rel of + LP.Ge -> Ge + LP.Le -> Le + LP.Eql -> Eql + case ind of + Nothing -> return (Rel (compileE lhs) rel2 (Const rhs)) + Just _ -> error "indicator constraint is not supported yet" + + ivs + | NoMIP `elem` opt = Set.empty + | otherwise = LP.integerVariables lp + + ivs2 = IS.fromList . map (nameToVar Map.!) . Set.toList $ ivs + + solveByQE = + case mapM LA.compileAtom (cs1 ++ cs2) of + Nothing -> do + putStrLn "s UNKNOWN" + exitFailure + Just cs -> + case f cs ivs2 of + Nothing -> do + putStrLn "s UNSATISFIABLE" + exitFailure + Just m -> do + putStrLn $ "o " ++ showValue (Data.Expr.eval m obj) + putStrLn "s SATISFIABLE" + let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] + printModel m2 + where + f = case solver of + "omega" -> OmegaTest.solveQFLA + "omega-test" -> OmegaTest.solveQFLA + "cooper" -> Cooper.solveQFLA + _ -> error "unknown solver" + + solveByMIP = + case MIPSolverHL.optimize (LP.dir lp) obj (cs1 ++ cs2) ivs2 of + OptUnknown -> do + putStrLn "s UNKNOWN" + exitFailure + OptUnsat -> do + putStrLn "s UNSATISFIABLE" + exitFailure + Unbounded -> do + putStrLn "s UNBOUNDED" + exitFailure + Optimum r m -> do + putStrLn $ "o " ++ showValue r + putStrLn "s OPTIMUM FOUND" + let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] + printModel m2 + + solveByMIP2 = do + solver <- Simplex2.newSolver + + let ps = last ("bland-rule" : [s | PivotStrategy s <- opt]) + case ps of + "bland-rule" -> Simplex2.setPivotStrategy solver Simplex2.PivotStrategyBlandRule + "largest-coefficient" -> Simplex2.setPivotStrategy solver Simplex2.PivotStrategyLargestCoefficient + _ -> error ("unknown pivot strategy \"" ++ ps ++ "\"") + + let nthreads = last (0 : [n | NThread n <- opt]) + + Simplex2.setLogger solver putCommentLine + replicateM (length vsAssoc) (Simplex2.newVar solver) -- XXX + Simplex2.setOptDir solver (LP.dir lp) + Simplex2.setObj solver $ fromJust (LA.compileExpr obj) + putCommentLine "Loading constraints... " + forM_ (cs1 ++ cs2) $ \c -> do + Simplex2.assertAtom solver $ fromJust (LA.compileAtom c) + putCommentLine "Loading constraints finished" + + mip <- MIPSolver2.newSolver solver ivs2 + MIPSolver2.setShowRational mip printRat + MIPSolver2.setLogger mip putCommentLine + ncap <- getNumCapabilities + MIPSolver2.setNThread mip $ + if nthreads >= 1 + then min ncap nthreads + else ncap + let update m val = do + putStrLn $ "o " ++ showValue val + ret <- MIPSolver2.optimize mip update + case ret of + Simplex2.Unsat -> do + putStrLn "s UNSATISFIABLE" + exitFailure + Simplex2.Unbounded -> do + putStrLn "s UNBOUNDED" + m <- MIPSolver2.model mip + let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] + printModel m2 + exitFailure + Simplex2.Optimum -> do + m <- MIPSolver2.model mip + r <- MIPSolver2.getObjValue mip + putStrLn "s OPTIMUM FOUND" + let m2 = Map.fromAscList [(v, m IM.! (nameToVar Map.! v)) | v <- Set.toList vs] + printModel m2 + + solveByCAD + | not (IS.null ivs2) = do + putStrLn "s UNKNOWN" + putCommentLine "integer variables are not supported by CAD" + exitFailure + | otherwise = do + let cs = map g $ cs1 ++ cs2 + case CAD.solve cs of + Nothing -> do + putStrLn "s UNSATISFIABLE" + exitFailure + Just m -> do + let m2 = IM.map (\x -> AReal.approx x (2^^(-64::Int))) $ + IM.fromAscList $ Map.toAscList $ m + putStrLn $ "o " ++ showValue (Data.Expr.eval m2 obj) + putStrLn "s SATISFIABLE" + let m3 = Map.fromAscList [(v, m2 IM.! (nameToVar Map.! v)) | v <- Set.toList vs] + printModel m3 + where + g (Rel lhs rel rhs) = Rel (f lhs) rel (f rhs) + + f (Const r) = P.constant r + f (Var v) = P.var v + f (e1 :+: e2) = f e1 + f e2 + f (e1 :*: e2) = f e1 * f e2 + f (e1 :/: e2) + | P.deg p > 0 = error "can't handle rational expression" + | otherwise = P.mapCoeff (/ c) $ f e1 + where + p = f e2 + c = P.coeff P.mmOne p + + solveByContiTraverso + | not (vs `Set.isSubsetOf` ivs) = do + putStrLn "s UNKNOWN" + putCommentLine "continuous variables are not supported by Conti-Traverso algorithm" + exitFailure + | otherwise = do + let tmp = do + linObj <- LA.compileExpr obj + linCon <- mapM LA.compileAtom (cs1 ++ cs2) + return (linObj, linCon) + case tmp of + Nothing -> do + putStrLn "s UNKNOWN" + putCommentLine "non-linear expressions are not supported by Conti-Traverso algorithm" + exitFailure + Just (linObj, linCon) -> do + case ContiTraverso.solve P.grlex (LP.dir lp) linObj linCon of + Nothing -> do + putStrLn "s UNSATISFIABLE" + exitFailure + Just m -> do + let m2 = IM.map fromInteger m + putStrLn $ "o " ++ showValue (Data.Expr.eval m2 obj) + putStrLn "s OPTIMUM FOUND" + let m3 = Map.fromAscList [(v, m2 IM.! (nameToVar Map.! v)) | v <- Set.toList vs] + printModel m3 + + printRat :: Bool + printRat = PrintRational `elem` opt + + showValue :: Rational -> String + showValue = showRational printRat + +lpPrintModel :: Handle -> Bool -> Map.Map String Rational -> IO () +lpPrintModel h asRat m = do + forM_ (Map.toList m) $ \(v, val) -> do + printf "v %s = %s\n" v (showRational asRat val) + + +putCommentLine :: String -> IO () +putCommentLine s = do + putStr "c " + putStrLn s + hFlush stdout + +-- --------------------------------------------------------------------------- + +getSolver :: [Flag] -> String +getSolver xs = last $ "mip" : [s | Solver s <- xs] + +main :: IO () +main = do + args <- getArgs + case getOpt Permute options args of + (o,_,[]) + | Help `elem` o -> putStrLn (usageInfo header options) + | Version `elem` o -> putStrLn (V.showVersion version) + (o,[fname],[]) -> do + + let mode = + case reverse [m | Mode m <- o] of + m:_ -> m + [] -> + case map toLower (takeExtension fname) of + ".cnf" -> ModeSAT + ".opb" -> ModePB + ".wbo" -> ModeWBO + ".wcnf" -> ModeMaxSAT + ".lp" -> ModeLP + ".mps" -> ModeLP + _ -> ModeLP + + case mode of + ModeSAT -> do + ret <- DIMACS.parseFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right cnf -> do + let (lp,mtrans) = CNF2LP.convert CNF2LP.ObjNone cnf + run (getSolver o) o lp $ \m -> do + let m2 = mtrans m + satPrintModel stdout m2 0 + writeSOLFileSAT o m2 + ModePB -> do + ret <- PBFile.parseOPBFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right pb -> do + let (lp,mtrans) = PB2LP.convert PB2LP.ObjNone pb + run (getSolver o) o lp $ \m -> do + let m2 = mtrans m + pbPrintModel stdout m2 0 + writeSOLFileSAT o m2 + ModeWBO -> do + ret <- PBFile.parseWBOFile fname + case ret of + Left err -> hPrint stderr err >> exitFailure + Right wbo -> do + let (lp,mtrans) = PB2LP.convertWBO False wbo + run (getSolver o) o lp $ \m -> do + let m2 = mtrans m + pbPrintModel stdout m2 0 + writeSOLFileSAT o m2 + ModeMaxSAT -> do + ret <- MaxSAT.parseWCNFFile fname + case ret of + Left err -> hPutStrLn stderr err >> exitFailure + Right wcnf -> do + let (lp,mtrans) = MaxSAT2LP.convert wcnf + run (getSolver o) o lp $ \m -> do + let m2 = mtrans m + maxsatPrintModel stdout m2 0 + writeSOLFileSAT o m2 + ModeLP -> do + ret <- LP.parseFile fname + lp <- case ret of + Right lp -> return lp + Left err -> do + ret <- MPS.parseFile fname + case ret of + Right lp -> return lp + Left err2 -> do + hPrint stderr err + hPrint stderr err2 + exitFailure + run (getSolver o) o lp $ \m -> do + lpPrintModel stdout (PrintRational `elem` o) m + writeSOLFileLP o m + (_,_,errs) -> + hPutStrLn stderr $ concat errs ++ usageInfo header options + +-- FIXME: 目的関数値を表示するように +writeSOLFileLP :: [Flag] -> Map.Map String Rational -> IO () +writeSOLFileLP opt m = do + forM_ [fname | WriteFile fname <- opt ] $ \fname -> do + let m2 = Map.map fromRational m + writeFile fname (GurobiSol.render m2 Nothing) + +-- FIXME: 目的関数値を表示するように +writeSOLFileSAT :: [Flag] -> SAT.Model -> IO () +writeSOLFileSAT opt m = do + let m2 = Map.fromList [("x" ++ show x, if b then 1 else 0) | (x,b) <- assocs m] + writeSOLFileLP opt m2