Safe Haskell	Safe-Inferred
Language	Haskell98

Numeric.COINOR.CLP

Synopsis

simplex :: (Coefficient a, Indexed sh, Index sh ~ ix) => Method -> Bounds ix -> Constraints a ix -> (Direction, Objective sh) -> Result sh
data Direction
- = Minimize
- | Maximize
data PlusMinusOne
- = MinusOne
- | PlusOne
data Term a ix = Term a ix
(.*) :: a -> ix -> Term a ix
type Constraints a ix = [Inequality [Term a ix]]
free :: x -> Inequality x
(<=.) :: x -> Double -> Inequality x
(>=.) :: x -> Double -> Inequality x
(==.) :: x -> Double -> Inequality x
(>=<.) :: x -> (Double, Double) -> Inequality x
data Method
dual :: Method
primal :: Method
initialSolve :: Method
initialDualSolve :: Method
initialPrimalSolve :: Method
initialBarrierSolve :: Method
initialBarrierNoCrossSolve :: Method
data FailureType
- = PrimalInfeasible
- | DualInfeasible
- | StoppedOnIterations
- | StoppedDueToErrors
type Result sh = Either FailureType (Double, Array sh Double)

Documentation

simplex :: (Coefficient a, Indexed sh, Index sh ~ ix) => Method -> Bounds ix -> Constraints a ix -> (Direction, Objective sh) -> Result sh Source #

>>> case Shape.indexTupleFromShape tripletShape of
      (x,y,z) ->
         mapSnd Array.toTuple <$>
         LP.simplex LP.dual []
            [[2.*x, 1.*y] <=. 10, [1.*y, (5::Double).*z] <=. 20]
            (LP.Maximize, Array.fromTuple (4,-3,2)
               :: Array.Array TripletShape Double)
Right (28.0,(5.0,0.0,4.0))

>>> case Shape.indexTupleFromShape tripletShape of
      (x,y,z) ->
         mapSnd Array.toTuple <$>
         LP.simplex LP.primal [y >=<. (-12,12)]
            [[1.*x, (-1).*y] <=. 10, [(-1).*y, (1::Double).*z] <=. 20]
            (LP.Maximize, Array.fromTuple (4,-3,2)
               :: Array.Array TripletShape Double)
Right (116.0,(22.0,12.0,32.0))

>>> case Shape.indexTupleFromShape tripletShape of
      (x,y,z) ->
         mapSnd Array.toTuple <$>
         LP.simplex LP.primal [y >=<. (-12,12)]
            [[PlusOne .* x, MinusOne .* y] <=. 10,
             [MinusOne .* y, PlusOne .* z] <=. 20]
            (LP.Maximize, Array.fromTuple (4,-3,2)
               :: Array.Array TripletShape Double)
Right (116.0,(22.0,12.0,32.0))

>>> case Shape.indexTupleFromShape tripletShape of
      (x,y,z) ->
         mapSnd Array.toTuple <$>
         LP.simplex LP.primal [y >=<. (-12,12)]
            [[1.*x, 1.*y] <=. 10, [1.*y, (-1::Double).*z] >=. 20]
            (LP.Maximize, Array.fromTuple (4,3,2)
               :: Array.Array TripletShape Double)
Left PrimalInfeasible

>>> case Shape.indexTupleFromShape tripletShape of
      (x,y,z) ->
         mapSnd Array.toTuple <$>
         LP.simplex LP.primal [y >=<. (-12,12)]
            [[1.*x, 1.*y] <=. 10, [1.*y, (1::Double).*z] >=. 20]
            (LP.Maximize, Array.fromTuple (4,3,2)
               :: Array.Array TripletShape Double)
Left DualInfeasible

forAllMethod $ \method (QC.Positive posWeight) (QC.Positive negWeight) target ->
   case Shape.indexTupleFromShape pairShape of
      (pos,neg) ->
         case mapSnd Array.toTuple <$>
               LP.simplex method []
                  [[1.*pos, (-1::Double).*neg] ==. target]
                  (LP.Minimize, Array.fromTuple (posWeight,negWeight)
                     :: Array.Array PairShape Double) of
            Left _ -> QC.property False
            Right (absol,(posResult,negResult)) ->
               QC.property (absol>=0)
               .&&.
               (posResult === 0 .||. negResult === 0)

forAllMethod $ \method target ->
   case Shape.indexTupleFromShape pairShape of
      (pos,neg) ->
         case mapSnd Array.toTuple <$>
               LP.simplex method []
                  [[1.*pos, (-1::Double).*neg] ==. target]
                  (LP.Minimize, Array.fromTuple (1,1)
                     :: Array.Array PairShape Double) of
            Left _ -> QC.property False
            Right (absol,(posResult,negResult)) ->
               QC.counterexample (show(absol,(posResult,negResult))) $
               QC.property (approxReal 0.001 absol (abs target))
               .&&.
               (posResult === 0 .||. negResult === 0)

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \(dir,obj) ->
   case LP.simplex method bounds constrs (dir,obj) of
      Left _ -> False
      Right _ -> True

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \(dir,obj) ->
   case LP.simplex method bounds constrs (dir,obj) of
      Left _ -> QC.property False
      Right (_,sol) -> TestLP.checkFeasibility 0.1 bounds constrs sol

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \(dir,obj) ->
   case LP.simplex method bounds constrs (dir,obj) of
      Left _ -> QC.property False
      Right (_,sol) ->
         QC.forAll (QC.choose (0,1)) $ \lambda ->
         TestLP.checkFeasibility 0.1 bounds constrs $
         TestLP.affineCombination lambda sol (Array.map fromIntegral origin)

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \(dir,obj) ->
   case LP.simplex method bounds constrs (dir,obj) of
      Left _ -> QC.property False
      Right (opt,sol) ->
         QC.forAll (QC.choose (0,1)) $ \lambda ->
            let val = TestLP.scalarProduct obj $
                        TestLP.affineCombination lambda sol (Array.map fromIntegral origin)
            in case dir of
                  LP.Minimize -> opt-0.01 <= val
                  LP.Maximize -> opt+0.01 >= val

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllBoundedProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \dirObjA ->
   QC.forAll (TestLP.genObjective origin) $ \dirObjB ->
   let solA = LP.simplex method bounds constrs dirObjA in
   let solB = LP.simplex method bounds constrs dirObjB in
   QC.counterexample (show (mapRight fst solA, mapRight fst solB)) $
   case (solA, solB) of
      (Right _, Right _) -> True
      (Left _, Left _) -> True
      _ -> False

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \(_dir,obj) ->
   case (LP.simplex method bounds constrs (LP.Minimize,obj),
         LP.simplex method bounds constrs (LP.Maximize,obj)) of
      (Right (optMin,_), Right (optMax,_)) ->
         QC.counterexample (show (optMin, optMax)) $ optMin <= optMax + 0.01
      _ -> QC.property False

forAllMethod $ \method ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds allConstrs ->
   QC.forAll (QC.sublistOf allConstrs) $ \someConstrs ->
   QC.forAll (TestLP.genObjective origin) $ \(dir,obj) ->
   case (LP.simplex method bounds allConstrs (dir,obj),
         LP.simplex method bounds someConstrs (dir,obj)) of
      (Right (optAll,_), Right (optSome,_)) ->
         QC.counterexample (show (optAll, optSome)) $
         case dir of
            LP.Minimize -> optAll >= optSome-0.01
            LP.Maximize -> optAll <= optSome+0.01
      _ -> QC.property False

forAllMethod $ \methodA ->
   forAllMethod $ \methodB ->
   TestLP.forAllOrigin $ \origin ->
   TestLP.forAllProblem origin $ \bounds constrs ->
   QC.forAll (TestLP.genObjective origin) $ \dirObj ->
   case (LP.simplex methodA bounds constrs dirObj,
         LP.simplex methodB bounds constrs dirObj) of
      (Right (optA,_), Right (optB,_)) ->
         QC.counterexample (show (optA, optB)) $
         approxReal 0.01 optA optB
      _ -> QC.property False

data Direction #

Constructors

Minimize
Maximize

Instances

Instances details

Bounded Direction
Instance details Defined in Numeric.LinearProgramming.Common Methods minBound :: Direction # maxBound :: Direction #
Enum Direction
Instance details Defined in Numeric.LinearProgramming.Common Methods succ :: Direction -> Direction # pred :: Direction -> Direction # toEnum :: Int -> Direction # fromEnum :: Direction -> Int # enumFrom :: Direction -> [Direction] # enumFromThen :: Direction -> Direction -> [Direction] # enumFromTo :: Direction -> Direction -> [Direction] # enumFromThenTo :: Direction -> Direction -> Direction -> [Direction] #
Show Direction
Instance details Defined in Numeric.LinearProgramming.Common Methods showsPrec :: Int -> Direction -> ShowS # show :: Direction -> String # showList :: [Direction] -> ShowS #
Eq Direction
Instance details Defined in Numeric.LinearProgramming.Common Methods (==) :: Direction -> Direction -> Bool # (/=) :: Direction -> Direction -> Bool #

data PlusMinusOne Source #

Constructors

MinusOne
PlusOne

Instances

Instances details

Show PlusMinusOne Source #
Instance details Defined in Numeric.COINOR.CLP Methods showsPrec :: Int -> PlusMinusOne -> ShowS # show :: PlusMinusOne -> String # showList :: [PlusMinusOne] -> ShowS #
Eq PlusMinusOne Source #
Instance details Defined in Numeric.COINOR.CLP Methods (==) :: PlusMinusOne -> PlusMinusOne -> Bool # (/=) :: PlusMinusOne -> PlusMinusOne -> Bool #

data Term a ix #

Constructors

Term a ix

Instances

Instances details

(Show a, Show ix) => Show (Term a ix)
Instance details Defined in Numeric.LinearProgramming.Common Methods showsPrec :: Int -> Term a ix -> ShowS # show :: Term a ix -> String # showList :: [Term a ix] -> ShowS #

(.*) :: a -> ix -> Term a ix infix 7 #

type Constraints a ix = [Inequality [Term a ix]] #

free :: x -> Inequality x #

(<=.) :: x -> Double -> Inequality x infix 4 #

(>=.) :: x -> Double -> Inequality x infix 4 #

(==.) :: x -> Double -> Inequality x infix 4 #

(>=<.) :: x -> (Double, Double) -> Inequality x infix 4 #

data Method Source #

dual :: Method Source #

primal :: Method Source #

initialSolve :: Method Source #

initialDualSolve :: Method Source #

initialPrimalSolve :: Method Source #

initialBarrierSolve :: Method Source #

initialBarrierNoCrossSolve :: Method Source #

data FailureType Source #

Constructors

PrimalInfeasible
DualInfeasible
StoppedOnIterations
StoppedDueToErrors

Instances

Instances details

Show FailureType Source #
Instance details Defined in Numeric.COINOR.CLP.Private Methods showsPrec :: Int -> FailureType -> ShowS # show :: FailureType -> String # showList :: [FailureType] -> ShowS #
Eq FailureType Source #
Instance details Defined in Numeric.COINOR.CLP.Private Methods (==) :: FailureType -> FailureType -> Bool # (/=) :: FailureType -> FailureType -> Bool #

type Result sh = Either FailureType (Double, Array sh Double) Source #