Documentation

>>> 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))

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