Copyright	(c) Andrew Lelechenko 2014-2015
License	GPL-3
Maintainer	andrew.lelechenko@gmail.com
Stability	experimental
Portability	POSIX
Safe Haskell	Safe
Language	Haskell2010

Math.ExpPairs.LinearForm

Description

Provides types for rational forms (to hold objective functions in Math.ExpPairs) and linear contraints (to hold constraints of optimization). Both of them are built atop of projective linear forms.

Synopsis

data LinearForm t = LinearForm !t !t !t
scaleLF :: (Num t, Eq t) => t -> LinearForm t -> LinearForm t
evalLF :: Num t => (t, t, t) -> LinearForm t -> t
substituteLF :: (Eq t, Num t) => (LinearForm t, LinearForm t, LinearForm t) -> LinearForm t -> LinearForm t
data RationalForm t = (LinearForm t) :/: (LinearForm t)
evalRF :: Real t => (Integer, Integer, Integer) -> RationalForm t -> RationalInf
data IneqType
- = Strict
- | NonStrict
data Constraint t = Constraint !(LinearForm t) !IneqType
checkConstraint :: (Num t, Ord t) => (Integer, Integer, Integer) -> Constraint t -> Bool

Documentation

data LinearForm t #

Define an affine linear form of three variables: a*k + b*l + c*m. First argument of LinearForm stands for a, second for b and third for c. Linear forms form a monoid by addition.

Constructors

LinearForm !t !t !t

Instances

Functor LinearForm #
Instance details Defined in Math.ExpPairs.LinearForm Methods fmap :: (a -> b) -> LinearForm a -> LinearForm b # (<$) :: a -> LinearForm b -> LinearForm a #
Foldable LinearForm #
Instance details Defined in Math.ExpPairs.LinearForm Methods fold :: Monoid m => LinearForm m -> m # foldMap :: Monoid m => (a -> m) -> LinearForm a -> m # foldr :: (a -> b -> b) -> b -> LinearForm a -> b # foldr' :: (a -> b -> b) -> b -> LinearForm a -> b # foldl :: (b -> a -> b) -> b -> LinearForm a -> b # foldl' :: (b -> a -> b) -> b -> LinearForm a -> b # foldr1 :: (a -> a -> a) -> LinearForm a -> a # foldl1 :: (a -> a -> a) -> LinearForm a -> a # toList :: LinearForm a -> [a] # null :: LinearForm a -> Bool # length :: LinearForm a -> Int # elem :: Eq a => a -> LinearForm a -> Bool # maximum :: Ord a => LinearForm a -> a # minimum :: Ord a => LinearForm a -> a # sum :: Num a => LinearForm a -> a # product :: Num a => LinearForm a -> a #
Eq t => Eq (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (==) :: LinearForm t -> LinearForm t -> Bool # (/=) :: LinearForm t -> LinearForm t -> Bool #
Num t => Num (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (+) :: LinearForm t -> LinearForm t -> LinearForm t # (-) :: LinearForm t -> LinearForm t -> LinearForm t # (*) :: LinearForm t -> LinearForm t -> LinearForm t # negate :: LinearForm t -> LinearForm t # abs :: LinearForm t -> LinearForm t # signum :: LinearForm t -> LinearForm t # fromInteger :: Integer -> LinearForm t #
Show t => Show (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods showsPrec :: Int -> LinearForm t -> ShowS # show :: LinearForm t -> String # showList :: [LinearForm t] -> ShowS #
Generic (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Associated Types type Rep (LinearForm t) :: * -> * # Methods from :: LinearForm t -> Rep (LinearForm t) x # to :: Rep (LinearForm t) x -> LinearForm t #
Num t => Semigroup (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (<>) :: LinearForm t -> LinearForm t -> LinearForm t # sconcat :: NonEmpty (LinearForm t) -> LinearForm t # stimes :: Integral b => b -> LinearForm t -> LinearForm t #
Num t => Monoid (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods mempty :: LinearForm t # mappend :: LinearForm t -> LinearForm t -> LinearForm t # mconcat :: [LinearForm t] -> LinearForm t #
NFData t => NFData (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods rnf :: LinearForm t -> () #
(Num t, Eq t, Pretty t) => Pretty (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods pretty :: LinearForm t -> Doc ann # prettyList :: [LinearForm t] -> Doc ann #
type Rep (LinearForm t) #
Instance details Defined in Math.ExpPairs.LinearForm type Rep (LinearForm t) = D1 (MetaData "LinearForm" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-A57bvNSkfW36XePlDuMIT4" False) (C1 (MetaCons "LinearForm" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 t) :: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 t) :: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 t))))

scaleLF :: (Num t, Eq t) => t -> LinearForm t -> LinearForm t #

Multiply a linear form by a given coefficient.

evalLF :: Num t => (t, t, t) -> LinearForm t -> t #

Evaluate a linear form a*k + b*l + c*m for given k, l and m.

substituteLF :: (Eq t, Num t) => (LinearForm t, LinearForm t, LinearForm t) -> LinearForm t -> LinearForm t #

Substitute linear forms k, l and m into a given linear form a*k + b*l + c*m to obtain a new linear form.

data RationalForm t #

Define a rational form of two variables, equal to the ratio of two LinearForm.

Constructors

(LinearForm t) :/: (LinearForm t) infix 5

Instances

Functor RationalForm #
Instance details Defined in Math.ExpPairs.LinearForm Methods fmap :: (a -> b) -> RationalForm a -> RationalForm b # (<$) :: a -> RationalForm b -> RationalForm a #
Foldable RationalForm #
Instance details Defined in Math.ExpPairs.LinearForm Methods fold :: Monoid m => RationalForm m -> m # foldMap :: Monoid m => (a -> m) -> RationalForm a -> m # foldr :: (a -> b -> b) -> b -> RationalForm a -> b # foldr' :: (a -> b -> b) -> b -> RationalForm a -> b # foldl :: (b -> a -> b) -> b -> RationalForm a -> b # foldl' :: (b -> a -> b) -> b -> RationalForm a -> b # foldr1 :: (a -> a -> a) -> RationalForm a -> a # foldl1 :: (a -> a -> a) -> RationalForm a -> a # toList :: RationalForm a -> [a] # null :: RationalForm a -> Bool # length :: RationalForm a -> Int # elem :: Eq a => a -> RationalForm a -> Bool # maximum :: Ord a => RationalForm a -> a # minimum :: Ord a => RationalForm a -> a # sum :: Num a => RationalForm a -> a # product :: Num a => RationalForm a -> a #
Eq t => Eq (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (==) :: RationalForm t -> RationalForm t -> Bool # (/=) :: RationalForm t -> RationalForm t -> Bool #
Num t => Fractional (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (/) :: RationalForm t -> RationalForm t -> RationalForm t # recip :: RationalForm t -> RationalForm t # fromRational :: Rational -> RationalForm t #
Num t => Num (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (+) :: RationalForm t -> RationalForm t -> RationalForm t # (-) :: RationalForm t -> RationalForm t -> RationalForm t # (*) :: RationalForm t -> RationalForm t -> RationalForm t # negate :: RationalForm t -> RationalForm t # abs :: RationalForm t -> RationalForm t # signum :: RationalForm t -> RationalForm t # fromInteger :: Integer -> RationalForm t #
Show t => Show (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods showsPrec :: Int -> RationalForm t -> ShowS # show :: RationalForm t -> String # showList :: [RationalForm t] -> ShowS #
Generic (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Associated Types type Rep (RationalForm t) :: * -> * # Methods from :: RationalForm t -> Rep (RationalForm t) x # to :: Rep (RationalForm t) x -> RationalForm t #
NFData t => NFData (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods rnf :: RationalForm t -> () #
(Num t, Eq t, Pretty t) => Pretty (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods pretty :: RationalForm t -> Doc ann # prettyList :: [RationalForm t] -> Doc ann #
type Rep (RationalForm t) #
Instance details Defined in Math.ExpPairs.LinearForm type Rep (RationalForm t) = D1 (MetaData "RationalForm" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-A57bvNSkfW36XePlDuMIT4" False) (C1 (MetaCons ":/:" (InfixI NotAssociative 5) False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (LinearForm t)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (LinearForm t))))

evalRF :: Real t => (Integer, Integer, Integer) -> RationalForm t -> RationalInf #

Evaluate a rational form (a*k + b*l + c*m) / (a'*k + b'*l + c'*m) for given k, l and m.

data IneqType #

Constants to specify the strictness of Constraint.

Constructors

Strict	Strict inequality (>0).
NonStrict	Non-strict inequality (≥0).

Instances

Bounded IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Methods minBound :: IneqType # maxBound :: IneqType #
Enum IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Methods succ :: IneqType -> IneqType # pred :: IneqType -> IneqType # toEnum :: Int -> IneqType # fromEnum :: IneqType -> Int # enumFrom :: IneqType -> [IneqType] # enumFromThen :: IneqType -> IneqType -> [IneqType] # enumFromTo :: IneqType -> IneqType -> [IneqType] # enumFromThenTo :: IneqType -> IneqType -> IneqType -> [IneqType] #
Eq IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Methods (==) :: IneqType -> IneqType -> Bool # (/=) :: IneqType -> IneqType -> Bool #
Ord IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Methods compare :: IneqType -> IneqType -> Ordering # (<) :: IneqType -> IneqType -> Bool # (<=) :: IneqType -> IneqType -> Bool # (>) :: IneqType -> IneqType -> Bool # (>=) :: IneqType -> IneqType -> Bool # max :: IneqType -> IneqType -> IneqType # min :: IneqType -> IneqType -> IneqType #
Show IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Methods showsPrec :: Int -> IneqType -> ShowS # show :: IneqType -> String # showList :: [IneqType] -> ShowS #
Generic IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Associated Types type Rep IneqType :: * -> * # Methods from :: IneqType -> Rep IneqType x # to :: Rep IneqType x -> IneqType #
Pretty IneqType #
Instance details Defined in Math.ExpPairs.LinearForm Methods pretty :: IneqType -> Doc ann # prettyList :: [IneqType] -> Doc ann #
type Rep IneqType #
Instance details Defined in Math.ExpPairs.LinearForm type Rep IneqType = D1 (MetaData "IneqType" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-A57bvNSkfW36XePlDuMIT4" False) (C1 (MetaCons "Strict" PrefixI False) (U1 :: * -> ) :+: C1 (MetaCons "NonStrict" PrefixI False) (U1 :: -> *))

data Constraint t #

A linear constraint of two variables.

Constructors

Constraint !(LinearForm t) !IneqType

Instances

Functor Constraint #
Instance details Defined in Math.ExpPairs.LinearForm Methods fmap :: (a -> b) -> Constraint a -> Constraint b # (<$) :: a -> Constraint b -> Constraint a #
Foldable Constraint #
Instance details Defined in Math.ExpPairs.LinearForm Methods fold :: Monoid m => Constraint m -> m # foldMap :: Monoid m => (a -> m) -> Constraint a -> m # foldr :: (a -> b -> b) -> b -> Constraint a -> b # foldr' :: (a -> b -> b) -> b -> Constraint a -> b # foldl :: (b -> a -> b) -> b -> Constraint a -> b # foldl' :: (b -> a -> b) -> b -> Constraint a -> b # foldr1 :: (a -> a -> a) -> Constraint a -> a # foldl1 :: (a -> a -> a) -> Constraint a -> a # toList :: Constraint a -> [a] # null :: Constraint a -> Bool # length :: Constraint a -> Int # elem :: Eq a => a -> Constraint a -> Bool # maximum :: Ord a => Constraint a -> a # minimum :: Ord a => Constraint a -> a # sum :: Num a => Constraint a -> a # product :: Num a => Constraint a -> a #
Eq t => Eq (Constraint t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods (==) :: Constraint t -> Constraint t -> Bool # (/=) :: Constraint t -> Constraint t -> Bool #
Show t => Show (Constraint t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods showsPrec :: Int -> Constraint t -> ShowS # show :: Constraint t -> String # showList :: [Constraint t] -> ShowS #
Generic (Constraint t) #
Instance details Defined in Math.ExpPairs.LinearForm Associated Types type Rep (Constraint t) :: * -> * # Methods from :: Constraint t -> Rep (Constraint t) x # to :: Rep (Constraint t) x -> Constraint t #
NFData t => NFData (Constraint t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods rnf :: Constraint t -> () #
(Num t, Eq t, Pretty t) => Pretty (Constraint t) #
Instance details Defined in Math.ExpPairs.LinearForm Methods pretty :: Constraint t -> Doc ann # prettyList :: [Constraint t] -> Doc ann #
type Rep (Constraint t) #
Instance details Defined in Math.ExpPairs.LinearForm type Rep (Constraint t) = D1 (MetaData "Constraint" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-A57bvNSkfW36XePlDuMIT4" False) (C1 (MetaCons "Constraint" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (LinearForm t)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 IneqType)))

checkConstraint :: (Num t, Ord t) => (Integer, Integer, Integer) -> Constraint t -> Bool #

Evaluate a rational form of constraint and compare its value with 0. Strictness depends on the given IneqType.