Math.ExpPairs.LinearForm

Linear forms, rational forms and constraints

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.

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

Defined in Math.ExpPairs.LinearForm

Methods

fmap :: (a -> b) -> LinearForm a -> LinearForm b

(<$) :: a -> LinearForm b -> LinearForm a

Foldable LinearForm

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

Traversable LinearForm

Defined in Math.ExpPairs.LinearForm

Methods

traverse :: Applicative f => (a -> f b) -> LinearForm a -> f (LinearForm b)

sequenceA :: Applicative f => LinearForm (f a) -> f (LinearForm a)

mapM :: Monad m => (a -> m b) -> LinearForm a -> m (LinearForm b)

sequence :: Monad m => LinearForm (m a) -> m (LinearForm a)

Eq t => Eq (LinearForm t)

Defined in Math.ExpPairs.LinearForm

Methods

(==) :: LinearForm t -> LinearForm t -> Bool

(/=) :: LinearForm t -> LinearForm t -> Bool

Num t => Num (LinearForm t)

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)

Defined in Math.ExpPairs.LinearForm

Methods

showsPrec :: Int -> LinearForm t -> ShowS

show :: LinearForm t -> String

showList :: [LinearForm t] -> ShowS

Generic (LinearForm t)

Defined in Math.ExpPairs.LinearForm

Associated Types

type Rep (LinearForm t) :: Type -> Type

Methods

from :: LinearForm t -> Rep (LinearForm t) x

to :: Rep (LinearForm t) x -> LinearForm t

Num t => Semigroup (LinearForm t)

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)

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)

Defined in Math.ExpPairs.LinearForm

Methods

rnf :: LinearForm t -> ()

(Num t, Eq t, Pretty t) => Pretty (LinearForm t)

Defined in Math.ExpPairs.LinearForm

Methods

pretty :: LinearForm t -> Doc ann

prettyList :: [LinearForm t] -> Doc ann

type Rep (LinearForm t)

Defined in Math.ExpPairs.LinearForm

type Rep (LinearForm t) = D1 (MetaData "LinearForm" "Math.ExpPairs.LinearForm" "exp-pairs-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" 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

Defined in Math.ExpPairs.LinearForm

Methods

fmap :: (a -> b) -> RationalForm a -> RationalForm b

(<$) :: a -> RationalForm b -> RationalForm a

Foldable RationalForm

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

Traversable RationalForm

Defined in Math.ExpPairs.LinearForm

Methods

traverse :: Applicative f => (a -> f b) -> RationalForm a -> f (RationalForm b)

sequenceA :: Applicative f => RationalForm (f a) -> f (RationalForm a)

mapM :: Monad m => (a -> m b) -> RationalForm a -> m (RationalForm b)

sequence :: Monad m => RationalForm (m a) -> m (RationalForm a)

Eq t => Eq (RationalForm t)

Defined in Math.ExpPairs.LinearForm

Methods

(==) :: RationalForm t -> RationalForm t -> Bool

(/=) :: RationalForm t -> RationalForm t -> Bool

Num t => Fractional (RationalForm t)

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)

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)

Defined in Math.ExpPairs.LinearForm

Methods

showsPrec :: Int -> RationalForm t -> ShowS

show :: RationalForm t -> String

showList :: [RationalForm t] -> ShowS

Generic (RationalForm t)

Defined in Math.ExpPairs.LinearForm

Associated Types

type Rep (RationalForm t) :: Type -> Type

Methods

from :: RationalForm t -> Rep (RationalForm t) x

to :: Rep (RationalForm t) x -> RationalForm t

NFData t => NFData (RationalForm t)

Defined in Math.ExpPairs.LinearForm

Methods

rnf :: RationalForm t -> ()

(Num t, Eq t, Pretty t) => Pretty (RationalForm t)

Defined in Math.ExpPairs.LinearForm

Methods

pretty :: RationalForm t -> Doc ann

prettyList :: [RationalForm t] -> Doc ann

type Rep (RationalForm t)

Defined in Math.ExpPairs.LinearForm

type Rep (RationalForm t) = D1 (MetaData "RationalForm" "Math.ExpPairs.LinearForm" "exp-pairs-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" 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

Defined in Math.ExpPairs.LinearForm

Methods

minBound :: IneqType

maxBound :: IneqType

Enum IneqType

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

Defined in Math.ExpPairs.LinearForm

Methods

(==) :: IneqType -> IneqType -> Bool

(/=) :: IneqType -> IneqType -> Bool

Ord IneqType

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

Defined in Math.ExpPairs.LinearForm

Methods

showsPrec :: Int -> IneqType -> ShowS

show :: IneqType -> String

showList :: [IneqType] -> ShowS

Generic IneqType

Defined in Math.ExpPairs.LinearForm

Associated Types

type Rep IneqType :: Type -> Type

Methods

from :: IneqType -> Rep IneqType x

to :: Rep IneqType x -> IneqType

Pretty IneqType

Defined in Math.ExpPairs.LinearForm

Methods

pretty :: IneqType -> Doc ann

prettyList :: [IneqType] -> Doc ann

type Rep IneqType

Defined in Math.ExpPairs.LinearForm

type Rep IneqType = D1 (MetaData "IneqType" "Math.ExpPairs.LinearForm" "exp-pairs-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" False) (C1 (MetaCons "Strict" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "NonStrict" PrefixI False) (U1 :: Type -> Type))

data Constraint t

A linear constraint of two variables.

Constructors

Constraint !(LinearForm t) !IneqType

Instances

Functor Constraint

Defined in Math.ExpPairs.LinearForm

Methods

fmap :: (a -> b) -> Constraint a -> Constraint b

(<$) :: a -> Constraint b -> Constraint a

Foldable Constraint

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

Traversable Constraint

Defined in Math.ExpPairs.LinearForm

Methods

traverse :: Applicative f => (a -> f b) -> Constraint a -> f (Constraint b)

sequenceA :: Applicative f => Constraint (f a) -> f (Constraint a)

mapM :: Monad m => (a -> m b) -> Constraint a -> m (Constraint b)

sequence :: Monad m => Constraint (m a) -> m (Constraint a)

Eq t => Eq (Constraint t)

Defined in Math.ExpPairs.LinearForm

Methods

(==) :: Constraint t -> Constraint t -> Bool

(/=) :: Constraint t -> Constraint t -> Bool

Show t => Show (Constraint t)

Defined in Math.ExpPairs.LinearForm

Methods

showsPrec :: Int -> Constraint t -> ShowS

show :: Constraint t -> String

showList :: [Constraint t] -> ShowS

Generic (Constraint t)

Defined in Math.ExpPairs.LinearForm

Associated Types

type Rep (Constraint t) :: Type -> Type

Methods

from :: Constraint t -> Rep (Constraint t) x

to :: Rep (Constraint t) x -> Constraint t

NFData t => NFData (Constraint t)

Defined in Math.ExpPairs.LinearForm

Methods

rnf :: Constraint t -> ()

(Num t, Eq t, Pretty t) => Pretty (Constraint t)

Defined in Math.ExpPairs.LinearForm

Methods

pretty :: Constraint t -> Doc ann

prettyList :: [Constraint t] -> Doc ann

type Rep (Constraint t)

Defined in Math.ExpPairs.LinearForm

type Rep (Constraint t) = D1 (MetaData "Constraint" "Math.ExpPairs.LinearForm" "exp-pairs-0.2.1.0-J4IGbuSTVwXCgBqjoU0P5n" 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.