Math.ExpPairs.LinearForm

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

Methods

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

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

Foldable 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)

Methods

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

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

Num t => Num (LinearForm t)

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)

Methods

showsPrec :: Int -> LinearForm t -> ShowS

show :: LinearForm t -> String

showList :: [LinearForm t] -> ShowS

Generic (LinearForm t)

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)

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)

Methods

mempty :: LinearForm t

mappend :: LinearForm t -> LinearForm t -> LinearForm t

mconcat :: [LinearForm t] -> LinearForm t

NFData t => NFData (LinearForm t)

Methods

rnf :: LinearForm t -> ()

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

Methods

pretty :: LinearForm t -> Doc ann

prettyList :: [LinearForm t] -> Doc ann

type Rep (LinearForm t)

type Rep (LinearForm t) = D1 * (MetaData "LinearForm" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-Gtd6e9LEtfhDqv5Iz3ymUo" False) (C1 * (MetaCons "LinearForm" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * t)) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * t)) (S1 * (MetaSel (Nothing 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

Methods

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

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

Foldable RationalForm

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)

Methods

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

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

Num t => Fractional (RationalForm t)

Methods

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

recip :: RationalForm t -> RationalForm t

fromRational :: Rational -> RationalForm t

Num t => Num (RationalForm t)

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)

Methods

showsPrec :: Int -> RationalForm t -> ShowS

show :: RationalForm t -> String

showList :: [RationalForm t] -> ShowS

Generic (RationalForm t)

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)

Methods

rnf :: RationalForm t -> ()

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

Methods

pretty :: RationalForm t -> Doc ann

prettyList :: [RationalForm t] -> Doc ann

type Rep (RationalForm t)

type Rep (RationalForm t) = D1 * (MetaData "RationalForm" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-Gtd6e9LEtfhDqv5Iz3ymUo" False) (C1 * (MetaCons ":/:" (InfixI NotAssociative 5) False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (LinearForm t))) (S1 * (MetaSel (Nothing 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

Methods

minBound :: IneqType

maxBound :: IneqType

Enum IneqType

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

Methods

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

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

Ord IneqType

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

Methods

showsPrec :: Int -> IneqType -> ShowS

show :: IneqType -> String

showList :: [IneqType] -> ShowS

Generic IneqType

Associated Types

type Rep IneqType :: * -> *

Methods

from :: IneqType -> Rep IneqType x

to :: Rep IneqType x -> IneqType

Pretty IneqType

Methods

pretty :: IneqType -> Doc ann

prettyList :: [IneqType] -> Doc ann

type Rep IneqType

type Rep IneqType = D1 * (MetaData "IneqType" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-Gtd6e9LEtfhDqv5Iz3ymUo" 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

Methods

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

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

Foldable Constraint

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)

Methods

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

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

Show t => Show (Constraint t)

Methods

showsPrec :: Int -> Constraint t -> ShowS

show :: Constraint t -> String

showList :: [Constraint t] -> ShowS

Generic (Constraint t)

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)

Methods

rnf :: Constraint t -> ()

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

Methods

pretty :: Constraint t -> Doc ann

prettyList :: [Constraint t] -> Doc ann

type Rep (Constraint t)

type Rep (Constraint t) = D1 * (MetaData "Constraint" "Math.ExpPairs.LinearForm" "exp-pairs-0.1.6.0-Gtd6e9LEtfhDqv5Iz3ymUo" False) (C1 * (MetaCons "Constraint" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * (LinearForm t))) (S1 * (MetaSel (Nothing 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.