module Math.ExpPairs.LinearForm
( LinearForm (..)
, evalLF
, substituteLF
, RationalForm (..)
, evalRF
, IneqType (..)
, Constraint (..)
, checkConstraint
) where
import Control.DeepSeq
import Data.Foldable (Foldable (..), toList)
import Data.List (intercalate)
import Data.Ratio (numerator, denominator)
import Data.Monoid (Monoid, mempty, mappend)
import GHC.Generics (Generic (..))
import Math.ExpPairs.RatioInf
data LinearForm t = LinearForm t t t
deriving (Eq, Functor, Foldable, Generic)
instance NFData t => NFData (LinearForm t) where
rnf = rnf . toList
instance (Num t, Eq t, Show t) => Show (LinearForm t) where
show (LinearForm a b c) = if (a==0) && (b==0) && (c==0)
then "0"
else "(" ++ intercalate " + " (filter (/=[]) $
[if a/= 0 then show a ++ "k" else []] ++
[if b/= 0 then show b ++ "l" else []] ++
[if c/= 0 then show c ++ "m" else []] ) ++ ")"
instance Num t => Num (LinearForm t) where
(LinearForm a b c) + (LinearForm d e f) = LinearForm (a+d) (b+e) (c+f)
(*) = error "Multiplication of LinearForm is undefined"
negate = fmap negate
abs = error "Absolute value of LinearForm is undefined"
signum = error "Signum of LinearForm is undefined"
fromInteger n = LinearForm 0 0 (fromInteger n)
instance Num t => Monoid (LinearForm t) where
mempty = 0
mappend = (+)
scaleLF :: (Num t, Eq t) => t -> LinearForm t -> LinearForm t
scaleLF 0 = const 0
scaleLF s = fmap (* s)
evalLF :: Num t => (t, t, t) -> LinearForm t -> t
evalLF (k, l, m) (LinearForm a b c) = a * k + l * b + m * c
substituteLF :: (Eq t, Num t) => (LinearForm t, LinearForm t, LinearForm t) -> LinearForm t -> LinearForm t
substituteLF (k, l, m) (LinearForm a b c) = scaleLF a k + scaleLF b l + scaleLF c m
data RationalForm t = RationalForm (LinearForm t) (LinearForm t)
deriving (Eq, Show, Functor, Foldable, Generic)
instance NFData t => NFData (RationalForm t) where
rnf = rnf . toList
instance Num t => Num (RationalForm t) where
(+) = error "Addition of RationalForm is undefined"
(*) = error "Multiplication of RationalForm is undefined"
negate (RationalForm a b) = RationalForm (negate a) b
abs = error "Absolute value of RationalForm is undefined"
signum = error "Signum of RationalForm is undefined"
fromInteger n = RationalForm (fromInteger n) 1
instance Num t => Fractional (RationalForm t) where
fromRational r = RationalForm (fromInteger $ numerator r) (fromInteger $ denominator r)
recip (RationalForm a b) = RationalForm b a
mapTriple :: (a -> b) -> (a, a, a) -> (b, b, b)
mapTriple f (x, y, z) = (f x, f y, f z)
evalRF :: (Real t, Num t) => (Integer, Integer, Integer) -> RationalForm t -> RationalInf
evalRF (k, l, m) (RationalForm num den) = if denom==0 then InfPlus else Finite (numer / denom) where
klm = mapTriple fromInteger (k, l, m)
numer = toRational $ evalLF klm num
denom = toRational $ evalLF klm den
data IneqType
= Strict
| NonStrict
deriving (Eq, Ord, Show, Enum, Bounded)
data Constraint t = Constraint (LinearForm t) IneqType
deriving (Eq, Show, Functor, Foldable, Generic)
instance NFData t => NFData (Constraint t) where
rnf (Constraint l i) = i `seq` rnf l
checkConstraint :: (Num t, Eq t) => (Integer, Integer, Integer) -> Constraint t -> Bool
checkConstraint (k, l, m) (Constraint lf ineq)
= if ineq==NonStrict
then signum numer /= 1
else signum numer == 1 where
klm = mapTriple fromInteger (k, l, m)
numer = evalLF klm lf