Copyright	(c) David Janin, 2016
License	see the LICENSE file in the distribution
Maintainer	janin@labri.fr
Stability	experimental
Safe Haskell	Safe
Language	Haskell2010

Duration.Affine

Description

An implementation of multi-variable linear polynoms. Associated partial order when variables are always assumed to have stricly positive values. This can also be seen as an algebra of (positive) delays with unknows.

Warning : the num and fractional instances are there for notational convinience. In order to stay within affine functions, the product fails over two non constant functions and teh inverse fails over a non constant function.

Synopsis

Documentation

data Affine d i Source #

Affine functions over a numeric space d and a set of variable index i.

Constructors

Affine !d ![(d, i)]

Instances

(Num d, Ord d, Ord i) => Eq (Affine d i) Source #	Semantical equality
Methods (==) :: Affine d i -> Affine d i -> Bool # (/=) :: Affine d i -> Affine d i -> Bool #
(Fractional d, Eq d, Ord i) => Fractional (Affine d i) Source #	For syntactic confort (with partially defined inverse)
Methods (/) :: Affine d i -> Affine d i -> Affine d i # recip :: Affine d i -> Affine d i # fromRational :: Rational -> Affine d i #
(Num d, Eq d, Ord i) => Num (Affine d i) Source #	For syntactic confort (with partially defined product)
Methods (+) :: Affine d i -> Affine d i -> Affine d i # (-) :: Affine d i -> Affine d i -> Affine d i # (*) :: Affine d i -> Affine d i -> Affine d i # negate :: Affine d i -> Affine d i # abs :: Affine d i -> Affine d i # signum :: Affine d i -> Affine d i # fromInteger :: Integer -> Affine d i #
(Num d, Ord d, Ord i) => Ord (Affine d i) Source #	Total order with possible error
Methods compare :: Affine d i -> Affine d i -> Ordering # (<) :: Affine d i -> Affine d i -> Bool # (<=) :: Affine d i -> Affine d i -> Bool # (>) :: Affine d i -> Affine d i -> Bool # (>=) :: Affine d i -> Affine d i -> Bool # max :: Affine d i -> Affine d i -> Affine d i # min :: Affine d i -> Affine d i -> Affine d i #
(Show d, Show i) => Show (Affine d i) Source #
Methods showsPrec :: Int -> Affine d i -> ShowS # show :: Affine d i -> String # showList :: [Affine d i] -> ShowS #
(Num d, Ord d, Ord i) => POrd (Affine d i) Source #	Semantical partial order (with positive variables)
Methods partialCompare :: Affine d i -> Affine d i -> Maybe Ordering Source # pLeq :: Affine d i -> Affine d i -> Bool Source # pOrdEq :: Affine d i -> Affine d i -> Bool Source # pOrdMin :: [Affine d i] -> Maybe (Affine d i) Source # pOrdMax :: [Affine d i] -> Maybe (Affine d i) Source # pOrdReduceMin :: [Affine d i] -> [Affine d i] Source # pOrdReduceMax :: [Affine d i] -> [Affine d i] Source #

affineFromID :: Num d => i -> Affine d i Source #

Creates the one variable affine function (X_i) from index i.

affineFromConst :: d -> Affine d i Source #

Creates the constant affine function (d) from value d.

shiftAffine :: (Eq d, Num d, Ord i) => d -> Affine d i -> Affine d i Source #

Replaces any variable X by X + d

setToZeroAffine :: (Num d, Ord i) => [i] -> Affine d i -> Affine d i Source #

Sets variables Xi with i in the list to zero

evalAffine :: (Eq d, Num d, Ord i) => d -> Affine d i -> Affine d i Source #

Evals an affine function on a point (for debug)

getNextKnownDelay :: (Eq d, Num d) => Affine d i -> Maybe d Source #

Gets the greatest stricly positive constant lower than an affine returns Nothing if its 0 error if there is no such value