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Added lots of comments to the solveConstraints function and made a few trivial tweaks

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This commit is contained in:
Neil Brown 2007-12-12 18:04:46 +00:00
parent 8d2751439b
commit 9082e5c887
1 changed files with 28 additions and 7 deletions
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35
transformations/ArrayUsageCheck.hs
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@ -67,8 +67,11 @@ type EqualityProblem = [EqualityConstraintEquation]
type InequalityConstraintEquation = Array CoeffIndex Integer
type InequalityProblem = [InequalityConstraintEquation]
type StIneq = StateT InequalityProblem Maybe
-- | Solves all the constraints in the Equality Problem (taking them to be == 0),
-- and transforms the InequalityProblems appropriately.
-- TODO the function currently doesn't record the relation between the transformed variables
-- (e.g. sigma for x_k) and the original variables (x_k). In order to feed back useful
-- information to the user, we should do this at some point in future.
solveConstraints :: EqualityProblem -> InequalityProblem -> Maybe InequalityProblem
solveConstraints p ineq
= normaliseEq p >>= (\p' -> execStateT (solve p') ineq)
@ -95,12 +98,19 @@ solveConstraints p ineq
solve [] = return ()
solve p = (solveUnits p >>* removeRedundant) >>= liftF checkFalsifiable >>= solveNext >>= solve
-- | Checks if any of the coefficients in the equation have an absolute value of 1.
-- Returns either Just <the first such coefficient> or Nothing (there are no such coefficients in the equation).
-- This function only looks at a_1 .. a_n. That is, a_0 is ignored.
checkForUnit :: EqualityConstraintEquation -> Maybe CoeffIndex
checkForUnit = listToMaybe . map fst . filter coeffAbsVal1 . tail . assocs
where
coeffAbsVal1 :: (a, Integer) -> Bool
coeffAbsVal1 (_,x) = (abs x) == 1
-- | Finds the first unit coefficient (|a_k| == 1) in a set of equality constraints.
-- Returns Nothing if there are no unit coefficients. Otherwise it returns
-- (Just (equation, indexOfUnitCoeff), otherEquations); that is, the specified equation is not
-- present in the list of equations.
findFirstUnit :: EqualityProblem -> (Maybe (EqualityConstraintEquation,CoeffIndex),EqualityProblem)
findFirstUnit [] = (Nothing,[])
findFirstUnit (e:es) = case checkForUnit e of
@ -108,6 +118,11 @@ solveConstraints p ineq
Nothing -> let (me,es') = findFirstUnit es in (me,e:es')
-- | Substitutes a value for x_k into an equation. Given k, the value for x_k in terms
-- of coefficients of other variables (let's call it x_k_val), it subsitutes this into
-- all the equations in the list by adding x_k_val (scaled by a_k) to each equation and
-- then zeroing out the a_k value. Note that the (x_k_val ! k) value will be ignored;
-- it should be zero, in any case (otherwise x_k would be defined in terms of itself!).
substIn :: CoeffIndex -> Array CoeffIndex Integer -> EqualityProblem -> EqualityProblem
substIn k x_k_val = map substIn'
where
@ -115,6 +130,7 @@ solveConstraints p ineq
where
scaled_x_k_val = amap (* (eq ! k)) x_k_val
-- | Solves (i.e. removes by substitution) all unit coefficients in the given list of equations.
solveUnits :: EqualityProblem -> StateT InequalityProblem Maybe EqualityProblem
solveUnits p
= case findFirstUnit p of
@ -137,12 +153,15 @@ solveConstraints p ineq
| origVal == 1 = negate -- Original coeff was 1; negate
| otherwise = id -- Original coeff was -1; don't do anything
-- | Finds the coefficient with the smallest absolute value of a_1 .. a_n (i.e. not a_0)
-- that is non-zero (i.e. zero coefficients are ignored).
findSmallestAbsCoeff :: EqualityConstraintEquation -> CoeffIndex
findSmallestAbsCoeff = fst. minimumBy (cmpAbsSnd) . filter ((/= 0) . snd) . tail . assocs
findSmallestAbsCoeff = fst . minimumBy cmpAbsSnd . filter ((/= 0) . snd) . tail . assocs
where
cmpAbsSnd :: (a,Integer) -> (a,Integer) -> Ordering
cmpAbsSnd (_,x) (_,y) = compare (abs x) (abs y)
-- | Solves the next equality and returns the new set of equalities.
solveNext :: EqualityProblem -> StateT InequalityProblem Maybe EqualityProblem
solveNext [] = return []
solveNext (e:es) = -- We transform the kth variable into sigma, effectively
@ -151,19 +170,21 @@ solveConstraints p ineq
-- that the multiple of sigma is added on properly)
modify (map alterEquation) >> (lift $ (normaliseEq . map alterEquation) (e:es))
where
-- | Adds a scaled version of x_k_eq onto the current equation, after zeroing out
-- the a_k coefficient in the current equation.
alterEquation :: EqualityConstraintEquation -> EqualityConstraintEquation
alterEquation eq = arrayZipWith (+) (eq // [(k,0)]) (amap (\x -> x * (eq ! k)) x_k_eq)
k = findSmallestAbsCoeff e
a_k = e ! k
m = (abs a_k) + 1
sign_a_k = signum a_k
x_k_eq = amap (\a_i -> sign_a_k * (a_i `mymod` m)) e // [(k,(- sign_a_k) * m)]
-- I think this is probably equivalent to mod, but let's follow the maths:
mymod :: Integer -> Integer -> Integer
mymod x y = x - (y * (floordivplushalf x y))
-- This is floor (x/y + 1/2). Probably a way to do it without reverting to float arithmetic:
floordivplushalf :: Integer -> Integer -> Integer
floordivplushalf x y = floor ((fromInteger x / fromInteger y) + (0.5 :: Double))