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https://gitlab.com/sheaf/metabrush.git
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Implement adaptive shaving algorithm
This commit is contained in:
sheaf
parent
01fdd9a126
commit
ced714987e
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@ -110,8 +110,7 @@ main = do
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putStrLn $ unlines
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[ replicate 40 '='
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, "Best time: " ++ show bestTime ++ "s"
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, "Best parameters:"
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--, show (testCuspOptions bestTest)
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, "Best parameters: " ++ show (testName bestTest)
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]
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benchTestCase :: TestCase -> IO Double
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@ -181,9 +180,15 @@ testCases = benchCases
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benchCases :: [ TestCase ]
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benchCases =
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[ ellipseTestCase opts "full" ( 0, 1 ) pi $ defaultStartBoxes [ 2 ] ] -- [ 0 .. 3 ] ]
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where
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opts = defaultRootIsolationOptions
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[ ellipseTestCase opts ("minWidth=" ++ show minWidth ++ ",ε=" ++ show narrowAbs) ( 0, 1 ) pi $ defaultStartBoxes [ 2 ]
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| minWidth <- [ 1e-5 ]
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, narrowAbs <- [ 1e-5, 1e-4, 1e-3, 5e-3, 8e-3, 1e-2, 2e-2, 3e-2, 4e-2, 5e-2, 1e-1 ]
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, let opts =
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RootIsolationOptions
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{ minWidth
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, cuspFindingAlgorithms = defaultRootIsolationAlgorithms minWidth narrowAbs
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}
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]
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--------------------------------------------------------------------------------
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@ -55,7 +55,8 @@ import Data.Semigroup
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import Numeric
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( showFFloat )
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import GHC.TypeNats
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( Nat, KnownNat )
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( Nat, KnownNat
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, type (<=) )
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-- containers
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import Data.Tree
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@ -285,10 +286,10 @@ defaultGaussSeidelOptions =
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defaultBisectionOptions
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:: forall n d
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. BoxCt n d
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. ( 1 <= n, BoxCt n d )
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=> Double -> Double
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-> Box n -> BisectionOptions n d
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defaultBisectionOptions _minWidth _narrowAbs box =
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defaultBisectionOptions minWidth _narrowAbs box =
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BisectionOptions
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{ canHaveSols =
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\ eqs box' ->
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@ -320,21 +321,20 @@ defaultBisectionOptions _minWidth _narrowAbs box =
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-- First, check if the largest dimension is over 10 times larger
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-- than the smallest dimension; if so bisect along that coordinate.
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--
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-- TODO: filter out dimensions smaller than minimum width.
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in case sortOnArg ( width . coordInterval ) datPerCoord of
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[] -> error "dimension 0"
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[] -> error "impossible: dimension 0"
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[Arg _ d] -> (coordIndex d, "")
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Arg w0 _ : ds ->
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let Arg w1 d1 = last ds
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in if w1 >= 10 * w0
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then ( coordIndex d1, "tooWide")
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then ( coordIndex d1, "tooWide" )
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-- Otherwise, pick the dimension with the largest spread = width * Jacobian column norm
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else case sortOnArg ( Dual . spread ) datPerCoord of
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[] -> error "dimension 0"
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Arg _ d : _ ->
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(coordIndex d, "spread")
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else case filter ( not . isTooSmall ) $ sortOnArg ( Dual . spread ) datPerCoord of
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[] -> ( coordIndex d1, "tooWide'" )
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Arg _ d : _ -> ( coordIndex d, "spread" )
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}
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where
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isTooSmall ( Arg ( Dual w ) _ ) = w < minWidth
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{-# INLINEABLE defaultBisectionOptions #-}
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sortOnArg :: Ord b => (a -> b) -> [a] -> [Arg b a]
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@ -494,7 +494,7 @@ bisect canHaveSols ( fallbackDim, why ) box =
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( oks, ("cd = " ++ show i, mid ) )
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Nothing ->
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case bisectInCoord box fallbackDim of
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( mid, (lo, hi) ) ->
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( mid, ( lo, hi ) ) ->
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( [ lo, hi ], ( why, mid ) )
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where
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solsList =
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@ -673,30 +673,27 @@ makeBox2Consistent
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-> Box2Options n d
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-> ( 𝕀ℝ n -> D 1 ( 𝕀ℝ n ) ( 𝕀ℝ d ) )
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-> Box n -> Box n
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makeBox2Consistent minWidth (Box2Options epsEq lambdaMin coordsToNarrow eqsToUse) eqs x0
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makeBox2Consistent minWidth (Box2Options ε_eq λMin coordsToNarrow eqsToUse) eqs x0
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= ( `State.evalState` False ) $ doLoop 0.25 x0
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where
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box1Options :: Box1Options n d
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box1Options = Box1Options epsEq coordsToNarrow eqsToUse
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box1Options = Box1Options ε_eq coordsToNarrow eqsToUse
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doBox1 :: Box n -> [ Box n ]
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doBox1 = makeBox1Consistent minWidth box1Options eqs
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doLoop :: Double -> Box n -> State Bool ( Box n )
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doLoop lambda x = do
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x'' <- forEachDim @n x $ \ i ->
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boundConsistency ( `index` i ) ( set i ) lambda
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doLoop λ x = do
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x'' <- forEachDim @n x $ boundConsistency λ
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modified <- State.get
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let lambda' = if modified then lambda else 0.5 * lambda
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if lambda' < lambdaMin
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let λ' = if modified then λ else 0.5 * λ
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if λ' < λMin
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then return x''
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else do { State.put False ; doLoop lambda' x'' }
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else do { State.put False ; doLoop λ' x'' }
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boundConsistency :: ( Box n -> 𝕀 Double )
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-> ( 𝕀 Double -> Box n -> Box n )
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-> Double -> Box n -> State Bool ( Box n )
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boundConsistency getter setter lambda box = do
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boundConsistency :: Double -> Fin n -> Box n -> State Bool ( Box n )
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boundConsistency λ i box = do
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let x@( 𝕀 x_inf x_sup ) = getter box
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c1 = ( 1 - lambda ) * x_inf + lambda * x_sup
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c2 = lambda * x_inf + ( 1 - lambda ) * x_sup
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c1 = ( 1 - λ ) * x_inf + λ * x_sup
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c2 = λ * x_inf + ( 1 - λ ) * x_sup
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x'_inf =
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case doBox1 ( setter ( 𝕀 x_inf c1 ) box ) of
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[] -> c1
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@ -706,9 +703,12 @@ makeBox2Consistent minWidth (Box2Options epsEq lambdaMin coordsToNarrow eqsToUse
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[] -> c2
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x's -> maximum $ map ( sup . getter ) x's
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x' = 𝕀 x'_inf x'_sup
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when ( width x - width x' >= epsEq ) $
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when ( width x - width x' >= ε_eq ) $
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State.put True
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return $ setter x' box
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where
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getter = ( `index` i )
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setter = set i
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-- | Pre-condition the system \( AX = B \).
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precondition
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@ -779,7 +779,7 @@ leftNarrow :: Double
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-> ( 𝕀 Double -> ( 𝕀 Double, 𝕀 Double ) )
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-> 𝕀 Double
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-> [ 𝕀 Double ]
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leftNarrow eps_equal eps_bisection ff' = left_narrow
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leftNarrow ε_eq ε_bis ff' = left_narrow
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where
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left_narrow ( 𝕀 x_inf x_sup ) =
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go x_sup ( 𝕀 x_inf ( if x_inf == x_sup then x_inf else succFP x_inf ) )
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@ -791,19 +791,18 @@ leftNarrow eps_equal eps_bisection ff' = left_narrow
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else
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let x = 𝕀 ( sup x_left ) x_sup
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( _f_x, f'_x ) = ff' x
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x's = do delta <- f_x_left `extendedDivide` f'_x --f'_x_left
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let x_new = x_left - delta
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x's = do δ <- f_x_left `extendedDivide` f'_x
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let x_new = x_left - δ
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map fst $ x_new `intersect` x
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in
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if | null x's
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-> []
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| ( width x - sum ( map width x's ) ) < eps_equal
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-- TODO: do a check with the relative reduction in size?
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| ( width x - sum ( map width x's ) ) < ε_eq
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-> x's
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| otherwise
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-> do
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x' <- x's
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if sup x' - inf x' < eps_bisection
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if sup x' - inf x' < ε_bis
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then return x'
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else left_narrow =<< bisectI x'
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@ -813,7 +812,7 @@ rightNarrow :: Double
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-> ( 𝕀 Double -> ( 𝕀 Double, 𝕀 Double ) )
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-> 𝕀 Double
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-> [ 𝕀 Double ]
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rightNarrow eps_equal eps_bisection ff' = right_narrow
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rightNarrow ε_eq ε_bis ff' = right_narrow
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where
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right_narrow ( 𝕀 x_inf x_sup ) =
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go x_inf ( 𝕀 ( if x_inf == x_sup then x_sup else prevFP x_sup ) x_sup )
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@ -825,19 +824,18 @@ rightNarrow eps_equal eps_bisection ff' = right_narrow
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else
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let x = 𝕀 x_inf ( inf x_right )
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( _f_x, f'_x ) = ff' x
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x's = do delta <- f_x_right `extendedDivide` f'_x --f'_x_right
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let x_new = x_right - delta
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x's = do δ <- f_x_right `extendedDivide` f'_x
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let x_new = x_right - δ
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map fst $ x_new `intersect` x
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in
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if | null x's
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-> []
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| ( width x - sum ( map width x's ) ) < eps_equal
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-- TODO: do a check with the relative reduction in size?
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| ( width x - sum ( map width x's ) ) < ε_eq
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-> x's
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| otherwise
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-> do
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x' <- x's
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if sup x' - inf x' < eps_bisection
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if sup x' - inf x' < ε_bis
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then return x'
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else right_narrow =<< bisectI x'
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@ -873,25 +871,21 @@ allNarrowingOperators
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-> Box1Options n d
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-> ( 𝕀ℝ n -> D 1 ( 𝕀ℝ n ) ( 𝕀ℝ d ) )
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-> [ Box n -> State Bool [ Box n ] ]
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allNarrowingOperators eps_bis ( Box1Options eps_eq coordsToNarrow eqsToUse ) eqs =
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allNarrowingOperators ε_bis ( Box1Options ε_eq coordsToNarrow eqsToUse ) eqs =
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[ \ cand ->
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let getter = ( `index` coordIndex )
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setter = set coordIndex
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newCands = map ( `setter` cand ) $ narrowFn eps_eq eps_bis ( \ x0 -> fn $ setter x0 cand ) ( getter cand )
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newCands = map ( `setter` cand ) $ narrowFn ( \ box -> ff' coordIndex eqnIndex $ setter box cand ) ( getter cand )
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in do
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when ( ( width ( getter cand ) - sum ( map ( width . getter ) newCands ) ) > eps_eq ) $
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when ( ( width ( getter cand ) - sum ( map ( width . getter ) newCands ) ) > ε_eq ) $
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-- TODO: do a check with the relative reduction in size?
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State.put True
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return newCands
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| narrowFn <- [ leftNarrow, rightNarrow ]
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, ( coordIndex, fn ) <-
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[ ( i, ff' i d )
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| i <- coordsToNarrow
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, d <- eqsToUse
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]
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| narrowFn <- [ leftNarrow ε_eq ε_bis, rightNarrow ε_eq ε_bis ]
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, coordIndex <- coordsToNarrow
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, eqnIndex <- eqsToUse
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]
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where
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ff' :: Fin n -> Fin d -> 𝕀ℝ n -> ( 𝕀 Double, 𝕀 Double )
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ff' i d ts =
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let df = eqs ts
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@ -900,3 +894,86 @@ allNarrowingOperators eps_bis ( Box1Options eps_eq coordsToNarrow eqsToUse ) eqs
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f' = df `monIndex` linearMonomial i
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in ( f `index` d, f' `index` d )
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{-# INLINEABLE allNarrowingOperators #-}
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data AdaptiveShavingOptions
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= AdaptiveShavingOptions
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{ γ_init, σ_good, σ_bad, β_good, β_bad :: !Double
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}
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defaultAdaptiveShavingOptions :: AdaptiveShavingOptions
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defaultAdaptiveShavingOptions =
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AdaptiveShavingOptions
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{ γ_init = 0.25
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, σ_good = 0.25
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, σ_bad = 0.75
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, β_good = 1.5
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, β_bad = 0.7
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}
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-- | Algorithm @lnar_sbc3ag@ (adaptive guessing) from the paper
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-- "Box Consistency through Adaptive Shaving" (Goldsztejn & Goualard, 2010).
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leftShave :: Double
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-> AdaptiveShavingOptions
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-> ( 𝕀 Double -> ( 𝕀 Double, 𝕀 Double ) )
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-> 𝕀 Double
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-> [ 𝕀 Double ]
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leftShave ε -- minimum width
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( AdaptiveShavingOptions { γ_init, σ_good, σ_bad, β_good, β_bad } )
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ff' i0 =
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left_narrow γ_init i0
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where
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w0 = width i0
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left_narrow :: Double -> 𝕀 Double -> [ 𝕀 Double ]
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left_narrow γ i@( 𝕀 x_inf x_sup )
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-- Stop if the box is too small.
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| width i < ε
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= [ i ]
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| otherwise
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= go γ x_sup ( 𝕀 x_inf ( if x_inf == x_sup then x_inf else succFP x_inf ) )
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go :: Double -> Double -> 𝕀 Double -> [ 𝕀 Double ]
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go γ x_sup x_left =
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let ( f_x_left, _f'_x_left ) = ff' x_left
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in
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if 0 `inside` f_x_left
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-- Box-consistency achieved; finish.
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then [ 𝕀 ( inf x_left ) x_sup ]
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else
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-- Otherwise, try to shave off a chunk on the left of the interval.
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let --x' = 𝕀 ( sup x_left ) x_sup
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inf_guess = sup x_left
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sup_guess = min x_sup ( inf_guess + γ * w0 ) -- * width x' )
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guess = 𝕀 inf_guess sup_guess
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-- NB: this always uses the initial width (to "avoid asymptotic behaviour" according to the paper)
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( f_guess, f'_guess ) = ff' guess
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x_minus_guess = 𝕀 ( min x_sup ( succFP $ sup guess ) ) x_sup
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in if not ( 0 `inside` f_guess )
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then
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-- We successfully shaved "guess" off; go round again after removing it.
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-- TODO: here we could go back to the top with a new "w" maybe?
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left_narrow ( β_good * γ ) x_minus_guess
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else
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-- Do a Newton step to try to reduce the guess interval.
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-- Starting from "guess", we get a collection of sub-intervals
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-- "guesses'" refining where the function can be zero.
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let guesses' :: [ ( 𝕀 Double ) ]
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guesses' = do
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δ <- f_x_left `extendedDivide` f'_guess
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let guess' = singleton ( inf guess ) - δ
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map fst $ guess' `intersect` guess
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w_guess = width guess
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w_guesses'
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| null guesses'
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= 0
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| otherwise
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= sup_guess - minimum ( map inf guesses' )
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γ' | w_guesses' < σ_good * w_guess
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-- Good improvement, try larger guesses in the future.
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= β_good * γ
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| w_guesses' > σ_bad * w_guess
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-- Poor improvement, try smaller guesses in the future.
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= β_bad * γ
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| otherwise
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-- Otherwise, keep the γ factor the same.
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= γ
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in left_narrow γ' =<< ( x_minus_guess : guesses' )
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