mirror of
https://gitlab.com/sheaf/metabrush.git
synced 2024-11-05 14:53:37 +00:00
make cusp-finding algorithm choice more configurable
This commit is contained in:
sheaf
parent
a183475985
commit
55470d1f0e
|
|
@ -250,7 +250,8 @@ benchmark cusps
|
|||
Main.hs
|
||||
|
||||
build-depends:
|
||||
brush-strokes
|
||||
brush-strokes
|
||||
, deepseq
|
||||
|
||||
type:
|
||||
exitcode-stdio-1.0
|
||||
|
|
|
|||
|
|
@ -25,7 +25,11 @@ import Data.Coerce
|
|||
import Data.Foldable
|
||||
( for_ )
|
||||
import Data.List
|
||||
( intercalate )
|
||||
( intercalate, sortOn )
|
||||
import Data.Traversable
|
||||
( for )
|
||||
import GHC.Clock
|
||||
( getMonotonicTime )
|
||||
import GHC.Exts
|
||||
( Proxy#, proxy# )
|
||||
import GHC.Generics
|
||||
|
|
@ -43,6 +47,13 @@ import qualified Data.Sequence as Seq
|
|||
import Data.Tree
|
||||
( foldTree )
|
||||
|
||||
-- deepseq
|
||||
import Control.DeepSeq
|
||||
( rnf )
|
||||
|
||||
-- gauge
|
||||
--import qualified Gauge
|
||||
|
||||
-- tree-view
|
||||
import Data.Tree.View
|
||||
( showTree )
|
||||
|
|
@ -64,11 +75,66 @@ import Math.Ring
|
|||
|
||||
--------------------------------------------------------------------------------
|
||||
|
||||
{-
|
||||
main :: IO ()
|
||||
main = Gauge.defaultMainWith benchConfig
|
||||
[ Gauge.bgroup "Cusp finding"
|
||||
[ Gauge.bench testName $ Gauge.nf benchTest benchCase
|
||||
| benchCase@( TestCase { testName } ) <- benchCases
|
||||
]
|
||||
]
|
||||
|
||||
benchConfig :: Gauge.Config
|
||||
benchConfig = Gauge.defaultConfig
|
||||
{ Gauge.timeLimit = Just 0
|
||||
, Gauge.minSamples = Nothing
|
||||
, Gauge.minDuration = 0
|
||||
}
|
||||
|
||||
benchTest :: TestCase -> ()
|
||||
benchTest ( TestCase { testBrushStroke, testCuspOptions, testStartBoxes } ) =
|
||||
let ( _, testStrokeFnI ) = brushStrokeFunctions testBrushStroke
|
||||
( _, ( dunno, sols ) ) = computeCusps testCuspOptions testStrokeFnI testStartBoxes
|
||||
in dunno `seq` sols `seq` ()
|
||||
-}
|
||||
|
||||
main :: IO ()
|
||||
main = do
|
||||
for_ testCases $ \ testCase@( TestCase { testName, testBrushStroke, testAlgorithmParams, testStartBoxes } ) -> do
|
||||
putStrLn "Running cusp-finding benchmarks."
|
||||
testsWithTime <-
|
||||
for testCases $ \ tst -> do { dt <- benchTestCase tst; return ( tst, dt ) }
|
||||
let (bestTest, bestTime) = head $ sortOn snd testsWithTime
|
||||
putStrLn $ unlines
|
||||
[ replicate 40 '='
|
||||
, "Best time: " ++ show bestTime ++ "s"
|
||||
, "Best parameters:"
|
||||
--, show (testCuspOptions bestTest)
|
||||
]
|
||||
|
||||
benchTestCase :: TestCase -> IO Double
|
||||
benchTestCase ( TestCase { testName, testBrushStroke, testCuspOptions, testStartBoxes } ) = do
|
||||
putStrLn $ unlines
|
||||
[ replicate 40 '='
|
||||
, "Test case " ++ testName ]
|
||||
before <- getMonotonicTime
|
||||
let ( _, testStrokeFnI ) = brushStrokeFunctions testBrushStroke
|
||||
( _newtTrees, ( dunno, sols ) ) = computeCusps testCuspOptions testStrokeFnI testStartBoxes
|
||||
rnf dunno `seq` rnf sols `seq` return ()
|
||||
after <- getMonotonicTime
|
||||
let dt = after - before
|
||||
putStrLn $ unlines
|
||||
[ " - #sols: " ++ show (length sols)
|
||||
, " - #dunno: " ++ show (length dunno)
|
||||
, " - Time elapsed: " ++ show dt ++ "s"
|
||||
, "" ]
|
||||
return dt
|
||||
|
||||
{-
|
||||
main :: IO ()
|
||||
main =
|
||||
for_ testCases $ \ testCase@( TestCase { testName, testBrushStroke, testCuspOptions, testStartBoxes } ) -> do
|
||||
let ( _, testStrokeFnI ) = brushStrokeFunctions testBrushStroke
|
||||
( newtTrees, ( dunno, sols ) ) = computeCusps testAlgorithmParams testStrokeFnI testStartBoxes
|
||||
( newtTrees, ( dunno, sols ) ) = computeCusps testCuspOptions testStrokeFnI testStartBoxes
|
||||
showedTrees = map ( uncurry showIntervalNewtonTree ) newtTrees
|
||||
testHeader =
|
||||
[ "", "Test case '" ++ testName ++ "':" ]
|
||||
|
|
@ -84,6 +150,7 @@ main = do
|
|||
-- logFileMVar <- newMVar "logs/fnData.log"
|
||||
-- logToFile logFileMVar (unlines logLines)
|
||||
-- `seq` return ()
|
||||
-}
|
||||
|
||||
testCases :: [ TestCase ]
|
||||
testCases = benchCases
|
||||
|
|
@ -103,7 +170,12 @@ testCases = benchCases
|
|||
-}
|
||||
|
||||
benchCases :: [ TestCase ]
|
||||
benchCases = [ ellipseTestCase "full" ( 0, 1 ) pi $ defaultStartBoxes [ 0 .. 3 ] ]
|
||||
benchCases =
|
||||
[ ellipseTestCase opts "full" ( 0, 1 ) pi $ defaultStartBoxes [ 0 .. 3 ] ]
|
||||
where
|
||||
opts = defaultCuspFindingOptions
|
||||
|
||||
|
||||
|
||||
--------------------------------------------------------------------------------
|
||||
|
||||
|
|
@ -117,10 +189,10 @@ data BrushStroke =
|
|||
|
||||
data TestCase =
|
||||
TestCase
|
||||
{ testName :: String
|
||||
, testBrushStroke :: BrushStroke
|
||||
, testAlgorithmParams :: CuspAlgorithmParams
|
||||
, testStartBoxes :: [ Box ]
|
||||
{ testName :: String
|
||||
, testBrushStroke :: BrushStroke
|
||||
, testCuspOptions :: CuspFindingOptions
|
||||
, testStartBoxes :: [ Box ]
|
||||
}
|
||||
|
||||
brushStrokeFunctions
|
||||
|
|
@ -176,7 +248,7 @@ take 10 $ Data.List.sortOn ( \ ( _, ℝ1 e, v) -> abs e + norm v ) [ let { v = m
|
|||
potentialCusp $ eval fI $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
|
||||
> True
|
||||
|
||||
let nbPotentialSols b = let ( _newtTrees, ( dunno, sols ) ) = intervalNewtonGSFrom NoPreconditioning 1e-7 fI b in length dunno + length sols
|
||||
let nbPotentialSols b = let ( _newtTrees, ( dunno, sols ) ) = findCuspsFrom NoPreconditioning 1e-7 fI b in length dunno + length sols
|
||||
|
||||
nbPotentialSols $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
|
||||
1
|
||||
|
|
@ -184,7 +256,7 @@ nbPotentialSols $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
|
|||
nbPotentialSols $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
|
||||
0
|
||||
|
||||
let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI b
|
||||
let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ findCuspsFrom NoPreconditioning 1e-7 fI b
|
||||
|
||||
putStrLn $ unlines $ map Data.Tree.View.showTree $ showTrees $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
|
||||
|
||||
|
|
@ -390,7 +462,7 @@ maximum [ _y $ sup $ unT $ _D12_v $ dEdsdcdt $ eval fI $ mkBox (t, t) 2 (s, s) |
|
|||
|
||||
|
||||
|
||||
let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI b
|
||||
let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ findCuspsFrom NoPreconditioning 1e-7 fI b
|
||||
|
||||
putStrLn $ unlines $ map Data.Tree.View.showTree $ showTrees $ mkBox (0.5486101933245248, 0.5486102071493622) 2 (0.548095036738487, 0.5480952)
|
||||
|
||||
|
|
@ -408,16 +480,12 @@ showD float = showFFloat (Just 6) float ""
|
|||
|
||||
--------------------------------------------------------------------------------
|
||||
|
||||
ellipseTestCase :: String -> ( Double, Double ) -> Double -> [ Box ] -> TestCase
|
||||
ellipseTestCase str k0k1 rot startBoxes =
|
||||
ellipseTestCase :: CuspFindingOptions -> String -> ( Double, Double ) -> Double -> [ Box ] -> TestCase
|
||||
ellipseTestCase opts str k0k1 rot startBoxes =
|
||||
TestCase
|
||||
{ testName = "ellipse (" ++ str ++ ")"
|
||||
, testBrushStroke = ellipseBrushStroke k0k1 rot
|
||||
, testAlgorithmParams =
|
||||
CuspAlgorithmParams
|
||||
{ preconditioning = InverseMidJacobian
|
||||
, maxWidth = 1e-7
|
||||
}
|
||||
, testCuspOptions = opts
|
||||
, testStartBoxes = startBoxes
|
||||
}
|
||||
|
||||
|
|
@ -442,11 +510,7 @@ trickyCusp2TestCase =
|
|||
TestCase
|
||||
{ testName = "trickyCusp2"
|
||||
, testBrushStroke = trickyCusp2BrushStroke
|
||||
, testAlgorithmParams =
|
||||
CuspAlgorithmParams
|
||||
{ preconditioning = InverseMidJacobian
|
||||
, maxWidth = 1e-7
|
||||
}
|
||||
, testCuspOptions = defaultCuspFindingOptions
|
||||
, testStartBoxes = defaultStartBoxes [ 0 .. 3 ]
|
||||
}
|
||||
|
||||
|
|
@ -496,13 +560,6 @@ data Point nbParams =
|
|||
deriving stock Generic
|
||||
deriving stock instance Show ( ℝ nbParams ) => Show ( Point nbParams )
|
||||
|
||||
data CuspAlgorithmParams =
|
||||
CuspAlgorithmParams
|
||||
{ preconditioning :: !Preconditioner
|
||||
, maxWidth :: !Double
|
||||
}
|
||||
deriving stock Show
|
||||
|
||||
type Brush nbParams
|
||||
= forall {t} k (i :: t)
|
||||
. DiffInterp k i ( ℝ nbParams )
|
||||
|
|
@ -543,14 +600,12 @@ getStrokeFunctions brush sp0 crv =
|
|||
{-# INLINEABLE getStrokeFunctions #-}
|
||||
|
||||
computeCusps
|
||||
:: CuspAlgorithmParams
|
||||
:: CuspFindingOptions
|
||||
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-> [ Box ]
|
||||
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||
computeCusps params eqs startBoxes =
|
||||
foldMap
|
||||
( intervalNewtonGSFrom ( preconditioning params ) ( maxWidth params ) eqs )
|
||||
startBoxes
|
||||
-> ( [ ( Box, RootFindingTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||
computeCusps cuspOpts eqs startBoxes =
|
||||
foldMap ( findCuspsFrom cuspOpts eqs ) startBoxes
|
||||
|
||||
defaultStartBoxes :: [ Int ] -> [ Box ]
|
||||
defaultStartBoxes is =
|
||||
|
|
@ -561,8 +616,8 @@ getR1 (ℝ1 u) = u
|
|||
{-
|
||||
|
||||
(f, fI) = brushStrokeFunctions $ ellipseBrushStroke (0,1) pi
|
||||
nbPotentialSols box = let ( _newtTrees, ( dunno, sols ) ) = intervalNewtonGSFrom NoPreconditioning 1e-7 fI box in length dunno + length sols
|
||||
showTrees box = putStrLn $ unlines $ map Data.Tree.View.showTree $ map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI box
|
||||
nbPotentialSols box = let ( _newtTrees, ( dunno, sols ) ) = findCuspsFrom NoPreconditioning 1e-7 fI box in length dunno + length sols
|
||||
showTrees box = putStrLn $ unlines $ map Data.Tree.View.showTree $ map ( uncurry showIntervalNewtonTree ) $ fst $ findCuspsFrom NoPreconditioning 1e-7 fI box
|
||||
|
||||
sol_t = 0.5486100729150693796677845183880669025324233347060776339185 :: Double
|
||||
sol_s = 0.5480950141859386853197594577293968665598143630958601978245 :: Double
|
||||
|
|
|
|||
|
|
@ -19,13 +19,14 @@ module Math.Bezier.Stroke
|
|||
, brushStrokeData, pathAndUsedParams
|
||||
|
||||
-- ** Cusp finding
|
||||
, Preconditioner(..)
|
||||
, IntervalNewtonTree(..), showIntervalNewtonTree
|
||||
, IntervalNewtonStep(..)
|
||||
, IntervalNewtonLeaf(..)
|
||||
, RootFindingTree(..), showRootFindingTree
|
||||
, RootFindingStep(..)
|
||||
, RootFindingLeaf(..)
|
||||
, Box
|
||||
, intervalNewtonGS, intervalNewtonGSFrom, gaussSeidel
|
||||
|
||||
, CuspFindingOptions(..), defaultCuspFindingOptions
|
||||
, RootFindingAlgorithm(..), defaultCuspFindingAlgorithms
|
||||
, Preconditioner(..)
|
||||
, findCusps, findCuspsFrom, gaussSeidel
|
||||
)
|
||||
where
|
||||
|
||||
|
|
@ -53,13 +54,11 @@ import Data.List
|
|||
import Data.List.NonEmpty
|
||||
( NonEmpty )
|
||||
import qualified Data.List.NonEmpty as NE
|
||||
( cons, singleton, unzip )
|
||||
( NonEmpty(..), cons, last, singleton, unzip )
|
||||
import Data.Maybe
|
||||
( fromMaybe, isJust, listToMaybe, mapMaybe )
|
||||
import Data.Semigroup
|
||||
( sconcat )
|
||||
import Data.Traversable
|
||||
( for )
|
||||
import GHC.Exts
|
||||
( newMutVar#, runRW#, inline
|
||||
, Proxy#, proxy#
|
||||
|
|
@ -263,6 +262,7 @@ computeStrokeOutline ::
|
|||
|
||||
)
|
||||
=> RootSolvingAlgorithm
|
||||
-> Maybe CuspFindingOptions
|
||||
-> FitParameters
|
||||
-> ( ptData -> usedParams )
|
||||
-> ( usedParams -> brushParams ) -- ^ assumed to be linear and non-decreasing
|
||||
|
|
@ -279,7 +279,7 @@ computeStrokeOutline ::
|
|||
, Seq FitPoint
|
||||
, [ Cusp ]
|
||||
)
|
||||
computeStrokeOutline rootAlgo fitParams ptParams toBrushParams brushFn spline@( Spline { splineStart = spt0 } ) = case ssplineType @clo of
|
||||
computeStrokeOutline rootAlgo mbCuspOptions fitParams ptParams toBrushParams brushFn spline@( Spline { splineStart = spt0 } ) = case ssplineType @clo of
|
||||
-- Open brush path with at least one segment.
|
||||
-- Need to add caps at both ends of the path.
|
||||
SOpen
|
||||
|
|
@ -381,7 +381,7 @@ computeStrokeOutline rootAlgo fitParams ptParams toBrushParams brushFn spline@(
|
|||
where
|
||||
|
||||
outlineInfo :: ptData -> Curve Open crvData ptData -> OutlineInfo
|
||||
outlineInfo = inline ( outlineFunction rootAlgo ptParams toBrushParams brushFn )
|
||||
outlineInfo = inline ( outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams brushFn )
|
||||
|
||||
outlineFns :: Seq OutlineInfo
|
||||
outlineFns = go spt0 ( openCurves $ splineCurves ( adjustSplineType @Open spline ) )
|
||||
|
|
@ -541,6 +541,7 @@ outlineFunction
|
|||
, Show ptData, Show brushParams
|
||||
)
|
||||
=> RootSolvingAlgorithm
|
||||
-> Maybe CuspFindingOptions
|
||||
-> ( ptData -> usedParams )
|
||||
-> ( usedParams -> brushParams ) -- ^ assumed to be linear and non-decreasing
|
||||
-> ( forall {t} k (i :: t)
|
||||
|
|
@ -553,7 +554,7 @@ outlineFunction
|
|||
-> ptData
|
||||
-> Curve Open crvData ptData
|
||||
-> OutlineInfo
|
||||
outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
||||
outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
||||
let
|
||||
|
||||
usedParams :: C 2 ( ℝ 1 ) usedParams
|
||||
|
|
@ -604,10 +605,11 @@ outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
|||
$ toBrushParams params_t
|
||||
|
||||
( newtTrees, ( newtDunno, newtSols ) ) =
|
||||
intervalNewtonGS
|
||||
InverseMidJacobian
|
||||
1e-7
|
||||
curvesI
|
||||
case mbCuspOptions of
|
||||
Just cuspOptions ->
|
||||
findCusps cuspOptions curvesI
|
||||
Nothing ->
|
||||
( [], ( [], [] ) )
|
||||
|
||||
showD :: Double -> String
|
||||
showD float = showFFloat (Just 6) float ""
|
||||
|
|
@ -627,7 +629,7 @@ outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
|||
]
|
||||
) ++ "}"
|
||||
]
|
||||
showedTrees = map ( uncurry showIntervalNewtonTree ) newtTrees
|
||||
showedTrees = map ( uncurry showRootFindingTree ) newtTrees
|
||||
solLines =
|
||||
[ " #sols: " ++ show (length newtSols)
|
||||
, "#dunno: " ++ show (length newtDunno)
|
||||
|
|
@ -638,7 +640,7 @@ outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
|||
|
||||
logContents = unlines $ functionDataLines ++ treeLines
|
||||
|
||||
in trace (unlines solLines) $
|
||||
in --trace (unlines solLines) $
|
||||
--logToFile cuspFindingMVar logContents `seq`
|
||||
OutlineInfo
|
||||
{ outlineFn = fwdBwd
|
||||
|
|
@ -1032,16 +1034,6 @@ solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strok
|
|||
|
||||
where
|
||||
|
||||
-- !_ = trace
|
||||
-- ( unlines
|
||||
-- [ "solveEnvelopeEquation"
|
||||
-- , " t: " ++ show _t
|
||||
-- , " pt: " ++ show path_t
|
||||
-- , " tgt: " ++ show path'_t
|
||||
-- , " fwdOffset: " ++ show fwdOffset
|
||||
-- , " bwdOffset: " ++ show bwdOffset ]
|
||||
-- ) True
|
||||
|
||||
fwdSol = findSolFrom "fwd" fwdOffset
|
||||
( bwdPt, bwdTgt ) = findSolFrom "bwd" bwdOffset
|
||||
|
||||
|
|
@ -1278,115 +1270,9 @@ gaussSeidel
|
|||
|
||||
return ( ( 𝕀 ( ℝ1 x1'_lo ) ( ℝ1 x1'_hi ), 𝕀 ( ℝ1 x2'_lo ) ( ℝ1 x2'_hi ) )
|
||||
, sub_x1 && sub_x2 )
|
||||
|
||||
{-
|
||||
gaussSeidel2 :: Int
|
||||
-> Double
|
||||
-> Double
|
||||
-> ( 𝕀ℝ 2, 𝕀ℝ 2 ) -- ^ columns of \( A \)
|
||||
-> 𝕀ℝ 2 -- ^ \( B \)
|
||||
-> ( 𝕀ℝ 1, 𝕀ℝ 1 ) -- ^ initial box \( X \)
|
||||
-> [ ( ( 𝕀ℝ 1, 𝕀ℝ 1 ), Bool ) ]
|
||||
gaussSeidel2 maxIters eps_abs eps_rel
|
||||
( 𝕀 ( ℝ2 a11_lo a21_lo ) ( ℝ2 a11_hi a21_hi )
|
||||
, 𝕀 ( ℝ2 a12_lo a22_lo ) ( ℝ2 a12_hi a22_hi ) )
|
||||
( 𝕀 ( ℝ2 b1_lo b2_lo ) ( ℝ2 b1_hi b2_hi ) )
|
||||
x0
|
||||
= let !a11 = 𝕀 a11_lo a11_hi
|
||||
!a12 = 𝕀 a12_lo a12_hi
|
||||
!a21 = 𝕀 a21_lo a21_hi
|
||||
!a22 = 𝕀 a22_lo a22_hi
|
||||
!b1 = 𝕀 b1_lo b1_hi
|
||||
!b2 = 𝕀 b2_lo b2_hi
|
||||
|
||||
-- See "Algorithm 2" in
|
||||
-- "Using interval unions to solve linear systems of equations with uncertainties"
|
||||
iter ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) ) = do
|
||||
let
|
||||
!x1 = 𝕀 x1_lo x1_hi
|
||||
!x2 = 𝕀 x2_lo x2_hi
|
||||
blah1 = do
|
||||
let s = b1 - a12 * x2
|
||||
let s1 = s `monus` ( a11 * x1 )
|
||||
y1 <-
|
||||
if not $ containsZero ( s1 - a11 * x1 )
|
||||
then []
|
||||
else
|
||||
if containsZero s1 && containsZero a11
|
||||
then [ ( x1, False ) ]
|
||||
else do
|
||||
x1'' <- s1 `extendedDivide` a11
|
||||
x1'' `intersect` x1
|
||||
|
||||
let s2 = s `monus` ( a12 * x2 )
|
||||
y2 <-
|
||||
if not $ containsZero ( s2 - a11 * x1 )
|
||||
then []
|
||||
else
|
||||
if containsZero s2 && containsZero a11
|
||||
then [ ( x1, False ) ]
|
||||
else do
|
||||
x1'' <- s2 `extendedDivide` a12
|
||||
x1'' `intersect` x1
|
||||
return ( y1 `cart` y2 )
|
||||
|
||||
blah2 = do
|
||||
let s = b2 - a21 * x1
|
||||
let s1 = s `monus` ( a21 * x1 )
|
||||
y1 <-
|
||||
if not $ containsZero ( s1 - a22 * x2 )
|
||||
then []
|
||||
else
|
||||
if containsZero s1 && containsZero a22
|
||||
then [ ( x1, False ) ]
|
||||
else do
|
||||
x1'' <- s1 `extendedDivide` a21
|
||||
x1'' `intersect` x1
|
||||
|
||||
let s2 = s `monus` ( a12 * x2 )
|
||||
y2 <-
|
||||
if not $ containsZero ( s2 - a22 * x2 )
|
||||
then []
|
||||
else
|
||||
if containsZero s2 && containsZero a22
|
||||
then [ ( x1, False ) ]
|
||||
else do
|
||||
x1'' <- s2 `extendedDivide` a22
|
||||
x1'' `intersect` x1
|
||||
return ( y1 `cart` y2 )
|
||||
|
||||
blah1 ++ blah2
|
||||
|
||||
go :: Int -> ( 𝕀ℝ 1, 𝕀ℝ 1 ) -> [ ( ( 𝕀ℝ 1, 𝕀ℝ 1 ), Bool ) ]
|
||||
go !i x
|
||||
= do { nxt@( x', sub ) <- iter x
|
||||
; let dw_abs = maxWidth x - maxWidth x'
|
||||
dw_rel = 1 - ( maxWidth x' / maxWidth x )
|
||||
; if sub
|
||||
|| i >= maxIters
|
||||
|| dw_abs < eps_abs
|
||||
|| dw_rel < eps_rel
|
||||
then return nxt
|
||||
else go ( i + 1 ) x'
|
||||
}
|
||||
|
||||
in go 1 x0
|
||||
where
|
||||
maxWidth :: ( 𝕀ℝ 1, 𝕀ℝ 1 ) -> Double
|
||||
maxWidth ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) )
|
||||
= max ( x1_hi - x1_lo ) ( x2_hi - x2_lo )
|
||||
containsZero :: 𝕀 Double -> Bool
|
||||
containsZero ( 𝕀 lo hi ) = lo <= 0 && hi >= 0
|
||||
monus :: 𝕀 Double -> 𝕀 Double -> 𝕀 Double
|
||||
monus ( 𝕀 lo1 hi1 ) ( 𝕀 lo2 hi2 )
|
||||
| hi1 - lo1 >= hi2 - lo2
|
||||
= 𝕀 ( lo1 - lo2 ) ( hi1 - hi2 )
|
||||
| otherwise
|
||||
= 𝕀 ( hi1 - hi2 ) ( lo1 - lo2 )
|
||||
cart :: ( 𝕀 Double, Bool ) -> ( 𝕀 Double, Bool ) -> ( ( 𝕀ℝ 1, 𝕀ℝ 1 ), Bool )
|
||||
cart ( 𝕀 lo1 hi1, sub1 ) ( 𝕀 lo2 hi2, sub2 ) =
|
||||
( ( 𝕀 ( ℝ1 lo1 ) ( ℝ1 hi1 ), 𝕀 ( ℝ1 lo2 ) ( ℝ1 hi2 ) ), sub1 && sub2 )
|
||||
-}
|
||||
-- TODO: try implementing the complete interval union Gauss–Seidel algorithm.
|
||||
-- See "Algorithm 2" in
|
||||
-- "Using interval unions to solve linear systems of equations with uncertainties"
|
||||
|
||||
-- | Compute the intersection of two intervals.
|
||||
--
|
||||
|
|
@ -1404,6 +1290,9 @@ intersect ( 𝕀 lo1 hi1 ) ( 𝕀 lo2 hi2 )
|
|||
|
||||
-- | Computes the brush stroke coordinates of a cusp from
|
||||
-- the @(t,s)@ parameter values.
|
||||
--
|
||||
-- TODO: use Newton's method starting at the midpoint of the box,
|
||||
-- instead of just taking the midpoint of the box.
|
||||
cuspCoords :: ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () ) )
|
||||
-> Box
|
||||
-> Cusp
|
||||
|
|
@ -1421,42 +1310,45 @@ cuspCoords eqs ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), i, 𝕀 ( ℝ1 s_lo ) ( ℝ1
|
|||
t_mid = 0.5 * ( t_lo + t_hi )
|
||||
s_mid = 0.5 * ( s_lo + s_hi )
|
||||
|
||||
|
||||
-- | Preconditioner to use with the interval Gauss–Seidel method.
|
||||
data Preconditioner
|
||||
= NoPreconditioning
|
||||
| InverseMidJacobian
|
||||
deriving stock Show
|
||||
|
||||
-- | A tree recording the steps taken with the interval Newton method.
|
||||
data IntervalNewtonTree d
|
||||
= IntervalNewtonLeaf (IntervalNewtonLeaf d)
|
||||
| IntervalNewtonStep (IntervalNewtonStep d) [(d, IntervalNewtonTree d)]
|
||||
-- | A tree recording the steps taken when doing cusp finding.
|
||||
data RootFindingTree d
|
||||
= RootFindingLeaf (RootFindingLeaf d)
|
||||
| RootFindingStep RootFindingStep [(d, RootFindingTree d)]
|
||||
|
||||
data IntervalNewtonStep d
|
||||
= IntervalNewtonContraction [d]
|
||||
| IntervalNewtonBisection (String, Double)
|
||||
-- | A description of a step taken in cusp-finding.
|
||||
data RootFindingStep
|
||||
= GaussSeidelStep
|
||||
| BisectionStep (String, Double)
|
||||
| Box1Step
|
||||
| Box2Step
|
||||
|
||||
instance Show d => Show (IntervalNewtonStep d) where
|
||||
showsPrec _ ( IntervalNewtonContraction v )
|
||||
= showString "N "
|
||||
. showsPrec 0 v
|
||||
showsPrec _ ( IntervalNewtonBisection (coord, w) )
|
||||
= showString "B "
|
||||
instance Show RootFindingStep where
|
||||
showsPrec _ GaussSeidelStep = showString "GS"
|
||||
showsPrec _ ( BisectionStep (coord, w) )
|
||||
= showString "bis "
|
||||
. showParen True
|
||||
( showString coord
|
||||
. showString " = "
|
||||
. showsPrec 0 w
|
||||
)
|
||||
showsPrec _ Box1Step = showString "box(1)"
|
||||
showsPrec _ Box2Step = showString "box(2)"
|
||||
|
||||
data IntervalNewtonLeaf d
|
||||
data RootFindingLeaf d
|
||||
= TooSmall d
|
||||
| NoSolution String d
|
||||
deriving stock Show
|
||||
|
||||
showIntervalNewtonTree :: Box -> IntervalNewtonTree Box -> Tree String
|
||||
showIntervalNewtonTree cand (IntervalNewtonLeaf l) = Node (show cand ++ " " ++ showArea (boxArea cand) ++ " " ++ show l) []
|
||||
showIntervalNewtonTree cand (IntervalNewtonStep s ts)
|
||||
= Node (show cand ++ " abc " ++ showArea (boxArea cand) ++ " " ++ show s) $ map (\ (c,t) -> showIntervalNewtonTree c t) ts
|
||||
showRootFindingTree :: Box -> RootFindingTree Box -> Tree String
|
||||
showRootFindingTree cand (RootFindingLeaf l) = Node (show cand ++ " " ++ showArea (boxArea cand) ++ " " ++ show l) []
|
||||
showRootFindingTree cand (RootFindingStep s ts)
|
||||
= Node (show cand ++ " abc " ++ showArea (boxArea cand) ++ " " ++ show s) $ map (\ (c,t) -> showRootFindingTree c t) ts
|
||||
|
||||
boxArea :: Box -> Double
|
||||
boxArea ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), _, 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
|
|
@ -1466,53 +1358,169 @@ showArea :: Double -> [Char]
|
|||
showArea area = "(area " ++ showFFloat (Just 6) area "" ++ ")"
|
||||
|
||||
type Box = ( 𝕀ℝ 1, Int, 𝕀ℝ 1 )
|
||||
type BoxHistory = [ NE.NonEmpty ( RootFindingStep, Box ) ]
|
||||
|
||||
intervalNewtonGS
|
||||
:: Preconditioner
|
||||
-> Double
|
||||
-- | Options for the cusp-finding methods in 'findCusps' and 'findCuspsFrom'.
|
||||
data CuspFindingOptions
|
||||
= CuspFindingOptions
|
||||
{ -- | Minimum width of a box.
|
||||
minWidth :: !Double
|
||||
-- | Given a box and its history, return a round of cusp-finding strategies
|
||||
-- to run, in sequence, on this box.
|
||||
, cuspFindingAlgorithms :: !( Box -> BoxHistory -> NonEmpty RootFindingAlgorithm )
|
||||
}
|
||||
|
||||
data RootFindingAlgorithm
|
||||
-- | Gauss–Seidel step with the given preconditioning method.
|
||||
= GaussSeidel GaussSeidelOptions
|
||||
-- | @box(1)@-consistency.
|
||||
| Box1 Box1Options
|
||||
-- | @box(2)@-consistency.
|
||||
| Box2 Box2Options
|
||||
-- | Bisection step.
|
||||
| Bisection BisectionOptions
|
||||
|
||||
-- | Options for the interval Gauss–Seidel method.
|
||||
data GaussSeidelOptions = GaussSeidelOptions { gsPreconditioner :: Preconditioner }
|
||||
|
||||
-- | Options for the @box(1)@-consistency method.
|
||||
data Box1Options = Box1Options { box1EpsEq :: !Double }
|
||||
|
||||
-- | Options for the @box(2)@-consistency method.
|
||||
data Box2Options = Box2Options { box2EpsEq :: !Double, box2LambdaMin :: !Double }
|
||||
|
||||
-- | Options for the bisection method.
|
||||
data BisectionOptions =
|
||||
BisectionOptions
|
||||
{ canHaveSols :: !( ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) ) -> Box -> Bool )
|
||||
, fallbackBisectionDim :: !( [ ( RootFindingStep, Box ) ] -> BoxHistory -> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) ) -> (Int, String) )
|
||||
}
|
||||
|
||||
defaultCuspFindingOptions :: CuspFindingOptions
|
||||
defaultCuspFindingOptions =
|
||||
CuspFindingOptions
|
||||
{ minWidth
|
||||
, cuspFindingAlgorithms = defaultCuspFindingAlgorithms minWidth 5e-3
|
||||
}
|
||||
where
|
||||
minWidth = 1e-5
|
||||
|
||||
defaultCuspFindingAlgorithms :: Double -> Double -> Box -> BoxHistory -> NonEmpty RootFindingAlgorithm
|
||||
defaultCuspFindingAlgorithms minWidth narrowAbs box history =
|
||||
case history of
|
||||
lastRoundBoxes : _
|
||||
-- If, in the last round of strategies, we didn't try bisection...
|
||||
| any ( \case { BisectionStep {} -> False; _ -> True } . fst ) lastRoundBoxes
|
||||
, (_, lastRoundFirstBox ) <- NE.last lastRoundBoxes
|
||||
-- ...and the last round didn't sufficiently reduce the size of the box...
|
||||
, not $ box `sufficientlySmallerThan` lastRoundFirstBox
|
||||
-- ...then try bisecting the box.
|
||||
-> Bisection ( defaultBisectionOptions minWidth narrowAbs box ) NE.:| []
|
||||
|
||||
-- Otherwise, do a normal round: try an interval Gauss–Seidel step followed by box(1)-consistency.
|
||||
_ -> GaussSeidel defaultGaussSeidelOptions
|
||||
NE.:| [ Box1 ( Box1Options { box1EpsEq = narrowAbs } ) ]
|
||||
where
|
||||
sufficientlySmallerThan :: Box -> Box -> Bool
|
||||
sufficientlySmallerThan ( t1, _, s1 ) ( t2, _, s2 ) =
|
||||
( wd t1 - wd t2 > narrowAbs )
|
||||
||
|
||||
( wd s1 - wd s2 > narrowAbs )
|
||||
wd :: 𝕀ℝ 1 -> Double
|
||||
wd ( 𝕀 ( ℝ1 lo ) ( ℝ1 hi ) ) = hi - lo
|
||||
|
||||
defaultGaussSeidelOptions :: GaussSeidelOptions
|
||||
defaultGaussSeidelOptions = GaussSeidelOptions { gsPreconditioner = InverseMidJacobian }
|
||||
|
||||
defaultBisectionOptions :: Double -> Double -> Box -> BisectionOptions
|
||||
defaultBisectionOptions
|
||||
_minWidth
|
||||
_narrowAbs
|
||||
( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||
, i
|
||||
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
)
|
||||
= BisectionOptions
|
||||
{ canHaveSols =
|
||||
\ eqs _box'@( _t', _i', _s' ) ->
|
||||
-- box(0)-consistency
|
||||
let dat' = ( eqs _t' `Seq.index` _i' ) _s'
|
||||
in ee_potential_zero dat' && 𝛿E𝛿sdcdt_potential_zero dat'
|
||||
|
||||
-- box(1)-consistency
|
||||
--not $ null $ makeBox1Consistent eqs _minWidth _narrowAbs _box'
|
||||
|
||||
-- box(2)-consistency
|
||||
--let ( t'', i'', s'') = makeBox2Consistent eqs _minWidth _narrowAbs 0.2 _box'
|
||||
-- dat'' = ( eqs t'' `Seq.index` i'' ) s''
|
||||
--in ee_potential_zero dat'' && 𝛿E𝛿sdcdt_potential_zero dat''
|
||||
, fallbackBisectionDim =
|
||||
\ _roundHist _prevRoundsHist eqs ->
|
||||
let StrokeDatum { ee = D22 _ ( T ee_t ) (T ee_s ) _ _ _
|
||||
, 𝛿E𝛿sdcdt = D12 _ ( T ( T f_t ) ) ( T ( T f_s ) ) }
|
||||
= ( eqs t `Seq.index` i ) s
|
||||
wd_t = t_hi - t_lo
|
||||
wd_s = s_hi - s_lo
|
||||
tJWidth = wd_t * normVI3 ee_t f_t
|
||||
sJWidth = wd_s * normVI3 ee_s f_s
|
||||
in if tJWidth >= sJWidth
|
||||
-- bisect along dimension that maximises width(x_j) * || J_j || ...
|
||||
-- ... but don't allow thin boxes
|
||||
|| ( wd_t >= 10 * wd_s )
|
||||
&& not ( wd_s >= 10 * wd_t )
|
||||
then (0, "")
|
||||
else (1, "")
|
||||
}
|
||||
|
||||
-- | Find cusps in the envelope for values of the parameters in
|
||||
-- \( 0 \leqslant t, s \leqslant 1 \), using interval arithmetic.
|
||||
--
|
||||
-- See 'findCuspsFrom' for details.
|
||||
findCusps
|
||||
:: CuspFindingOptions
|
||||
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||
intervalNewtonGS precondMethod minWidth eqs =
|
||||
foldMap
|
||||
( intervalNewtonGSFrom precondMethod minWidth eqs )
|
||||
initBoxes
|
||||
-> ( [ ( Box, RootFindingTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||
findCusps opts eqs = foldMap ( findCuspsFrom opts eqs ) initBoxes
|
||||
where
|
||||
initBoxes =
|
||||
[ ( 𝕀 ( ℝ1 zero ) ( ℝ1 one ), i, 𝕀 ( ℝ1 zero ) ( ℝ1 one ) )
|
||||
| i <- [ 0 .. length ( eqs ( 𝕀 ( ℝ1 zero ) ( ℝ1 one ) ) ) - 1 ]
|
||||
]
|
||||
|
||||
-- | Interval Newton method with Gauss–Seidel step for inversion
|
||||
-- of the interval Jacobian.
|
||||
-- | Use the following algorithms using interal arithmetic in order
|
||||
-- to find cusps in the envelope:
|
||||
--
|
||||
-- - interval Newton method with Gauss–Seidel step for inversion
|
||||
-- of the interval Jacobian,
|
||||
-- - coordinate-wise Newton method (@box(1)@-consistency algorithm),
|
||||
-- - @box(2)@-consistency algorithm,
|
||||
-- - bisection.
|
||||
--
|
||||
-- Returns @(tree, (dunno, sols))@ where @tree@ is the full tree (useful for debugging),
|
||||
-- @sols@ are boxes that contain a unique solution (and to which Newton's method
|
||||
-- will converge starting from anywhere inside the box), and @dunno@ are small
|
||||
-- boxes which might or might not contain solutions.
|
||||
intervalNewtonGSFrom
|
||||
:: Preconditioner
|
||||
-> Double
|
||||
findCuspsFrom
|
||||
:: CuspFindingOptions
|
||||
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-> Box
|
||||
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||
intervalNewtonGSFrom precondMethod minWidth eqs initBox =
|
||||
runWriter $
|
||||
map ( initBox , ) <$> go initBox
|
||||
-> ( [ ( Box, RootFindingTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||
findCuspsFrom
|
||||
( CuspFindingOptions
|
||||
{ minWidth
|
||||
, cuspFindingAlgorithms
|
||||
}
|
||||
)
|
||||
eqs initBox = runWriter $ map ( initBox , ) <$> go [] initBox
|
||||
|
||||
where
|
||||
|
||||
recur :: ( cand -> Writer ( [ Box ], [ Box ] ) [ IntervalNewtonTree Box ] )
|
||||
-> ( [ ( cand, IntervalNewtonTree Box ) ] -> IntervalNewtonTree Box )
|
||||
-> [ cand ]
|
||||
-> Writer ( [Box], [Box] ) [ IntervalNewtonTree Box ]
|
||||
recur r f cands = do
|
||||
rest <- traverse ( \ c -> do { trees <- r c; return [ (c, tree) | tree <- trees ] } ) cands
|
||||
return [ f $ concat rest ]
|
||||
|
||||
go :: Box -- box to work on
|
||||
go :: BoxHistory
|
||||
-> Box -- box to work on
|
||||
-> Writer ( [ Box ], [ Box ] )
|
||||
[ IntervalNewtonTree Box ]
|
||||
go cand@( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||
[ RootFindingTree Box ]
|
||||
go history
|
||||
cand@( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||
, i
|
||||
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
)
|
||||
|
|
@ -1520,212 +1528,251 @@ intervalNewtonGSFrom precondMethod minWidth eqs initBox =
|
|||
| t_hi - t_lo < minWidth && s_hi - s_lo < minWidth
|
||||
= do let res = TooSmall cand
|
||||
tell ( [ cand ], [] )
|
||||
return [ IntervalNewtonLeaf res ]
|
||||
return [ RootFindingLeaf res ]
|
||||
| -- Check the envelope equation interval contains zero.
|
||||
ee_potential_zero sd
|
||||
-- Check the 𝛿E𝛿sdcdt interval contains zero.
|
||||
, 𝛿E𝛿sdcdt_potential_zero sd
|
||||
= continue cand
|
||||
= doStrategies history ( cuspFindingAlgorithms cand history ) cand
|
||||
-- Box doesn't contain a solution: discard it.
|
||||
| otherwise
|
||||
= return [ IntervalNewtonLeaf $ NoSolution ( if ee_potential_zero sd then "dc/dt" else "ee" ) cand ]
|
||||
, let whyNoSol = if ee_potential_zero sd then "dc/dt" else "ee"
|
||||
= return [ RootFindingLeaf $ NoSolution whyNoSol cand ]
|
||||
where
|
||||
sd = ( eqs t `Seq.index` i ) s
|
||||
|
||||
continue :: Box
|
||||
-> Writer ( [ Box ], [ Box ] )
|
||||
[ IntervalNewtonTree Box ]
|
||||
continue
|
||||
cand@( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||
, i
|
||||
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
)
|
||||
| StrokeDatum { ee = D22 _ ( T ee_t ) (T ee_s ) _ _ _
|
||||
, 𝛿E𝛿sdcdt = D12 _ ( T ( T f_t ) ) ( T ( T f_s ) ) }
|
||||
<- ( eqs t `Seq.index` i ) s
|
||||
, StrokeDatum { ee = D22 _ee_mid _ _ _ _ _
|
||||
, 𝛿E𝛿sdcdt = D12 ( T f_mid ) ( T ( T _f_t_mid ) ) ( T ( T _f_s_mid ) ) }
|
||||
<- ( eqs i_t_mid `Seq.index` i ) i_s_mid
|
||||
= let -- Interval Newton method: take one Gauss–Seidel step
|
||||
-- for the equation f'(x) v = - f(x_mid),
|
||||
-- where f = 𝛿E/𝛿s * dc/dt
|
||||
!( a, b ) = precondition precondMethod
|
||||
( midI f_t, midI f_s )
|
||||
( f_t, f_s ) ( neg f_mid )
|
||||
--(a, b)
|
||||
-- | 𝕀 (ℝ1 ee_lo) (ℝ1 ee_hi) <- ee_mid
|
||||
-- , 𝕀 (ℝ1 ee_t_lo) (ℝ1 ee_t_hi) <- ee_t
|
||||
-- , 𝕀 (ℝ1 ee_s_lo) (ℝ1 ee_s_hi) <- ee_s
|
||||
-- , 𝕀 (ℝ2 fx_lo fy_lo) (ℝ2 fx_hi fy_hi) <- f_mid
|
||||
-- , 𝕀 (ℝ2 f_tx_lo f_ty_lo) (ℝ2 f_tx_hi f_ty_hi) <- f_t
|
||||
-- , 𝕀 (ℝ2 f_sx_lo f_sy_lo) (ℝ2 f_sx_hi f_sy_hi) <- f_s
|
||||
-- = ( ( 𝕀 (ℝ2 f_tx_lo ee_t_lo) (ℝ2 f_tx_hi ee_t_hi)
|
||||
-- , 𝕀 (ℝ2 f_sx_lo ee_s_lo) (ℝ2 f_sx_hi ee_s_hi)
|
||||
-- )
|
||||
-- , neg $ 𝕀 (ℝ2 fx_lo ee_lo) (ℝ2 fx_hi ee_hi)
|
||||
-- )
|
||||
|
||||
!gsGuesses = gaussSeidel a b
|
||||
( coerce ( (-) @( 𝕀 Double ) ) t i_t_mid
|
||||
, coerce ( (-) @( 𝕀 Double ) ) s i_s_mid )
|
||||
in if any ( smaller . fst ) gsGuesses
|
||||
then
|
||||
-- If the Gauss–Seidel step was a contraction, then the box
|
||||
-- contains a unique solution (by the Banach fixed point theorem).
|
||||
--
|
||||
-- These boxes can thus be directly added to the solution set:
|
||||
-- Newton's method is guaranteed to converge to the unique solution.
|
||||
let !(done, todo) = bimap ( map ( mkGuess . fst ) ) ( map ( mkGuess . fst ) )
|
||||
$ partition snd gsGuesses
|
||||
in do tell ([], done)
|
||||
case todo of
|
||||
[] -> return [ IntervalNewtonLeaf $ NoSolution "GaussSeidel" cand ]
|
||||
_ -> recur go ( IntervalNewtonStep ( IntervalNewtonContraction done ) )
|
||||
todo
|
||||
else
|
||||
-- Gauss–Seidel failed to shrink the boxes, so bisect instead.
|
||||
-- We have to pick along which dimension to bisect:
|
||||
-- - if bisecting along a particular dimension discards one of
|
||||
-- the boxes, do that;
|
||||
-- - otherwise, bisect along the dimension j that maximises
|
||||
-- width(x_j) * || J_j ||.
|
||||
let l_t = 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_mid )
|
||||
r_t = 𝕀 ( ℝ1 t_mid ) ( ℝ1 t_hi )
|
||||
d_s = 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_mid )
|
||||
u_s = 𝕀 ( ℝ1 s_mid ) ( ℝ1 s_hi )
|
||||
l = ( l_t, i, s )
|
||||
r = ( r_t, i, s )
|
||||
d = ( t, i, d_s )
|
||||
u = ( t, i, u_s )
|
||||
l_dat = ( eqs l_t `Seq.index` i ) s
|
||||
r_dat = ( eqs r_t `Seq.index` i ) s
|
||||
d_dat = ( eqs t `Seq.index` i ) d_s
|
||||
u_dat = ( eqs t `Seq.index` i ) u_s
|
||||
l_skip =
|
||||
not ( ee_potential_zero l_dat )
|
||||
|| not ( 𝛿E𝛿sdcdt_potential_zero l_dat )
|
||||
r_skip =
|
||||
not ( ee_potential_zero r_dat )
|
||||
|| not ( 𝛿E𝛿sdcdt_potential_zero r_dat )
|
||||
d_skip =
|
||||
not ( ee_potential_zero d_dat )
|
||||
|| not ( 𝛿E𝛿sdcdt_potential_zero d_dat )
|
||||
u_skip =
|
||||
not ( ee_potential_zero u_dat )
|
||||
|| not ( 𝛿E𝛿sdcdt_potential_zero u_dat )
|
||||
tJWidth = ( t_hi - t_lo ) * normVI3 ee_t f_t
|
||||
sJWidth = ( s_hi - s_lo ) * normVI3 ee_s f_s
|
||||
( bisGuesses, whatBis )
|
||||
| l_skip && r_skip
|
||||
= ( [], ( "lr", t_mid ) )
|
||||
| d_skip && u_skip
|
||||
= ( [], ( "du", s_mid ) )
|
||||
| l_skip
|
||||
= ( [ r ], ( "r", t_mid ) )
|
||||
| r_skip
|
||||
= ( [ l ], ( "l", t_mid ) )
|
||||
| d_skip
|
||||
= ( [ u ], ( "u", s_mid ) )
|
||||
| u_skip
|
||||
= ( [ d ], ( "d", s_mid ) )
|
||||
| tJWidth >= sJWidth
|
||||
-- ... but don't allow thin boxes.
|
||||
|| ( t_hi - t_lo >= 10 * ( s_hi - s_lo ) )
|
||||
&& not ( s_hi - s_lo >= 10 * ( t_hi - t_lo ) )
|
||||
= ( [ l, r ], ( "t", t_mid ) )
|
||||
| otherwise
|
||||
= ( [ d, u ], ( "s", s_mid ) )
|
||||
in recur go ( IntervalNewtonStep ( IntervalNewtonBisection whatBis ) )
|
||||
( doStrategy =<< bisGuesses )
|
||||
-- Run a round of cusp finding strategies, then recur.
|
||||
doStrategies
|
||||
:: BoxHistory
|
||||
-> NonEmpty RootFindingAlgorithm
|
||||
-> Box
|
||||
-> Writer ( [ Box ], [ Box ] )
|
||||
[ RootFindingTree Box ]
|
||||
doStrategies hist0 = do_strats []
|
||||
where
|
||||
t_mid = 0.5 * ( t_lo + t_hi )
|
||||
do_strats :: [ ( RootFindingStep, Box ) ]
|
||||
-> NE.NonEmpty RootFindingAlgorithm
|
||||
-> Box
|
||||
-> Writer ( [ Box ], [ Box ] )
|
||||
[ RootFindingTree Box ]
|
||||
do_strats stratsHist ( algo NE.:| algos ) box = do
|
||||
-- Run one strategy in the round.
|
||||
( step, boxes ) <- doStrategy stratsHist hist0 eqs minWidth algo box
|
||||
case algos of
|
||||
-- If there are other algorithms to run in this round, run them next.
|
||||
nextAlgo : otherAlgos ->
|
||||
let stratsHist' = ( step, box ) : stratsHist
|
||||
in recur step ( do_strats stratsHist' ( nextAlgo NE.:| otherAlgos ) ) boxes
|
||||
-- Otherwise, we have done one full round of strategies.
|
||||
-- Recur back to the top (calling 'go').
|
||||
[] ->
|
||||
let stratsHist' = ( step, box ) NE.:| stratsHist
|
||||
history = stratsHist' : hist0
|
||||
in recur step ( go history ) boxes
|
||||
|
||||
recur :: RootFindingStep
|
||||
-> ( Box -> Writer ( [ Box ], [ Box ] ) [ RootFindingTree Box ] )
|
||||
-> [ Box ]
|
||||
-> Writer ( [Box], [Box] ) [ RootFindingTree Box ]
|
||||
recur step r cands = do
|
||||
rest <- traverse ( \ c -> do { trees <- r c; return [ (c, tree) | tree <- trees ] } ) cands
|
||||
return [ RootFindingStep step $ concat rest ]
|
||||
|
||||
|
||||
-- | Execute a cusp-finding strategy, replacing the input box with
|
||||
-- (hopefully smaller) output boxes.
|
||||
doStrategy :: [ ( RootFindingStep, Box ) ]
|
||||
-> BoxHistory
|
||||
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-> Double
|
||||
-> RootFindingAlgorithm
|
||||
-> Box
|
||||
-> Writer ( [ Box ], [ Box ] )
|
||||
( RootFindingStep, [ Box ] )
|
||||
doStrategy roundHistory previousRoundsHistory eqs minWidth algo box =
|
||||
case algo of
|
||||
GaussSeidel ( GaussSeidelOptions { gsPreconditioner } ) -> do
|
||||
boxes <- intervalGaussSeidel eqs gsPreconditioner box
|
||||
return ( GaussSeidelStep, boxes )
|
||||
Box1 ( Box1Options { box1EpsEq } ) ->
|
||||
return ( Box1Step, makeBox1Consistent eqs minWidth box1EpsEq box )
|
||||
Box2 ( Box2Options { box2LambdaMin, box2EpsEq } ) ->
|
||||
return ( Box2Step, [ makeBox2Consistent eqs minWidth box2EpsEq box2LambdaMin box ] )
|
||||
Bisection ( BisectionOptions { canHaveSols, fallbackBisectionDim } ) -> do
|
||||
let ( boxes, whatBis ) = bisect ( canHaveSols eqs ) ( fallbackBisectionDim roundHistory previousRoundsHistory eqs ) box
|
||||
return ( BisectionStep whatBis, boxes )
|
||||
|
||||
-- | Bisect the given box.
|
||||
--
|
||||
-- (The difficult part lies in determining along which dimension to bisect.)
|
||||
bisect :: ( Box -> Bool )
|
||||
-- ^ how to check whether a box contains solutions
|
||||
-> ( Int, String )
|
||||
-- ^ fall-back choice of dimension (and "why" we chose it)
|
||||
-> Box
|
||||
-> ( [ Box ], ( String, Double ) )
|
||||
bisect canHaveSols ( dim, why )
|
||||
( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||
, i
|
||||
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
)
|
||||
-- We try to bisect along a dimension which eliminates zeros from one of the
|
||||
-- sub-regions.
|
||||
--
|
||||
-- If this fails, we fall-back to the provided dimension choice.
|
||||
= let t_mid = 0.5 * ( t_lo + t_hi )
|
||||
s_mid = 0.5 * ( s_lo + s_hi )
|
||||
i_t_mid = singleton ( ℝ1 t_mid )
|
||||
i_s_mid = singleton ( ℝ1 s_mid )
|
||||
mkGuess ( t0, s0 ) = ( coerce ( (+) @( 𝕀 Double ) ) t0 i_t_mid
|
||||
, i
|
||||
, coerce ( (+) @( 𝕀 Double ) ) s0 i_s_mid )
|
||||
smaller ( 𝕀 ( ℝ1 t0_lo ) ( ℝ1 t0_hi ), 𝕀 ( ℝ1 s0_lo ) ( ℝ1 s0_hi ) )
|
||||
= ( t0_lo + t_mid ) > t_lo + 0.25 * minWidth
|
||||
|| ( t0_hi + t_mid ) < t_hi - 0.25 * minWidth
|
||||
|| ( s0_lo + s_mid ) > s_lo + 0.25 * minWidth
|
||||
|| ( s0_hi + s_mid ) < s_hi - 0.25 * minWidth
|
||||
neg ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) )
|
||||
= let !( 𝕀 x'_lo x'_hi ) = negate $ 𝕀 x_lo x_hi
|
||||
!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
|
||||
in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
|
||||
l_t = 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_mid )
|
||||
r_t = 𝕀 ( ℝ1 t_mid ) ( ℝ1 t_hi )
|
||||
d_s = 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_mid )
|
||||
u_s = 𝕀 ( ℝ1 s_mid ) ( ℝ1 s_hi )
|
||||
l = ( l_t, i, s )
|
||||
r = ( r_t, i, s )
|
||||
d = ( t , i, d_s )
|
||||
u = ( t , i, u_s )
|
||||
l_skip = not $ canHaveSols l
|
||||
r_skip = not $ canHaveSols r
|
||||
d_skip = not $ canHaveSols d
|
||||
u_skip = not $ canHaveSols u
|
||||
|
||||
-- Attempting to implement Algorithm 6 "Heuristic to apply bound-consistency"
|
||||
-- from the paper
|
||||
-- "Parallelization of a bound-consistency enforcing procedure and its application in solving nonlinear systems"
|
||||
doStrategy box@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), _, 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
| eps_box1 > eps_box2
|
||||
= if | w_t > ebs_box1 || w_s > ebs_box1
|
||||
-> makeBox1Consistent box
|
||||
| w_t > ebs_box2 || w_s > ebs_box2
|
||||
-> [ makeBox2Consistent box ]
|
||||
| otherwise
|
||||
-> [ box ]
|
||||
| otherwise
|
||||
= if | w_t > ebs_box2 || w_s > ebs_box2
|
||||
-> [ makeBox2Consistent box ]
|
||||
| w_t > ebs_box1 || w_s > ebs_box1
|
||||
-> makeBox1Consistent box
|
||||
| otherwise
|
||||
-> [ box ]
|
||||
where
|
||||
eps_box1 = 0.4
|
||||
eps_box2 = 0.1
|
||||
w_t = t_hi - t_lo
|
||||
w_s = s_hi - s_lo
|
||||
( bisGuesses, whatBis )
|
||||
| l_skip && r_skip
|
||||
= ( [], ( "lr", t_mid ) )
|
||||
| d_skip && u_skip
|
||||
= ( [], ( "du", s_mid ) )
|
||||
| l_skip
|
||||
= ( [ r ], ( "r", t_mid ) )
|
||||
| r_skip
|
||||
= ( [ l ], ( "l", t_mid ) )
|
||||
| d_skip
|
||||
= ( [ u ], ( "u", s_mid ) )
|
||||
| u_skip
|
||||
= ( [ d ], ( "d", s_mid ) )
|
||||
| otherwise
|
||||
= let why' = case why of
|
||||
"" -> ""
|
||||
_ -> " (" ++ why ++ ")"
|
||||
in case dim of
|
||||
0 -> ( [ l, r ], ( "t" ++ why', t_mid ) )
|
||||
1 -> ( [ d, u ], ( "s" ++ why', s_mid ) )
|
||||
_ -> error "bisect: fall-back bisection dimension should be either 0 or 1"
|
||||
in ( bisGuesses, whatBis )
|
||||
|
||||
-- An implementation of "bound-consistency" from the paper
|
||||
-- "Parallelization of a bound-consistency enforcing procedure and its application in solving nonlinear systems"
|
||||
makeBox2Consistent :: Box -> Box
|
||||
makeBox2Consistent x = ( `State.evalState` False ) $ doLoop 0.25 x
|
||||
where
|
||||
doLoop :: Double -> Box -> State Bool Box
|
||||
doLoop lambda x = do
|
||||
x' <- boundConsistency get_t set_t lambda x
|
||||
x'' <- boundConsistency get_s set_s lambda x'
|
||||
modified <- State.get
|
||||
let lambda' = if modified then lambda else 0.5 * lambda
|
||||
if lambda' < 0.001
|
||||
then return x''
|
||||
else do { State.put False ; doLoop lambda' x'' }
|
||||
-- | Interval Newton method with Gauss–Seidel step.
|
||||
intervalGaussSeidel
|
||||
:: ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-- ^ equations
|
||||
-> Preconditioner
|
||||
-- ^ preconditioner to use for the Gauss–Seidel step
|
||||
-> Box
|
||||
-> Writer ( [ Box ], [ Box ] ) [ Box ]
|
||||
intervalGaussSeidel
|
||||
eqs
|
||||
precondMethod
|
||||
( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||
, i
|
||||
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||
)
|
||||
| StrokeDatum { 𝛿E𝛿sdcdt = D12 _ ( T ( T f_t ) ) ( T ( T f_s ) ) }
|
||||
<- ( eqs t `Seq.index` i ) s
|
||||
, StrokeDatum { ee = D22 _ee_mid _ _ _ _ _
|
||||
, 𝛿E𝛿sdcdt = D12 ( T f_mid ) ( T ( T _f_t_mid ) ) ( T ( T _f_s_mid ) ) }
|
||||
<- ( eqs i_t_mid `Seq.index` i ) i_s_mid
|
||||
= let -- Interval Newton method: take one Gauss–Seidel step
|
||||
-- for the equation f'(x) v = - f(x_mid),
|
||||
-- where f = 𝛿E/𝛿s * dc/dt
|
||||
( a, b ) = precondition precondMethod
|
||||
( midI f_t, midI f_s )
|
||||
( f_t, f_s ) ( neg f_mid )
|
||||
--(a, b)
|
||||
-- | 𝕀 (ℝ1 ee_lo) (ℝ1 ee_hi) <- ee_mid
|
||||
-- , 𝕀 (ℝ1 ee_t_lo) (ℝ1 ee_t_hi) <- ee_t
|
||||
-- , 𝕀 (ℝ1 ee_s_lo) (ℝ1 ee_s_hi) <- ee_s
|
||||
-- , 𝕀 (ℝ2 fx_lo fy_lo) (ℝ2 fx_hi fy_hi) <- f_mid
|
||||
-- , 𝕀 (ℝ2 f_tx_lo f_ty_lo) (ℝ2 f_tx_hi f_ty_hi) <- f_t
|
||||
-- , 𝕀 (ℝ2 f_sx_lo f_sy_lo) (ℝ2 f_sx_hi f_sy_hi) <- f_s
|
||||
-- = ( ( 𝕀 (ℝ2 f_tx_lo ee_t_lo) (ℝ2 f_tx_hi ee_t_hi)
|
||||
-- , 𝕀 (ℝ2 f_sx_lo ee_s_lo) (ℝ2 f_sx_hi ee_s_hi)
|
||||
-- )
|
||||
-- , neg $ 𝕀 (ℝ2 fx_lo ee_lo) (ℝ2 fx_hi ee_hi)
|
||||
-- )
|
||||
|
||||
boundConsistency :: ( Box -> 𝕀 Double )
|
||||
-> ( 𝕀 Double -> Box -> Box )
|
||||
-> Double -> Box -> State Bool Box
|
||||
boundConsistency getter setter lambda box = do
|
||||
let x@( 𝕀 x_inf x_sup ) = getter box
|
||||
c1 = ( 1 - lambda ) * x_inf + lambda * x_sup
|
||||
c2 = lambda * x_inf + ( 1 - lambda ) * x_sup
|
||||
x'_inf =
|
||||
case makeBox1Consistent ( setter ( 𝕀 x_inf c1 ) box ) of
|
||||
[] -> c1
|
||||
x's -> minimum $ map ( inf . getter ) x's
|
||||
x'_sup =
|
||||
case makeBox1Consistent ( setter ( 𝕀 c2 x_sup ) box ) of
|
||||
[] -> c2
|
||||
x's -> maximum $ map ( sup . getter ) x's
|
||||
x' = 𝕀 x'_inf x'_sup
|
||||
when ( width x - width x' >= eps_eq ) $
|
||||
State.put True
|
||||
return $ setter x' box
|
||||
gsGuesses = gaussSeidel a b
|
||||
( coerce ( (-) @( 𝕀 Double ) ) t i_t_mid
|
||||
, coerce ( (-) @( 𝕀 Double ) ) s i_s_mid )
|
||||
in
|
||||
-- If the Gauss–Seidel step was a contraction, then the box
|
||||
-- contains a unique solution (by the Banach fixed point theorem).
|
||||
--
|
||||
-- These boxes can thus be directly added to the solution set:
|
||||
-- Newton's method is guaranteed to converge to the unique solution.
|
||||
let !(done, todo) = bimap ( map ( mkGuess . fst ) ) ( map ( mkGuess . fst ) )
|
||||
$ partition snd gsGuesses
|
||||
in do tell ([], done)
|
||||
return todo
|
||||
where
|
||||
t_mid = 0.5 * ( t_lo + t_hi )
|
||||
s_mid = 0.5 * ( s_lo + s_hi )
|
||||
i_t_mid = singleton ( ℝ1 t_mid )
|
||||
i_s_mid = singleton ( ℝ1 s_mid )
|
||||
mkGuess ( t0, s0 ) = ( coerce ( (+) @( 𝕀 Double ) ) t0 i_t_mid
|
||||
, i
|
||||
, coerce ( (+) @( 𝕀 Double ) ) s0 i_s_mid )
|
||||
neg ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) )
|
||||
= let !( 𝕀 x'_lo x'_hi ) = negate $ 𝕀 x_lo x_hi
|
||||
!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
|
||||
in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
|
||||
|
||||
-- An implementation of "bc_enforce" from the paper
|
||||
-- "Parallelization of a bound-consistency enforcing procedure and its application in solving nonlinear systems"
|
||||
--
|
||||
-- See also
|
||||
-- "Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems"
|
||||
makeBox1Consistent :: Box -> [ Box ]
|
||||
makeBox1Consistent x =
|
||||
( `State.evalState` False ) $
|
||||
pipeFunctionsWhileTrue (allNarrowingOperators eps_eq eps_bis eqs) x
|
||||
eps_eq = 1e-5 -- TODO: this is an additive constant,
|
||||
-- but I think we also want a multiplicative constant?
|
||||
eps_bis = minWidth
|
||||
-- | An implementation of "bc_enforce" from the paper
|
||||
-- "Parallelization of a bound-consistency enforcing procedure and its application in solving nonlinear systems"
|
||||
--
|
||||
-- See also
|
||||
-- "Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems"
|
||||
makeBox1Consistent
|
||||
:: ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-> Double -> Double
|
||||
-> Box -> [ Box ]
|
||||
makeBox1Consistent eqs minWidth epsEq x =
|
||||
( `State.evalState` False ) $
|
||||
pipeFunctionsWhileTrue (allNarrowingOperators epsEq minWidth eqs) x
|
||||
|
||||
-- | An implementation of "bound-consistency" from the paper
|
||||
-- "Parallelization of a bound-consistency enforcing procedure and its application in solving nonlinear systems"
|
||||
makeBox2Consistent
|
||||
:: ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||
-> Double -> Double -> Double
|
||||
-> Box -> Box
|
||||
makeBox2Consistent eqs minWidth epsEq lambdaMin x0 = ( `State.evalState` False ) $ doLoop 0.25 x0
|
||||
where
|
||||
doLoop :: Double -> Box -> State Bool Box
|
||||
doLoop lambda x = do
|
||||
x' <- boundConsistency get_t set_t lambda x
|
||||
x'' <- boundConsistency get_s set_s lambda x'
|
||||
modified <- State.get
|
||||
let lambda' = if modified then lambda else 0.5 * lambda
|
||||
if lambda' < lambdaMin
|
||||
then return x''
|
||||
else do { State.put False ; doLoop lambda' x'' }
|
||||
|
||||
boundConsistency :: ( Box -> 𝕀 Double )
|
||||
-> ( 𝕀 Double -> Box -> Box )
|
||||
-> Double -> Box -> State Bool Box
|
||||
boundConsistency getter setter lambda box = do
|
||||
let x@( 𝕀 x_inf x_sup ) = getter box
|
||||
c1 = ( 1 - lambda ) * x_inf + lambda * x_sup
|
||||
c2 = lambda * x_inf + ( 1 - lambda ) * x_sup
|
||||
x'_inf =
|
||||
case makeBox1Consistent eqs minWidth epsEq ( setter ( 𝕀 x_inf c1 ) box ) of
|
||||
[] -> c1
|
||||
x's -> minimum $ map ( inf . getter ) x's
|
||||
x'_sup =
|
||||
case makeBox1Consistent eqs minWidth epsEq ( setter ( 𝕀 c2 x_sup ) box ) of
|
||||
[] -> c2
|
||||
x's -> maximum $ map ( sup . getter ) x's
|
||||
x' = 𝕀 x'_inf x'_sup
|
||||
when ( width x - width x' >= epsEq ) $
|
||||
State.put True
|
||||
return $ setter x' box
|
||||
|
||||
ee_potential_zero :: StrokeDatum 3 𝕀 -> Bool
|
||||
ee_potential_zero dat =
|
||||
|
|
@ -1736,7 +1783,6 @@ ee_potential_zero dat =
|
|||
cmpℝ2 (<=) ( inf $ unT $ _D12_v $ 𝛿E𝛿sdcdt dat ) ( ℝ2 0 0 )
|
||||
&& cmpℝ2 (>=) ( sup $ unT $ _D12_v $ 𝛿E𝛿sdcdt dat ) ( ℝ2 0 0 )
|
||||
|
||||
|
||||
zero, one :: Double
|
||||
zero = 1e-6
|
||||
one = 1 - zero
|
||||
|
|
@ -1841,7 +1887,7 @@ leftNarrow eps_equal eps_bisection ff' = left_narrow
|
|||
x' <- x's
|
||||
if sup x' - inf x' < eps_bisection
|
||||
then return x'
|
||||
else left_narrow =<< bisect x'
|
||||
else left_narrow =<< bisectI x'
|
||||
|
||||
-- TODO: de-duplicate with 'leftNarrow'?
|
||||
rightNarrow :: Double
|
||||
|
|
@ -1875,10 +1921,10 @@ rightNarrow eps_equal eps_bisection ff' = right_narrow
|
|||
x' <- x's
|
||||
if sup x' - inf x' < eps_bisection
|
||||
then return x'
|
||||
else right_narrow =<< bisect x'
|
||||
else right_narrow =<< bisectI x'
|
||||
|
||||
bisect :: 𝕀 Double -> [ 𝕀 Double ]
|
||||
bisect x@( 𝕀 x_inf x_sup )
|
||||
bisectI :: 𝕀 Double -> [ 𝕀 Double ]
|
||||
bisectI x@( 𝕀 x_inf x_sup )
|
||||
| x_inf == x_sup
|
||||
= [ x ]
|
||||
| otherwise
|
||||
|
|
@ -1953,7 +1999,10 @@ allNarrowingOperators eps_eq eps_bis eqs =
|
|||
} = 𝛿E𝛿sdcdt $ ( eqs t `Seq.index` i ) s
|
||||
in ( 𝕀 y_inf y_sup, 𝕀 y'_inf y'_sup )
|
||||
|
||||
get_t, get_s :: Box -> 𝕀 Double
|
||||
get_t ( 𝕀 ( ℝ1 t_inf ) ( ℝ1 t_sup ), _, _ ) = 𝕀 t_inf t_sup
|
||||
|
||||
set_t, set_s :: 𝕀 Double -> Box -> Box
|
||||
set_t ( 𝕀 t_inf t_sup ) ( _, i, s ) = ( 𝕀 ( ℝ1 t_inf ) ( ℝ1 t_sup ), i, s )
|
||||
get_s ( _ , _, 𝕀 ( ℝ1 s_inf ) ( ℝ1 s_sup ) ) = 𝕀 s_inf s_sup
|
||||
set_s ( 𝕀 s_inf s_sup ) ( t, i, _ ) = ( t, i, 𝕀 ( ℝ1 s_inf ) ( ℝ1 s_sup ) )
|
||||
|
|
@ -78,7 +78,10 @@ import Math.Bezier.Cubic.Fit
|
|||
import Math.Bezier.Spline
|
||||
( Spline(..), Curves(..), Curve(..), NextPoint(..) )
|
||||
import Math.Bezier.Stroke
|
||||
( RootSolvingAlgorithm(..), invalidateCache )
|
||||
( RootSolvingAlgorithm(..)
|
||||
, CuspFindingOptions(..), Preconditioner(..)
|
||||
, invalidateCache
|
||||
)
|
||||
import Math.Linear
|
||||
( ℝ(..) )
|
||||
import MetaBrush.Action
|
||||
|
|
@ -212,6 +215,8 @@ runApplication application = do
|
|||
--HalleyM2
|
||||
NewtonRaphson
|
||||
{ maxIters = 20, precision = 8 }
|
||||
cuspFindingOptionsTVar <- STM.newTVarIO @( Maybe CuspFindingOptions ) $
|
||||
Just defaultCuspFindingOptions
|
||||
|
||||
-- Put all these stateful variables in a record for conciseness.
|
||||
let
|
||||
|
|
@ -337,6 +342,7 @@ runApplication application = do
|
|||
debug <- STM.readTVar debugTVar
|
||||
fitParameters <- STM.readTVar fitParametersTVar
|
||||
rootsAlgo <- STM.readTVar rootsAlgoTVar
|
||||
mbCuspOptions <- STM.readTVar cuspFindingOptionsTVar
|
||||
STM.writeTVar recomputeStrokesTVar False
|
||||
let
|
||||
addRulers :: ( ( Int32, Int32 ) -> Cairo.Render () ) -> ( ( Int32, Int32 ) -> Cairo.Render () )
|
||||
|
|
@ -348,7 +354,9 @@ runApplication application = do
|
|||
doc
|
||||
pure
|
||||
( addRulers <$> getDocumentRender
|
||||
colours rootsAlgo fitParameters mode debug
|
||||
colours
|
||||
rootsAlgo mbCuspOptions fitParameters
|
||||
mode debug
|
||||
modifiers mbMousePos mbHoldAction mbPartialPath
|
||||
doc
|
||||
)
|
||||
|
|
|
|||
|
|
@ -74,7 +74,7 @@ import Math.Bezier.Spline
|
|||
import Math.Bezier.Stroke
|
||||
( Cusp(..), CachedStroke(..), invalidateCache
|
||||
, computeStrokeOutline
|
||||
, RootSolvingAlgorithm
|
||||
, RootSolvingAlgorithm, CuspFindingOptions
|
||||
)
|
||||
import Math.Linear
|
||||
( ℝ(..), T(..) )
|
||||
|
|
@ -148,12 +148,16 @@ blankRender :: Colours -> Cairo.Render ()
|
|||
blankRender _ = pure ()
|
||||
|
||||
getDocumentRender
|
||||
:: Colours -> RootSolvingAlgorithm -> FitParameters -> Mode -> Bool
|
||||
:: Colours
|
||||
-> RootSolvingAlgorithm -> Maybe CuspFindingOptions -> FitParameters
|
||||
-> Mode -> Bool
|
||||
-> Set Modifier -> Maybe ( ℝ 2 ) -> Maybe HoldAction -> Maybe PartialPath
|
||||
-> Document
|
||||
-> ST RealWorld ( ( Int32, Int32 ) -> Cairo.Render () )
|
||||
getDocumentRender
|
||||
cols rootAlgo fitParams mode debug
|
||||
cols
|
||||
rootAlgo mbCuspOptions fitParams
|
||||
mode debug
|
||||
modifiers mbMousePos mbHoldEvent mbPartialPath
|
||||
doc@( Document { viewportCenter = ℝ2 cx cy, zoomFactor, documentContent = content } )
|
||||
= do
|
||||
|
|
@ -215,7 +219,10 @@ getDocumentRender
|
|||
-> previewStroke :<| foldMap visibleStrokes ( strokes content )
|
||||
_ -> foldMap visibleStrokes ( strokes content )
|
||||
|
||||
strokesRenderData <- traverseMaybe ( sequenceA . strokeRenderData rootAlgo fitParams ) modifiedStrokes
|
||||
strokesRenderData <-
|
||||
traverseMaybe
|
||||
( sequenceA . strokeRenderData rootAlgo mbCuspOptions fitParams )
|
||||
modifiedStrokes
|
||||
|
||||
let
|
||||
renderSelectionRect :: Cairo.Render ()
|
||||
|
|
@ -276,8 +283,13 @@ instance NFData StrokeRenderData where
|
|||
-- - the computed outline (using fitting algorithm),
|
||||
-- - the brush shape function.
|
||||
-- - Otherwise, this consists of the underlying spline path only.
|
||||
strokeRenderData :: RootSolvingAlgorithm -> FitParameters -> Stroke -> Maybe ( ST RealWorld StrokeRenderData )
|
||||
strokeRenderData rootAlgo fitParams
|
||||
strokeRenderData
|
||||
:: RootSolvingAlgorithm
|
||||
-> Maybe CuspFindingOptions
|
||||
-> FitParameters
|
||||
-> Stroke
|
||||
-> Maybe ( ST RealWorld StrokeRenderData )
|
||||
strokeRenderData rootAlgo mbCuspOptions fitParams
|
||||
( Stroke
|
||||
{ strokeSpline = spline :: StrokeSpline clo ( Record pointFields )
|
||||
, strokeBrush = ( strokeBrush :: Maybe ( Brush brushFields ) )
|
||||
|
|
@ -302,7 +314,7 @@ strokeRenderData rootAlgo fitParams
|
|||
|
||||
-- Compute the outline using the brush function.
|
||||
( outline, fitPts, cusps ) <-
|
||||
computeStrokeOutline @clo rootAlgo fitParams
|
||||
computeStrokeOutline @clo rootAlgo mbCuspOptions fitParams
|
||||
( toUsedParams . brushParams ) embedUsedParams brushFn
|
||||
spline
|
||||
pure $
|
||||
|
|
|
|||
Loading…
Reference in a new issue