mirror of
https://gitlab.com/sheaf/metabrush.git
synced 2024-11-05 14:53:37 +00:00
precondition before taking Gauss-Seidel step
This commit is contained in:
sheaf
parent
78c03b99e1
commit
1ae84fec97
|
|
@ -25,7 +25,7 @@ import Control.Arrow
|
|||
import Control.Applicative
|
||||
( Applicative(..) )
|
||||
import Control.Monad
|
||||
( guard, unless )
|
||||
( unless )
|
||||
import Control.Monad.ST
|
||||
( RealWorld, ST )
|
||||
import Data.Bifunctor
|
||||
|
|
@ -33,7 +33,7 @@ import Data.Bifunctor
|
|||
import Data.Coerce
|
||||
( Coercible, coerce )
|
||||
import Data.Foldable
|
||||
( for_, toList )
|
||||
( for_ )
|
||||
import Data.Functor.Identity
|
||||
( Identity(..) )
|
||||
import Data.List
|
||||
|
|
@ -88,6 +88,8 @@ import qualified Control.Parallel.Strategies as Strats
|
|||
-- rounded-hw
|
||||
import Numeric.Rounded.Hardware
|
||||
( Rounded(..) )
|
||||
import Numeric.Rounded.Hardware.Interval.NonEmpty
|
||||
( Interval(..) )
|
||||
import qualified Numeric.Rounded.Hardware.Interval.NonEmpty as Interval
|
||||
|
||||
-- transformers
|
||||
|
|
@ -122,7 +124,7 @@ import Math.Differentiable
|
|||
, type ExtentOrder
|
||||
)
|
||||
import Math.Epsilon
|
||||
( epsilon )
|
||||
( epsilon, nearZero )
|
||||
import Math.Interval
|
||||
import Math.Linear
|
||||
import Math.Module
|
||||
|
|
@ -339,8 +341,7 @@ computeStrokeOutline fitParams ptParams toBrushParams brushFn spline@( Spline {
|
|||
( ( _, startTgtFwd), ( _, startTgtBwd ) ) = outlineFn firstOutlineFn $ ℝ1 0
|
||||
( ( _, endTgtFwd ), ( _, endTgtBwd ) ) = outlineFn lastOutlineFn $ ℝ1 1
|
||||
fwdStartCap, bwdStartCap :: SplinePts Open
|
||||
cusps :: [ Cusp ]
|
||||
OutlineData ( fmap fst -> TwoSided fwdStartCap bwdStartCap ) cusps
|
||||
OutlineData ( fmap fst -> TwoSided fwdStartCap bwdStartCap ) _
|
||||
= snd . runWriter
|
||||
$ tellBrushJoin ( endTgt, endTgtFwd, endTgtBwd ) spt0 ( startTgt, startTgtFwd, startTgtBwd )
|
||||
-> do
|
||||
|
|
@ -596,7 +597,7 @@ outlineFunction ptParams toBrushParams brushFromParams sp0 crv =
|
|||
$ runD ( brushFromParams @Point proxy# id )
|
||||
$ toBrushParams params_t
|
||||
|
||||
( newtDunno, newtSols ) = intervalNewtonGS 0.0001 curvesI
|
||||
( newtDunno, newtSols ) = intervalNewtonGS InverseMidJacobian 0.0001 curvesI
|
||||
|
||||
in --trace
|
||||
-- ( unlines $
|
||||
|
|
@ -1184,9 +1185,14 @@ cuspCoords eqs ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), i, 𝕀 ( ℝ1 s_lo ) ( ℝ1
|
|||
}
|
||||
where
|
||||
t_mid = 0.5 * ( t_lo + t_hi )
|
||||
s_mid = 0.5 * ( t_lo + t_hi )
|
||||
s_mid = 0.5 * ( s_lo + s_hi )
|
||||
|
||||
|
||||
data Preconditioner
|
||||
= NoPreconditioning
|
||||
| InverseMidJacobian
|
||||
deriving stock Show
|
||||
|
||||
-- | Interval Newton method with Gauss–Seidel step for inversion
|
||||
-- of the interval Jacobian.
|
||||
--
|
||||
|
|
@ -1194,10 +1200,11 @@ cuspCoords eqs ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), i, 𝕀 ( ℝ1 s_lo ) ( ℝ1
|
|||
-- (and to which Newton's method will converge starting from anywhere inside
|
||||
-- the box), and @dunno@ which are small boxes which might or might not
|
||||
-- contain solutions.
|
||||
intervalNewtonGS :: Double
|
||||
intervalNewtonGS :: Preconditioner
|
||||
-> Double
|
||||
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 'Interval ) )
|
||||
-> ( [ ( 𝕀ℝ 1, Int, 𝕀ℝ 1 ) ], [ ( 𝕀ℝ 1, Int, 𝕀ℝ 1 ) ] )
|
||||
intervalNewtonGS minWidth eqs =
|
||||
intervalNewtonGS precondMethod minWidth eqs =
|
||||
go [ ( 𝕀 ( ℝ1 0 ) ( ℝ1 1 ), i, 𝕀 ( ℝ1 0 ) ( ℝ1 1 ) )
|
||||
| i <- [ 0 .. length ( eqs ( 𝕀 ( ℝ1 0 ) ( ℝ1 1 ) ) ) - 1 ]
|
||||
]
|
||||
|
|
@ -1231,13 +1238,11 @@ intervalNewtonGS minWidth eqs =
|
|||
, cmpℝ2 (>) ( getRounded ( Interval.sup $ ival f ) ) ( ℝ2 0 0 )
|
||||
-> let -- Interval Newton method: take one Gauss–Seidel step
|
||||
-- for the equation f'(X) v = - f(x_mid).
|
||||
-- !precond = matInverse ( f_t_mid, f_s_mid )
|
||||
-- !a = matMul precond ( f_t, f_s )
|
||||
-- !b = matMulVec precond ( neg f_mid )
|
||||
-- !gsGuesses = gaussSeidel a b ( t, s )
|
||||
!gsGuesses = gaussSeidel
|
||||
( f_t, f_s )
|
||||
( neg f_mid )
|
||||
!( a, b ) = precondition precondMethod
|
||||
( f_t_mid, f_s_mid )
|
||||
( f_t, f_s ) ( neg f_mid )
|
||||
|
||||
!gsGuesses = gaussSeidel a b
|
||||
( coerce ( (-) @( 𝕀 Double ) ) t i_t_mid
|
||||
, coerce ( (-) @( 𝕀 Double ) ) s i_s_mid )
|
||||
in if all ( smaller . fst ) gsGuesses
|
||||
|
|
@ -1283,6 +1288,50 @@ intervalNewtonGS minWidth eqs =
|
|||
!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
|
||||
in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
|
||||
|
||||
precondition :: Preconditioner
|
||||
-> ( 𝕀ℝ 2, 𝕀ℝ 2 )
|
||||
-> ( 𝕀ℝ 2, 𝕀ℝ 2 )
|
||||
-> 𝕀ℝ 2
|
||||
-> ( ( 𝕀ℝ 2, 𝕀ℝ 2 ), 𝕀ℝ 2 )
|
||||
precondition meth jac_mid a@( a1, a2 ) b =
|
||||
case meth of
|
||||
NoPreconditioning
|
||||
-> ( a, b )
|
||||
InverseMidJacobian
|
||||
| ( 𝕀 ( ℝ2 a11_lo a21_lo ) ( ℝ2 a11_hi a21_hi )
|
||||
, 𝕀 ( ℝ2 a12_lo a22_lo ) ( ℝ2 a12_hi a22_hi ) ) <- jac_mid
|
||||
, let !a11 = 0.5 * ( a11_lo + a11_hi )
|
||||
!a12 = 0.5 * ( a12_lo + a12_hi )
|
||||
!a21 = 0.5 * ( a21_lo + a21_hi )
|
||||
!a22 = 0.5 * ( a22_lo + a22_hi )
|
||||
!d = a11 * a22 - a12 * a21
|
||||
, not ( nearZero d )
|
||||
, let !precond = ( ℝ2 a22 -a21, ℝ2 -a12 a11 )
|
||||
!inv = recip d
|
||||
f x = scale inv $ matMulVec precond x
|
||||
-> ( ( f a1, f a2 ), f b )
|
||||
| otherwise
|
||||
-> ( a, b )
|
||||
|
||||
scale :: Double -> 𝕀ℝ 2 -> 𝕀ℝ 2
|
||||
scale s ( 𝕀 ( ℝ2 a1_lo a2_lo ) ( ℝ2 a1_hi a2_hi ) )
|
||||
| I ( Rounded b1_lo ) ( Rounded b1_hi )
|
||||
<- I ( Rounded s ) ( Rounded s ) * I ( Rounded a1_lo ) ( Rounded a1_hi )
|
||||
, I ( Rounded b2_lo ) ( Rounded b2_hi )
|
||||
<- I ( Rounded s ) ( Rounded s ) * I ( Rounded a2_lo ) ( Rounded a2_hi )
|
||||
= 𝕀 ( ℝ2 b1_lo b2_lo ) ( ℝ2 b1_hi b2_hi )
|
||||
|
||||
matMulVec :: ( ℝ 2, ℝ 2 ) -> 𝕀ℝ 2 -> 𝕀ℝ 2
|
||||
matMulVec ( ℝ2 a11 a21, ℝ2 a12 a22 ) ( 𝕀 ( ℝ2 u_lo v_lo ) ( ℝ2 u_hi v_hi ) ) =
|
||||
let !( I ( Rounded u'_lo ) ( Rounded u'_hi ) ) =
|
||||
I ( Rounded a11 ) ( Rounded a11 ) * I ( Rounded u_lo ) ( Rounded u_hi )
|
||||
+ I ( Rounded a12 ) ( Rounded a12 ) * I ( Rounded v_lo ) ( Rounded v_hi )
|
||||
!( I ( Rounded v'_lo ) ( Rounded v'_hi ) ) =
|
||||
I ( Rounded a21 ) ( Rounded a21 ) * I ( Rounded u_lo ) ( Rounded u_hi )
|
||||
+ I ( Rounded a22 ) ( Rounded a22 ) * I ( Rounded v_lo ) ( Rounded v_hi )
|
||||
in 𝕀 ( ℝ2 u'_lo v'_lo ) ( ℝ2 u'_hi v'_hi )
|
||||
|
||||
|
||||
cmpℝ2 :: ( Double -> Double -> Bool ) -> ℝ 2 -> ℝ 2 -> Bool
|
||||
cmpℝ2 cmp ( ℝ2 x1 y1 ) ( ℝ2 x2 y2 )
|
||||
= cmp x1 x2 && cmp y1 y2
|
||||
|
|
|
|||
Loading…
Reference in a new issue