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Always run Gauss-Seidel at tiny sizes to rule out fake solutions

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sheaf 2024-04-22 01:52:29 +02:00
parent 0e59d85143
commit b1df0d04e6
1 changed files with 19 additions and 18 deletions
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37
brush-strokes/src/lib/Math/Root/Isolation.hs
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@ -250,26 +250,27 @@ defaultRootIsolationAlgorithms
:: forall n d
. BoxCt n d
=> Double -> Double -> Box n -> BoxHistory n -> Either String ( NE.NonEmpty ( RootIsolationAlgorithm n d ) )
defaultRootIsolationAlgorithms minWidth ε_eq box history
-- All the box widths are lower than the minimum width: give up.
| and $ ( \ cd -> width cd <= minWidth ) <$> coordinates box
= Left $ "widths <= " ++ show minWidth
| otherwise
= Right $ case history of
lastRoundBoxes : _
-- If, in the last round of strategies, we didn't try bisection...
| any ( \case { BisectionStep {} -> False; _ -> True } . fst ) lastRoundBoxes
, ( _step, 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.
-> NE.singleton $ Bisection ( defaultBisectionOptions minWidth ε_eq box )
-- Otherwise, do a normal round.
-- Currently: we try an interval Gauss–Seidel step followed by box(1)-consistency.
_ -> GaussSeidel _gaussSeidelOptions
NE.:| [ Box1 _box1Options ]
defaultRootIsolationAlgorithms minWidth ε_eq 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
, ( _step, 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...
-- ...unless the box is already too small, in which case we give up.
-> if verySmall
then Left $ "widths <= " ++ show minWidth
else Right $ NE.singleton $ Bisection ( defaultBisectionOptions minWidth ε_eq box )
-- Otherwise, do a normal round.
-- Currently: we try an interval Gauss–Seidel step followed by box(1)-consistency.
_ -> Right $ GaussSeidel _gaussSeidelOptions
NE.:| [ Box1 _box1Options | not verySmall ]
where
verySmall = and $ ( \ cd -> width cd <= minWidth ) <$> coordinates box
_box1Options :: Box1Options n d
_box1Options =
Box1Options