| Copyright | (c) Justus Sagemüller 2016 |
|---|---|
| License | GPL v3 |
| Maintainer | (@) sagemueller $ geo.uni-koeln.de |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.Manifold.DifferentialEquation
Description
- type DifferentialEqn x y = Shade (x, y) -> LocalDifferentialEqn x y
- constLinearODE :: forall x y. (WithField ℝ LinearManifold x, SimpleSpace x, WithField ℝ LinearManifold y, SimpleSpace y) => ((x +> y) +> y) -> DifferentialEqn x y
- constLinearPDE :: forall x y y'. (WithField ℝ LinearManifold x, SimpleSpace x, WithField ℝ LinearManifold y, SimpleSpace y, FiniteFreeSpace y, WithField ℝ LinearManifold y', SimpleSpace y') => ((x +> (y, y')) +> (y, y')) -> DifferentialEqn x (y, y')
- filterDEqnSolution_static :: forall x y m. (WithField ℝ Manifold x, SimpleSpace (Needle x), Refinable y, Geodesic (Interior y)) => InconsistencyStrategy m x (Shade' y) -> DifferentialEqn x y -> PointsWeb x (Shade' y) -> m (PointsWeb x (Shade' y))
- iterateFilterDEqn_static :: (WithField ℝ Manifold x, SimpleSpace (Needle x), Refinable y, Geodesic (Interior y), Applicative m) => InconsistencyStrategy m x (Shade' y) -> DifferentialEqn x y -> PointsWeb x (Shade' y) -> [PointsWeb x (Shade' y)]
- maxDeviationsGoal :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => [Needle y] -> x -> Shade' y -> ℝ
- uncertaintyGoal :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => Metric' y -> x -> Shade' y -> ℝ
- uncertaintyGoal' :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => (x -> Metric' y) -> x -> Shade' y -> ℝ
- euclideanVolGoal :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => ℝ -> x -> Shade' y -> ℝ
- data InconsistencyStrategy m x y where
Formulating simple differential eqns.
type DifferentialEqn x y = Shade (x, y) -> LocalDifferentialEqn x y Source
constLinearODE :: forall x y. (WithField ℝ LinearManifold x, SimpleSpace x, WithField ℝ LinearManifold y, SimpleSpace y) => ((x +> y) +> y) -> DifferentialEqn x y Source
constLinearPDE :: forall x y y'. (WithField ℝ LinearManifold x, SimpleSpace x, WithField ℝ LinearManifold y, SimpleSpace y, FiniteFreeSpace y, WithField ℝ LinearManifold y', SimpleSpace y') => ((x +> (y, y')) +> (y, y')) -> DifferentialEqn x (y, y') Source
filterDEqnSolution_static :: forall x y m. (WithField ℝ Manifold x, SimpleSpace (Needle x), Refinable y, Geodesic (Interior y)) => InconsistencyStrategy m x (Shade' y) -> DifferentialEqn x y -> PointsWeb x (Shade' y) -> m (PointsWeb x (Shade' y)) Source
iterateFilterDEqn_static :: (WithField ℝ Manifold x, SimpleSpace (Needle x), Refinable y, Geodesic (Interior y), Applicative m) => InconsistencyStrategy m x (Shade' y) -> DifferentialEqn x y -> PointsWeb x (Shade' y) -> [PointsWeb x (Shade' y)] Source
Cost functions for error bounds
maxDeviationsGoal :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => [Needle y] -> x -> Shade' y -> ℝ Source
uncertaintyGoal :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => Metric' y -> x -> Shade' y -> ℝ Source
uncertaintyGoal' :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => (x -> Metric' y) -> x -> Shade' y -> ℝ Source
euclideanVolGoal :: (WithField ℝ EuclidSpace y, SimpleSpace (Needle y)) => ℝ -> x -> Shade' y -> ℝ Source
Solver configuration
data InconsistencyStrategy m x y where Source
Constructors
| AbortOnInconsistency :: InconsistencyStrategy Maybe x y | |
| IgnoreInconsistencies :: InconsistencyStrategy Identity x y | |
| HighlightInconsistencies :: y -> InconsistencyStrategy Identity x y |
Instances