Data.Manifold.DifferentialEquation

Formulating simple differential eqns.

type DifferentialEqn ㄇ x y = Shade (x, y) -> LocalDifferentialEqn ㄇ x y

type ODE x y = DifferentialEqn AffineModel x y

An ordinary differential equation is one that does not need any a-priori partial derivatives to compute the derivative for integration in some propagation direction. Classically, ODEs are usually understood as DifferentialEquation ℝ ℝ⁰ y, but actually x can at least be an arbitrary one-dimensional space (i.e. basically real intervals or 'S¹'). In these cases, there is always only one partial derivative: that which we integrate over, in the only possible direction for propagation.

constLinearDEqn :: forall x y. (SimpleSpace x, SimpleSpace y, AffineManifold y, Scalar x ~ ℝ, Scalar y ~ ℝ) => (y +> (x +> y)) -> ((x +> y) +> y) -> DifferentialEqn QuadraticModel x y

constLinearODE :: forall x y. (SimpleSpace x, Scalar x ~ ℝ, AffineManifold y, SimpleSpace y, Scalar y ~ ℝ) => ((x +> y) +> y) -> ODE x y

iterateFilterDEqn_static :: (ModellableRelation x y, MonadPlus m, LocalModel ㄇ) => InformationMergeStrategy [] m (x, Shade' y) iy -> Embedding (->) (Shade' y) iy -> DifferentialEqn ㄇ x y -> PointsWeb x (Shade' y) -> Cofree m (PointsWeb x (Shade' y))

Cost functions for error bounds

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

Solver configuration

data InconsistencyStrategy m x y where

Constructors

AbortOnInconsistency :: InconsistencyStrategy Maybe x y

IgnoreInconsistencies :: InconsistencyStrategy Identity x y

HighlightInconsistencies :: y -> InconsistencyStrategy Identity x y

Instances

Functor (InconsistencyStrategy m x)

Methods

fmap :: (a -> b) -> InconsistencyStrategy m x a -> InconsistencyStrategy m x b

(<$) :: a -> InconsistencyStrategy m x b -> InconsistencyStrategy m x a