Copyright	(c) Justus Sagemüller 2017
License	GPL v3
Maintainer	(@) jsagemue $ uni-koeln.de
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.Manifold.Function.LocalModel

Contents

The model class

Description

Synopsis

class LocalModel ㄇ where
- fitLocally :: ModellableRelation x y => [(Needle x, Shade' y)] -> Maybe (ㄇ x y)
- tweakLocalOffset :: ModellableRelation x y => Lens' (ㄇ x y) (Shade y)
- evalLocalModel :: ModellableRelation x y => ㄇ x y -> Needle x -> Shade' y
type ModellableRelation x y = (WithField ℝ Manifold x, Refinable y, Geodesic y, FlatSpace (Needle x), FlatSpace (Needle y))
data AffineModel x y = AffineModel {
- _affineModelOffset :: Shade y
- _affineModelLCoeff :: Shade (Needle x +> Needle y)
}
data QuadraticModel x y = QuadraticModel {
- _quadraticModelOffset :: Shade y
- _quadraticModelLCoeff :: Shade (Needle x +> Needle y)
- _quadraticModelQCoeff :: Shade (Needle x ⊗〃+> Needle y)
}
estimateLocalJacobian :: forall x y. (WithField ℝ Manifold x, Refinable y, SimpleSpace (Needle x), SimpleSpace (Needle y)) => Metric x -> [(Local x, Shade' y)] -> Maybe (Shade' (LocalLinear x y))
estimateLocalHessian :: forall x y. (WithField ℝ Manifold x, Refinable y, Geodesic y, FlatSpace (Needle x), FlatSpace (Needle y)) => NonEmpty (Local x, Shade' y) -> QuadraticModel x y
propagationCenteredModel :: forall x y ㄇ. (ModellableRelation x y, LocalModel ㄇ) => LocalDataPropPlan x (Shade' y) -> ㄇ x y
propagationCenteredQuadraticModel :: forall x y. ModellableRelation x y => LocalDataPropPlan x (Shade' y) -> QuadraticModel x y
quadraticModel_derivatives :: forall x y. (PseudoAffine x, PseudoAffine y, SimpleSpace (Needle x), SimpleSpace (Needle y), Scalar (Needle y) ~ Scalar (Needle x)) => QuadraticModel x y -> (Shade' y, (Shade' (LocalLinear x y), Shade' (LocalBilinear x y)))
type DifferentialEqn ㄇ x y = Shade (x, y) -> LocalDifferentialEqn ㄇ x y
newtype LocalDifferentialEqn ㄇ x y = LocalDifferentialEqn {
- _rescanDifferentialEqn :: ㄇ x y -> (Maybe (Shade' y), Maybe (Shade' (LocalLinear x y)))
}
propagateDEqnSolution_loc :: forall x y ㄇ. (ModellableRelation x y, LocalModel ㄇ) => DifferentialEqn ㄇ x y -> LocalDataPropPlan x (Shade' y) -> Maybe (Shade' y)
data LocalDataPropPlan x y = LocalDataPropPlan {
- _sourcePosition :: !(Interior x)
- _targetPosOffset :: !(Needle x)
- _sourceData, _targetAPrioriData :: !y
- _relatedData :: [(Needle x, y)]
}
rangeWithinVertices :: forall s i m t. (RealFrac' s, WithField s PseudoAffine i, WithField s PseudoAffine m, Geodesic i, Geodesic m, SimpleSpace (Needle i), SimpleSpace (Needle m), AffineManifold (Interior i), AffineManifold (Interior m), Object (Affine s) (Interior i), Object (Affine s) (Interior m), Traversable t) => (Interior i, Interior m) -> t (i, m) -> Maybe (Shade i -> Shade m)

The model class

class LocalModel ㄇ where Source #

Methods

fitLocally :: ModellableRelation x y => [(Needle x, Shade' y)] -> Maybe (ㄇ x y) Source #

tweakLocalOffset :: ModellableRelation x y => Lens' (ㄇ x y) (Shade y) Source #

evalLocalModel :: ModellableRelation x y => ㄇ x y -> Needle x -> Shade' y Source #

Instances

LocalModel AffineModel Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods fitLocally :: ModellableRelation x y => [(Needle x, Shade' y)] -> Maybe (AffineModel x y) Source # tweakLocalOffset :: ModellableRelation x y => Lens' (AffineModel x y) (Shade y) Source # evalLocalModel :: ModellableRelation x y => AffineModel x y -> Needle x -> Shade' y Source #
LocalModel QuadraticModel Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods fitLocally :: ModellableRelation x y => [(Needle x, Shade' y)] -> Maybe (QuadraticModel x y) Source # tweakLocalOffset :: ModellableRelation x y => Lens' (QuadraticModel x y) (Shade y) Source # evalLocalModel :: ModellableRelation x y => QuadraticModel x y -> Needle x -> Shade' y Source #

type ModellableRelation x y = (WithField ℝ Manifold x, Refinable y, Geodesic y, FlatSpace (Needle x), FlatSpace (Needle y)) Source #

Local data fit models

data AffineModel x y Source #

Constructors

AffineModel
Fields _affineModelOffset :: Shade y _affineModelLCoeff :: Shade (Needle x +> Needle y)

Instances

LocalModel AffineModel Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods fitLocally :: ModellableRelation x y => [(Needle x, Shade' y)] -> Maybe (AffineModel x y) Source # tweakLocalOffset :: ModellableRelation x y => Lens' (AffineModel x y) (Shade y) Source # evalLocalModel :: ModellableRelation x y => AffineModel x y -> Needle x -> Shade' y Source #
(Show (Shade y), Show (Shade (Needle x +> Needle y))) => Show (AffineModel x y) Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods showsPrec :: Int -> AffineModel x y -> ShowS # show :: AffineModel x y -> String # showList :: [AffineModel x y] -> ShowS #

data QuadraticModel x y Source #

Constructors

QuadraticModel
Fields _quadraticModelOffset :: Shade y _quadraticModelLCoeff :: Shade (Needle x +> Needle y) _quadraticModelQCoeff :: Shade (Needle x ⊗〃+> Needle y)

Instances

LocalModel QuadraticModel Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods fitLocally :: ModellableRelation x y => [(Needle x, Shade' y)] -> Maybe (QuadraticModel x y) Source # tweakLocalOffset :: ModellableRelation x y => Lens' (QuadraticModel x y) (Shade y) Source # evalLocalModel :: ModellableRelation x y => QuadraticModel x y -> Needle x -> Shade' y Source #
(Show (Shade y), Show (Shade (Needle x +> Needle y)), Show (Shade (Needle x ⊗〃+> Needle y))) => Show (QuadraticModel x y) Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods showsPrec :: Int -> QuadraticModel x y -> ShowS # show :: QuadraticModel x y -> String # showList :: [QuadraticModel x y] -> ShowS #

estimateLocalJacobian :: forall x y. (WithField ℝ Manifold x, Refinable y, SimpleSpace (Needle x), SimpleSpace (Needle y)) => Metric x -> [(Local x, Shade' y)] -> Maybe (Shade' (LocalLinear x y)) Source #

Deprecated: Use fitLocally

estimateLocalHessian :: forall x y. (WithField ℝ Manifold x, Refinable y, Geodesic y, FlatSpace (Needle x), FlatSpace (Needle y)) => NonEmpty (Local x, Shade' y) -> QuadraticModel x y Source #

Deprecated: Use fitLocally

propagationCenteredModel :: forall x y ㄇ. (ModellableRelation x y, LocalModel ㄇ) => LocalDataPropPlan x (Shade' y) -> ㄇ x y Source #

propagationCenteredQuadraticModel :: forall x y. ModellableRelation x y => LocalDataPropPlan x (Shade' y) -> QuadraticModel x y Source #

quadraticModel_derivatives :: forall x y. (PseudoAffine x, PseudoAffine y, SimpleSpace (Needle x), SimpleSpace (Needle y), Scalar (Needle y) ~ Scalar (Needle x)) => QuadraticModel x y -> (Shade' y, (Shade' (LocalLinear x y), Shade' (LocalBilinear x y))) Source #

Differential equations

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

newtype LocalDifferentialEqn ㄇ x y Source #

Constructors

LocalDifferentialEqn
Fields _rescanDifferentialEqn :: ㄇ x y -> (Maybe (Shade' y), Maybe (Shade' (LocalLinear x y)))

propagateDEqnSolution_loc :: forall x y ㄇ. (ModellableRelation x y, LocalModel ㄇ) => DifferentialEqn ㄇ x y -> LocalDataPropPlan x (Shade' y) -> Maybe (Shade' y) Source #

data LocalDataPropPlan x y Source #

Constructors

LocalDataPropPlan
Fields _sourcePosition :: !(Interior x) _targetPosOffset :: !(Needle x) _sourceData, _targetAPrioriData :: !y _relatedData :: [(Needle x, y)]

Instances

(Show (Interior x), Show y, Show (Needle x)) => Show (LocalDataPropPlan x y) Source #
Instance details Defined in Data.Manifold.Function.LocalModel Methods showsPrec :: Int -> LocalDataPropPlan x y -> ShowS # show :: LocalDataPropPlan x y -> String # showList :: [LocalDataPropPlan x y] -> ShowS #

Range interpolation

rangeWithinVertices :: forall s i m t. (RealFrac' s, WithField s PseudoAffine i, WithField s PseudoAffine m, Geodesic i, Geodesic m, SimpleSpace (Needle i), SimpleSpace (Needle m), AffineManifold (Interior i), AffineManifold (Interior m), Object (Affine s) (Interior i), Object (Affine s) (Interior m), Traversable t) => (Interior i, Interior m) -> t (i, m) -> Maybe (Shade i -> Shade m) Source #