Data.Function.Affine

Documentation

data Affine s d c where

Constructors

Affine :: (ChartIndex d :->: (c, LinearMap s (Needle d) (Needle c))) -> Affine s d c

Instances

Category (Affine s :: Type -> Type -> Type)

Defined in Data.Function.Affine

Associated Types

type Object (Affine s) o

Methods

id :: forall (a :: κ). Object (Affine s) a => Affine s a a

(.) :: forall (a :: κ) (b :: κ) (c :: κ). (Object (Affine s) a, Object (Affine s) b, Object (Affine s) c) => Affine s b c -> Affine s a b -> Affine s a c

(ScalarManifold s, Eq s) => Morphism (Affine s)

Defined in Data.Function.Affine

Methods

first :: (ObjectPair (Affine s) b d, ObjectPair (Affine s) c d) => Affine s b c -> Affine s (b, d) (c, d)

second :: (ObjectPair (Affine s) d b, ObjectPair (Affine s) d c) => Affine s b c -> Affine s (d, b) (d, c)

(***) :: (ObjectPair (Affine s) b b', ObjectPair (Affine s) c c') => Affine s b c -> Affine s b' c' -> Affine s (b, b') (c, c')

(ScalarManifold s, Eq s) => PreArrow (Affine s)

Defined in Data.Function.Affine

Methods

(&&&) :: (Object (Affine s) b, ObjectPair (Affine s) c c') => Affine s b c -> Affine s b c' -> Affine s b (c, c')

terminal :: Object (Affine s) b => Affine s b (UnitObject (Affine s))

fst :: ObjectPair (Affine s) x y => Affine s (x, y) x

snd :: ObjectPair (Affine s) x y => Affine s (x, y) y

(ScalarManifold s, Eq s) => WellPointed (Affine s)

Defined in Data.Function.Affine

Associated Types

type PointObject (Affine s) x

Methods

globalElement :: ObjectPoint (Affine s) x => x -> Affine s (UnitObject (Affine s)) x

unit :: CatTagged (Affine s) (UnitObject (Affine s))

const :: (Object (Affine s) b, ObjectPoint (Affine s) x) => x -> Affine s b x

(ScalarManifold s, Eq s) => Cartesian (Affine s)

Defined in Data.Function.Affine

Associated Types

type PairObjects (Affine s) a b

type UnitObject (Affine s)

Methods

swap :: (ObjectPair (Affine s) a b, ObjectPair (Affine s) b a) => Affine s (a, b) (b, a)

attachUnit :: (unit ~ UnitObject (Affine s), ObjectPair (Affine s) a unit) => Affine s a (a, unit)

detachUnit :: (unit ~ UnitObject (Affine s), ObjectPair (Affine s) a unit) => Affine s (a, unit) a

regroup :: (ObjectPair (Affine s) a b, ObjectPair (Affine s) b c, ObjectPair (Affine s) a (b, c), ObjectPair (Affine s) (a, b) c) => Affine s (a, (b, c)) ((a, b), c)

regroup' :: (ObjectPair (Affine s) a b, ObjectPair (Affine s) b c, ObjectPair (Affine s) a (b, c), ObjectPair (Affine s) (a, b) c) => Affine s ((a, b), c) (a, (b, c))

EnhancedCat (Affine s) (LinearMap s)

Defined in Data.Function.Affine

Methods

arr :: (Object (LinearMap s) b, Object (LinearMap s) c, Object (Affine s) b, Object (Affine s) c) => LinearMap s b c -> Affine s b c

EnhancedCat ((->) :: Type -> Type -> Type) (Affine s)

Defined in Data.Function.Affine

Methods

arr :: (Object (Affine s) b, Object (Affine s) c, Object (->) b, Object (->) c) => Affine s b c -> b -> c

(Atlas x, HasTrie (ChartIndex x), LinearManifold (Needle x), Scalar (Needle x) ~ s, LinearManifold y, Scalar y ~ s, Num' s) => AdditiveGroup (Affine s x y)

Defined in Data.Function.Affine

Methods

zeroV :: Affine s x y

(^+^) :: Affine s x y -> Affine s x y -> Affine s x y

negateV :: Affine s x y -> Affine s x y

(^-^) :: Affine s x y -> Affine s x y -> Affine s x y

(Atlas x, HasTrie (ChartIndex x), LinearManifold (Needle x), Scalar (Needle x) ~ s, LinearManifold y, Scalar y ~ s, Num' s) => VectorSpace (Affine s x y)

Defined in Data.Function.Affine

Associated Types

type Scalar (Affine s x y)

Methods

(*^) :: Scalar (Affine s x y) -> Affine s x y -> Affine s x y

(Atlas x, HasTrie (ChartIndex x), LinearManifold (Needle x), Scalar (Needle x) ~ s, LinearManifold (Needle y), Scalar (Needle y) ~ s, Manifold y, Scalar (Needle y) ~ s) => AffineSpace (Affine s x y)

Defined in Data.Function.Affine

Associated Types

type Diff (Affine s x y)

Methods

(.-.) :: Affine s x y -> Affine s x y -> Diff (Affine s x y)

(.+^) :: Affine s x y -> Diff (Affine s x y) -> Affine s x y

(Atlas x, HasTrie (ChartIndex x), Manifold y, LinearManifold (Needle x), Scalar (Needle x) ~ s, LinearManifold (Needle y), Scalar (Needle y) ~ s) => PseudoAffine (Affine s x y)

Defined in Data.Function.Affine

Methods

(.-~.) :: Affine s x y -> Affine s x y -> Maybe (Needle (Affine s x y))

(.-~!) :: Affine s x y -> Affine s x y -> Needle (Affine s x y)

pseudoAffineWitness :: PseudoAffineWitness (Affine s x y)

(Atlas x, HasTrie (ChartIndex x), Manifold y, LinearManifold (Needle x), Scalar (Needle x) ~ s, LinearManifold (Needle y), Scalar (Needle y) ~ s) => Semimanifold (Affine s x y)

Defined in Data.Function.Affine

Associated Types

type Needle (Affine s x y)

Methods

(.+~^) :: Affine s x y -> Needle (Affine s x y) -> Affine s x y

(.-~^) :: Affine s x y -> Needle (Affine s x y) -> Affine s x y

semimanifoldWitness :: SemimanifoldWitness (Affine s x y)

type Object (Affine s :: Type -> Type -> Type) (x :: Type)

Defined in Data.Function.Affine

type Object (Affine s :: Type -> Type -> Type) (x :: Type) = (Manifold x, Atlas' x, Scalar (Needle x) ~ s)

type UnitObject (Affine s)

Defined in Data.Function.Affine

type UnitObject (Affine s) = ZeroDim s

type PointObject (Affine s) x

Defined in Data.Function.Affine

type PointObject (Affine s) x = ()

type PairObjects (Affine s) a b

Defined in Data.Function.Affine

type PairObjects (Affine s) a b = ()

type Scalar (Affine s x y)

Defined in Data.Function.Affine

type Scalar (Affine s x y) = s

type Diff (Affine s x y)

Defined in Data.Function.Affine

type Diff (Affine s x y) = Affine s x (Needle y)

type Needle (Affine s x y)

Defined in Data.Function.Affine

type Needle (Affine s x y) = Affine s x (Needle y)

evalAffine :: forall x y s. (Manifold x, Atlas x, HasTrie (ChartIndex x), Manifold y, s ~ Scalar (Needle x), s ~ Scalar (Needle y)) => Affine s x y -> x -> (y, LinearMap s (Needle x) (Needle y))

fromOffsetSlope :: forall x y s. (LinearSpace x, Atlas x, HasTrie (ChartIndex x), Manifold y, s ~ Scalar x, s ~ Scalar (Needle y)) => y -> LinearMap s x (Needle y) -> Affine s x y

Misc

lensEmbedding :: forall k x c s. (Num' s, LinearSpace x, LinearSpace c, Object k x, Object k c, Scalar x ~ s, Scalar c ~ s, EnhancedCat k (LinearMap s)) => Lens' x c -> Embedding k c x

correspondingDirections :: forall x c t s. (WithField s AffineManifold c, WithField s AffineManifold x, SemiInner (Needle c), SemiInner (Needle x), RealFrac' s, Traversable t) => (c, x) -> t (Needle c, Needle x) -> Maybe (Embedding (Affine s) c x)