Math.VectorSpace.DimensionAware

Documentation

data DimensionalityWitness v where

Low-level case distinction between spaces with a dimension that is both fixed and low enough that it makes sense to treat it this way, and more general spaces where this is not feasible.

Use this type only when defining instances of DimensionAware. When making decisions based on dimensionality, DimensionalityCases is more convenient.

Constructors

IsStaticDimensional :: n `Dimensional` v => DimensionalityWitness v

IsFlexibleDimensional :: StaticDimension v ~ 'Nothing => DimensionalityWitness v

class VectorSpace v => DimensionAware v where

This class does not really pose any restrictions on a vector space type, but allows it to express its dimension. This is for optimisation purposes only, specifically to allow low-dimensional vectors to be represented efficiently in unboxed arrays / matrices.

Associated Types

type StaticDimension v :: Maybe Nat

If this is Nothing, it can mean the dimension is infinite, or just big, or simply unknown / not considered in the implementation.

type StaticDimension v = 'Nothing

Methods

dimensionalityWitness :: DimensionalityWitness v

Instances

DimensionAware Integer

Defined in Math.VectorSpace.DimensionAware

Associated Types

type StaticDimension Integer :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness Integer

DimensionAware Double

Defined in Math.VectorSpace.DimensionAware

Associated Types

type StaticDimension Double :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness Double

DimensionAware Float

Defined in Math.VectorSpace.DimensionAware

Associated Types

type StaticDimension Float :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness Float

DimensionAware Int

Defined in Math.VectorSpace.DimensionAware

Associated Types

type StaticDimension Int :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness Int

Integral n => DimensionAware (Ratio n)

Defined in Math.VectorSpace.DimensionAware

Associated Types

type StaticDimension (Ratio n) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (Ratio n)

(Num' n, Unbox n) => DimensionAware (FinSuppSeq n)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (FinSuppSeq n) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (FinSuppSeq n)

(Num' n, Unbox n) => DimensionAware (Sequence n)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (Sequence n) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (Sequence n)

(Num' s, Eq s) => DimensionAware (V0 s)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (V0 s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (V0 s)

(Num' s, Eq s) => DimensionAware (V1 s)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (V1 s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (V1 s)

(Num' s, Eq s) => DimensionAware (V2 s)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (V2 s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (V2 s)

(Num' s, Eq s) => DimensionAware (V3 s)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (V3 s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (V3 s)

(Num' s, Eq s) => DimensionAware (V4 s)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (V4 s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (V4 s)

(Semimanifold m, DimensionAware (Needle (VRep m)), Scalar (Needle m) ~ Scalar (Needle (VRep m))) => DimensionAware (GenericNeedle m)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (GenericNeedle m) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (GenericNeedle m)

DimensionAware (ZeroDim s)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (ZeroDim s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (ZeroDim s)

(Num' s, TensorSpace v, Scalar v ~ s) => DimensionAware (SymmetricTensor s v)

Defined in Math.LinearMap.Category.Instances

Associated Types

type StaticDimension (SymmetricTensor s v) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (SymmetricTensor s v)

(DimensionAware u, DimensionAware v, Scalar u ~ Scalar v) => DimensionAware (u, v)

Defined in Math.VectorSpace.DimensionAware

Associated Types

type StaticDimension (u, v) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (u, v)

DimensionAware v => DimensionAware (Rec0 v s)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (Rec0 v s) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (Rec0 v s)

(LinearSpace u, LinearSpace v, DimensionAware u, DimensionAware v, Scalar u ~ s, Scalar v ~ s) => DimensionAware (LinearFunction s u v)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (LinearFunction s u v) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (LinearFunction s u v)

(LinearSpace u, TensorSpace v, Scalar u ~ s, Scalar v ~ s) => DimensionAware (LinearMap s u v)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (LinearMap s u v) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (LinearMap s u v)

(TensorSpace u, TensorSpace v, Scalar u ~ s, Scalar v ~ s) => DimensionAware (Tensor s u v)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (Tensor s u v) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (Tensor s u v)

(DimensionAware (f p), DimensionAware (g p), Scalar (f p) ~ Scalar (g p)) => DimensionAware ((f :*: g) p)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension ((f :*: g) p) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness ((f :*: g) p)

DimensionAware (f p) => DimensionAware (M1 i c f p)

Defined in Math.LinearMap.Category.Class

Associated Types

type StaticDimension (M1 i c f p) :: Maybe Nat

Methods

dimensionalityWitness :: DimensionalityWitness (M1 i c f p)

class (DimensionAware v, StaticDimension v ~ 'Just n) => Dimensional n v | v -> n where

Minimal complete definition

unsafeFromArrayWithOffset, unsafeWriteArrayWithOffset

Methods

knownDimensionalitySing :: Sing n

default knownDimensionalitySing :: KnownNat n => Sing n

unsafeFromArrayWithOffset :: Vector α (Scalar v) => Int -> α (Scalar v) -> v

Read basis expansion from an array, starting at the specified offset. The array must have at least length n + offset, else the behaviour is undefined.

unsafeWriteArrayWithOffset :: Vector α (Scalar v) => Mutable α σ (Scalar v) -> Int -> v -> ST σ ()

Instances

Dimensional 1 Integer

Defined in Math.VectorSpace.DimensionAware

Methods

knownDimensionalitySing :: Sing 1

unsafeFromArrayWithOffset :: Vector α (Scalar Integer) => Int -> α (Scalar Integer) -> Integer

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar Integer) => Mutable α σ (Scalar Integer) -> Int -> Integer -> ST σ ()

Dimensional 1 Double

Defined in Math.VectorSpace.DimensionAware

Methods

knownDimensionalitySing :: Sing 1

unsafeFromArrayWithOffset :: Vector α (Scalar Double) => Int -> α (Scalar Double) -> Double

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar Double) => Mutable α σ (Scalar Double) -> Int -> Double -> ST σ ()

Dimensional 1 Float

Defined in Math.VectorSpace.DimensionAware

Methods

knownDimensionalitySing :: Sing 1

unsafeFromArrayWithOffset :: Vector α (Scalar Float) => Int -> α (Scalar Float) -> Float

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar Float) => Mutable α σ (Scalar Float) -> Int -> Float -> ST σ ()

Dimensional 1 Int

Defined in Math.VectorSpace.DimensionAware

Methods

knownDimensionalitySing :: Sing 1

unsafeFromArrayWithOffset :: Vector α (Scalar Int) => Int -> α (Scalar Int) -> Int

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar Int) => Mutable α σ (Scalar Int) -> Int -> Int -> ST σ ()

(Semimanifold m, Dimensional n (Needle (VRep m)), Scalar (Needle m) ~ Scalar (Needle (VRep m))) => Dimensional n (GenericNeedle m)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing n

unsafeFromArrayWithOffset :: Vector α (Scalar (GenericNeedle m)) => Int -> α (Scalar (GenericNeedle m)) -> GenericNeedle m

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (GenericNeedle m)) => Mutable α σ (Scalar (GenericNeedle m)) -> Int -> GenericNeedle m -> ST σ ()

(Num' s, Eq s) => Dimensional 0 (V0 s)

Defined in Math.LinearMap.Category.Instances

Methods

knownDimensionalitySing :: Sing 0

unsafeFromArrayWithOffset :: Vector α (Scalar (V0 s)) => Int -> α (Scalar (V0 s)) -> V0 s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (V0 s)) => Mutable α σ (Scalar (V0 s)) -> Int -> V0 s -> ST σ ()

Dimensional 0 (ZeroDim s)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing 0

unsafeFromArrayWithOffset :: Vector α (Scalar (ZeroDim s)) => Int -> α (Scalar (ZeroDim s)) -> ZeroDim s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (ZeroDim s)) => Mutable α σ (Scalar (ZeroDim s)) -> Int -> ZeroDim s -> ST σ ()

Integral n => Dimensional 1 (Ratio n)

Defined in Math.VectorSpace.DimensionAware

Methods

knownDimensionalitySing :: Sing 1

unsafeFromArrayWithOffset :: Vector α (Scalar (Ratio n)) => Int -> α (Scalar (Ratio n)) -> Ratio n

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (Ratio n)) => Mutable α σ (Scalar (Ratio n)) -> Int -> Ratio n -> ST σ ()

(Num' s, Eq s) => Dimensional 1 (V1 s)

Defined in Math.LinearMap.Category.Instances

Methods

knownDimensionalitySing :: Sing 1

unsafeFromArrayWithOffset :: Vector α (Scalar (V1 s)) => Int -> α (Scalar (V1 s)) -> V1 s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (V1 s)) => Mutable α σ (Scalar (V1 s)) -> Int -> V1 s -> ST σ ()

(Num' s, Eq s) => Dimensional 2 (V2 s)

Defined in Math.LinearMap.Category.Instances

Methods

knownDimensionalitySing :: Sing 2

unsafeFromArrayWithOffset :: Vector α (Scalar (V2 s)) => Int -> α (Scalar (V2 s)) -> V2 s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (V2 s)) => Mutable α σ (Scalar (V2 s)) -> Int -> V2 s -> ST σ ()

(Num' s, Eq s) => Dimensional 3 (V3 s)

Defined in Math.LinearMap.Category.Instances

Methods

knownDimensionalitySing :: Sing 3

unsafeFromArrayWithOffset :: Vector α (Scalar (V3 s)) => Int -> α (Scalar (V3 s)) -> V3 s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (V3 s)) => Mutable α σ (Scalar (V3 s)) -> Int -> V3 s -> ST σ ()

(Num' s, Eq s) => Dimensional 4 (V4 s)

Defined in Math.LinearMap.Category.Instances

Methods

knownDimensionalitySing :: Sing 4

unsafeFromArrayWithOffset :: Vector α (Scalar (V4 s)) => Int -> α (Scalar (V4 s)) -> V4 s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (V4 s)) => Mutable α σ (Scalar (V4 s)) -> Int -> V4 s -> ST σ ()

(Num' s, Dimensional n v, TensorSpace v, Scalar v ~ s, m ~ TriangularNum n) => Dimensional m (SymmetricTensor s v)

Defined in Math.LinearMap.Category.Instances

Methods

knownDimensionalitySing :: Sing m

unsafeFromArrayWithOffset :: Vector α (Scalar (SymmetricTensor s v)) => Int -> α (Scalar (SymmetricTensor s v)) -> SymmetricTensor s v

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (SymmetricTensor s v)) => Mutable α σ (Scalar (SymmetricTensor s v)) -> Int -> SymmetricTensor s v -> ST σ ()

(Dimensional n u, Dimensional m v, Scalar u ~ Scalar v, nm ~ (n + m)) => Dimensional nm (u, v)

Defined in Math.VectorSpace.DimensionAware

Methods

knownDimensionalitySing :: Sing nm

unsafeFromArrayWithOffset :: Vector α (Scalar (u, v)) => Int -> α (Scalar (u, v)) -> (u, v)

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (u, v)) => Mutable α σ (Scalar (u, v)) -> Int -> (u, v) -> ST σ ()

Dimensional n v => Dimensional n (Rec0 v s)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing n

unsafeFromArrayWithOffset :: Vector α (Scalar (Rec0 v s)) => Int -> α (Scalar (Rec0 v s)) -> Rec0 v s

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (Rec0 v s)) => Mutable α σ (Scalar (Rec0 v s)) -> Int -> Rec0 v s -> ST σ ()

(Dimensional n u, Dimensional m v, LinearSpace u, LinearSpace v, Scalar u ~ s, Scalar v ~ s, nm ~ (n * m)) => Dimensional nm (LinearFunction s u v)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing nm

unsafeFromArrayWithOffset :: Vector α (Scalar (LinearFunction s u v)) => Int -> α (Scalar (LinearFunction s u v)) -> LinearFunction s u v

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (LinearFunction s u v)) => Mutable α σ (Scalar (LinearFunction s u v)) -> Int -> LinearFunction s u v -> ST σ ()

(Dimensional n u, Dimensional m v, LinearSpace u, TensorSpace v, Scalar u ~ s, Scalar v ~ s, nm ~ (n * m)) => Dimensional nm (LinearMap s u v)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing nm

unsafeFromArrayWithOffset :: Vector α (Scalar (LinearMap s u v)) => Int -> α (Scalar (LinearMap s u v)) -> LinearMap s u v

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (LinearMap s u v)) => Mutable α σ (Scalar (LinearMap s u v)) -> Int -> LinearMap s u v -> ST σ ()

(Dimensional n u, Dimensional m v, TensorSpace u, TensorSpace v, Scalar u ~ s, Scalar v ~ s, nm ~ (n * m)) => Dimensional nm (Tensor s u v)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing nm

unsafeFromArrayWithOffset :: Vector α (Scalar (Tensor s u v)) => Int -> α (Scalar (Tensor s u v)) -> Tensor s u v

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (Tensor s u v)) => Mutable α σ (Scalar (Tensor s u v)) -> Int -> Tensor s u v -> ST σ ()

(Dimensional n (f p), Dimensional m (g p), Scalar (f p) ~ Scalar (g p), nm ~ (n + m)) => Dimensional nm ((f :*: g) p)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing nm

unsafeFromArrayWithOffset :: Vector α (Scalar ((f :*: g) p)) => Int -> α (Scalar ((f :*: g) p)) -> (f :*: g) p

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar ((f :*: g) p)) => Mutable α σ (Scalar ((f :*: g) p)) -> Int -> (f :*: g) p -> ST σ ()

Dimensional n (f p) => Dimensional n (M1 i c f p)

Defined in Math.LinearMap.Category.Class

Methods

knownDimensionalitySing :: Sing n

unsafeFromArrayWithOffset :: Vector α (Scalar (M1 i c f p)) => Int -> α (Scalar (M1 i c f p)) -> M1 i c f p

unsafeWriteArrayWithOffset :: forall (α :: Type -> Type) σ. Vector α (Scalar (M1 i c f p)) => Mutable α σ (Scalar (M1 i c f p)) -> Int -> M1 i c f p -> ST σ ()

data DimensionalityCases v where

Batteries-included version of DimensionalityWitness.

Constructors

StaticDimensionalCase :: (KnownNat n, n `Dimensional` v) => DimensionalityCases v

FlexibleDimensionalCase :: StaticDimension v ~ 'Nothing => DimensionalityCases v

type Dimension v = FromJust (StaticDimension v)

class DimensionAware v => StaticDimensional v where

Methods

dimensionIsStatic :: forall r. (forall n. (KnownNat n, n `Dimensional` v) => r) -> r

Instances

(DimensionAware v, IsJust (StaticDimension v) ~ 'True) => StaticDimensional v

Defined in Math.VectorSpace.DimensionAware

Methods

dimensionIsStatic :: (forall (n :: Nat). (KnownNat n, Dimensional n v) => r) -> r

dimensionalitySing :: forall v n. n `Dimensional` v => Sing n

dimensionality :: forall v. DimensionAware v => DimensionalityCases v

dimension :: forall v n a. (n `Dimensional` v, Integral a) => a

dimensionOf :: forall v n a. (n `Dimensional` v, Integral a) => v -> a

Convenience function. The result does never depend on the runtime input, only on its type.

unsafeFromArray :: forall v n α. (n `Dimensional` v, Vector α (Scalar v)) => α (Scalar v) -> v

Read basis expansion from an array. The array must have length n, else the behaviour is undefined.

fromArray :: forall v n α. (n `Dimensional` v, Vector α (Scalar v)) => α (Scalar v) -> Maybe v

Read basis expansion from an array, if the size equals the dimension.

toArray :: forall v n α. (n `Dimensional` v, Vector α (Scalar v)) => v -> α (Scalar v)

Write out basis expansion to an array, whose length will always be n.

staticDimensionSing :: forall v. DimensionAware v => Sing (StaticDimension v)

scalarUnsafeFromArrayWithOffset :: (v ~ Scalar v, Vector α v) => Int -> α v -> v

scalarUnsafeWriteArrayWithOffset :: (v ~ Scalar v, Vector α v) => Mutable α σ v -> Int -> v -> ST σ ()

unsafeFromArrayWithOffsetViaList :: forall v n α. (n `Dimensional` v, Vector α (Scalar v)) => ([Scalar v] -> v) -> Int -> α (Scalar v) -> v

unsafeWriteArrayWithOffsetViaList :: forall v n α σ. (n `Dimensional` v, Vector α (Scalar v)) => (v -> [Scalar v]) -> Mutable α σ (Scalar v) -> Int -> v -> ST σ ()

notStaticDimensionalContradiction :: forall v n r. StaticDimension v ~ 'Nothing => r

To be used as an “absurd” values for implementing methods whose constraints combine to require both static- and flexible dimensionality (which can thus never be called).

The actual type of this should be

  notStaticDimensionalContradiction :: ∀ v n r
    . (nDimensionalv, StaticDimension v ~ 'Nothing) => r

GHC 9.6 baulks at that, though. It is a self-contradicting type, but that's the whole point...