Data.VectorSpace.Free.Sequence

Documentation

type Sequence = GSequence Vector

type BoxSequence = GSequence Vector

data GSequence array n

The space of possibly-infinite sequences, isomorphic to the space of all lists but implemented more efficiently (with exponentially-growing chunks of unboxed data, so the overhead is amortised). In other words, this is a type of spine-lazy but element-strict arrays.

This space is dual to FinSuppSeq, which is completely strict.

Constructors

Sequence

Fields

• sequenceHeads :: !(array n)

  Length must be at most minimumChunkSize in the outer constructor and double in each deeper layer. (Specification subject to future change!) If the length at depth 𝑑 is less than 2^𝑑, the remaining entries are treated as zeroes.

• sequenceRemain :: GSequence array n

SoloChunk

Fields

• chunkOffset :: !Int
• soloChunk :: !(array n)

  Length plus offset must be at most minimumChunkSize if this is the outer constructor and can double in each deeper layer.

Instances

Functor BoxSequence

Defined in Data.VectorSpace.Free.Sequence

Methods

fmap :: (a -> b) -> BoxSequence a -> BoxSequence b

(<$) :: a -> BoxSequence b -> BoxSequence a

(Unbox n, Num n) => IsList (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

Associated Types

type Item (Sequence n)

Methods

fromList :: [Item (Sequence n)] -> Sequence n

fromListN :: Int -> [Item (Sequence n)] -> Sequence n

toList :: Sequence n -> [Item (Sequence n)]

(Unbox n, Show n, Num n) => Show (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

Methods

showsPrec :: Int -> Sequence n -> ShowS

show :: Sequence n -> String

showList :: [Sequence n] -> ShowS

(Num n, Unbox n) => AffineSpace (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

Associated Types

type Diff (Sequence n)

Methods

(.-.) :: Sequence n -> Sequence n -> Diff (Sequence n)

(.+^) :: Sequence n -> Diff (Sequence n) -> Sequence n

(Num n, Unbox n) => HasBasis (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

Associated Types

type Basis (Sequence n)

Methods

basisValue :: Basis (Sequence n) -> Sequence n

decompose :: Sequence n -> [(Basis (Sequence n), Scalar (Sequence n))]

decompose' :: Sequence n -> Basis (Sequence n) -> Scalar (Sequence n)

(Num n, Unbox n) => VectorSpace (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

Associated Types

type Scalar (Sequence n)

Methods

(*^) :: Scalar (Sequence n) -> Sequence n -> Sequence n

(Num n, Unbox n) => AdditiveGroup (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

Methods

zeroV :: Sequence n

(^+^) :: Sequence n -> Sequence n -> Sequence n

negateV :: Sequence n -> Sequence n

(^-^) :: Sequence n -> Sequence n -> Sequence n

type Item (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

type Item (Sequence n) = n

type Diff (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

type Diff (Sequence n) = Sequence n

type Basis (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

type Basis (Sequence n) = Int

type Scalar (Sequence n)

Defined in Data.VectorSpace.Free.Sequence

type Scalar (Sequence n) = n

minimumChunkSize :: Int