Numeric.Dimensions.Idx

Provides a data type Idx that enumerates through multiple dimensions. Lower indices go first, i.e. assumed enumeration is i = i1 + i2*n1 + i3*n1*n2 + ... + ik*n1*n2*...*n(k-1). This is also to encourage column-first matrix enumeration and array layout.

Data types

data Idx ds where

Type-level dimensional indexing with arbitrary Int values inside

Constructors

Z :: Idx '[]

Zero-rank dimensionality - scalar

(:!) :: !Int -> !(Idx ds) -> Idx (d ': ds) infixr 5

List-like concatenation of indices

Instances

IsList (Idx ds)

Associated Types

type Item (Idx ds) :: *

Methods

fromList :: [Item (Idx ds)] -> Idx ds

fromListN :: Int -> [Item (Idx ds)] -> Idx ds

toList :: Idx ds -> [Item (Idx ds)]

Dimensions ds => Bounded (Idx ds)

Methods

minBound :: Idx ds

maxBound :: Idx ds

Dimensions ds => Enum (Idx ds)

Methods

succ :: Idx ds -> Idx ds

pred :: Idx ds -> Idx ds

toEnum :: Int -> Idx ds

fromEnum :: Idx ds -> Int

enumFrom :: Idx ds -> [Idx ds]

enumFromThen :: Idx ds -> Idx ds -> [Idx ds]

enumFromTo :: Idx ds -> Idx ds -> [Idx ds]

enumFromThenTo :: Idx ds -> Idx ds -> Idx ds -> [Idx ds]

Eq (Idx ds)

Methods

(==) :: Idx ds -> Idx ds -> Bool

(/=) :: Idx ds -> Idx ds -> Bool

Num (Idx ((:) Nat n ([] Nat)))

With this instance we can slightly reduce indexing expressions e.g. x ! (1 :! 2 :! 4) == x ! (1 :! 2 :! 4 :! Z)

Methods

(+) :: Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat])

(-) :: Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat])

(*) :: Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat])

negate :: Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat])

abs :: Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat])

signum :: Idx ((Nat ': n) [Nat]) -> Idx ((Nat ': n) [Nat])

fromInteger :: Integer -> Idx ((Nat ': n) [Nat])

Ord (Idx ds)

Methods

compare :: Idx ds -> Idx ds -> Ordering

(<) :: Idx ds -> Idx ds -> Bool

(<=) :: Idx ds -> Idx ds -> Bool

(>) :: Idx ds -> Idx ds -> Bool

(>=) :: Idx ds -> Idx ds -> Bool

max :: Idx ds -> Idx ds -> Idx ds

min :: Idx ds -> Idx ds -> Idx ds

Show (Idx ds)

Methods

showsPrec :: Int -> Idx ds -> ShowS

show :: Idx ds -> String

showList :: [Idx ds] -> ShowS

type Item (Idx ds)

type Item (Idx ds) = Int

appendIdx :: forall as b. Idx as -> Int -> Idx (as +: b)

Append index dimension

splitIdx :: forall as bs. FiniteList as => Idx (as ++ bs) -> (Idx as, Idx bs)

Split index into prefix and suffix dimensioned indices