Data.TypeList.MultiIndex

We define the a multidimensional array of indices called MultiIndex. The canonical implementation of a MultiIndex is an heterogeneous list of Ordinals. Below we illustrate some example of MultiIndex types and the elements they contain.

Three :|: Nil = {(1),(2),(3)}

Three :|: (Two :|: Nil) = {(1,1),(1,2),(2,1),(2,2),(3,1),(3,2)}

Three :|: (Two :|: (Two :|: Nil)) = {(1,1,1),(1,1,2),(1,2,1),(1,2,2),(2,1,1),(2,1,2),(2,2,1),(2,2,2),(3,1,1),(3,1,2),(3,2,1),(3,2,2)}

Documentation

data Nil

Constructors

Nil

Instances

Bounded Nil

Eq Nil

Show Nil

Generic Nil

Cardinality Nil

Random Nil

ReverseList Nil

TypeList Nil

Dimensions Nil

MultiIndex Nil

Extend Nil l'

TypeList l => TailRevList Nil l

DropList Zero Nil

TakeList Zero Nil

TypeList l => AppendList Nil l

(Ordinal i, Ordinal j) => Matrix i j (Tensor (:|: i (:|: j Nil)) e)

Functor (Tensor Nil)

Applicative (Tensor Nil)

FromList (Tensor Nil)

(Ordinal i, Sum i i) => SquareMatrix (Tensor (:|: i (:|: i Nil)))

Eq e => Eq (Tensor Nil e)

Show e => Show (Tensor Nil e)

(Ordinal i, Ordinal j) => Transpose (Tensor (:|: i (:|: j Nil)) e)

Tensor (Tensor Nil e)

Dimensions (Tensor Nil e)

(Eq e, Fractional e, Ordinal i, Ordinal j) => LinearSystem (Tensor (:|: i (:|: j Nil)) e) (Tensor (:|: i Nil) e)

(Eq e, Fractional e, Ordinal i, Ordinal j, Ordinal k, Sum j k) => LinearSystem (Tensor (:|: i (:|: j Nil)) e) (Tensor (:|: i (:|: k Nil)) e)

data a :|: b

This is the constructor for heterogeneous lists, equivalent to : for standard lists. Nil is used to end the lists, just like '[]'.

Constructors

a :|: b

Instances

(Ordinal i, Ordinal j) => Matrix i j (Tensor (:|: i (:|: j Nil)) e)

DropList Zero l => DropList Zero (:|: e l)

TakeList Zero l => TakeList Zero (:|: e l)

(Ordinal i1, Ordinal i2, Sum i1 i2, MultiIndex is) => MultiIndexConcat Zero (:|: i1 is) (:|: i2 is)

(MultiIndex is, Ordinal n, Functor (Tensor is), Functor (Tensor (:|: n is))) => Functor (Tensor (:|: (Succ n) is))

(MultiIndex is, Functor (Tensor is)) => Functor (Tensor (:|: One is))

(MultiIndex is, Ordinal n, Applicative (Tensor is), Applicative (Tensor (:|: n is))) => Applicative (Tensor (:|: (Succ n) is))

(MultiIndex is, Applicative (Tensor is)) => Applicative (Tensor (:|: One is))

(FromList (Tensor is), FromList (Tensor (:|: n is)), Ordinal n, MultiIndex is) => FromList (Tensor (:|: (Succ n) is))

(FromList (Tensor is), MultiIndex is) => FromList (Tensor (:|: One is))

(Ordinal i, Sum i i) => SquareMatrix (Tensor (:|: i (:|: i Nil)))

DropList n l => DropList (Succ n) (:|: e l)

TakeList n l => TakeList (Succ n) (:|: e l)

(Cardinal n, Ordinal i, MultiIndex js, MultiIndex ks, MultiIndexConcat n js ks) => MultiIndexConcat (Succ n) (:|: i js) (:|: i ks)

(Bounded e, Bounded l) => Bounded (:|: e l)

(Eq a, Eq b) => Eq (:|: a b)

(MultiIndex is, Ordinal n, Eq (Tensor is e), Eq (Tensor (:|: n is) e)) => Eq (Tensor (:|: (Succ n) is) e)

(MultiIndex is, Eq (Tensor is e)) => Eq (Tensor (:|: One is) e)

(Ordinal i, MultiIndex is) => Show (:|: i is)

(MultiIndex is, Ordinal n, Show (Tensor is e), Show (Tensor (:|: n is) e)) => Show (Tensor (:|: (Succ n) is) e)

(MultiIndex is, Show (Tensor is e)) => Show (Tensor (:|: One is) e)

Generic (:|: a b)

(Ordinal i, Ordinal j) => Transpose (Tensor (:|: i (:|: j Nil)) e)

(MultiIndex is, Ordinal n, Tensor (Tensor is e), Tensor (Tensor (:|: n is) e), ~ * e (Elem (Tensor is e)), ~ * is (Index (Tensor is e)), ~ * e (Elem (Tensor (:|: n is) e)), ~ * (Index (Tensor (:|: n is) e)) (:|: n is)) => Tensor (Tensor (:|: (Succ n) is) e)

(MultiIndex is, Tensor (Tensor is e), ~ * e (Elem (Tensor is e)), ~ * is (Index (Tensor is e))) => Tensor (Tensor (:|: One is) e)

(Cardinality e, Cardinality l, Cardinal (:*: (Card e) (Card l))) => Cardinality (:|: e l)

(Random e, Random l) => Random (:|: e l)

(TailRevList l Nil, TailRevList (:|: e l) Nil) => ReverseList (:|: e l)

TypeList l => HeadTail (:|: e l)

TypeList l => TypeList (:|: e l)

(Ordinal i, Dimensions is) => Dimensions (:|: i is)

Dimensions (Tensor (:|: n is) e) => Dimensions (Tensor (:|: (Succ n) is) e)

Dimensions (Tensor is e) => Dimensions (Tensor (:|: One is) e)

(Ordinal i, MultiIndex is) => MultiIndex (:|: i is)

(TailRevList l (:|: e l'), TypeList l') => TailRevList (:|: e l) l'

AppendList l l' => AppendList (:|: e l) l'

Extend l l' => Extend (:|: e l) (:|: e l')

(Eq e, Fractional e, Ordinal i, Ordinal j) => LinearSystem (Tensor (:|: i (:|: j Nil)) e) (Tensor (:|: i Nil) e)

(Eq e, Fractional e, Ordinal i, Ordinal j, Ordinal k, Sum j k) => LinearSystem (Tensor (:|: i (:|: j Nil)) e) (Tensor (:|: i (:|: k Nil)) e)

module Data.Ordinal

module Data.TypeList

class (Dimensions i, TypeList i) => MultiIndex i where

Methods

fromMultiIndex :: Num n => i -> [n]

toMultiIndex :: (Eq n, Num n) => [n] -> i

Instances

MultiIndex Nil

(Ordinal i, MultiIndex is) => MultiIndex (:|: i is)

multiIndex2Linear :: (MultiIndex i, Num n) => i -> n

class Dimensions i where

Class for types having multiple dimensions, like MultiIndexes or Tensors.

Methods

dimensions :: Num n => i -> [n]

Returns the dimensions list. It should always be independent on its argument and work on undefined.

Instances

Dimensions Nil

(Ordinal i, Dimensions is) => Dimensions (:|: i is)

Dimensions (Tensor (:|: n is) e) => Dimensions (Tensor (:|: (Succ n) is) e)

Dimensions (Tensor is e) => Dimensions (Tensor (:|: One is) e)

Dimensions (Tensor Nil e)

Dimensions i => Dimensions (Tensor i e)

class (Cardinal n, MultiIndex is, MultiIndex js) => MultiIndexConcat n is js

Associated Types

type Concat n is js

Instances

(Ordinal i1, Ordinal i2, Sum i1 i2, MultiIndex is) => MultiIndexConcat Zero (:|: i1 is) (:|: i2 is)

(Cardinal n, Ordinal i, MultiIndex js, MultiIndex ks, MultiIndexConcat n js ks) => MultiIndexConcat (Succ n) (:|: i js) (:|: i ks)