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

Ord Nil

Show Nil

Generic Nil

Cardinality Nil

ReverseList Nil

TypeList Nil

Dimensions Nil

MultiIndex Nil

Extend Nil l'

(TypeList Nil, TypeList l) => TailRevList Nil l

DropList Zero Nil

TakeList Zero Nil

(TypeList Nil, TypeList l) => AppendList Nil l

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

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

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

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

(Cardinal Zero, TypeList (:|: e l), DropList Zero l) => DropList Zero (:|: e l)

(Cardinal Zero, TypeList (:|: e l), TakeList Zero l) => TakeList Zero (:|: e l)

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

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

(Cardinal (Succ n), TypeList (:|: e l), DropList n l) => DropList (Succ n) (:|: e l)

(Cardinal (Succ n), TypeList (:|: e l), TakeList n l) => TakeList (Succ n) (:|: e l)

(Cardinal (Succ n), MultiIndex (:|: i js), MultiIndex (:|: i ks), 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)

(Eq (:|: e l), Ord e, Ord l) => Ord (:|: e l)

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

Generic (:|: a b)

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

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

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

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

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

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

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

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

(TypeList (:|: e l), TypeList 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.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

(Dimensions (:|: i is), TypeList (:|: i is), 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 i => Dimensions (Tensor i e)

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

Associated Types

type Concat n is js

Instances

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

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