Data.Repa.Array.Generic.Index

Shapes and Indices

Shapes

class Eq sh => Shape sh where

Class of types that can be used as array shapes and indices.

Minimal complete definition

rank, zeroDim, unitDim, intersectDim, addDim, size, inShapeRange, listOfShape, shapeOfList

Methods

rank :: sh -> Int

Get the number of dimensions in a shape.

zeroDim :: sh

The shape of an array of size zero, with a particular dimensionality.

unitDim :: sh

The shape of an array with size one, with a particular dimensionality.

intersectDim :: sh -> sh -> sh

Compute the intersection of two shapes.

addDim :: sh -> sh -> sh

Add the coordinates of two shapes componentwise

size :: sh -> Int

Get the total number of elements in an array with this shape.

inShapeRange :: sh -> sh -> sh -> Bool

Given a starting and ending index, check if some index is with that range.

listOfShape :: sh -> [Int]

Convert a shape into its list of dimensions.

shapeOfList :: [Int] -> Maybe sh

Convert a list of dimensions to a shape

Instances

Shape Int

Methods

rank :: Int -> Int

zeroDim :: Int

unitDim :: Int

intersectDim :: Int -> Int -> Int

addDim :: Int -> Int -> Int

size :: Int -> Int

inShapeRange :: Int -> Int -> Int -> Bool

listOfShape :: Int -> [Int]

shapeOfList :: [Int] -> Maybe Int

Shape Z

Methods

rank :: Z -> Int

zeroDim :: Z

unitDim :: Z

intersectDim :: Z -> Z -> Z

addDim :: Z -> Z -> Z

size :: Z -> Int

inShapeRange :: Z -> Z -> Z -> Bool

listOfShape :: Z -> [Int]

shapeOfList :: [Int] -> Maybe Z

Shape sh => Shape (RW sh)

Methods

rank :: RW sh -> Int

zeroDim :: RW sh

unitDim :: RW sh

intersectDim :: RW sh -> RW sh -> RW sh

addDim :: RW sh -> RW sh -> RW sh

size :: RW sh -> Int

inShapeRange :: RW sh -> RW sh -> RW sh -> Bool

listOfShape :: RW sh -> [Int]

shapeOfList :: [Int] -> Maybe (RW sh)

Shape sh => Shape ((:.) sh Int)

Methods

rank :: (sh :. Int) -> Int

zeroDim :: sh :. Int

unitDim :: sh :. Int

intersectDim :: (sh :. Int) -> (sh :. Int) -> sh :. Int

addDim :: (sh :. Int) -> (sh :. Int) -> sh :. Int

size :: (sh :. Int) -> Int

inShapeRange :: (sh :. Int) -> (sh :. Int) -> (sh :. Int) -> Bool

listOfShape :: (sh :. Int) -> [Int]

shapeOfList :: [Int] -> Maybe (sh :. Int)

inShape :: Shape sh => sh -> sh -> Bool

Given an array shape and index, check whether the index is in the shape.

showShape :: Shape sh => sh -> String

Nicely format a shape as a string

Polymorphic Shapes

data Z

An index of dimension zero

Constructors

Z

Instances

Eq Z

Methods

(==) :: Z -> Z -> Bool

(/=) :: Z -> Z -> Bool

Ord Z

Methods

compare :: Z -> Z -> Ordering

(<) :: Z -> Z -> Bool

(<=) :: Z -> Z -> Bool

(>) :: Z -> Z -> Bool

(>=) :: Z -> Z -> Bool

max :: Z -> Z -> Z

min :: Z -> Z -> Z

Read Z

Methods

readsPrec :: Int -> ReadS Z

readList :: ReadS [Z]

readPrec :: ReadPrec Z

readListPrec :: ReadPrec [Z]

Show Z

Methods

showsPrec :: Int -> Z -> ShowS

show :: Z -> String

showList :: [Z] -> ShowS

Shape Z

Methods

rank :: Z -> Int

zeroDim :: Z

unitDim :: Z

intersectDim :: Z -> Z -> Z

addDim :: Z -> Z -> Z

size :: Z -> Int

inShapeRange :: Z -> Z -> Z -> Bool

listOfShape :: Z -> [Int]

shapeOfList :: [Int] -> Maybe Z

Slice Z

Methods

sliceOfFull :: Z -> FullShape Z -> SliceShape Z

fullOfSlice :: Z -> SliceShape Z -> FullShape Z

Eq (Name (RW Z))

Methods

(==) :: Name (RW Z) -> Name (RW Z) -> Bool

(/=) :: Name (RW Z) -> Name (RW Z) -> Bool

Show (Name (RW Z))

Methods

showsPrec :: Int -> Name (RW Z) -> ShowS

show :: Name (RW Z) -> String

showList :: [Name (RW Z)] -> ShowS

Layout (RW Z)

Associated Types

data Name (RW Z) :: *

type Index (RW Z) :: *

Methods

name :: Name (RW Z)

create :: Name (RW Z) -> Index (RW Z) -> RW Z

extent :: RW Z -> Index (RW Z)

toIndex :: RW Z -> Index (RW Z) -> Int

fromIndex :: RW Z -> Int -> Index (RW Z)

type SliceShape Z

type SliceShape Z = Z

type FullShape Z

type FullShape Z = Z

data Name (RW Z)

data Name (RW Z) = RZ

type Index (RW Z)

type Index (RW Z) = Z

data tail :. head infixl 3

Our index type, used for both shapes and indices.

Constructors

!tail :. !head infixl 3

Instances

Eq (Name (RW sh)) => Eq (Name (RW ((:.) sh Int)))

Methods

(==) :: Name (RW (sh :. Int)) -> Name (RW (sh :. Int)) -> Bool

(/=) :: Name (RW (sh :. Int)) -> Name (RW (sh :. Int)) -> Bool

Show (Name (RW sh)) => Show (Name (RW ((:.) sh Int)))

Methods

showsPrec :: Int -> Name (RW (sh :. Int)) -> ShowS

show :: Name (RW (sh :. Int)) -> String

showList :: [Name (RW (sh :. Int))] -> ShowS

(Layout (RW sh), (~) * (Index (RW sh)) sh) => Layout (RW ((:.) sh Int))

Associated Types

data Name (RW ((:.) sh Int)) :: *

type Index (RW ((:.) sh Int)) :: *

Methods

name :: Name (RW (sh :. Int))

create :: Name (RW (sh :. Int)) -> Index (RW (sh :. Int)) -> RW (sh :. Int)

extent :: RW (sh :. Int) -> Index (RW (sh :. Int))

toIndex :: RW (sh :. Int) -> Index (RW (sh :. Int)) -> Int

fromIndex :: RW (sh :. Int) -> Int -> Index (RW (sh :. Int))

(Eq tail, Eq head) => Eq ((:.) tail head)

Methods

(==) :: (tail :. head) -> (tail :. head) -> Bool

(/=) :: (tail :. head) -> (tail :. head) -> Bool

(Ord tail, Ord head) => Ord ((:.) tail head)

Methods

compare :: (tail :. head) -> (tail :. head) -> Ordering

(<) :: (tail :. head) -> (tail :. head) -> Bool

(<=) :: (tail :. head) -> (tail :. head) -> Bool

(>) :: (tail :. head) -> (tail :. head) -> Bool

(>=) :: (tail :. head) -> (tail :. head) -> Bool

max :: (tail :. head) -> (tail :. head) -> tail :. head

min :: (tail :. head) -> (tail :. head) -> tail :. head

(Read tail, Read head) => Read ((:.) tail head)

Methods

readsPrec :: Int -> ReadS (tail :. head)

readList :: ReadS [tail :. head]

readPrec :: ReadPrec (tail :. head)

readListPrec :: ReadPrec [tail :. head]

(Show tail, Show head) => Show ((:.) tail head)

Methods

showsPrec :: Int -> (tail :. head) -> ShowS

show :: (tail :. head) -> String

showList :: [tail :. head] -> ShowS

Shape sh => Shape ((:.) sh Int)

Methods

rank :: (sh :. Int) -> Int

zeroDim :: sh :. Int

unitDim :: sh :. Int

intersectDim :: (sh :. Int) -> (sh :. Int) -> sh :. Int

addDim :: (sh :. Int) -> (sh :. Int) -> sh :. Int

size :: (sh :. Int) -> Int

inShapeRange :: (sh :. Int) -> (sh :. Int) -> (sh :. Int) -> Bool

listOfShape :: (sh :. Int) -> [Int]

shapeOfList :: [Int] -> Maybe (sh :. Int)

Slice sl => Slice ((:.) sl All)

Methods

sliceOfFull :: (sl :. All) -> FullShape (sl :. All) -> SliceShape (sl :. All)

fullOfSlice :: (sl :. All) -> SliceShape (sl :. All) -> FullShape (sl :. All)

Slice sl => Slice ((:.) sl Int)

Methods

sliceOfFull :: (sl :. Int) -> FullShape (sl :. Int) -> SliceShape (sl :. Int)

fullOfSlice :: (sl :. Int) -> SliceShape (sl :. Int) -> FullShape (sl :. Int)

data Name (RW ((:.) sh Int))

data Name (RW ((:.) sh Int)) = RC (Name (RW sh))

type Index (RW ((:.) sh Int))

type Index (RW ((:.) sh Int)) = (:.) sh Int

type SliceShape ((:.) sl All)

type SliceShape ((:.) sl All) = (:.) (SliceShape sl) Int

type SliceShape ((:.) sl Int)

type SliceShape ((:.) sl Int) = SliceShape sl

type FullShape ((:.) sl All)

type FullShape ((:.) sl All) = (:.) (FullShape sl) Int

type FullShape ((:.) sl Int)

type FullShape ((:.) sl Int) = (:.) (FullShape sl) Int

Synonyms for common layouts.

type SH0 = Z

type SH1 = SH0 :. Int

type SH2 = SH1 :. Int

type SH3 = SH2 :. Int

type SH4 = SH3 :. Int

type SH5 = SH4 :. Int

Helpers that constrain the coordinates to be Ints.

ish0 :: SH0

ish1 :: Int -> SH1

ish2 :: Int -> Int -> SH2

ish3 :: Int -> Int -> Int -> SH3

ish4 :: Int -> Int -> Int -> Int -> SH4

ish5 :: Int -> Int -> Int -> Int -> Int -> SH5

Layouts

class Shape (Index l) => Layout l where

A layout provides a total order on the elements of an index space.

We can talk about the n-th element of an array, independent of its shape and dimensionality.

Minimal complete definition

name, create, extent, toIndex, fromIndex

Associated Types

data Name l

Short name for a layout which does not include details of the exact extent.

type Index l

Type used to index into this array layout.

Methods

name :: Name l

O(1). Proxy for the layout name.

create :: Name l -> Index l -> l

O(1). Create a default layout of the given extent.

extent :: l -> Index l

O(1). Yield the extent of the layout.

toIndex :: l -> Index l -> Int

O(1). Convert a polymorphic index to a linear one.

fromIndex :: l -> Int -> Index l

O(1). Convert a linear index to a polymorphic one.

Instances

Layout L

Linear layout.

Associated Types

data Name L :: *

type Index L :: *

Methods

name :: Name L

create :: Name L -> Index L -> L

extent :: L -> Index L

toIndex :: L -> Index L -> Int

fromIndex :: L -> Int -> Index L

Layout B

Boxed arrays.

Associated Types

data Name B :: *

type Index B :: *

Methods

name :: Name B

create :: Name B -> Index B -> B

extent :: B -> Index B

toIndex :: B -> Index B -> Int

fromIndex :: B -> Int -> Index B

Layout F

Foreign arrays.

Associated Types

data Name F :: *

type Index F :: *

Methods

name :: Name F

create :: Name F -> Index F -> F

extent :: F -> Index F

toIndex :: F -> Index F -> Int

fromIndex :: F -> Int -> Index F

Layout U

Unboxed arrays.

Associated Types

data Name U :: *

type Index U :: *

Methods

name :: Name U

create :: Name U -> Index U -> U

extent :: U -> Index U

toIndex :: U -> Index U -> Int

fromIndex :: U -> Int -> Index U

Layout N

Nested arrays.

Associated Types

data Name N :: *

type Index N :: *

Methods

name :: Name N

create :: Name N -> Index N -> N

extent :: N -> Index N

toIndex :: N -> Index N -> Int

fromIndex :: N -> Int -> Index N

Layout A

Associated Types

data Name A :: *

type Index A :: *

Methods

name :: Name A

create :: Name A -> Index A -> A

extent :: A -> Index A

toIndex :: A -> Index A -> Int

fromIndex :: A -> Int -> Index A

Layout l => Layout (W l)

Windowed arrays.

Associated Types

data Name (W l) :: *

type Index (W l) :: *

Methods

name :: Name (W l)

create :: Name (W l) -> Index (W l) -> W l

extent :: W l -> Index (W l)

toIndex :: W l -> Index (W l) -> Int

fromIndex :: W l -> Int -> Index (W l)

(Layout (RW sh), (~) * (Index (RW sh)) sh) => Layout (RW ((:.) sh Int))

Associated Types

data Name (RW ((:.) sh Int)) :: *

type Index (RW ((:.) sh Int)) :: *

Methods

name :: Name (RW (sh :. Int))

create :: Name (RW (sh :. Int)) -> Index (RW (sh :. Int)) -> RW (sh :. Int)

extent :: RW (sh :. Int) -> Index (RW (sh :. Int))

toIndex :: RW (sh :. Int) -> Index (RW (sh :. Int)) -> Int

fromIndex :: RW (sh :. Int) -> Int -> Index (RW (sh :. Int))

Layout (RW Z)

Associated Types

data Name (RW Z) :: *

type Index (RW Z) :: *

Methods

name :: Name (RW Z)

create :: Name (RW Z) -> Index (RW Z) -> RW Z

extent :: RW Z -> Index (RW Z)

toIndex :: RW Z -> Index (RW Z) -> Int

fromIndex :: RW Z -> Int -> Index (RW Z)

Layout l => Layout (D l)

Delayed arrays.

Associated Types

data Name (D l) :: *

type Index (D l) :: *

Methods

name :: Name (D l)

create :: Name (D l) -> Index (D l) -> D l

extent :: D l -> Index (D l)

toIndex :: D l -> Index (D l) -> Int

fromIndex :: D l -> Int -> Index (D l)

(Layout l1, Layout l2, (~) * (Index l1) (Index l2)) => Layout (D2 l1 l2)

Delayed arrays.

Associated Types

data Name (D2 l1 l2) :: *

type Index (D2 l1 l2) :: *

Methods

name :: Name (D2 l1 l2)

create :: Name (D2 l1 l2) -> Index (D2 l1 l2) -> D2 l1 l2

extent :: D2 l1 l2 -> Index (D2 l1 l2)

toIndex :: D2 l1 l2 -> Index (D2 l1 l2) -> Int

fromIndex :: D2 l1 l2 -> Int -> Index (D2 l1 l2)

((~) * (Index r) Int, Layout r, Layout l) => Layout (E r l)

Dense arrays.

Associated Types

data Name (E r l) :: *

type Index (E r l) :: *

Methods

name :: Name (E r l)

create :: Name (E r l) -> Index (E r l) -> E r l

extent :: E r l -> Index (E r l)

toIndex :: E r l -> Index (E r l) -> Int

fromIndex :: E r l -> Int -> Index (E r l)

((~) * (Index l1) (Index l2), Layout l1, Layout l2) => Layout (T2 l1 l2)

Associated Types

data Name (T2 l1 l2) :: *

type Index (T2 l1 l2) :: *

Methods

name :: Name (T2 l1 l2)

create :: Name (T2 l1 l2) -> Index (T2 l1 l2) -> T2 l1 l2

extent :: T2 l1 l2 -> Index (T2 l1 l2)

toIndex :: T2 l1 l2 -> Index (T2 l1 l2) -> Int

fromIndex :: T2 l1 l2 -> Int -> Index (T2 l1 l2)

type LayoutI l = (Layout l, Index l ~ Int)