Copyright	(c) Christopher Chalmers
License	BSD3
Maintainer	Christopher Chalmers
Stability	provisional
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Dense

Contents

Array types
Indexing
Construction
Functions on arrays
Mutable
Delayed
- Generating delayed
- Helpful reexports
Focused
Stencils
- Constructing stencils
- Using stencils
Common shapes
- Extra planes

Description

This module provides a large subset of the full functionality of "dense" without exporting names that conflict with names in prelude, so it can often be imported unqualified. It also includes reexported classes and data types from other modules. However it does not contain much functions necessary to construct arrays, for that see Data.Dense.Generic or one of the type specific modules intended to be imported qualified. Typical imports for shaped will look like this:

import           Data.Dense
import qualified Data.Dense.Unboxed as U

For boxed-specific arrays (a la Data.Vector) see Data.Dense.Boxed.

Synopsis

Array types

data Array v f a Source #

An Array is a vector with a shape.

Instances

Shape f => HasLayout f (Array v f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Methods layout :: Lens' (Array v f a) (Layout f) Source #
(Boxed v, Shape f) => FunctorWithIndex (f Int) (Array v f) Source #
Methods imap :: (f Int -> a -> b) -> Array v f a -> Array v f b # imapped :: (Indexable (f Int) p, Settable f) => p a (f b) -> Array v f a -> f (Array v f b) #
(Boxed v, Shape f) => FoldableWithIndex (f Int) (Array v f) Source #
Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Array v f a -> m # ifolded :: (Indexable (f Int) p, Contravariant f, Applicative f) => p a (f a) -> Array v f a -> f (Array v f a) # ifoldr :: (f Int -> a -> b -> b) -> b -> Array v f a -> b # ifoldl :: (f Int -> b -> a -> b) -> b -> Array v f a -> b # ifoldr' :: (f Int -> a -> b -> b) -> b -> Array v f a -> b # ifoldl' :: (f Int -> b -> a -> b) -> b -> Array v f a -> b #
(Boxed v, Shape f) => TraversableWithIndex (f Int) (Array v f) Source #
Methods itraverse :: Applicative f => (f Int -> a -> f b) -> Array v f a -> f (Array v f b) # itraversed :: (Indexable (f Int) p, Applicative f) => p a (f b) -> Array v f a -> f (Array v f b) #
Boxed v => Functor (Array v f) Source #
Methods fmap :: (a -> b) -> Array v f a -> Array v f b # (<$) :: a -> Array v f b -> Array v f a #
Boxed v => Foldable (Array v f) Source #
Methods fold :: Monoid m => Array v f m -> m # foldMap :: Monoid m => (a -> m) -> Array v f a -> m # foldr :: (a -> b -> b) -> b -> Array v f a -> b # foldr' :: (a -> b -> b) -> b -> Array v f a -> b # foldl :: (b -> a -> b) -> b -> Array v f a -> b # foldl' :: (b -> a -> b) -> b -> Array v f a -> b # foldr1 :: (a -> a -> a) -> Array v f a -> a # foldl1 :: (a -> a -> a) -> Array v f a -> a # toList :: Array v f a -> [a] # null :: Array v f a -> Bool # length :: Array v f a -> Int # elem :: Eq a => a -> Array v f a -> Bool # maximum :: Ord a => Array v f a -> a # minimum :: Ord a => Array v f a -> a # sum :: Num a => Array v f a -> a # product :: Num a => Array v f a -> a #
Boxed v => Traversable (Array v f) Source #
Methods traverse :: Applicative f => (a -> f b) -> Array v f a -> f (Array v f b) # sequenceA :: Applicative f => Array v f (f a) -> f (Array v f a) # mapM :: Monad m => (a -> m b) -> Array v f a -> m (Array v f b) # sequence :: Monad m => Array v f (m a) -> m (Array v f a) #
(Boxed v, Eq1 f) => Eq1 (Array v f) Source #
Methods liftEq :: (a -> b -> Bool) -> Array v f a -> Array v f b -> Bool #
(Boxed v, Read1 f) => Read1 (Array v f) Source #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Array v f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Array v f a] #
(Boxed v, Shape f, Serial1 f) => Serial1 (Array v f) Source #
Methods serializeWith :: MonadPut m => (a -> m ()) -> Array v f a -> m () # deserializeWith :: MonadGet m => m a -> m (Array v f a) #
(Vector v a, (~) (* -> *) f V1) => Vector (Array v f) a Source #	1D Arrays can be used as a generic `Vector`.
Methods basicUnsafeFreeze :: PrimMonad m => Mutable (Array v f) (PrimState m) a -> m (Array v f a) # basicUnsafeThaw :: PrimMonad m => Array v f a -> m (Mutable (Array v f) (PrimState m) a) # basicLength :: Array v f a -> Int # basicUnsafeSlice :: Int -> Int -> Array v f a -> Array v f a # basicUnsafeIndexM :: Monad m => Array v f a -> Int -> m a # basicUnsafeCopy :: PrimMonad m => Mutable (Array v f) (PrimState m) a -> Array v f a -> m () # elemseq :: Array v f a -> a -> b -> b #
(Vector v a, Eq1 f, Eq a) => Eq (Array v f a) Source #
Methods (==) :: Array v f a -> Array v f a -> Bool # (/=) :: Array v f a -> Array v f a -> Bool #
(Typeable (* -> ) f, Typeable ( -> ) v, Typeable a, Data (f Int), Data (v a)) => Data (Array v f a) Source #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Array v f a -> c (Array v f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Array v f a) # toConstr :: Array v f a -> Constr # dataTypeOf :: Array v f a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Array v f a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Array v f a)) # gmapT :: (forall b. Data b => b -> b) -> Array v f a -> Array v f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Array v f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Array v f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Array v f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Array v f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Array v f a -> m (Array v f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Array v f a -> m (Array v f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Array v f a -> m (Array v f a) #
(Vector v a, Read1 f, Read a) => Read (Array v f a) Source #
Methods readsPrec :: Int -> ReadS (Array v f a) # readList :: ReadS [Array v f a] # readPrec :: ReadPrec (Array v f a) # readListPrec :: ReadPrec [Array v f a] #
(Vector v a, Show1 f, Show a) => Show (Array v f a) Source #
Methods showsPrec :: Int -> Array v f a -> ShowS # show :: Array v f a -> String # showList :: [Array v f a] -> ShowS #
(Vector v a, Shape f, Binary (f Int), Binary a) => Binary (Array v f a) Source #
Methods put :: Array v f a -> Put # get :: Get (Array v f a) # putList :: [Array v f a] -> Put #
(Vector v a, Shape f, Serial1 f, Serial a) => Serial (Array v f a) Source #
Methods serialize :: MonadPut m => Array v f a -> m () # deserialize :: MonadGet m => m (Array v f a) #
(Vector v a, Shape f, Serialize (f Int), Serialize a) => Serialize (Array v f a) Source #
Methods put :: Putter (Array v f a) # get :: Get (Array v f a) #
(NFData (f Int), NFData (v a)) => NFData (Array v f a) Source #
Methods rnf :: Array v f a -> () #
(Vector v a, Foldable f, Hashable a) => Hashable (Array v f a) Source #
Methods hashWithSalt :: Int -> Array v f a -> Int # hash :: Array v f a -> Int #
(Shape f, Vector v a) => Ixed (Array v f a) Source #
Methods ix :: Index (Array v f a) -> Traversal' (Array v f a) (IxValue (Array v f a)) #
(Shape f, Vector v a) => AsEmpty (Array v f a) Source #
Methods _Empty :: Prism' (Array v f a) () #
(Vector v a, Vector v b) => Each (Array v f a) (Array v f b) a b Source #
Methods each :: Traversal (Array v f a) (Array v f b) a b #
type Mutable (Array v f) Source #
type Mutable (Array v f) = MArray (Mutable v) f
type Index (Array v f a) Source #
type Index (Array v f a) = f Int
type IxValue (Array v f a) Source #
type IxValue (Array v f a) = a

type BArray = Array Vector Source #

Boxed array.

type UArray = Array Vector Source #

Unboxed array.

type SArray = Array Vector Source #

Storeable array.

type PArray = Array Vector Source #

Prim array.

Indexing

type Layout f = f Int Source #

A Layout is the full size of an array. This alias is used to help distinguish between the layout of an array and an index (usually just l Int) in a type signature.

class Shape f => HasLayout f a | a -> f where Source #

Class of things that have a Layout. This means we can use the same functions for the various different arrays in the library.

Methods

layout :: Lens' a (Layout f) Source #

Lens onto the Layout of something.

layout :: a ~ f Int => (Layout f -> g (Layout f)) -> a -> g a Source #

Lens onto the Layout of something.

Instances

(~) * i Int => HasLayout V4 (V4 i) Source #
Methods layout :: Lens' (V4 i) (Layout V4) Source #
(~) * i Int => HasLayout V3 (V3 i) Source #
Methods layout :: Lens' (V3 i) (Layout V3) Source #
(~) * i Int => HasLayout V2 (V2 i) Source #
Methods layout :: Lens' (V2 i) (Layout V2) Source #
(~) * i Int => HasLayout V1 (V1 i) Source #
Methods layout :: Lens' (V1 i) (Layout V1) Source #
(~) * i Int => HasLayout V0 (V0 i) Source #
Methods layout :: Lens' (V0 i) (Layout V0) Source #
Shape f => HasLayout f (Focused f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Methods layout :: Lens' (Focused f a) (Layout f) Source #
Shape f => HasLayout f (Delayed f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Methods layout :: Lens' (Delayed f a) (Layout f) Source #
Shape f => HasLayout f (Array v f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Methods layout :: Lens' (Array v f a) (Layout f) Source #
Shape f => HasLayout f (MArray v f s a) Source #
Methods layout :: Lens' (MArray v f s a) (Layout f) Source #

class (Eq1 f, Additive f, Traversable f) => Shape f Source #

Class for types that can be converted to and from linear indexes.

Instances

Shape V4 Source #
Methods shapeToIndex :: Layout V4 -> V4 Int -> Int Source # shapeFromIndex :: Layout V4 -> Int -> V4 Int Source # shapeIntersect :: Layout V4 -> Layout V4 -> Layout V4 Source # unsafeShapeStep :: Layout V4 -> V4 Int -> V4 Int Source # shapeStep :: Layout V4 -> V4 Int -> Maybe (V4 Int) Source # shapeStepBetween :: V4 Int -> Layout V4 -> V4 Int -> Maybe (V4 Int) Source # shapeInRange :: Layout V4 -> V4 Int -> Bool Source # shapeSize :: Layout V4 -> Int Source #
Shape V3 Source #
Methods shapeToIndex :: Layout V3 -> V3 Int -> Int Source # shapeFromIndex :: Layout V3 -> Int -> V3 Int Source # shapeIntersect :: Layout V3 -> Layout V3 -> Layout V3 Source # unsafeShapeStep :: Layout V3 -> V3 Int -> V3 Int Source # shapeStep :: Layout V3 -> V3 Int -> Maybe (V3 Int) Source # shapeStepBetween :: V3 Int -> Layout V3 -> V3 Int -> Maybe (V3 Int) Source # shapeInRange :: Layout V3 -> V3 Int -> Bool Source # shapeSize :: Layout V3 -> Int Source #
Shape V2 Source #
Methods shapeToIndex :: Layout V2 -> V2 Int -> Int Source # shapeFromIndex :: Layout V2 -> Int -> V2 Int Source # shapeIntersect :: Layout V2 -> Layout V2 -> Layout V2 Source # unsafeShapeStep :: Layout V2 -> V2 Int -> V2 Int Source # shapeStep :: Layout V2 -> V2 Int -> Maybe (V2 Int) Source # shapeStepBetween :: V2 Int -> Layout V2 -> V2 Int -> Maybe (V2 Int) Source # shapeInRange :: Layout V2 -> V2 Int -> Bool Source # shapeSize :: Layout V2 -> Int Source #
Shape V1 Source #
Methods shapeToIndex :: Layout V1 -> V1 Int -> Int Source # shapeFromIndex :: Layout V1 -> Int -> V1 Int Source # shapeIntersect :: Layout V1 -> Layout V1 -> Layout V1 Source # unsafeShapeStep :: Layout V1 -> V1 Int -> V1 Int Source # shapeStep :: Layout V1 -> V1 Int -> Maybe (V1 Int) Source # shapeStepBetween :: V1 Int -> Layout V1 -> V1 Int -> Maybe (V1 Int) Source # shapeInRange :: Layout V1 -> V1 Int -> Bool Source # shapeSize :: Layout V1 -> Int Source #
Shape V0 Source #
Methods shapeToIndex :: Layout V0 -> V0 Int -> Int Source # shapeFromIndex :: Layout V0 -> Int -> V0 Int Source # shapeIntersect :: Layout V0 -> Layout V0 -> Layout V0 Source # unsafeShapeStep :: Layout V0 -> V0 Int -> V0 Int Source # shapeStep :: Layout V0 -> V0 Int -> Maybe (V0 Int) Source # shapeStepBetween :: V0 Int -> Layout V0 -> V0 Int -> Maybe (V0 Int) Source # shapeInRange :: Layout V0 -> V0 Int -> Bool Source # shapeSize :: Layout V0 -> Int Source #

extent :: HasLayout f a => a -> f Int Source #

Get the extent of an array.

extent :: Array v f a    -> f Int
extent :: MArray v f s a -> f Int
extent :: Delayed f a    -> f Int
extent :: Focused f a    -> f Int

size :: HasLayout f a => a -> Int Source #

Get the total number of elements in an array.

size :: Array v f a    -> Int
size :: MArray v f s a -> Int
size :: Delayed f a    -> Int
size :: Focused f a    -> Int

Folds over indexes

indexes :: HasLayout f a => IndexedFold Int a (f Int) Source #

Indexed fold for all the indexes in the layout.

indexesBetween :: HasLayout f a => f Int -> f Int -> IndexedFold Int a (f Int) Source #

Indexed fold between the two indexes where the index is the linear index for the original layout.

indexesFrom :: HasLayout f a => f Int -> IndexedFold Int a (f Int) Source #

Indexed fold starting starting from some point, where the index is the linear index for the original layout.

Lenses

vector :: (Vector v a, Vector w b) => IndexedLens (Layout f) (Array v f a) (Array w f b) (v a) (w b) Source #

Indexed lens over the underlying vector of an array. The index is the extent of the array. You must _not_ change the length of the vector, otherwise an error will be thrown (even for V1 layouts, use flat for V1).

Traversals

values :: (Shape f, Vector v a, Vector w b) => IndexedTraversal (f Int) (Array v f a) (Array w f b) a b Source #

Indexed traversal over the elements of an array. The index is the current position in the array.

values' :: (Shape f, Vector v a, Vector v b) => IndexedTraversal (f Int) (Array v f a) (Array v f b) a b Source #

Same as values but restrictive in the vector type.

valuesBetween :: (Shape f, Vector v a) => f Int -> f Int -> IndexedTraversal' (f Int) (Array v f a) a Source #

Traverse over the values between two indexes.

Construction

Flat arrays

flat :: Vector w b => Iso (Array v V1 a) (Array w V1 b) (v a) (w b) Source #

1D arrays are just vectors. You are free to change the length of the vector when going over this Iso (unlike linear).

Note that V1 arrays are an instance of Vector so you can use any of the functions in Data.Vector.Generic on them without needing to convert.

Shaped from lists

fromListInto :: (Shape f, Vector v a) => Layout f -> [a] -> Maybe (Array v f a) Source #

O(n) Convert the first n elements of a list to an Array with the given shape. Returns Nothing if there are not enough elements in the list.

fromListInto_ :: (Shape f, Vector v a) => Layout f -> [a] -> Array v f a Source #

O(n) Convert the first n elements of a list to an Array with the given shape. Throw an error if the list is not long enough.

Shaped from vectors

fromVectorInto :: (Shape f, Vector v a) => Layout f -> v a -> Maybe (Array v f a) Source #

Create an array from a vector and a layout. Return Nothing if the vector is not the right shape.

fromVectorInto_ :: (Shape f, Vector v a) => Layout f -> v a -> Array v f a Source #

Create an array from a vector and a layout. Throws an error if the vector is not the right shape.

Generating

See Data.Shaped.Generic.

Functions on arrays

Empty arrays

See AsEmpty class or Data.Shaped.Generic.

Indexing

See Ixed class.

Modifying arrays

See Data.Shaped.Generic.

Slices

Matrix

ixRow :: Vector v a => Int -> IndexedTraversal' Int (Array v V2 a) (v a) Source #

Affine traversal over a single row in a matrix.

>>> traverseOf_ rows print $ m & ixRow 1 . each *~ 2
[a,b,c,d]
[e * 2,f * 2,g * 2,h * 2]
[i,j,k,l]

The row vector should remain the same size to satisfy traversal laws but give reasonable behaviour if the size differs:

>>> traverseOf_ rows print $ m & ixRow 1 .~ B.fromList [0,1]
[a,b,c,d]
[0,1,g,h]
[i,j,k,l]

>>> traverseOf_ rows print $ m & ixRow 1 .~ B.fromList [0..100]
[a,b,c,d]
[0,1,2,3]
[i,j,k,l]

rows :: (Vector v a, Vector w b) => IndexedTraversal Int (Array v V2 a) (Array w V2 b) (v a) (w b) Source #

Indexed traversal over the rows of a matrix. Each row is an efficient slice of the original vector.

>>> traverseOf_ rows print m
[a,b,c,d]
[e,f,g,h]
[i,j,k,l]

ixColumn :: Vector v a => Int -> IndexedTraversal' Int (Array v V2 a) (v a) Source #

Affine traversal over a single column in a matrix.

>>> traverseOf_ rows print $ m & ixColumn 2 . each +~ 1
[a,b,c + 1,d]
[e,f,g + 1,h]
[i,j,k + 1,l]

columns :: (Vector v a, Vector w b) => IndexedTraversal Int (Array v V2 a) (Array w V2 b) (v a) (w b) Source #

Indexed traversal over the columns of a matrix. Unlike rows, each column is a new separate vector.

>>> traverseOf_ columns print m
[a,e,i]
[b,f,j]
[c,g,k]
[d,h,l]

>>> traverseOf_ rows print $ m & columns . indices odd . each .~ 0
[a,0,c,0]
[e,0,g,0]
[i,0,k,0]

The vectors should be the same size to be a valid traversal. If the vectors are different sizes, the number of rows in the new array will be the length of the smallest vector.

3D

ixPlane :: Vector v a => ALens' (V3 Int) (V2 Int) -> Int -> IndexedTraversal' Int (Array v V3 a) (Array v V2 a) Source #

Traversal over a single plane of a 3D array given a lens onto that plane (like _xy, _yz, _zx).

planes :: (Vector v a, Vector w b) => ALens' (V3 Int) (V2 Int) -> IndexedTraversal Int (Array v V3 a) (Array w V3 b) (Array v V2 a) (Array w V2 b) Source #

Traversal over all planes of 3D array given a lens onto that plane (like _xy, _yz, _zx).

flattenPlane :: (Vector v a, Vector w b) => ALens' (V3 Int) (V2 Int) -> (v a -> b) -> Array v V3 a -> Array w V2 b Source #

Flatten a plane by reducing a vector in the third dimension to a single value.

Mutable

data MArray v l s a Source #

A mutable array with a shape.

Instances

Shape f => HasLayout f (MArray v f s a) Source #
Methods layout :: Lens' (MArray v f s a) (Layout f) Source #
(MVector v a, (~) (* -> *) f V1) => MVector (MArray v f) a Source #
Methods basicLength :: MArray v f s a -> Int # basicUnsafeSlice :: Int -> Int -> MArray v f s a -> MArray v f s a # basicOverlaps :: MArray v f s a -> MArray v f s a -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MArray v f (PrimState m) a) # basicInitialize :: PrimMonad m => MArray v f (PrimState m) a -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> a -> m (MArray v f (PrimState m) a) # basicUnsafeRead :: PrimMonad m => MArray v f (PrimState m) a -> Int -> m a # basicUnsafeWrite :: PrimMonad m => MArray v f (PrimState m) a -> Int -> a -> m () # basicClear :: PrimMonad m => MArray v f (PrimState m) a -> m () # basicSet :: PrimMonad m => MArray v f (PrimState m) a -> a -> m () # basicUnsafeCopy :: PrimMonad m => MArray v f (PrimState m) a -> MArray v f (PrimState m) a -> m () # basicUnsafeMove :: PrimMonad m => MArray v f (PrimState m) a -> MArray v f (PrimState m) a -> m () # basicUnsafeGrow :: PrimMonad m => MArray v f (PrimState m) a -> Int -> m (MArray v f (PrimState m) a) #

type BMArray = MArray MVector Source #

Boxed mutable array.

type UMArray = MArray MVector Source #

Unboxed mutable array.

type SMArray = MArray MVector Source #

Storable mutable array.

type PMArray = MArray MVector Source #

Primitive mutable array.

Delayed

data Delayed f a Source #

A delayed representation of an array. This useful for mapping over an array in parallel.

Instances

Shape f => HasLayout f (Delayed f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Methods layout :: Lens' (Delayed f a) (Layout f) Source #
Functor (Delayed f) Source #
Methods fmap :: (a -> b) -> Delayed f a -> Delayed f b # (<$) :: a -> Delayed f b -> Delayed f a #
Shape f => Foldable (Delayed f) Source #	`foldMap` in parallel.
Methods fold :: Monoid m => Delayed f m -> m # foldMap :: Monoid m => (a -> m) -> Delayed f a -> m # foldr :: (a -> b -> b) -> b -> Delayed f a -> b # foldr' :: (a -> b -> b) -> b -> Delayed f a -> b # foldl :: (b -> a -> b) -> b -> Delayed f a -> b # foldl' :: (b -> a -> b) -> b -> Delayed f a -> b # foldr1 :: (a -> a -> a) -> Delayed f a -> a # foldl1 :: (a -> a -> a) -> Delayed f a -> a # toList :: Delayed f a -> [a] # null :: Delayed f a -> Bool # length :: Delayed f a -> Int # elem :: Eq a => a -> Delayed f a -> Bool # maximum :: Ord a => Delayed f a -> a # minimum :: Ord a => Delayed f a -> a # sum :: Num a => Delayed f a -> a # product :: Num a => Delayed f a -> a #
Shape f => Traversable (Delayed f) Source #
Methods traverse :: Applicative f => (a -> f b) -> Delayed f a -> f (Delayed f b) # sequenceA :: Applicative f => Delayed f (f a) -> f (Delayed f a) # mapM :: Monad m => (a -> m b) -> Delayed f a -> m (Delayed f b) # sequence :: Monad m => Delayed f (m a) -> m (Delayed f a) #
Shape f => Metric (Delayed f) Source #
Methods dot :: Num a => Delayed f a -> Delayed f a -> a # quadrance :: Num a => Delayed f a -> a # qd :: Num a => Delayed f a -> Delayed f a -> a # distance :: Floating a => Delayed f a -> Delayed f a -> a # norm :: Floating a => Delayed f a -> a # signorm :: Floating a => Delayed f a -> Delayed f a #
Shape f => Additive (Delayed f) Source #
Methods zero :: Num a => Delayed f a # (^+^) :: Num a => Delayed f a -> Delayed f a -> Delayed f a # (^-^) :: Num a => Delayed f a -> Delayed f a -> Delayed f a # lerp :: Num a => a -> Delayed f a -> Delayed f a -> Delayed f a # liftU2 :: (a -> a -> a) -> Delayed f a -> Delayed f a -> Delayed f a # liftI2 :: (a -> b -> c) -> Delayed f a -> Delayed f b -> Delayed f c #
Shape f => Apply (Delayed f) Source #
Methods (<.>) :: Delayed f (a -> b) -> Delayed f a -> Delayed f b # (.>) :: Delayed f a -> Delayed f b -> Delayed f b # (<.) :: Delayed f a -> Delayed f b -> Delayed f a #
FunctorWithIndex (f Int) (Delayed f) Source #
Methods imap :: (f Int -> a -> b) -> Delayed f a -> Delayed f b # imapped :: (Indexable (f Int) p, Settable f) => p a (f b) -> Delayed f a -> f (Delayed f b) #
Shape f => FoldableWithIndex (f Int) (Delayed f) Source #	`ifoldMap` in parallel.
Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Delayed f a -> m # ifolded :: (Indexable (f Int) p, Contravariant f, Applicative f) => p a (f a) -> Delayed f a -> f (Delayed f a) # ifoldr :: (f Int -> a -> b -> b) -> b -> Delayed f a -> b # ifoldl :: (f Int -> b -> a -> b) -> b -> Delayed f a -> b # ifoldr' :: (f Int -> a -> b -> b) -> b -> Delayed f a -> b # ifoldl' :: (f Int -> b -> a -> b) -> b -> Delayed f a -> b #
Shape f => TraversableWithIndex (f Int) (Delayed f) Source #
Methods itraverse :: Applicative f => (f Int -> a -> f b) -> Delayed f a -> f (Delayed f b) # itraversed :: (Indexable (f Int) p, Applicative f) => p a (f b) -> Delayed f a -> f (Delayed f b) #
(Shape f, Show1 f, Show a) => Show (Delayed f a) Source #
Methods showsPrec :: Int -> Delayed f a -> ShowS # show :: Delayed f a -> String # showList :: [Delayed f a] -> ShowS #
Shape f => Ixed (Delayed f a) Source #
Methods ix :: Index (Delayed f a) -> Traversal' (Delayed f a) (IxValue (Delayed f a)) #
Shape f => AsEmpty (Delayed f a) Source #
Methods _Empty :: Prism' (Delayed f a) () #
Shape f => Each (Delayed f a) (Delayed f b) a b Source #
Methods each :: Traversal (Delayed f a) (Delayed f b) a b #
type Index (Delayed f a) Source #
type Index (Delayed f a) = f Int
type IxValue (Delayed f a) Source #
type IxValue (Delayed f a) = a

Generating delayed

delayed :: (Vector v a, Vector w b, Shape f, Shape g) => Iso (Array v f a) (Array w g b) (Delayed f a) (Delayed g b) Source #

Isomorphism between an array and its delayed representation. Conversion to the array is done in parallel.

seqDelayed :: (Vector v a, Vector w b, Shape f, Shape g) => Iso (Array v f a) (Array w g b) (Delayed f a) (Delayed g b) Source #

Isomorphism between an array and its delayed representation. Conversion to the array is done in parallel.

delay :: (Vector v a, Shape f) => Array v f a -> Delayed f a Source #

Turn a material array into a delayed one with the same shape.

manifest :: (Vector v a, Shape f) => Delayed f a -> Array v f a Source #

Parallel manifestation of a delayed array into a material one.

seqManifest :: (Vector v a, Shape f) => Delayed f a -> Array v f a Source #

Sequential manifestation of a delayed array.

genDelayed :: Layout f -> (f Int -> a) -> Delayed f a Source #

Generate a Delayed array using the given Layout and construction function.

indexDelayed :: Shape f => Delayed f a -> f Int -> a Source #

Index a delayed array, returning a IndexOutOfBounds exception if the index is out of range.

affirm :: (Shape f, Unbox a) => Delayed f a -> Delayed f a Source #

manifest an array to a UArray and delay again. See Data.Dense.Boxed or Data.Dense.Storable to affirm for other types of arrays.

seqAffirm :: (Shape f, Unbox a) => Delayed f a -> Delayed f a Source #

seqManifest an array to a UArray and delay again. See Data.Dense.Boxed or Data.Dense.Storable to affirm for other types of arrays.

Helpful reexports

(*^) :: (Functor f, Num a) => a -> f a -> f a infixl 7 #

Compute the left scalar product

>>> 2 *^ V2 3 4
V2 6 8

(^*) :: (Functor f, Num a) => f a -> a -> f a infixl 7 #

Compute the right scalar product

>>> V2 3 4 ^* 2
V2 6 8

(^/) :: (Functor f, Fractional a) => f a -> a -> f a infixl 7 #

Compute division by a scalar on the right.

class Functor f => Additive f where #

A vector is an additive group with additional structure.

Minimal complete definition

Nothing

Instances

Additive []
Methods zero :: Num a => [a] # (^+^) :: Num a => [a] -> [a] -> [a] # (^-^) :: Num a => [a] -> [a] -> [a] # lerp :: Num a => a -> [a] -> [a] -> [a] # liftU2 :: (a -> a -> a) -> [a] -> [a] -> [a] # liftI2 :: (a -> b -> c) -> [a] -> [b] -> [c] #
Additive Maybe
Methods zero :: Num a => Maybe a # (^+^) :: Num a => Maybe a -> Maybe a -> Maybe a # (^-^) :: Num a => Maybe a -> Maybe a -> Maybe a # lerp :: Num a => a -> Maybe a -> Maybe a -> Maybe a # liftU2 :: (a -> a -> a) -> Maybe a -> Maybe a -> Maybe a # liftI2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c #
Additive Identity
Methods zero :: Num a => Identity a # (^+^) :: Num a => Identity a -> Identity a -> Identity a # (^-^) :: Num a => Identity a -> Identity a -> Identity a # lerp :: Num a => a -> Identity a -> Identity a -> Identity a # liftU2 :: (a -> a -> a) -> Identity a -> Identity a -> Identity a # liftI2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c #
Additive Complex
Methods zero :: Num a => Complex a # (^+^) :: Num a => Complex a -> Complex a -> Complex a # (^-^) :: Num a => Complex a -> Complex a -> Complex a # lerp :: Num a => a -> Complex a -> Complex a -> Complex a # liftU2 :: (a -> a -> a) -> Complex a -> Complex a -> Complex a # liftI2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c #
Additive ZipList
Methods zero :: Num a => ZipList a # (^+^) :: Num a => ZipList a -> ZipList a -> ZipList a # (^-^) :: Num a => ZipList a -> ZipList a -> ZipList a # lerp :: Num a => a -> ZipList a -> ZipList a -> ZipList a # liftU2 :: (a -> a -> a) -> ZipList a -> ZipList a -> ZipList a # liftI2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c #
Additive IntMap
Methods zero :: Num a => IntMap a # (^+^) :: Num a => IntMap a -> IntMap a -> IntMap a # (^-^) :: Num a => IntMap a -> IntMap a -> IntMap a # lerp :: Num a => a -> IntMap a -> IntMap a -> IntMap a # liftU2 :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a # liftI2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c #
Additive Vector
Methods zero :: Num a => Vector a # (^+^) :: Num a => Vector a -> Vector a -> Vector a # (^-^) :: Num a => Vector a -> Vector a -> Vector a # lerp :: Num a => a -> Vector a -> Vector a -> Vector a # liftU2 :: (a -> a -> a) -> Vector a -> Vector a -> Vector a # liftI2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #
Additive Quaternion
Methods zero :: Num a => Quaternion a # (^+^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # (^-^) :: Num a => Quaternion a -> Quaternion a -> Quaternion a # lerp :: Num a => a -> Quaternion a -> Quaternion a -> Quaternion a # liftU2 :: (a -> a -> a) -> Quaternion a -> Quaternion a -> Quaternion a # liftI2 :: (a -> b -> c) -> Quaternion a -> Quaternion b -> Quaternion c #
Additive Plucker
Methods zero :: Num a => Plucker a # (^+^) :: Num a => Plucker a -> Plucker a -> Plucker a # (^-^) :: Num a => Plucker a -> Plucker a -> Plucker a # lerp :: Num a => a -> Plucker a -> Plucker a -> Plucker a # liftU2 :: (a -> a -> a) -> Plucker a -> Plucker a -> Plucker a # liftI2 :: (a -> b -> c) -> Plucker a -> Plucker b -> Plucker c #
Additive V4
Methods zero :: Num a => V4 a # (^+^) :: Num a => V4 a -> V4 a -> V4 a # (^-^) :: Num a => V4 a -> V4 a -> V4 a # lerp :: Num a => a -> V4 a -> V4 a -> V4 a # liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a # liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #
Additive V3
Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Additive V2
Methods zero :: Num a => V2 a # (^+^) :: Num a => V2 a -> V2 a -> V2 a # (^-^) :: Num a => V2 a -> V2 a -> V2 a # lerp :: Num a => a -> V2 a -> V2 a -> V2 a # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Additive V1
Methods zero :: Num a => V1 a # (^+^) :: Num a => V1 a -> V1 a -> V1 a # (^-^) :: Num a => V1 a -> V1 a -> V1 a # lerp :: Num a => a -> V1 a -> V1 a -> V1 a # liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a # liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #
Additive V0
Methods zero :: Num a => V0 a # (^+^) :: Num a => V0 a -> V0 a -> V0 a # (^-^) :: Num a => V0 a -> V0 a -> V0 a # lerp :: Num a => a -> V0 a -> V0 a -> V0 a # liftU2 :: (a -> a -> a) -> V0 a -> V0 a -> V0 a # liftI2 :: (a -> b -> c) -> V0 a -> V0 b -> V0 c #
Additive ((->) b)
Methods zero :: Num a => b -> a # (^+^) :: Num a => (b -> a) -> (b -> a) -> b -> a # (^-^) :: Num a => (b -> a) -> (b -> a) -> b -> a # lerp :: Num a => a -> (b -> a) -> (b -> a) -> b -> a # liftU2 :: (a -> a -> a) -> (b -> a) -> (b -> a) -> b -> a # liftI2 :: (a -> b -> c) -> (b -> a) -> (b -> b) -> b -> c #
Ord k => Additive (Map k)
Methods zero :: Num a => Map k a # (^+^) :: Num a => Map k a -> Map k a -> Map k a # (^-^) :: Num a => Map k a -> Map k a -> Map k a # lerp :: Num a => a -> Map k a -> Map k a -> Map k a # liftU2 :: (a -> a -> a) -> Map k a -> Map k a -> Map k a # liftI2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c #
(Eq k, Hashable k) => Additive (HashMap k)
Methods zero :: Num a => HashMap k a # (^+^) :: Num a => HashMap k a -> HashMap k a -> HashMap k a # (^-^) :: Num a => HashMap k a -> HashMap k a -> HashMap k a # lerp :: Num a => a -> HashMap k a -> HashMap k a -> HashMap k a # liftU2 :: (a -> a -> a) -> HashMap k a -> HashMap k a -> HashMap k a # liftI2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c #
Shape f => Additive (Delayed f) #
Methods zero :: Num a => Delayed f a # (^+^) :: Num a => Delayed f a -> Delayed f a -> Delayed f a # (^-^) :: Num a => Delayed f a -> Delayed f a -> Delayed f a # lerp :: Num a => a -> Delayed f a -> Delayed f a -> Delayed f a # liftU2 :: (a -> a -> a) -> Delayed f a -> Delayed f a -> Delayed f a # liftI2 :: (a -> b -> c) -> Delayed f a -> Delayed f b -> Delayed f c #
Dim k n => Additive (V k n)
Methods zero :: Num a => V k n a # (^+^) :: Num a => V k n a -> V k n a -> V k n a # (^-^) :: Num a => V k n a -> V k n a -> V k n a # lerp :: Num a => a -> V k n a -> V k n a -> V k n a # liftU2 :: (a -> a -> a) -> V k n a -> V k n a -> V k n a # liftI2 :: (a -> b -> c) -> V k n a -> V k n b -> V k n c #

class Additive f => Metric f where #

Free and sparse inner product/metric spaces.

Minimal complete definition

Nothing

Instances

Metric []
Methods dot :: Num a => [a] -> [a] -> a # quadrance :: Num a => [a] -> a # qd :: Num a => [a] -> [a] -> a # distance :: Floating a => [a] -> [a] -> a # norm :: Floating a => [a] -> a # signorm :: Floating a => [a] -> [a] #
Metric Maybe
Methods dot :: Num a => Maybe a -> Maybe a -> a # quadrance :: Num a => Maybe a -> a # qd :: Num a => Maybe a -> Maybe a -> a # distance :: Floating a => Maybe a -> Maybe a -> a # norm :: Floating a => Maybe a -> a # signorm :: Floating a => Maybe a -> Maybe a #
Metric Identity
Methods dot :: Num a => Identity a -> Identity a -> a # quadrance :: Num a => Identity a -> a # qd :: Num a => Identity a -> Identity a -> a # distance :: Floating a => Identity a -> Identity a -> a # norm :: Floating a => Identity a -> a # signorm :: Floating a => Identity a -> Identity a #
Metric ZipList
Methods dot :: Num a => ZipList a -> ZipList a -> a # quadrance :: Num a => ZipList a -> a # qd :: Num a => ZipList a -> ZipList a -> a # distance :: Floating a => ZipList a -> ZipList a -> a # norm :: Floating a => ZipList a -> a # signorm :: Floating a => ZipList a -> ZipList a #
Metric IntMap
Methods dot :: Num a => IntMap a -> IntMap a -> a # quadrance :: Num a => IntMap a -> a # qd :: Num a => IntMap a -> IntMap a -> a # distance :: Floating a => IntMap a -> IntMap a -> a # norm :: Floating a => IntMap a -> a # signorm :: Floating a => IntMap a -> IntMap a #
Metric Vector
Methods dot :: Num a => Vector a -> Vector a -> a # quadrance :: Num a => Vector a -> a # qd :: Num a => Vector a -> Vector a -> a # distance :: Floating a => Vector a -> Vector a -> a # norm :: Floating a => Vector a -> a # signorm :: Floating a => Vector a -> Vector a #
Metric Quaternion
Methods dot :: Num a => Quaternion a -> Quaternion a -> a # quadrance :: Num a => Quaternion a -> a # qd :: Num a => Quaternion a -> Quaternion a -> a # distance :: Floating a => Quaternion a -> Quaternion a -> a # norm :: Floating a => Quaternion a -> a # signorm :: Floating a => Quaternion a -> Quaternion a #
Metric Plucker
Methods dot :: Num a => Plucker a -> Plucker a -> a # quadrance :: Num a => Plucker a -> a # qd :: Num a => Plucker a -> Plucker a -> a # distance :: Floating a => Plucker a -> Plucker a -> a # norm :: Floating a => Plucker a -> a # signorm :: Floating a => Plucker a -> Plucker a #
Metric V4
Methods dot :: Num a => V4 a -> V4 a -> a # quadrance :: Num a => V4 a -> a # qd :: Num a => V4 a -> V4 a -> a # distance :: Floating a => V4 a -> V4 a -> a # norm :: Floating a => V4 a -> a # signorm :: Floating a => V4 a -> V4 a #
Metric V3
Methods dot :: Num a => V3 a -> V3 a -> a # quadrance :: Num a => V3 a -> a # qd :: Num a => V3 a -> V3 a -> a # distance :: Floating a => V3 a -> V3 a -> a # norm :: Floating a => V3 a -> a # signorm :: Floating a => V3 a -> V3 a #
Metric V2
Methods dot :: Num a => V2 a -> V2 a -> a # quadrance :: Num a => V2 a -> a # qd :: Num a => V2 a -> V2 a -> a # distance :: Floating a => V2 a -> V2 a -> a # norm :: Floating a => V2 a -> a # signorm :: Floating a => V2 a -> V2 a #
Metric V1
Methods dot :: Num a => V1 a -> V1 a -> a # quadrance :: Num a => V1 a -> a # qd :: Num a => V1 a -> V1 a -> a # distance :: Floating a => V1 a -> V1 a -> a # norm :: Floating a => V1 a -> a # signorm :: Floating a => V1 a -> V1 a #
Metric V0
Methods dot :: Num a => V0 a -> V0 a -> a # quadrance :: Num a => V0 a -> a # qd :: Num a => V0 a -> V0 a -> a # distance :: Floating a => V0 a -> V0 a -> a # norm :: Floating a => V0 a -> a # signorm :: Floating a => V0 a -> V0 a #
Ord k => Metric (Map k)
Methods dot :: Num a => Map k a -> Map k a -> a # quadrance :: Num a => Map k a -> a # qd :: Num a => Map k a -> Map k a -> a # distance :: Floating a => Map k a -> Map k a -> a # norm :: Floating a => Map k a -> a # signorm :: Floating a => Map k a -> Map k a #
(Hashable k, Eq k) => Metric (HashMap k)
Methods dot :: Num a => HashMap k a -> HashMap k a -> a # quadrance :: Num a => HashMap k a -> a # qd :: Num a => HashMap k a -> HashMap k a -> a # distance :: Floating a => HashMap k a -> HashMap k a -> a # norm :: Floating a => HashMap k a -> a # signorm :: Floating a => HashMap k a -> HashMap k a #
Shape f => Metric (Delayed f) #
Methods dot :: Num a => Delayed f a -> Delayed f a -> a # quadrance :: Num a => Delayed f a -> a # qd :: Num a => Delayed f a -> Delayed f a -> a # distance :: Floating a => Delayed f a -> Delayed f a -> a # norm :: Floating a => Delayed f a -> a # signorm :: Floating a => Delayed f a -> Delayed f a #
Dim k n => Metric (V k n)
Methods dot :: Num a => V k n a -> V k n a -> a # quadrance :: Num a => V k n a -> a # qd :: Num a => V k n a -> V k n a -> a # distance :: Floating a => V k n a -> V k n a -> a # norm :: Floating a => V k n a -> a # signorm :: Floating a => V k n a -> V k n a #

Focused

data Focused f a Source #

A delayed representation of an array with a focus on a single element. This element is the target of extract.

Instances

Shape f => HasLayout f (Focused f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Methods layout :: Lens' (Focused f a) (Layout f) Source #
Functor (Focused f) Source #
Methods fmap :: (a -> b) -> Focused f a -> Focused f b # (<$) :: a -> Focused f b -> Focused f a #
Shape f => Foldable (Focused f) Source #
Methods fold :: Monoid m => Focused f m -> m # foldMap :: Monoid m => (a -> m) -> Focused f a -> m # foldr :: (a -> b -> b) -> b -> Focused f a -> b # foldr' :: (a -> b -> b) -> b -> Focused f a -> b # foldl :: (b -> a -> b) -> b -> Focused f a -> b # foldl' :: (b -> a -> b) -> b -> Focused f a -> b # foldr1 :: (a -> a -> a) -> Focused f a -> a # foldl1 :: (a -> a -> a) -> Focused f a -> a # toList :: Focused f a -> [a] # null :: Focused f a -> Bool # length :: Focused f a -> Int # elem :: Eq a => a -> Focused f a -> Bool # maximum :: Ord a => Focused f a -> a # minimum :: Ord a => Focused f a -> a # sum :: Num a => Focused f a -> a # product :: Num a => Focused f a -> a #
Shape f => Traversable (Focused f) Source #
Methods traverse :: Applicative f => (a -> f b) -> Focused f a -> f (Focused f b) # sequenceA :: Applicative f => Focused f (f a) -> f (Focused f a) # mapM :: Monad m => (a -> m b) -> Focused f a -> m (Focused f b) # sequence :: Monad m => Focused f (m a) -> m (Focused f a) #
Shape f => Comonad (Focused f) Source #
Methods extract :: Focused f a -> a # duplicate :: Focused f a -> Focused f (Focused f a) # extend :: (Focused f a -> b) -> Focused f a -> Focused f b #
Shape f => Extend (Focused f) Source #
Methods duplicated :: Focused f a -> Focused f (Focused f a) # extended :: (Focused f a -> b) -> Focused f a -> Focused f b #
Shape f => ComonadStore (f Int) (Focused f) Source #
Methods pos :: Focused f a -> f Int # peek :: f Int -> Focused f a -> a # peeks :: (f Int -> f Int) -> Focused f a -> a # seek :: f Int -> Focused f a -> Focused f a # seeks :: (f Int -> f Int) -> Focused f a -> Focused f a # experiment :: Functor f => (f Int -> f (f Int)) -> Focused f a -> f a #
Shape f => FunctorWithIndex (f Int) (Focused f) Source #	Index relative to focus.
Methods imap :: (f Int -> a -> b) -> Focused f a -> Focused f b # imapped :: (Indexable (f Int) p, Settable f) => p a (f b) -> Focused f a -> f (Focused f b) #
Shape f => FoldableWithIndex (f Int) (Focused f) Source #	Index relative to focus.
Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Focused f a -> m # ifolded :: (Indexable (f Int) p, Contravariant f, Applicative f) => p a (f a) -> Focused f a -> f (Focused f a) # ifoldr :: (f Int -> a -> b -> b) -> b -> Focused f a -> b # ifoldl :: (f Int -> b -> a -> b) -> b -> Focused f a -> b # ifoldr' :: (f Int -> a -> b -> b) -> b -> Focused f a -> b # ifoldl' :: (f Int -> b -> a -> b) -> b -> Focused f a -> b #
Shape f => TraversableWithIndex (f Int) (Focused f) Source #	Index relative to focus.
Methods itraverse :: Applicative f => (f Int -> a -> f b) -> Focused f a -> f (Focused f b) # itraversed :: (Indexable (f Int) p, Applicative f) => p a (f b) -> Focused f a -> f (Focused f b) #
(Shape f, Show1 f, Show a) => Show (Focused f a) Source #
Methods showsPrec :: Int -> Focused f a -> ShowS # show :: Focused f a -> String # showList :: [Focused f a] -> ShowS #
Shape f => Ixed (Focused f a) Source #	Index relative to focus.
Methods ix :: Index (Focused f a) -> Traversal' (Focused f a) (IxValue (Focused f a)) #
type Index (Focused f a) Source #
type Index (Focused f a) = f Int
type IxValue (Focused f a) Source #
type IxValue (Focused f a) = a

Generating focused

focusOn :: f Int -> Delayed f a -> Focused f a Source #

Focus on a particular element of a delayed array.

unfocus :: Focused f a -> Delayed f a Source #

Discard the focus to retrieve the delayed array.

unfocused :: IndexedLens (f Int) (Focused f a) (Focused f b) (Delayed f a) (Delayed f b) Source #

Indexed lens onto the delayed array, indexed at the focus.

extendFocus :: Shape f => (Focused f a -> b) -> Delayed f a -> Delayed f b Source #

Modify a Delayed array by extracting a value from a Focused each point.

Focus location

locale :: ComonadStore s w => Lens' (w a) s Source #

Lens onto the position of a ComonadStore.

locale :: Lens' (Focused l a) (l Int)

shiftFocus :: Applicative f => f Int -> Focused f a -> Focused f a Source #

Focus on a neighbouring element, relative to the current focus.

Boundary

data Boundary Source #

The boundary condition used for indexing relative elements in a Focused.

Constructors

Clamp	clamp coordinates to the extent of the array
Mirror	mirror coordinates beyond the array extent
Wrap	wrap coordinates around on each dimension

Instances

Read Boundary Source #
Methods readsPrec :: Int -> ReadS Boundary # readList :: ReadS [Boundary] # readPrec :: ReadPrec Boundary # readListPrec :: ReadPrec [Boundary] #
Show Boundary Source #
Methods showsPrec :: Int -> Boundary -> ShowS # show :: Boundary -> String # showList :: [Boundary] -> ShowS #

peekB :: Shape f => Boundary -> f Int -> Focused f a -> a Source #

Index a focused using a Boundary condition.

peeksB :: Shape f => Boundary -> (f Int -> f Int) -> Focused f a -> a Source #

Index an element by applying a function the current position, using a boundary condition.

peekRelativeB :: Shape f => Boundary -> f Int -> Focused f a -> a Source #

Index an element relative to the current focus using a Boundary condition.

Helpful reexports

class Functor w => Comonad w where #

There are two ways to define a comonad:

I. Provide definitions for extract and extend satisfying these laws:

extend extract      = id
extract . extend f  = f
extend f . extend g = extend (f . extend g)

In this case, you may simply set fmap = liftW.

These laws are directly analogous to the laws for monads and perhaps can be made clearer by viewing them as laws stating that Cokleisli composition must be associative, and has extract for a unit:

f =>= extract   = f
extract =>= f   = f
(f =>= g) =>= h = f =>= (g =>= h)

II. Alternately, you may choose to provide definitions for fmap, extract, and duplicate satisfying these laws:

extract . duplicate      = id
fmap extract . duplicate = id
duplicate . duplicate    = fmap duplicate . duplicate

In this case you may not rely on the ability to define fmap in terms of liftW.

You may of course, choose to define both duplicate and extend. In that case you must also satisfy these laws:

extend f  = fmap f . duplicate
duplicate = extend id
fmap f    = extend (f . extract)

These are the default definitions of extend and duplicate and the definition of liftW respectively.

Minimal complete definition

extract, (duplicate | extend)

Instances

Comonad Identity
Methods extract :: Identity a -> a # duplicate :: Identity a -> Identity (Identity a) # extend :: (Identity a -> b) -> Identity a -> Identity b #
Comonad NonEmpty
Methods extract :: NonEmpty a -> a # duplicate :: NonEmpty a -> NonEmpty (NonEmpty a) # extend :: (NonEmpty a -> b) -> NonEmpty a -> NonEmpty b #
Comonad Tree
Methods extract :: Tree a -> a # duplicate :: Tree a -> Tree (Tree a) # extend :: (Tree a -> b) -> Tree a -> Tree b #
Monoid m => Comonad ((->) m)
Methods extract :: (m -> a) -> a # duplicate :: (m -> a) -> m -> m -> a # extend :: ((m -> a) -> b) -> (m -> a) -> m -> b #
Comonad ((,) e)
Methods extract :: (e, a) -> a # duplicate :: (e, a) -> (e, (e, a)) # extend :: ((e, a) -> b) -> (e, a) -> (e, b) #
(Representable f, Monoid (Rep f)) => Comonad (Co f)
Methods extract :: Co f a -> a # duplicate :: Co f a -> Co f (Co f a) # extend :: (Co f a -> b) -> Co f a -> Co f b #
Comonad (Arg e)
Methods extract :: Arg e a -> a # duplicate :: Arg e a -> Arg e (Arg e a) # extend :: (Arg e a -> b) -> Arg e a -> Arg e b #
Functor f => Comonad (Cofree f)
Methods extract :: Cofree f a -> a # duplicate :: Cofree f a -> Cofree f (Cofree f a) # extend :: (Cofree f a -> b) -> Cofree f a -> Cofree f b #
Comonad w => Comonad (Yoneda w)
Methods extract :: Yoneda w a -> a # duplicate :: Yoneda w a -> Yoneda w (Yoneda w a) # extend :: (Yoneda w a -> b) -> Yoneda w a -> Yoneda w b #
Monoid s => Comonad (ReifiedGetter s)
Methods extract :: ReifiedGetter s a -> a # duplicate :: ReifiedGetter s a -> ReifiedGetter s (ReifiedGetter s a) # extend :: (ReifiedGetter s a -> b) -> ReifiedGetter s a -> ReifiedGetter s b #
Comonad f => Comonad (MaybeApply f)
Methods extract :: MaybeApply f a -> a # duplicate :: MaybeApply f a -> MaybeApply f (MaybeApply f a) # extend :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b #
Shape f => Comonad (Focused f) #
Methods extract :: Focused f a -> a # duplicate :: Focused f a -> Focused f (Focused f a) # extend :: (Focused f a -> b) -> Focused f a -> Focused f b #
(Comonad w, Monoid m) => Comonad (TracedT m w)
Methods extract :: TracedT m w a -> a # duplicate :: TracedT m w a -> TracedT m w (TracedT m w a) # extend :: (TracedT m w a -> b) -> TracedT m w a -> TracedT m w b #
Comonad w => Comonad (StoreT s w)
Methods extract :: StoreT s w a -> a # duplicate :: StoreT s w a -> StoreT s w (StoreT s w a) # extend :: (StoreT s w a -> b) -> StoreT s w a -> StoreT s w b #
Comonad w => Comonad (EnvT e w)
Methods extract :: EnvT e w a -> a # duplicate :: EnvT e w a -> EnvT e w (EnvT e w a) # extend :: (EnvT e w a -> b) -> EnvT e w a -> EnvT e w b #
Comonad w => Comonad (IdentityT * w)
Methods extract :: IdentityT * w a -> a # duplicate :: IdentityT * w a -> IdentityT * w (IdentityT * w a) # extend :: (IdentityT * w a -> b) -> IdentityT * w a -> IdentityT * w b #
(~) * a b => Comonad (Context a b)
Methods extract :: Context a b a -> a # duplicate :: Context a b a -> Context a b (Context a b a) # extend :: (Context a b a -> b) -> Context a b a -> Context a b b #
Comonad (Tagged * s)
Methods extract :: Tagged * s a -> a # duplicate :: Tagged * s a -> Tagged * s (Tagged * s a) # extend :: (Tagged * s a -> b) -> Tagged * s a -> Tagged * s b #
(Comonad f, Comonad g) => Comonad (Sum * f g)
Methods extract :: Sum * f g a -> a # duplicate :: Sum * f g a -> Sum * f g (Sum * f g a) # extend :: (Sum * f g a -> b) -> Sum * f g a -> Sum * f g b #
(~) * a b => Comonad (Molten i a b)
Methods extract :: Molten i a b a -> a # duplicate :: Molten i a b a -> Molten i a b (Molten i a b a) # extend :: (Molten i a b a -> b) -> Molten i a b a -> Molten i a b b #
((~) * a b, Conjoined p) => Comonad (Pretext p a b)
Methods extract :: Pretext p a b a -> a # duplicate :: Pretext p a b a -> Pretext p a b (Pretext p a b a) # extend :: (Pretext p a b a -> b) -> Pretext p a b a -> Pretext p a b b #
((~) * a b, Conjoined p) => Comonad (PretextT p g a b)
Methods extract :: PretextT p g a b a -> a # duplicate :: PretextT p g a b a -> PretextT p g a b (PretextT p g a b a) # extend :: (PretextT p g a b a -> b) -> PretextT p g a b a -> PretextT p g a b b #

class Comonad w => ComonadStore s w | w -> s where #

Minimal complete definition

pos, peek

Instances

ComonadStore s w => ComonadStore s (Cofree w)
Methods pos :: Cofree w a -> s # peek :: s -> Cofree w a -> a # peeks :: (s -> s) -> Cofree w a -> a # seek :: s -> Cofree w a -> Cofree w a # seeks :: (s -> s) -> Cofree w a -> Cofree w a # experiment :: Functor f => (s -> f s) -> Cofree w a -> f a #
(ComonadStore s w, Monoid m) => ComonadStore s (TracedT m w)
Methods pos :: TracedT m w a -> s # peek :: s -> TracedT m w a -> a # peeks :: (s -> s) -> TracedT m w a -> a # seek :: s -> TracedT m w a -> TracedT m w a # seeks :: (s -> s) -> TracedT m w a -> TracedT m w a # experiment :: Functor f => (s -> f s) -> TracedT m w a -> f a #
Comonad w => ComonadStore s (StoreT s w)
Methods pos :: StoreT s w a -> s # peek :: s -> StoreT s w a -> a # peeks :: (s -> s) -> StoreT s w a -> a # seek :: s -> StoreT s w a -> StoreT s w a # seeks :: (s -> s) -> StoreT s w a -> StoreT s w a # experiment :: Functor f => (s -> f s) -> StoreT s w a -> f a #
ComonadStore s w => ComonadStore s (IdentityT * w)
Methods pos :: IdentityT * w a -> s # peek :: s -> IdentityT * w a -> a # peeks :: (s -> s) -> IdentityT * w a -> a # seek :: s -> IdentityT * w a -> IdentityT * w a # seeks :: (s -> s) -> IdentityT * w a -> IdentityT * w a # experiment :: Functor f => (s -> f s) -> IdentityT * w a -> f a #
ComonadStore s w => ComonadStore s (EnvT e w)
Methods pos :: EnvT e w a -> s # peek :: s -> EnvT e w a -> a # peeks :: (s -> s) -> EnvT e w a -> a # seek :: s -> EnvT e w a -> EnvT e w a # seeks :: (s -> s) -> EnvT e w a -> EnvT e w a # experiment :: Functor f => (s -> f s) -> EnvT e w a -> f a #
(~) * a b => ComonadStore a (Context a b)
Methods pos :: Context a b a -> a # peek :: a -> Context a b a -> a # peeks :: (a -> a) -> Context a b a -> a # seek :: a -> Context a b a -> Context a b a # seeks :: (a -> a) -> Context a b a -> Context a b a # experiment :: Functor f => (a -> f a) -> Context a b a -> f a #
((~) * a b, Conjoined p) => ComonadStore a (Pretext p a b)
Methods pos :: Pretext p a b a -> a # peek :: a -> Pretext p a b a -> a # peeks :: (a -> a) -> Pretext p a b a -> a # seek :: a -> Pretext p a b a -> Pretext p a b a # seeks :: (a -> a) -> Pretext p a b a -> Pretext p a b a # experiment :: Functor f => (a -> f a) -> Pretext p a b a -> f a #
((~) * a b, Conjoined p) => ComonadStore a (PretextT p g a b)
Methods pos :: PretextT p g a b a -> a # peek :: a -> PretextT p g a b a -> a # peeks :: (a -> a) -> PretextT p g a b a -> a # seek :: a -> PretextT p g a b a -> PretextT p g a b a # seeks :: (a -> a) -> PretextT p g a b a -> PretextT p g a b a # experiment :: Functor f => (a -> f a) -> PretextT p g a b a -> f a #
Shape f => ComonadStore (f Int) (Focused f) #
Methods pos :: Focused f a -> f Int # peek :: f Int -> Focused f a -> a # peeks :: (f Int -> f Int) -> Focused f a -> a # seek :: f Int -> Focused f a -> Focused f a # seeks :: (f Int -> f Int) -> Focused f a -> Focused f a # experiment :: Functor f => (f Int -> f (f Int)) -> Focused f a -> f a #

Stencils

data Stencil f a Source #

Stencils are used to fold over neighbouring array sites. To construct a stencil use mkStencil, mkStencilUnboxed. For static sized stencils you can use the quasiquoter stencil.

To use a stencil you can use stencilSum or use the Foldable and FoldableWithIndex instances.

Instances

Functor (Stencil f) Source #
Methods fmap :: (a -> b) -> Stencil f a -> Stencil f b # (<$) :: a -> Stencil f b -> Stencil f a #
Foldable (Stencil f) Source #
Methods fold :: Monoid m => Stencil f m -> m # foldMap :: Monoid m => (a -> m) -> Stencil f a -> m # foldr :: (a -> b -> b) -> b -> Stencil f a -> b # foldr' :: (a -> b -> b) -> b -> Stencil f a -> b # foldl :: (b -> a -> b) -> b -> Stencil f a -> b # foldl' :: (b -> a -> b) -> b -> Stencil f a -> b # foldr1 :: (a -> a -> a) -> Stencil f a -> a # foldl1 :: (a -> a -> a) -> Stencil f a -> a # toList :: Stencil f a -> [a] # null :: Stencil f a -> Bool # length :: Stencil f a -> Int # elem :: Eq a => a -> Stencil f a -> Bool # maximum :: Ord a => Stencil f a -> a # minimum :: Ord a => Stencil f a -> a # sum :: Num a => Stencil f a -> a # product :: Num a => Stencil f a -> a #
FoldableWithIndex (f Int) (Stencil f) Source #
Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Stencil f a -> m # ifolded :: (Indexable (f Int) p, Contravariant f, Applicative f) => p a (f a) -> Stencil f a -> f (Stencil f a) # ifoldr :: (f Int -> a -> b -> b) -> b -> Stencil f a -> b # ifoldl :: (f Int -> b -> a -> b) -> b -> Stencil f a -> b # ifoldr' :: (f Int -> a -> b -> b) -> b -> Stencil f a -> b # ifoldl' :: (f Int -> b -> a -> b) -> b -> Stencil f a -> b #
(Show1 f, Show a) => Show (Stencil f a) Source #
Methods showsPrec :: Int -> Stencil f a -> ShowS # show :: Stencil f a -> String # showList :: [Stencil f a] -> ShowS #

Constructing stencils

stencil :: QuasiQuoter Source #

QuasiQuoter for producing a static stencil definition. This is a versatile parser for 1D, 2D and 3D stencils. The parsing is similar to dense but stencil also supports _, which means ignore this element. Also, stencils should have an odd length in all dimensions so there is always a center element (which is used as zero).

Examples

1D stencils are of the form

[stencil| 5 -3 1 -3 5 |] :: Num a => Stencil V1 a

2D stencils are of the form

myStencil2 :: Num a => Stencil V2 a
myStencil2 = [stencil|
  0 1 0
  1 0 1
  0 1 0
|]

3D stencils have gaps between planes.

myStencil3 :: Fractional a => Stencil V3 a
myStencil3 :: [stencil|
  1/20 3/10 1/20
  3/10  1   3/10
  1/20 3/10 1/20

  3/10  1   3/10
   1    _    1
  3/10  1   3/10

  1/20 3/10 1/20
  3/10  1   3/10
  1/20 3/10 1/20
|]

Variables can also be used

myStencil2' :: a -> a -> a -> Stencil V2 a
myStencil2' a b c = [stencil|
  c b c
  b a b
  c b c
|]

mkStencil :: [(f Int, a)] -> Stencil f a Source #

Make a stencil folding over a list.

If the list is staticlly known this should expand at compile time via rewrite rules, similar to makeStencilTH but less reliable. If that does not happen the resulting could be slow. If the list is not know at compile time, mkStencilUnboxed can be signifcantly faster (but isn't subject expending via rewrite rules).

mkStencilTH :: (ShapeLift f, Lift a) => [(f Int, a)] -> Q Exp Source #

Construct a Stencil by unrolling the list at compile time. For example

ifoldr f b $(mkStencilTH [(V1 (-1), 5), (V1 0, 3), (V1 1, 5)])

will be get turned into

f (V1 (-1)) 5 (f (V1 0) 3 (f (V1 1) 5 b))

at compile time. Since there are no loops and all target indexes are known at compile time, this can lead to more optimisations and faster execution times. This can lead to around a 2x speed up compared to folding over unboxed vectors.

myStencil = $(mkStencilTH (as :: [(f Int, a)])) :: Stencil f a

Using stencils

stencilSum :: (Shape f, Num a) => Boundary -> Stencil f a -> Focused f a -> a Source #

Sum the elements around a Focused using a Boundary condition and a Stencil.

This is often used in conjunction with extendFocus.

Common shapes

newtype V1 a :: * -> * #

A 1-dimensional vector

>>> pure 1 :: V1 Int
V1 1

>>> V1 2 + V1 3
V1 5

>>> V1 2 * V1 3
V1 6

>>> sum (V1 2)
2

Constructors

V1 a

Instances

Monad V1
Methods (>>=) :: V1 a -> (a -> V1 b) -> V1 b # (>>) :: V1 a -> V1 b -> V1 b # return :: a -> V1 a # fail :: String -> V1 a #
Functor V1
Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
MonadFix V1
Methods mfix :: (a -> V1 a) -> V1 a #
Applicative V1
Methods pure :: a -> V1 a # (<>) :: V1 (a -> b) -> V1 a -> V1 b # (>) :: V1 a -> V1 b -> V1 b # (<*) :: V1 a -> V1 b -> V1 a #
Foldable V1
Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # toList :: V1 a -> [a] # null :: V1 a -> Bool # length :: V1 a -> Int # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # minimum :: Ord a => V1 a -> a # sum :: Num a => V1 a -> a # product :: Num a => V1 a -> a #
Traversable V1
Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Generic1 V1
Associated Types type Rep1 (V1 :: * -> ) :: -> * # Methods from1 :: V1 a -> Rep1 V1 a # to1 :: Rep1 V1 a -> V1 a #
Distributive V1
Methods distribute :: Functor f => f (V1 a) -> V1 (f a) # collect :: Functor f => (a -> V1 b) -> f a -> V1 (f b) # distributeM :: Monad m => m (V1 a) -> V1 (m a) # collectM :: Monad m => (a -> V1 b) -> m a -> V1 (m b) #
Representable V1
Associated Types type Rep (V1 :: * -> ) :: # Methods tabulate :: (Rep V1 -> a) -> V1 a # index :: V1 a -> Rep V1 -> a #
Eq1 V1
Methods liftEq :: (a -> b -> Bool) -> V1 a -> V1 b -> Bool #
Ord1 V1
Methods liftCompare :: (a -> b -> Ordering) -> V1 a -> V1 b -> Ordering #
Read1 V1
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V1 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V1 a] #
Show1 V1
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V1 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V1 a] -> ShowS #
MonadZip V1
Methods mzip :: V1 a -> V1 b -> V1 (a, b) # mzipWith :: (a -> b -> c) -> V1 a -> V1 b -> V1 c # munzip :: V1 (a, b) -> (V1 a, V1 b) #
Serial1 V1
Methods serializeWith :: MonadPut m => (a -> m ()) -> V1 a -> m () # deserializeWith :: MonadGet m => m a -> m (V1 a) #
Traversable1 V1
Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
R1 V1
Methods _x :: Functor f => (a -> f a) -> V1 a -> f (V1 a) #
Metric V1
Methods dot :: Num a => V1 a -> V1 a -> a # quadrance :: Num a => V1 a -> a # qd :: Num a => V1 a -> V1 a -> a # distance :: Floating a => V1 a -> V1 a -> a # norm :: Floating a => V1 a -> a # signorm :: Floating a => V1 a -> V1 a #
Additive V1
Methods zero :: Num a => V1 a # (^+^) :: Num a => V1 a -> V1 a -> V1 a # (^-^) :: Num a => V1 a -> V1 a -> V1 a # lerp :: Num a => a -> V1 a -> V1 a -> V1 a # liftU2 :: (a -> a -> a) -> V1 a -> V1 a -> V1 a # liftI2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #
Apply V1
Methods (<.>) :: V1 (a -> b) -> V1 a -> V1 b # (.>) :: V1 a -> V1 b -> V1 b # (<.) :: V1 a -> V1 b -> V1 a #
Bind V1
Methods (>>-) :: V1 a -> (a -> V1 b) -> V1 b # join :: V1 (V1 a) -> V1 a #
Foldable1 V1
Methods fold1 :: Semigroup m => V1 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V1 a -> m #
Shape V1 Source #
Methods shapeToIndex :: Layout V1 -> V1 Int -> Int Source # shapeFromIndex :: Layout V1 -> Int -> V1 Int Source # shapeIntersect :: Layout V1 -> Layout V1 -> Layout V1 Source # unsafeShapeStep :: Layout V1 -> V1 Int -> V1 Int Source # shapeStep :: Layout V1 -> V1 Int -> Maybe (V1 Int) Source # shapeStepBetween :: V1 Int -> Layout V1 -> V1 Int -> Maybe (V1 Int) Source # shapeInRange :: Layout V1 -> V1 Int -> Bool Source # shapeSize :: Layout V1 -> Int Source #
ShapeLift V1 Source #
Methods liftShape :: Lift a => V1 a -> Q Exp Source # liftShape' :: Lift a => V1 a -> Q Exp Source #
Unbox a => Vector Vector (V1 a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V1 a) -> m (Vector (V1 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V1 a) -> m (Mutable Vector (PrimState m) (V1 a)) # basicLength :: Vector (V1 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V1 a) -> Vector (V1 a) # basicUnsafeIndexM :: Monad m => Vector (V1 a) -> Int -> m (V1 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V1 a) -> Vector (V1 a) -> m () # elemseq :: Vector (V1 a) -> V1 a -> b -> b #
Unbox a => MVector MVector (V1 a)
Methods basicLength :: MVector s (V1 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V1 a) -> MVector s (V1 a) # basicOverlaps :: MVector s (V1 a) -> MVector s (V1 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V1 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V1 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V1 a -> m (MVector (PrimState m) (V1 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> m (V1 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> V1 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V1 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V1 a) -> V1 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V1 a) -> MVector (PrimState m) (V1 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V1 a) -> MVector (PrimState m) (V1 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V1 a) -> Int -> m (MVector (PrimState m) (V1 a)) #
(~) * i Int => HasLayout V1 (V1 i) Source #
Methods layout :: Lens' (V1 i) (Layout V1) Source #
Bounded a => Bounded (V1 a)
Methods minBound :: V1 a # maxBound :: V1 a #
Eq a => Eq (V1 a)
Methods (==) :: V1 a -> V1 a -> Bool # (/=) :: V1 a -> V1 a -> Bool #
Floating a => Floating (V1 a)
Methods pi :: V1 a # exp :: V1 a -> V1 a # log :: V1 a -> V1 a # sqrt :: V1 a -> V1 a # (**) :: V1 a -> V1 a -> V1 a # logBase :: V1 a -> V1 a -> V1 a # sin :: V1 a -> V1 a # cos :: V1 a -> V1 a # tan :: V1 a -> V1 a # asin :: V1 a -> V1 a # acos :: V1 a -> V1 a # atan :: V1 a -> V1 a # sinh :: V1 a -> V1 a # cosh :: V1 a -> V1 a # tanh :: V1 a -> V1 a # asinh :: V1 a -> V1 a # acosh :: V1 a -> V1 a # atanh :: V1 a -> V1 a # log1p :: V1 a -> V1 a # expm1 :: V1 a -> V1 a # log1pexp :: V1 a -> V1 a # log1mexp :: V1 a -> V1 a #
Fractional a => Fractional (V1 a)
Methods (/) :: V1 a -> V1 a -> V1 a # recip :: V1 a -> V1 a # fromRational :: Rational -> V1 a #
Data a => Data (V1 a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V1 a -> c (V1 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V1 a) # toConstr :: V1 a -> Constr # dataTypeOf :: V1 a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (V1 a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V1 a)) # gmapT :: (forall b. Data b => b -> b) -> V1 a -> V1 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V1 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V1 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V1 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V1 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V1 a -> m (V1 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V1 a -> m (V1 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V1 a -> m (V1 a) #
Num a => Num (V1 a)
Methods (+) :: V1 a -> V1 a -> V1 a # (-) :: V1 a -> V1 a -> V1 a # (*) :: V1 a -> V1 a -> V1 a # negate :: V1 a -> V1 a # abs :: V1 a -> V1 a # signum :: V1 a -> V1 a # fromInteger :: Integer -> V1 a #
Ord a => Ord (V1 a)
Methods compare :: V1 a -> V1 a -> Ordering # (<) :: V1 a -> V1 a -> Bool # (<=) :: V1 a -> V1 a -> Bool # (>) :: V1 a -> V1 a -> Bool # (>=) :: V1 a -> V1 a -> Bool # max :: V1 a -> V1 a -> V1 a # min :: V1 a -> V1 a -> V1 a #
Read a => Read (V1 a)
Methods readsPrec :: Int -> ReadS (V1 a) # readList :: ReadS [V1 a] # readPrec :: ReadPrec (V1 a) # readListPrec :: ReadPrec [V1 a] #
Show a => Show (V1 a)
Methods showsPrec :: Int -> V1 a -> ShowS # show :: V1 a -> String # showList :: [V1 a] -> ShowS #
Ix a => Ix (V1 a)
Methods range :: (V1 a, V1 a) -> [V1 a] # index :: (V1 a, V1 a) -> V1 a -> Int # unsafeIndex :: (V1 a, V1 a) -> V1 a -> Int inRange :: (V1 a, V1 a) -> V1 a -> Bool # rangeSize :: (V1 a, V1 a) -> Int # unsafeRangeSize :: (V1 a, V1 a) -> Int
Generic (V1 a)
Associated Types type Rep (V1 a) :: * -> * # Methods from :: V1 a -> Rep (V1 a) x # to :: Rep (V1 a) x -> V1 a #
Storable a => Storable (V1 a)
Methods sizeOf :: V1 a -> Int # alignment :: V1 a -> Int # peekElemOff :: Ptr (V1 a) -> Int -> IO (V1 a) # pokeElemOff :: Ptr (V1 a) -> Int -> V1 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V1 a) # pokeByteOff :: Ptr b -> Int -> V1 a -> IO () # peek :: Ptr (V1 a) -> IO (V1 a) # poke :: Ptr (V1 a) -> V1 a -> IO () #
Binary a => Binary (V1 a)
Methods put :: V1 a -> Put # get :: Get (V1 a) # putList :: [V1 a] -> Put #
Serial a => Serial (V1 a)
Methods serialize :: MonadPut m => V1 a -> m () # deserialize :: MonadGet m => m (V1 a) #
Serialize a => Serialize (V1 a)
Methods put :: Putter (V1 a) # get :: Get (V1 a) #
NFData a => NFData (V1 a)
Methods rnf :: V1 a -> () #
Hashable a => Hashable (V1 a)
Methods hashWithSalt :: Int -> V1 a -> Int # hash :: V1 a -> Int #
Unbox a => Unbox (V1 a)

Ixed (V1 a)
Methods ix :: Index (V1 a) -> Traversal' (V1 a) (IxValue (V1 a)) #
Epsilon a => Epsilon (V1 a)
Methods nearZero :: V1 a -> Bool #
FunctorWithIndex (E V1) V1
Methods imap :: (E V1 -> a -> b) -> V1 a -> V1 b # imapped :: (Indexable (E V1) p, Settable f) => p a (f b) -> V1 a -> f (V1 b) #
FoldableWithIndex (E V1) V1
Methods ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m # ifolded :: (Indexable (E V1) p, Contravariant f, Applicative f) => p a (f a) -> V1 a -> f (V1 a) # ifoldr :: (E V1 -> a -> b -> b) -> b -> V1 a -> b # ifoldl :: (E V1 -> b -> a -> b) -> b -> V1 a -> b # ifoldr' :: (E V1 -> a -> b -> b) -> b -> V1 a -> b # ifoldl' :: (E V1 -> b -> a -> b) -> b -> V1 a -> b #
TraversableWithIndex (E V1) V1
Methods itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: (Indexable (E V1) p, Applicative f) => p a (f b) -> V1 a -> f (V1 b) #
Each (V1 a) (V1 b) a b
Methods each :: Traversal (V1 a) (V1 b) a b #
type Rep1 V1
type Rep1 V1 = D1 (MetaData "V1" "Linear.V1" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" True) (C1 (MetaCons "V1" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))
type Rep V1
type Rep V1 = E V1
data MVector s (V1 a)
data MVector s (V1 a) = MV_V1 (MVector s a)
type Rep (V1 a)
type Rep (V1 a) = D1 (MetaData "V1" "Linear.V1" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" True) (C1 (MetaCons "V1" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
data Vector (V1 a)
data Vector (V1 a) = V_V1 (Vector a)
type Index (V1 a)
type Index (V1 a) = E V1
type IxValue (V1 a)
type IxValue (V1 a) = a

data V2 a :: * -> * #

A 2-dimensional vector

>>> pure 1 :: V2 Int
V2 1 1

>>> V2 1 2 + V2 3 4
V2 4 6

>>> V2 1 2 * V2 3 4
V2 3 8

>>> sum (V2 1 2)
3

Constructors

V2 ~a ~a

Instances

Monad V2
Methods (>>=) :: V2 a -> (a -> V2 b) -> V2 b # (>>) :: V2 a -> V2 b -> V2 b # return :: a -> V2 a # fail :: String -> V2 a #
Functor V2
Methods fmap :: (a -> b) -> V2 a -> V2 b # (<$) :: a -> V2 b -> V2 a #
MonadFix V2
Methods mfix :: (a -> V2 a) -> V2 a #
Applicative V2
Methods pure :: a -> V2 a # (<>) :: V2 (a -> b) -> V2 a -> V2 b # (>) :: V2 a -> V2 b -> V2 b # (<*) :: V2 a -> V2 b -> V2 a #
Foldable V2
Methods fold :: Monoid m => V2 m -> m # foldMap :: Monoid m => (a -> m) -> V2 a -> m # foldr :: (a -> b -> b) -> b -> V2 a -> b # foldr' :: (a -> b -> b) -> b -> V2 a -> b # foldl :: (b -> a -> b) -> b -> V2 a -> b # foldl' :: (b -> a -> b) -> b -> V2 a -> b # foldr1 :: (a -> a -> a) -> V2 a -> a # foldl1 :: (a -> a -> a) -> V2 a -> a # toList :: V2 a -> [a] # null :: V2 a -> Bool # length :: V2 a -> Int # elem :: Eq a => a -> V2 a -> Bool # maximum :: Ord a => V2 a -> a # minimum :: Ord a => V2 a -> a # sum :: Num a => V2 a -> a # product :: Num a => V2 a -> a #
Traversable V2
Methods traverse :: Applicative f => (a -> f b) -> V2 a -> f (V2 b) # sequenceA :: Applicative f => V2 (f a) -> f (V2 a) # mapM :: Monad m => (a -> m b) -> V2 a -> m (V2 b) # sequence :: Monad m => V2 (m a) -> m (V2 a) #
Generic1 V2
Associated Types type Rep1 (V2 :: * -> ) :: -> * # Methods from1 :: V2 a -> Rep1 V2 a # to1 :: Rep1 V2 a -> V2 a #
Distributive V2
Methods distribute :: Functor f => f (V2 a) -> V2 (f a) # collect :: Functor f => (a -> V2 b) -> f a -> V2 (f b) # distributeM :: Monad m => m (V2 a) -> V2 (m a) # collectM :: Monad m => (a -> V2 b) -> m a -> V2 (m b) #
Representable V2
Associated Types type Rep (V2 :: * -> ) :: # Methods tabulate :: (Rep V2 -> a) -> V2 a # index :: V2 a -> Rep V2 -> a #
Eq1 V2
Methods liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool #
Ord1 V2
Methods liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering #
Read1 V2
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] #
Show1 V2
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS #
MonadZip V2
Methods mzip :: V2 a -> V2 b -> V2 (a, b) # mzipWith :: (a -> b -> c) -> V2 a -> V2 b -> V2 c # munzip :: V2 (a, b) -> (V2 a, V2 b) #
Serial1 V2
Methods serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () # deserializeWith :: MonadGet m => m a -> m (V2 a) #
Traversable1 V2
Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) # sequence1 :: Apply f => V2 (f b) -> f (V2 b) #
R2 V2
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) #
R1 V2
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) #
Metric V2
Methods dot :: Num a => V2 a -> V2 a -> a # quadrance :: Num a => V2 a -> a # qd :: Num a => V2 a -> V2 a -> a # distance :: Floating a => V2 a -> V2 a -> a # norm :: Floating a => V2 a -> a # signorm :: Floating a => V2 a -> V2 a #
Additive V2
Methods zero :: Num a => V2 a # (^+^) :: Num a => V2 a -> V2 a -> V2 a # (^-^) :: Num a => V2 a -> V2 a -> V2 a # lerp :: Num a => a -> V2 a -> V2 a -> V2 a # liftU2 :: (a -> a -> a) -> V2 a -> V2 a -> V2 a # liftI2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Apply V2
Methods (<.>) :: V2 (a -> b) -> V2 a -> V2 b # (.>) :: V2 a -> V2 b -> V2 b # (<.) :: V2 a -> V2 b -> V2 a #
Bind V2
Methods (>>-) :: V2 a -> (a -> V2 b) -> V2 b # join :: V2 (V2 a) -> V2 a #
Foldable1 V2
Methods fold1 :: Semigroup m => V2 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m #
Shape V2 Source #
Methods shapeToIndex :: Layout V2 -> V2 Int -> Int Source # shapeFromIndex :: Layout V2 -> Int -> V2 Int Source # shapeIntersect :: Layout V2 -> Layout V2 -> Layout V2 Source # unsafeShapeStep :: Layout V2 -> V2 Int -> V2 Int Source # shapeStep :: Layout V2 -> V2 Int -> Maybe (V2 Int) Source # shapeStepBetween :: V2 Int -> Layout V2 -> V2 Int -> Maybe (V2 Int) Source # shapeInRange :: Layout V2 -> V2 Int -> Bool Source # shapeSize :: Layout V2 -> Int Source #
ShapeLift V2 Source #
Methods liftShape :: Lift a => V2 a -> Q Exp Source # liftShape' :: Lift a => V2 a -> Q Exp Source #
Unbox a => Vector Vector (V2 a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> m (Vector (V2 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V2 a) -> m (Mutable Vector (PrimState m) (V2 a)) # basicLength :: Vector (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V2 a) -> Vector (V2 a) # basicUnsafeIndexM :: Monad m => Vector (V2 a) -> Int -> m (V2 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V2 a) -> Vector (V2 a) -> m () # elemseq :: Vector (V2 a) -> V2 a -> b -> b #
Unbox a => MVector MVector (V2 a)
Methods basicLength :: MVector s (V2 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V2 a) -> MVector s (V2 a) # basicOverlaps :: MVector s (V2 a) -> MVector s (V2 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V2 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V2 a -> m (MVector (PrimState m) (V2 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (V2 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> V2 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V2 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V2 a) -> V2 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V2 a) -> MVector (PrimState m) (V2 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V2 a) -> Int -> m (MVector (PrimState m) (V2 a)) #
(~) * i Int => HasLayout V2 (V2 i) Source #
Methods layout :: Lens' (V2 i) (Layout V2) Source #
Bounded a => Bounded (V2 a)
Methods minBound :: V2 a # maxBound :: V2 a #
Eq a => Eq (V2 a)
Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Floating a => Floating (V2 a)
Methods pi :: V2 a # exp :: V2 a -> V2 a # log :: V2 a -> V2 a # sqrt :: V2 a -> V2 a # (**) :: V2 a -> V2 a -> V2 a # logBase :: V2 a -> V2 a -> V2 a # sin :: V2 a -> V2 a # cos :: V2 a -> V2 a # tan :: V2 a -> V2 a # asin :: V2 a -> V2 a # acos :: V2 a -> V2 a # atan :: V2 a -> V2 a # sinh :: V2 a -> V2 a # cosh :: V2 a -> V2 a # tanh :: V2 a -> V2 a # asinh :: V2 a -> V2 a # acosh :: V2 a -> V2 a # atanh :: V2 a -> V2 a # log1p :: V2 a -> V2 a # expm1 :: V2 a -> V2 a # log1pexp :: V2 a -> V2 a # log1mexp :: V2 a -> V2 a #
Fractional a => Fractional (V2 a)
Methods (/) :: V2 a -> V2 a -> V2 a # recip :: V2 a -> V2 a # fromRational :: Rational -> V2 a #
Data a => Data (V2 a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V2 a -> c (V2 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V2 a) # toConstr :: V2 a -> Constr # dataTypeOf :: V2 a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (V2 a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V2 a)) # gmapT :: (forall b. Data b => b -> b) -> V2 a -> V2 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V2 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V2 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V2 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V2 a -> m (V2 a) #
Num a => Num (V2 a)
Methods (+) :: V2 a -> V2 a -> V2 a # (-) :: V2 a -> V2 a -> V2 a # (*) :: V2 a -> V2 a -> V2 a # negate :: V2 a -> V2 a # abs :: V2 a -> V2 a # signum :: V2 a -> V2 a # fromInteger :: Integer -> V2 a #
Ord a => Ord (V2 a)
Methods compare :: V2 a -> V2 a -> Ordering # (<) :: V2 a -> V2 a -> Bool # (<=) :: V2 a -> V2 a -> Bool # (>) :: V2 a -> V2 a -> Bool # (>=) :: V2 a -> V2 a -> Bool # max :: V2 a -> V2 a -> V2 a # min :: V2 a -> V2 a -> V2 a #
Read a => Read (V2 a)
Methods readsPrec :: Int -> ReadS (V2 a) # readList :: ReadS [V2 a] # readPrec :: ReadPrec (V2 a) # readListPrec :: ReadPrec [V2 a] #
Show a => Show (V2 a)
Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Ix a => Ix (V2 a)
Methods range :: (V2 a, V2 a) -> [V2 a] # index :: (V2 a, V2 a) -> V2 a -> Int # unsafeIndex :: (V2 a, V2 a) -> V2 a -> Int inRange :: (V2 a, V2 a) -> V2 a -> Bool # rangeSize :: (V2 a, V2 a) -> Int # unsafeRangeSize :: (V2 a, V2 a) -> Int
Generic (V2 a)
Associated Types type Rep (V2 a) :: * -> * # Methods from :: V2 a -> Rep (V2 a) x # to :: Rep (V2 a) x -> V2 a #
Storable a => Storable (V2 a)
Methods sizeOf :: V2 a -> Int # alignment :: V2 a -> Int # peekElemOff :: Ptr (V2 a) -> Int -> IO (V2 a) # pokeElemOff :: Ptr (V2 a) -> Int -> V2 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V2 a) # pokeByteOff :: Ptr b -> Int -> V2 a -> IO () # peek :: Ptr (V2 a) -> IO (V2 a) # poke :: Ptr (V2 a) -> V2 a -> IO () #
Binary a => Binary (V2 a)
Methods put :: V2 a -> Put # get :: Get (V2 a) # putList :: [V2 a] -> Put #
Serial a => Serial (V2 a)
Methods serialize :: MonadPut m => V2 a -> m () # deserialize :: MonadGet m => m (V2 a) #
Serialize a => Serialize (V2 a)
Methods put :: Putter (V2 a) # get :: Get (V2 a) #
NFData a => NFData (V2 a)
Methods rnf :: V2 a -> () #
Hashable a => Hashable (V2 a)
Methods hashWithSalt :: Int -> V2 a -> Int # hash :: V2 a -> Int #
Unbox a => Unbox (V2 a)

Ixed (V2 a)
Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #
Epsilon a => Epsilon (V2 a)
Methods nearZero :: V2 a -> Bool #
FunctorWithIndex (E V2) V2
Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: (Indexable (E V2) p, Settable f) => p a (f b) -> V2 a -> f (V2 b) #
FoldableWithIndex (E V2) V2
Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: (Indexable (E V2) p, Contravariant f, Applicative f) => p a (f a) -> V2 a -> f (V2 a) # ifoldr :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl :: (E V2 -> b -> a -> b) -> b -> V2 a -> b # ifoldr' :: (E V2 -> a -> b -> b) -> b -> V2 a -> b # ifoldl' :: (E V2 -> b -> a -> b) -> b -> V2 a -> b #
TraversableWithIndex (E V2) V2
Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: (Indexable (E V2) p, Applicative f) => p a (f b) -> V2 a -> f (V2 b) #
Each (V2 a) (V2 b) a b
Methods each :: Traversal (V2 a) (V2 b) a b #
type Rep1 V2
type Rep1 V2 = D1 (MetaData "V2" "Linear.V2" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" False) (C1 (MetaCons "V2" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)))
type Rep V2
type Rep V2 = E V2
data MVector s (V2 a)
data MVector s (V2 a) = MV_V2 ~Int ~(MVector s a)
type Rep (V2 a)
type Rep (V2 a) = D1 (MetaData "V2" "Linear.V2" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" False) (C1 (MetaCons "V2" PrefixI False) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))))
data Vector (V2 a)
data Vector (V2 a) = V_V2 ~Int ~(Vector a)
type Index (V2 a)
type Index (V2 a) = E V2
type IxValue (V2 a)
type IxValue (V2 a) = a

data V3 a :: * -> * #

A 3-dimensional vector

Constructors

V3 ~a ~a ~a

Instances

Monad V3
Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a # fail :: String -> V3 a #
Functor V3
Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Methods mfix :: (a -> V3 a) -> V3 a #
Applicative V3
Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Foldable V3
Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> m # foldr :: (a -> b -> b) -> b -> V3 a -> b # foldr' :: (a -> b -> b) -> b -> V3 a -> b # foldl :: (b -> a -> b) -> b -> V3 a -> b # foldl' :: (b -> a -> b) -> b -> V3 a -> b # foldr1 :: (a -> a -> a) -> V3 a -> a # foldl1 :: (a -> a -> a) -> V3 a -> a # toList :: V3 a -> [a] # null :: V3 a -> Bool # length :: V3 a -> Int # elem :: Eq a => a -> V3 a -> Bool # maximum :: Ord a => V3 a -> a # minimum :: Ord a => V3 a -> a # sum :: Num a => V3 a -> a # product :: Num a => V3 a -> a #
Traversable V3
Methods traverse :: Applicative f => (a -> f b) -> V3 a -> f (V3 b) # sequenceA :: Applicative f => V3 (f a) -> f (V3 a) # mapM :: Monad m => (a -> m b) -> V3 a -> m (V3 b) # sequence :: Monad m => V3 (m a) -> m (V3 a) #
Generic1 V3
Associated Types type Rep1 (V3 :: * -> ) :: -> * # Methods from1 :: V3 a -> Rep1 V3 a # to1 :: Rep1 V3 a -> V3 a #
Distributive V3
Methods distribute :: Functor f => f (V3 a) -> V3 (f a) # collect :: Functor f => (a -> V3 b) -> f a -> V3 (f b) # distributeM :: Monad m => m (V3 a) -> V3 (m a) # collectM :: Monad m => (a -> V3 b) -> m a -> V3 (m b) #
Representable V3
Associated Types type Rep (V3 :: * -> ) :: # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Eq1 V3
Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] #
Show1 V3
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
MonadZip V3
Methods mzip :: V3 a -> V3 b -> V3 (a, b) # mzipWith :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # munzip :: V3 (a, b) -> (V3 a, V3 b) #
Serial1 V3
Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Traversable1 V3
Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
R3 V3
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) #
R2 V3
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) #
R1 V3
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) #
Metric V3
Methods dot :: Num a => V3 a -> V3 a -> a # quadrance :: Num a => V3 a -> a # qd :: Num a => V3 a -> V3 a -> a # distance :: Floating a => V3 a -> V3 a -> a # norm :: Floating a => V3 a -> a # signorm :: Floating a => V3 a -> V3 a #
Additive V3
Methods zero :: Num a => V3 a # (^+^) :: Num a => V3 a -> V3 a -> V3 a # (^-^) :: Num a => V3 a -> V3 a -> V3 a # lerp :: Num a => a -> V3 a -> V3 a -> V3 a # liftU2 :: (a -> a -> a) -> V3 a -> V3 a -> V3 a # liftI2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Apply V3
Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a #
Bind V3
Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Foldable1 V3
Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m #
Shape V3 Source #
Methods shapeToIndex :: Layout V3 -> V3 Int -> Int Source # shapeFromIndex :: Layout V3 -> Int -> V3 Int Source # shapeIntersect :: Layout V3 -> Layout V3 -> Layout V3 Source # unsafeShapeStep :: Layout V3 -> V3 Int -> V3 Int Source # shapeStep :: Layout V3 -> V3 Int -> Maybe (V3 Int) Source # shapeStepBetween :: V3 Int -> Layout V3 -> V3 Int -> Maybe (V3 Int) Source # shapeInRange :: Layout V3 -> V3 Int -> Bool Source # shapeSize :: Layout V3 -> Int Source #
ShapeLift V3 Source #
Methods liftShape :: Lift a => V3 a -> Q Exp Source # liftShape' :: Lift a => V3 a -> Q Exp Source #
Unbox a => Vector Vector (V3 a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> m (Vector (V3 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V3 a) -> m (Mutable Vector (PrimState m) (V3 a)) # basicLength :: Vector (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V3 a) -> Vector (V3 a) # basicUnsafeIndexM :: Monad m => Vector (V3 a) -> Int -> m (V3 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V3 a) -> Vector (V3 a) -> m () # elemseq :: Vector (V3 a) -> V3 a -> b -> b #
Unbox a => MVector MVector (V3 a)
Methods basicLength :: MVector s (V3 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V3 a) -> MVector s (V3 a) # basicOverlaps :: MVector s (V3 a) -> MVector s (V3 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V3 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V3 a -> m (MVector (PrimState m) (V3 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (V3 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> V3 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V3 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V3 a) -> V3 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V3 a) -> MVector (PrimState m) (V3 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V3 a) -> Int -> m (MVector (PrimState m) (V3 a)) #
(~) * i Int => HasLayout V3 (V3 i) Source #
Methods layout :: Lens' (V3 i) (Layout V3) Source #
Bounded a => Bounded (V3 a)
Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Floating a => Floating (V3 a)
Methods pi :: V3 a # exp :: V3 a -> V3 a # log :: V3 a -> V3 a # sqrt :: V3 a -> V3 a # (**) :: V3 a -> V3 a -> V3 a # logBase :: V3 a -> V3 a -> V3 a # sin :: V3 a -> V3 a # cos :: V3 a -> V3 a # tan :: V3 a -> V3 a # asin :: V3 a -> V3 a # acos :: V3 a -> V3 a # atan :: V3 a -> V3 a # sinh :: V3 a -> V3 a # cosh :: V3 a -> V3 a # tanh :: V3 a -> V3 a # asinh :: V3 a -> V3 a # acosh :: V3 a -> V3 a # atanh :: V3 a -> V3 a # log1p :: V3 a -> V3 a # expm1 :: V3 a -> V3 a # log1pexp :: V3 a -> V3 a # log1mexp :: V3 a -> V3 a #
Fractional a => Fractional (V3 a)
Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Data a => Data (V3 a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V3 a -> c (V3 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V3 a) # toConstr :: V3 a -> Constr # dataTypeOf :: V3 a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (V3 a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V3 a)) # gmapT :: (forall b. Data b => b -> b) -> V3 a -> V3 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V3 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V3 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V3 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V3 a -> m (V3 a) #
Num a => Num (V3 a)
Methods (+) :: V3 a -> V3 a -> V3 a # (-) :: V3 a -> V3 a -> V3 a # (*) :: V3 a -> V3 a -> V3 a # negate :: V3 a -> V3 a # abs :: V3 a -> V3 a # signum :: V3 a -> V3 a # fromInteger :: Integer -> V3 a #
Ord a => Ord (V3 a)
Methods compare :: V3 a -> V3 a -> Ordering # (<) :: V3 a -> V3 a -> Bool # (<=) :: V3 a -> V3 a -> Bool # (>) :: V3 a -> V3 a -> Bool # (>=) :: V3 a -> V3 a -> Bool # max :: V3 a -> V3 a -> V3 a # min :: V3 a -> V3 a -> V3 a #
Read a => Read (V3 a)
Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Show a => Show (V3 a)
Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Ix a => Ix (V3 a)
Methods range :: (V3 a, V3 a) -> [V3 a] # index :: (V3 a, V3 a) -> V3 a -> Int # unsafeIndex :: (V3 a, V3 a) -> V3 a -> Int inRange :: (V3 a, V3 a) -> V3 a -> Bool # rangeSize :: (V3 a, V3 a) -> Int # unsafeRangeSize :: (V3 a, V3 a) -> Int
Generic (V3 a)
Associated Types type Rep (V3 a) :: * -> * # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Storable a => Storable (V3 a)
Methods sizeOf :: V3 a -> Int # alignment :: V3 a -> Int # peekElemOff :: Ptr (V3 a) -> Int -> IO (V3 a) # pokeElemOff :: Ptr (V3 a) -> Int -> V3 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V3 a) # pokeByteOff :: Ptr b -> Int -> V3 a -> IO () # peek :: Ptr (V3 a) -> IO (V3 a) # poke :: Ptr (V3 a) -> V3 a -> IO () #
Binary a => Binary (V3 a)
Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Methods rnf :: V3 a -> () #
Hashable a => Hashable (V3 a)
Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Unbox a => Unbox (V3 a)

Ixed (V3 a)
Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Epsilon a => Epsilon (V3 a)
Methods nearZero :: V3 a -> Bool #
FunctorWithIndex (E V3) V3
Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: (Indexable (E V3) p, Settable f) => p a (f b) -> V3 a -> f (V3 b) #
FoldableWithIndex (E V3) V3
Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: (Indexable (E V3) p, Contravariant f, Applicative f) => p a (f a) -> V3 a -> f (V3 a) # ifoldr :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl :: (E V3 -> b -> a -> b) -> b -> V3 a -> b # ifoldr' :: (E V3 -> a -> b -> b) -> b -> V3 a -> b # ifoldl' :: (E V3 -> b -> a -> b) -> b -> V3 a -> b #
TraversableWithIndex (E V3) V3
Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: (Indexable (E V3) p, Applicative f) => p a (f b) -> V3 a -> f (V3 b) #
Each (V3 a) (V3 b) a b
Methods each :: Traversal (V3 a) (V3 b) a b #
type Rep1 V3
type Rep1 V3 = D1 (MetaData "V3" "Linear.V3" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" False) (C1 (MetaCons "V3" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))))
type Rep V3
type Rep V3 = E V3
data MVector s (V3 a)
data MVector s (V3 a) = MV_V3 ~Int ~(MVector s a)
type Rep (V3 a)
type Rep (V3 a) = D1 (MetaData "V3" "Linear.V3" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" False) (C1 (MetaCons "V3" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)))))
data Vector (V3 a)
data Vector (V3 a) = V_V3 ~Int ~(Vector a)
type Index (V3 a)
type Index (V3 a) = E V3
type IxValue (V3 a)
type IxValue (V3 a) = a

data V4 a :: * -> * #

A 4-dimensional vector.

Constructors

V4 ~a ~a ~a ~a

Instances

Monad V4
Methods (>>=) :: V4 a -> (a -> V4 b) -> V4 b # (>>) :: V4 a -> V4 b -> V4 b # return :: a -> V4 a # fail :: String -> V4 a #
Functor V4
Methods fmap :: (a -> b) -> V4 a -> V4 b # (<$) :: a -> V4 b -> V4 a #
MonadFix V4
Methods mfix :: (a -> V4 a) -> V4 a #
Applicative V4
Methods pure :: a -> V4 a # (<>) :: V4 (a -> b) -> V4 a -> V4 b # (>) :: V4 a -> V4 b -> V4 b # (<*) :: V4 a -> V4 b -> V4 a #
Foldable V4
Methods fold :: Monoid m => V4 m -> m # foldMap :: Monoid m => (a -> m) -> V4 a -> m # foldr :: (a -> b -> b) -> b -> V4 a -> b # foldr' :: (a -> b -> b) -> b -> V4 a -> b # foldl :: (b -> a -> b) -> b -> V4 a -> b # foldl' :: (b -> a -> b) -> b -> V4 a -> b # foldr1 :: (a -> a -> a) -> V4 a -> a # foldl1 :: (a -> a -> a) -> V4 a -> a # toList :: V4 a -> [a] # null :: V4 a -> Bool # length :: V4 a -> Int # elem :: Eq a => a -> V4 a -> Bool # maximum :: Ord a => V4 a -> a # minimum :: Ord a => V4 a -> a # sum :: Num a => V4 a -> a # product :: Num a => V4 a -> a #
Traversable V4
Methods traverse :: Applicative f => (a -> f b) -> V4 a -> f (V4 b) # sequenceA :: Applicative f => V4 (f a) -> f (V4 a) # mapM :: Monad m => (a -> m b) -> V4 a -> m (V4 b) # sequence :: Monad m => V4 (m a) -> m (V4 a) #
Generic1 V4
Associated Types type Rep1 (V4 :: * -> ) :: -> * # Methods from1 :: V4 a -> Rep1 V4 a # to1 :: Rep1 V4 a -> V4 a #
Distributive V4
Methods distribute :: Functor f => f (V4 a) -> V4 (f a) # collect :: Functor f => (a -> V4 b) -> f a -> V4 (f b) # distributeM :: Monad m => m (V4 a) -> V4 (m a) # collectM :: Monad m => (a -> V4 b) -> m a -> V4 (m b) #
Representable V4
Associated Types type Rep (V4 :: * -> ) :: # Methods tabulate :: (Rep V4 -> a) -> V4 a # index :: V4 a -> Rep V4 -> a #
Eq1 V4
Methods liftEq :: (a -> b -> Bool) -> V4 a -> V4 b -> Bool #
Ord1 V4
Methods liftCompare :: (a -> b -> Ordering) -> V4 a -> V4 b -> Ordering #
Read1 V4
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V4 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V4 a] #
Show1 V4
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V4 a] -> ShowS #
MonadZip V4
Methods mzip :: V4 a -> V4 b -> V4 (a, b) # mzipWith :: (a -> b -> c) -> V4 a -> V4 b -> V4 c # munzip :: V4 (a, b) -> (V4 a, V4 b) #
Serial1 V4
Methods serializeWith :: MonadPut m => (a -> m ()) -> V4 a -> m () # deserializeWith :: MonadGet m => m a -> m (V4 a) #
Traversable1 V4
Methods traverse1 :: Apply f => (a -> f b) -> V4 a -> f (V4 b) # sequence1 :: Apply f => V4 (f b) -> f (V4 b) #
R4 V4
Methods _w :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xyzw :: Functor f => (V4 a -> f (V4 a)) -> V4 a -> f (V4 a) #
R3 V4
Methods _z :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V4 a -> f (V4 a) #
R2 V4
Methods _y :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 a) #
R1 V4
Methods _x :: Functor f => (a -> f a) -> V4 a -> f (V4 a) #
Metric V4
Methods dot :: Num a => V4 a -> V4 a -> a # quadrance :: Num a => V4 a -> a # qd :: Num a => V4 a -> V4 a -> a # distance :: Floating a => V4 a -> V4 a -> a # norm :: Floating a => V4 a -> a # signorm :: Floating a => V4 a -> V4 a #
Additive V4
Methods zero :: Num a => V4 a # (^+^) :: Num a => V4 a -> V4 a -> V4 a # (^-^) :: Num a => V4 a -> V4 a -> V4 a # lerp :: Num a => a -> V4 a -> V4 a -> V4 a # liftU2 :: (a -> a -> a) -> V4 a -> V4 a -> V4 a # liftI2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #
Apply V4
Methods (<.>) :: V4 (a -> b) -> V4 a -> V4 b # (.>) :: V4 a -> V4 b -> V4 b # (<.) :: V4 a -> V4 b -> V4 a #
Bind V4
Methods (>>-) :: V4 a -> (a -> V4 b) -> V4 b # join :: V4 (V4 a) -> V4 a #
Foldable1 V4
Methods fold1 :: Semigroup m => V4 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V4 a -> m #
Shape V4 Source #
Methods shapeToIndex :: Layout V4 -> V4 Int -> Int Source # shapeFromIndex :: Layout V4 -> Int -> V4 Int Source # shapeIntersect :: Layout V4 -> Layout V4 -> Layout V4 Source # unsafeShapeStep :: Layout V4 -> V4 Int -> V4 Int Source # shapeStep :: Layout V4 -> V4 Int -> Maybe (V4 Int) Source # shapeStepBetween :: V4 Int -> Layout V4 -> V4 Int -> Maybe (V4 Int) Source # shapeInRange :: Layout V4 -> V4 Int -> Bool Source # shapeSize :: Layout V4 -> Int Source #
ShapeLift V4 Source #
Methods liftShape :: Lift a => V4 a -> Q Exp Source # liftShape' :: Lift a => V4 a -> Q Exp Source #
Unbox a => Vector Vector (V4 a)
Methods basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> m (Vector (V4 a)) # basicUnsafeThaw :: PrimMonad m => Vector (V4 a) -> m (Mutable Vector (PrimState m) (V4 a)) # basicLength :: Vector (V4 a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (V4 a) -> Vector (V4 a) # basicUnsafeIndexM :: Monad m => Vector (V4 a) -> Int -> m (V4 a) # basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (V4 a) -> Vector (V4 a) -> m () # elemseq :: Vector (V4 a) -> V4 a -> b -> b #
Unbox a => MVector MVector (V4 a)
Methods basicLength :: MVector s (V4 a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (V4 a) -> MVector s (V4 a) # basicOverlaps :: MVector s (V4 a) -> MVector s (V4 a) -> Bool # basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (V4 a)) # basicInitialize :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () # basicUnsafeReplicate :: PrimMonad m => Int -> V4 a -> m (MVector (PrimState m) (V4 a)) # basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (V4 a) # basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> V4 a -> m () # basicClear :: PrimMonad m => MVector (PrimState m) (V4 a) -> m () # basicSet :: PrimMonad m => MVector (PrimState m) (V4 a) -> V4 a -> m () # basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () # basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (V4 a) -> MVector (PrimState m) (V4 a) -> m () # basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (V4 a) -> Int -> m (MVector (PrimState m) (V4 a)) #
(~) * i Int => HasLayout V4 (V4 i) Source #
Methods layout :: Lens' (V4 i) (Layout V4) Source #
Bounded a => Bounded (V4 a)
Methods minBound :: V4 a # maxBound :: V4 a #
Eq a => Eq (V4 a)
Methods (==) :: V4 a -> V4 a -> Bool # (/=) :: V4 a -> V4 a -> Bool #
Floating a => Floating (V4 a)
Methods pi :: V4 a # exp :: V4 a -> V4 a # log :: V4 a -> V4 a # sqrt :: V4 a -> V4 a # (**) :: V4 a -> V4 a -> V4 a # logBase :: V4 a -> V4 a -> V4 a # sin :: V4 a -> V4 a # cos :: V4 a -> V4 a # tan :: V4 a -> V4 a # asin :: V4 a -> V4 a # acos :: V4 a -> V4 a # atan :: V4 a -> V4 a # sinh :: V4 a -> V4 a # cosh :: V4 a -> V4 a # tanh :: V4 a -> V4 a # asinh :: V4 a -> V4 a # acosh :: V4 a -> V4 a # atanh :: V4 a -> V4 a # log1p :: V4 a -> V4 a # expm1 :: V4 a -> V4 a # log1pexp :: V4 a -> V4 a # log1mexp :: V4 a -> V4 a #
Fractional a => Fractional (V4 a)
Methods (/) :: V4 a -> V4 a -> V4 a # recip :: V4 a -> V4 a # fromRational :: Rational -> V4 a #
Data a => Data (V4 a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V4 a -> c (V4 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V4 a) # toConstr :: V4 a -> Constr # dataTypeOf :: V4 a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (V4 a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V4 a)) # gmapT :: (forall b. Data b => b -> b) -> V4 a -> V4 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V4 a -> r # gmapQ :: (forall d. Data d => d -> u) -> V4 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V4 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V4 a -> m (V4 a) #
Num a => Num (V4 a)
Methods (+) :: V4 a -> V4 a -> V4 a # (-) :: V4 a -> V4 a -> V4 a # (*) :: V4 a -> V4 a -> V4 a # negate :: V4 a -> V4 a # abs :: V4 a -> V4 a # signum :: V4 a -> V4 a # fromInteger :: Integer -> V4 a #
Ord a => Ord (V4 a)
Methods compare :: V4 a -> V4 a -> Ordering # (<) :: V4 a -> V4 a -> Bool # (<=) :: V4 a -> V4 a -> Bool # (>) :: V4 a -> V4 a -> Bool # (>=) :: V4 a -> V4 a -> Bool # max :: V4 a -> V4 a -> V4 a # min :: V4 a -> V4 a -> V4 a #
Read a => Read (V4 a)
Methods readsPrec :: Int -> ReadS (V4 a) # readList :: ReadS [V4 a] # readPrec :: ReadPrec (V4 a) # readListPrec :: ReadPrec [V4 a] #
Show a => Show (V4 a)
Methods showsPrec :: Int -> V4 a -> ShowS # show :: V4 a -> String # showList :: [V4 a] -> ShowS #
Ix a => Ix (V4 a)
Methods range :: (V4 a, V4 a) -> [V4 a] # index :: (V4 a, V4 a) -> V4 a -> Int # unsafeIndex :: (V4 a, V4 a) -> V4 a -> Int inRange :: (V4 a, V4 a) -> V4 a -> Bool # rangeSize :: (V4 a, V4 a) -> Int # unsafeRangeSize :: (V4 a, V4 a) -> Int
Generic (V4 a)
Associated Types type Rep (V4 a) :: * -> * # Methods from :: V4 a -> Rep (V4 a) x # to :: Rep (V4 a) x -> V4 a #
Storable a => Storable (V4 a)
Methods sizeOf :: V4 a -> Int # alignment :: V4 a -> Int # peekElemOff :: Ptr (V4 a) -> Int -> IO (V4 a) # pokeElemOff :: Ptr (V4 a) -> Int -> V4 a -> IO () # peekByteOff :: Ptr b -> Int -> IO (V4 a) # pokeByteOff :: Ptr b -> Int -> V4 a -> IO () # peek :: Ptr (V4 a) -> IO (V4 a) # poke :: Ptr (V4 a) -> V4 a -> IO () #
Binary a => Binary (V4 a)
Methods put :: V4 a -> Put # get :: Get (V4 a) # putList :: [V4 a] -> Put #
Serial a => Serial (V4 a)
Methods serialize :: MonadPut m => V4 a -> m () # deserialize :: MonadGet m => m (V4 a) #
Serialize a => Serialize (V4 a)
Methods put :: Putter (V4 a) # get :: Get (V4 a) #
NFData a => NFData (V4 a)
Methods rnf :: V4 a -> () #
Hashable a => Hashable (V4 a)
Methods hashWithSalt :: Int -> V4 a -> Int # hash :: V4 a -> Int #
Unbox a => Unbox (V4 a)

Ixed (V4 a)
Methods ix :: Index (V4 a) -> Traversal' (V4 a) (IxValue (V4 a)) #
Epsilon a => Epsilon (V4 a)
Methods nearZero :: V4 a -> Bool #
FunctorWithIndex (E V4) V4
Methods imap :: (E V4 -> a -> b) -> V4 a -> V4 b # imapped :: (Indexable (E V4) p, Settable f) => p a (f b) -> V4 a -> f (V4 b) #
FoldableWithIndex (E V4) V4
Methods ifoldMap :: Monoid m => (E V4 -> a -> m) -> V4 a -> m # ifolded :: (Indexable (E V4) p, Contravariant f, Applicative f) => p a (f a) -> V4 a -> f (V4 a) # ifoldr :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl :: (E V4 -> b -> a -> b) -> b -> V4 a -> b # ifoldr' :: (E V4 -> a -> b -> b) -> b -> V4 a -> b # ifoldl' :: (E V4 -> b -> a -> b) -> b -> V4 a -> b #
TraversableWithIndex (E V4) V4
Methods itraverse :: Applicative f => (E V4 -> a -> f b) -> V4 a -> f (V4 b) # itraversed :: (Indexable (E V4) p, Applicative f) => p a (f b) -> V4 a -> f (V4 b) #
Each (V4 a) (V4 b) a b
Methods each :: Traversal (V4 a) (V4 b) a b #
type Rep1 V4
type Rep1 V4 = D1 (MetaData "V4" "Linear.V4" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" False) (C1 (MetaCons "V4" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1)) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) Par1))))
type Rep V4
type Rep V4 = E V4
data MVector s (V4 a)
data MVector s (V4 a) = MV_V4 ~Int ~(MVector s a)
type Rep (V4 a)
type Rep (V4 a) = D1 (MetaData "V4" "Linear.V4" "linear-1.20.5-7wYpWNZANRhKtNZ0kWxto6" False) (C1 (MetaCons "V4" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a))) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)))))
data Vector (V4 a)
data Vector (V4 a) = V_V4 ~Int ~(Vector a)
type Index (V4 a)
type Index (V4 a) = E V4
type IxValue (V4 a)
type IxValue (V4 a) = a

class R1 t where #

A space that has at least 1 basis vector _x.

Minimal complete definition

Nothing

Instances

R1 Identity
Methods _x :: Functor f => (a -> f a) -> Identity a -> f (Identity a) #
R1 V4
Methods _x :: Functor f => (a -> f a) -> V4 a -> f (V4 a) #
R1 V3
Methods _x :: Functor f => (a -> f a) -> V3 a -> f (V3 a) #
R1 V2
Methods _x :: Functor f => (a -> f a) -> V2 a -> f (V2 a) #
R1 V1
Methods _x :: Functor f => (a -> f a) -> V1 a -> f (V1 a) #

class R1 t => R2 t where #

A space that distinguishes 2 orthogonal basis vectors _x and _y, but may have more.

Minimal complete definition

Nothing

Instances

R2 V4
Methods _y :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V4 a -> f (V4 a) #
R2 V3
Methods _y :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V3 a -> f (V3 a) #
R2 V2
Methods _y :: Functor f => (a -> f a) -> V2 a -> f (V2 a) # _xy :: Functor f => (V2 a -> f (V2 a)) -> V2 a -> f (V2 a) #

class R2 t => R3 t where #

A space that distinguishes 3 orthogonal basis vectors: _x, _y, and _z. (It may have more)

Minimal complete definition

Nothing

Instances

R3 V4
Methods _z :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V4 a -> f (V4 a) #
R3 V3
Methods _z :: Functor f => (a -> f a) -> V3 a -> f (V3 a) # _xyz :: Functor f => (V3 a -> f (V3 a)) -> V3 a -> f (V3 a) #

class R3 t => R4 t where #

A space that distinguishes orthogonal basis vectors _x, _y, _z, _w. (It may have more.)

Minimal complete definition

Nothing

Instances

R4 V4
Methods _w :: Functor f => (a -> f a) -> V4 a -> f (V4 a) # _xyzw :: Functor f => (V4 a -> f (V4 a)) -> V4 a -> f (V4 a) #

Extra planes

_xz :: R3 t => Lens' (t a) (V2 a) #

_yz :: R3 t => Lens' (t a) (V2 a) #

_yx :: R2 t => Lens' (t a) (V2 a) #

>>> V2 1 2 ^. _yx
V2 2 1

_zy :: R3 t => Lens' (t a) (V2 a) #

_zx :: R3 t => Lens' (t a) (V2 a) #