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

data Array v f a
type BArray = Array Vector
type UArray = Array Vector
type SArray = Array Vector
type PArray = Array Vector
type Layout f = f Int
class Shape f => HasLayout f a | a -> f where
- layout :: Lens' a (Layout f)
class (Eq1 f, Additive f, Traversable f) => Shape f
extent :: HasLayout f a => a -> f Int
size :: HasLayout f a => a -> Int
indexes :: HasLayout f a => IndexedFold Int a (f Int)
indexesBetween :: HasLayout f a => f Int -> f Int -> IndexedFold Int a (f Int)
indexesFrom :: HasLayout f a => f Int -> IndexedFold Int a (f Int)
vector :: (Vector v a, Vector w b) => IndexedLens (Layout f) (Array v f a) (Array w f b) (v a) (w b)
values :: (Shape f, Vector v a, Vector w b) => IndexedTraversal (f Int) (Array v f a) (Array w f b) a b
values' :: (Shape f, Vector v a, Vector v b) => IndexedTraversal (f Int) (Array v f a) (Array v f b) a b
valuesBetween :: (Shape f, Vector v a) => f Int -> f Int -> IndexedTraversal' (f Int) (Array v f a) a
flat :: Vector w b => Iso (Array v V1 a) (Array w V1 b) (v a) (w b)
fromListInto :: (Shape f, Vector v a) => Layout f -> [a] -> Maybe (Array v f a)
fromListInto_ :: (Shape f, Vector v a) => Layout f -> [a] -> Array v f a
fromVectorInto :: (Shape f, Vector v a) => Layout f -> v a -> Maybe (Array v f a)
fromVectorInto_ :: (Shape f, Vector v a) => Layout f -> v a -> Array v f a
ixRow :: Vector v a => Int -> IndexedTraversal' Int (Array v V2 a) (v a)
rows :: (Vector v a, Vector w b) => IndexedTraversal Int (Array v V2 a) (Array w V2 b) (v a) (w b)
ixColumn :: Vector v a => Int -> IndexedTraversal' Int (Array v V2 a) (v a)
columns :: (Vector v a, Vector w b) => IndexedTraversal Int (Array v V2 a) (Array w V2 b) (v a) (w b)
ixPlane :: Vector v a => ALens' (V3 Int) (V2 Int) -> Int -> IndexedTraversal' Int (Array v V3 a) (Array v V2 a)
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)
flattenPlane :: (Vector v a, Vector w b) => ALens' (V3 Int) (V2 Int) -> (v a -> b) -> Array v V3 a -> Array w V2 b
data MArray v l s a
type BMArray = MArray MVector
type UMArray = MArray MVector
type SMArray = MArray MVector
type PMArray = MArray MVector
data Delayed f a
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)
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)
delay :: (Vector v a, Shape f) => Array v f a -> Delayed f a
manifest :: (Vector v a, Shape f) => Delayed f a -> Array v f a
seqManifest :: (Vector v a, Shape f) => Delayed f a -> Array v f a
genDelayed :: Layout f -> (f Int -> a) -> Delayed f a
indexDelayed :: Shape f => Delayed f a -> f Int -> a
affirm :: (Shape f, Unbox a) => Delayed f a -> Delayed f a
seqAffirm :: (Shape f, Unbox a) => Delayed f a -> Delayed f a
(*^) :: (Functor f, Num a) => a -> f a -> f a
(^*) :: (Functor f, Num a) => f a -> a -> f a
(^/) :: (Functor f, Fractional a) => f a -> a -> f a
class Functor f => Additive (f :: Type -> Type) where
- zero :: Num a => f a
- (^+^) :: Num a => f a -> f a -> f a
- (^-^) :: Num a => f a -> f a -> f a
- lerp :: Num a => a -> f a -> f a -> f a
- liftU2 :: (a -> a -> a) -> f a -> f a -> f a
- liftI2 :: (a -> b -> c) -> f a -> f b -> f c
class Additive f => Metric (f :: Type -> Type) where
- dot :: Num a => f a -> f a -> a
- quadrance :: Num a => f a -> a
- qd :: Num a => f a -> f a -> a
- distance :: Floating a => f a -> f a -> a
- norm :: Floating a => f a -> a
- signorm :: Floating a => f a -> f a
data Focused f a
focusOn :: f Int -> Delayed f a -> Focused f a
unfocus :: Focused f a -> Delayed f a
unfocused :: IndexedLens (f Int) (Focused f a) (Focused f b) (Delayed f a) (Delayed f b)
extendFocus :: Shape f => (Focused f a -> b) -> Delayed f a -> Delayed f b
locale :: ComonadStore s w => Lens' (w a) s
shiftFocus :: Applicative f => f Int -> Focused f a -> Focused f a
data Boundary
- = Clamp
- | Mirror
- | Wrap
peekB :: Shape f => Boundary -> f Int -> Focused f a -> a
peeksB :: Shape f => Boundary -> (f Int -> f Int) -> Focused f a -> a
peekRelativeB :: Shape f => Boundary -> f Int -> Focused f a -> a
class Functor w => Comonad (w :: Type -> Type) where
- extract :: w a -> a
- duplicate :: w a -> w (w a)
- extend :: (w a -> b) -> w a -> w b
class Comonad w => ComonadStore s (w :: Type -> Type) | w -> s where
- pos :: w a -> s
- peek :: s -> w a -> a
- peeks :: (s -> s) -> w a -> a
- seek :: s -> w a -> w a
- seeks :: (s -> s) -> w a -> w a
- experiment :: Functor f => (s -> f s) -> w a -> f a
data Stencil f a
stencil :: QuasiQuoter
mkStencil :: [(f Int, a)] -> Stencil f a
mkStencilTH :: (ShapeLift f, Lift a) => [(f Int, a)] -> Q Exp
stencilSum :: (Shape f, Num a) => Boundary -> Stencil f a -> Focused f a -> a
newtype V1 a = V1 a
data V2 a = V2 !a !a
data V3 a = V3 !a !a !a
data V4 a = V4 !a !a !a !a
class R1 (t :: Type -> Type) where
- _x :: Lens' (t a) a
class R1 t => R2 (t :: Type -> Type) where
- _y :: Lens' (t a) a
- _xy :: Lens' (t a) (V2 a)
class R2 t => R3 (t :: Type -> Type) where
- _z :: Lens' (t a) a
- _xyz :: Lens' (t a) (V3 a)
class R3 t => R4 (t :: Type -> Type) where
- _w :: Lens' (t a) a
- _xyzw :: Lens' (t a) (V4 a)
_xz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_yz :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_yx :: forall (t :: Type -> Type) a. R2 t => Lens' (t a) (V2 a)
_zy :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)
_zx :: forall (t :: Type -> Type) a. R3 t => Lens' (t a) (V2 a)

Array types

data Array v f a Source #

An Array is a vector with a shape.

Instances

Instances details

Shape f => HasLayout f (Array v f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Instance details Defined in Data.Dense.Base Methods layout :: Lens' (Array v f a) (Layout f) Source #
(Boxed v, Shape f) => FunctorWithIndex (f Int) (Array v f) Source #
Instance details Defined in Data.Dense.Base Methods imap :: (f Int -> a -> b) -> Array v f a -> Array v f b # imapped :: IndexedSetter (f Int) (Array v f a) (Array v f b) a b #
(Boxed v, Shape f) => FoldableWithIndex (f Int) (Array v f) Source #
Instance details Defined in Data.Dense.Base Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Array v f a -> m # ifolded :: IndexedFold (f Int) (Array v f a) 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 #
Instance details Defined in Data.Dense.Base Methods itraverse :: Applicative f0 => (f Int -> a -> f0 b) -> Array v f a -> f0 (Array v f b) # itraversed :: IndexedTraversal (f Int) (Array v f a) (Array v f b) a b #
Boxed v => Functor (Array v f) Source #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base Methods fold :: Monoid m => Array v f m -> m # foldMap :: Monoid m => (a -> m) -> Array v f a -> 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 #
Instance details Defined in Data.Dense.Base Methods traverse :: Applicative f0 => (a -> f0 b) -> Array v f a -> f0 (Array v f b) # sequenceA :: Applicative f0 => Array v f (f0 a) -> f0 (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 #
Instance details Defined in Data.Dense.Base Methods liftEq :: (a -> b -> Bool) -> Array v f a -> Array v f b -> Bool #
(Boxed v, Read1 f) => Read1 (Array v f) Source #
Instance details Defined in Data.Dense.Base Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Array v f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Array v f a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Array v f a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Array v f a] #
(Boxed v, Shape f, Serial1 f) => Serial1 (Array v f) Source #
Instance details Defined in Data.Dense.Base 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`.
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 :: forall r r'. (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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base Methods rnf :: Array v f a -> () #
(Vector v a, Foldable f, Hashable a) => Hashable (Array v f a) Source #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base Methods each :: Traversal (Array v f a) (Array v f b) a b #
type Mutable (Array v f) Source #
Instance details Defined in Data.Dense.Base type Mutable (Array v f) = MArray (Mutable v) f
type Index (Array v f a) Source #
Instance details Defined in Data.Dense.Base type Index (Array v f a) = f Int
type IxValue (Array v f a) Source #
Instance details Defined in Data.Dense.Base 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.

Minimal complete definition

Nothing

Methods

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

Lens onto the Layout of something.

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

Instances

Instances details

i ~ Int => HasLayout V0 (V0 i) Source #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V0 i) (Layout V0) Source #
i ~ Int => HasLayout V4 (V4 i) Source #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V4 i) (Layout V4) Source #
i ~ Int => HasLayout V3 (V3 i) Source #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V3 i) (Layout V3) Source #
i ~ Int => HasLayout V2 (V2 i) Source #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V2 i) (Layout V2) Source #
i ~ Int => HasLayout V1 (V1 i) Source #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V1 i) (Layout V1) Source #
Shape f => HasLayout f (Focused f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Instance details Defined in Data.Dense.Base 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.
Instance details Defined in Data.Dense.Base 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.
Instance details Defined in Data.Dense.Base Methods layout :: Lens' (Array v f a) (Layout f) Source #
Shape f => HasLayout f (MArray v f s a) Source #
Instance details Defined in Data.Dense.Mutable 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

Instances details

Shape V0 Source #
Instance details Defined in Data.Dense.Index 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 #
Shape V4 Source #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.Index 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 #

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

Instances details

Shape f => HasLayout f (MArray v f s a) Source #
Instance details Defined in Data.Dense.Mutable Methods layout :: Lens' (MArray v f s a) (Layout f) Source #
(MVector v a, f ~ V1) => MVector (MArray v f) a Source #
Instance details Defined in Data.Dense.Mutable 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

Instances details

Shape f => HasLayout f (Delayed f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Instance details Defined in Data.Dense.Base Methods layout :: Lens' (Delayed f a) (Layout f) Source #
Functor (Delayed f) Source #
Instance details Defined in Data.Dense.Base 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.
Instance details Defined in Data.Dense.Base Methods fold :: Monoid m => Delayed f m -> m # foldMap :: Monoid m => (a -> m) -> Delayed f a -> 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 #
Instance details Defined in Data.Dense.Base Methods traverse :: Applicative f0 => (a -> f0 b) -> Delayed f a -> f0 (Delayed f b) # sequenceA :: Applicative f0 => Delayed f (f0 a) -> f0 (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 => Apply (Delayed f) Source #
Instance details Defined in Data.Dense.Base 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 # liftF2 :: (a -> b -> c) -> Delayed f a -> Delayed f b -> Delayed f c #
Shape f => Metric (Delayed f) Source #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
FunctorWithIndex (f Int) (Delayed f) Source #
Instance details Defined in Data.Dense.Base Methods imap :: (f Int -> a -> b) -> Delayed f a -> Delayed f b # imapped :: IndexedSetter (f Int) (Delayed f a) (Delayed f b) a b #
Shape f => FoldableWithIndex (f Int) (Delayed f) Source #	`ifoldMap` in parallel.
Instance details Defined in Data.Dense.Base Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Delayed f a -> m # ifolded :: IndexedFold (f Int) (Delayed f a) 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 #
Instance details Defined in Data.Dense.Base Methods itraverse :: Applicative f0 => (f Int -> a -> f0 b) -> Delayed f a -> f0 (Delayed f b) # itraversed :: IndexedTraversal (f Int) (Delayed f a) (Delayed f b) a b #
(Shape f, Show1 f, Show a) => Show (Delayed f a) Source #
Instance details Defined in Data.Dense.Base Methods showsPrec :: Int -> Delayed f a -> ShowS # show :: Delayed f a -> String # showList :: [Delayed f a] -> ShowS #
Shape f => Ixed (Delayed f a) Source #
Instance details Defined in Data.Dense.Base Methods ix :: Index (Delayed f a) -> Traversal' (Delayed f a) (IxValue (Delayed f a)) #
Shape f => AsEmpty (Delayed f a) Source #
Instance details Defined in Data.Dense.Base Methods _Empty :: Prism' (Delayed f a) () #
Shape f => Each (Delayed f a) (Delayed f b) a b Source #
Instance details Defined in Data.Dense.Base Methods each :: Traversal (Delayed f a) (Delayed f b) a b #
type Index (Delayed f a) Source #
Instance details Defined in Data.Dense.Base type Index (Delayed f a) = f Int
type IxValue (Delayed f a) Source #
Instance details Defined in Data.Dense.Base 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 :: Type -> Type) where #

A vector is an additive group with additional structure.

Minimal complete definition

Nothing

Methods

zero :: Num a => f a #

The zero vector

(^+^) :: Num a => f a -> f a -> f a infixl 6 #

Compute the sum of two vectors

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

(^-^) :: Num a => f a -> f a -> f a infixl 6 #

Compute the difference between two vectors

>>> V2 4 5 ^-^ V2 3 1
V2 1 4

lerp :: Num a => a -> f a -> f a -> f a #

Linearly interpolate between two vectors.

liftU2 :: (a -> a -> a) -> f a -> f a -> f a #

Apply a function to merge the 'non-zero' components of two vectors, unioning the rest of the values.

For a dense vector this is equivalent to liftA2.
For a sparse vector this is equivalent to unionWith.

liftI2 :: (a -> b -> c) -> f a -> f b -> f c #

Apply a function to the components of two vectors.

For a dense vector this is equivalent to liftA2.
For a sparse vector this is equivalent to intersectionWith.

Instances

Instances details

Additive []
Instance details Defined in Linear.Vector 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
Instance details Defined in Linear.Vector 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 Complex
Instance details Defined in Linear.Vector 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
Instance details Defined in Linear.Vector 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 Identity
Instance details Defined in Linear.Vector 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 IntMap
Instance details Defined in Linear.Vector 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
Instance details Defined in Linear.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 Plucker
Instance details Defined in Linear.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 Quaternion
Instance details Defined in Linear.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 V0
Instance details Defined in Linear.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 V4
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Ord k => Additive (Map k)
Instance details Defined in Linear.Vector 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)
Instance details Defined in Linear.Vector 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) Source #
Instance details Defined in Data.Dense.Base 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 n => Additive (V n)
Instance details Defined in Linear.V Methods zero :: Num a => V n a # (^+^) :: Num a => V n a -> V n a -> V n a # (^-^) :: Num a => V n a -> V n a -> V n a # lerp :: Num a => a -> V n a -> V n a -> V n a # liftU2 :: (a -> a -> a) -> V n a -> V n a -> V n a # liftI2 :: (a -> b -> c) -> V n a -> V n b -> V n c #
Additive ((->) b :: Type -> Type)
Instance details Defined in Linear.Vector 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 -> b0 -> c) -> (b -> a) -> (b -> b0) -> b -> c #
(Additive f, Additive g) => Additive (Product f g)
Instance details Defined in Linear.Vector Methods zero :: Num a => Product f g a # (^+^) :: Num a => Product f g a -> Product f g a -> Product f g a # (^-^) :: Num a => Product f g a -> Product f g a -> Product f g a # lerp :: Num a => a -> Product f g a -> Product f g a -> Product f g a # liftU2 :: (a -> a -> a) -> Product f g a -> Product f g a -> Product f g a # liftI2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c #
(Additive f, Additive g) => Additive (Compose f g)
Instance details Defined in Linear.Vector Methods zero :: Num a => Compose f g a # (^+^) :: Num a => Compose f g a -> Compose f g a -> Compose f g a # (^-^) :: Num a => Compose f g a -> Compose f g a -> Compose f g a # lerp :: Num a => a -> Compose f g a -> Compose f g a -> Compose f g a # liftU2 :: (a -> a -> a) -> Compose f g a -> Compose f g a -> Compose f g a # liftI2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c #

class Additive f => Metric (f :: Type -> Type) where #

Free and sparse inner product/metric spaces.

Minimal complete definition

Nothing

Methods

dot :: Num a => f a -> f a -> a #

Compute the inner product of two vectors or (equivalently) convert a vector f a into a covector f a -> a.

>>> V2 1 2 `dot` V2 3 4
11

quadrance :: Num a => f a -> a #

Compute the squared norm. The name quadrance arises from Norman J. Wildberger's rational trigonometry.

qd :: Num a => f a -> f a -> a #

Compute the quadrance of the difference

distance :: Floating a => f a -> f a -> a #

Compute the distance between two vectors in a metric space

norm :: Floating a => f a -> a #

Compute the norm of a vector in a metric space

signorm :: Floating a => f a -> f a #

Convert a non-zero vector to unit vector.

Instances

Instances details

Metric []
Instance details Defined in Linear.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
Instance details Defined in Linear.Metric 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 ZipList
Instance details Defined in Linear.Metric 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 Identity
Instance details Defined in Linear.Metric 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 IntMap
Instance details Defined in Linear.Metric 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
Instance details Defined in Linear.Metric 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 Plucker
Instance details Defined in Linear.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 Quaternion
Instance details Defined in Linear.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 V0
Instance details Defined in Linear.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 #
Metric V4
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Ord k => Metric (Map k)
Instance details Defined in Linear.Metric 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)
Instance details Defined in Linear.Metric 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) Source #
Instance details Defined in Data.Dense.Base 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 n => Metric (V n)
Instance details Defined in Linear.V Methods dot :: Num a => V n a -> V n a -> a # quadrance :: Num a => V n a -> a # qd :: Num a => V n a -> V n a -> a # distance :: Floating a => V n a -> V n a -> a # norm :: Floating a => V n a -> a # signorm :: Floating a => V n a -> V n a #
(Metric f, Metric g) => Metric (Product f g)
Instance details Defined in Linear.Metric Methods dot :: Num a => Product f g a -> Product f g a -> a # quadrance :: Num a => Product f g a -> a # qd :: Num a => Product f g a -> Product f g a -> a # distance :: Floating a => Product f g a -> Product f g a -> a # norm :: Floating a => Product f g a -> a # signorm :: Floating a => Product f g a -> Product f g a #
(Metric f, Metric g) => Metric (Compose f g)
Instance details Defined in Linear.Metric Methods dot :: Num a => Compose f g a -> Compose f g a -> a # quadrance :: Num a => Compose f g a -> a # qd :: Num a => Compose f g a -> Compose f g a -> a # distance :: Floating a => Compose f g a -> Compose f g a -> a # norm :: Floating a => Compose f g a -> a # signorm :: Floating a => Compose f g a -> Compose f g 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

Instances details

Shape f => HasLayout f (Focused f a) Source #	The `size` of the `layout` must remain the same or an error is thrown.
Instance details Defined in Data.Dense.Base Methods layout :: Lens' (Focused f a) (Layout f) Source #
Functor (Focused f) Source #
Instance details Defined in Data.Dense.Base Methods fmap :: (a -> b) -> Focused f a -> Focused f b # (<$) :: a -> Focused f b -> Focused f a #
Shape f => Foldable (Focused f) Source #
Instance details Defined in Data.Dense.Base Methods fold :: Monoid m => Focused f m -> m # foldMap :: Monoid m => (a -> m) -> Focused f a -> 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 #
Instance details Defined in Data.Dense.Base Methods traverse :: Applicative f0 => (a -> f0 b) -> Focused f a -> f0 (Focused f b) # sequenceA :: Applicative f0 => Focused f (f0 a) -> f0 (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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 #
Instance details Defined in Data.Dense.Base 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 f0 => (f Int -> f0 (f Int)) -> Focused f a -> f0 a #
Shape f => FunctorWithIndex (f Int) (Focused f) Source #	Index relative to focus.
Instance details Defined in Data.Dense.Base Methods imap :: (f Int -> a -> b) -> Focused f a -> Focused f b # imapped :: IndexedSetter (f Int) (Focused f a) (Focused f b) a b #
Shape f => FoldableWithIndex (f Int) (Focused f) Source #	Index relative to focus.
Instance details Defined in Data.Dense.Base Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Focused f a -> m # ifolded :: IndexedFold (f Int) (Focused f a) 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.
Instance details Defined in Data.Dense.Base Methods itraverse :: Applicative f0 => (f Int -> a -> f0 b) -> Focused f a -> f0 (Focused f b) # itraversed :: IndexedTraversal (f Int) (Focused f a) (Focused f b) a b #
(Shape f, Show1 f, Show a) => Show (Focused f a) Source #
Instance details Defined in Data.Dense.Base 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.
Instance details Defined in Data.Dense.Base Methods ix :: Index (Focused f a) -> Traversal' (Focused f a) (IxValue (Focused f a)) #
type Index (Focused f a) Source #
Instance details Defined in Data.Dense.Base type Index (Focused f a) = f Int
type IxValue (Focused f a) Source #
Instance details Defined in Data.Dense.Base 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

Instances details

Read Boundary Source #
Instance details Defined in Data.Dense.Generic Methods readsPrec :: Int -> ReadS Boundary # readList :: ReadS [Boundary] # readPrec :: ReadPrec Boundary # readListPrec :: ReadPrec [Boundary] #
Show Boundary Source #
Instance details Defined in Data.Dense.Generic 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 :: Type -> Type) 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)

Methods

extract :: w a -> a #

extract . fmap f = f . extract

duplicate :: w a -> w (w a) #

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

extend :: (w a -> b) -> w a -> w b #

extend f = fmap f . duplicate

Instances

Instances details

Comonad Identity
Instance details Defined in Control.Comonad Methods extract :: Identity a -> a # duplicate :: Identity a -> Identity (Identity a) # extend :: (Identity a -> b) -> Identity a -> Identity b #
Comonad NonEmpty
Instance details Defined in Control.Comonad Methods extract :: NonEmpty a -> a # duplicate :: NonEmpty a -> NonEmpty (NonEmpty a) # extend :: (NonEmpty a -> b) -> NonEmpty a -> NonEmpty b #
Comonad Tree
Instance details Defined in Control.Comonad Methods extract :: Tree a -> a # duplicate :: Tree a -> Tree (Tree a) # extend :: (Tree a -> b) -> Tree a -> Tree b #
Comonad ((,) e)
Instance details Defined in Control.Comonad 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)
Instance details Defined in Data.Functor.Rep 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)
Instance details Defined in Control.Comonad 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)
Instance details Defined in Control.Comonad.Cofree 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)
Instance details Defined in Data.Functor.Yoneda 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)
Instance details Defined in Control.Lens.Reified 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)
Instance details Defined in Data.Functor.Bind.Class 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) Source #
Instance details Defined in Data.Dense.Base 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)
Instance details Defined in Control.Comonad.Trans.Traced 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)
Instance details Defined in Control.Comonad.Trans.Store 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)
Instance details Defined in Control.Comonad.Trans.Env 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)
Instance details Defined in Control.Comonad 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 #
(Functor f, Comonad w) => Comonad (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods extract :: CofreeT f w a -> a # duplicate :: CofreeT f w a -> CofreeT f w (CofreeT f w a) # extend :: (CofreeT f w a -> b) -> CofreeT f w a -> CofreeT f w b #
(Comonad f, Comonad g) => Comonad (Day f g)
Instance details Defined in Data.Functor.Day Methods extract :: Day f g a -> a # duplicate :: Day f g a -> Day f g (Day f g a) # extend :: (Day f g a -> b) -> Day f g a -> Day f g b #
Comonad (Tagged s)
Instance details Defined in Control.Comonad 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 #
a ~ b => Comonad (Context a b)
Instance details Defined in Control.Lens.Internal.Context Methods extract :: Context a b a0 -> a0 # duplicate :: Context a b a0 -> Context a b (Context a b a0) # extend :: (Context a b a0 -> b0) -> Context a b a0 -> Context a b b0 #
Monoid m => Comonad ((->) m :: Type -> Type)
Instance details Defined in Control.Comonad Methods extract :: (m -> a) -> a # duplicate :: (m -> a) -> m -> (m -> a) # extend :: ((m -> a) -> b) -> (m -> a) -> m -> b #
(Comonad f, Comonad g) => Comonad (Sum f g)
Instance details Defined in Control.Comonad 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)
Instance details Defined in Control.Lens.Internal.Magma Methods extract :: Molten i a b a0 -> a0 # duplicate :: Molten i a b a0 -> Molten i a b (Molten i a b a0) # extend :: (Molten i a b a0 -> b0) -> Molten i a b a0 -> Molten i a b b0 #
(a ~ b, Conjoined p) => Comonad (Bazaar p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar p a b a0 -> a0 # duplicate :: Bazaar p a b a0 -> Bazaar p a b (Bazaar p a b a0) # extend :: (Bazaar p a b a0 -> b0) -> Bazaar p a b a0 -> Bazaar p a b b0 #
(a ~ b, Conjoined p) => Comonad (Bazaar1 p a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: Bazaar1 p a b a0 -> a0 # duplicate :: Bazaar1 p a b a0 -> Bazaar1 p a b (Bazaar1 p a b a0) # extend :: (Bazaar1 p a b a0 -> b0) -> Bazaar1 p a b a0 -> Bazaar1 p a b b0 #
(a ~ b, Conjoined p) => Comonad (Pretext p a b)
Instance details Defined in Control.Lens.Internal.Context Methods extract :: Pretext p a b a0 -> a0 # duplicate :: Pretext p a b a0 -> Pretext p a b (Pretext p a b a0) # extend :: (Pretext p a b a0 -> b0) -> Pretext p a b a0 -> Pretext p a b b0 #
(a ~ b, Conjoined p) => Comonad (BazaarT p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: BazaarT p g a b a0 -> a0 # duplicate :: BazaarT p g a b a0 -> BazaarT p g a b (BazaarT p g a b a0) # extend :: (BazaarT p g a b a0 -> b0) -> BazaarT p g a b a0 -> BazaarT p g a b b0 #
(a ~ b, Conjoined p) => Comonad (BazaarT1 p g a b)
Instance details Defined in Control.Lens.Internal.Bazaar Methods extract :: BazaarT1 p g a b a0 -> a0 # duplicate :: BazaarT1 p g a b a0 -> BazaarT1 p g a b (BazaarT1 p g a b a0) # extend :: (BazaarT1 p g a b a0 -> b0) -> BazaarT1 p g a b a0 -> BazaarT1 p g a b b0 #
(a ~ b, Conjoined p) => Comonad (PretextT p g a b)
Instance details Defined in Control.Lens.Internal.Context Methods extract :: PretextT p g a b a0 -> a0 # duplicate :: PretextT p g a b a0 -> PretextT p g a b (PretextT p g a b a0) # extend :: (PretextT p g a b a0 -> b0) -> PretextT p g a b a0 -> PretextT p g a b b0 #

class Comonad w => ComonadStore s (w :: Type -> Type) | w -> s where #

Minimal complete definition

pos, peek

Methods

pos :: w a -> s #

peek :: s -> w a -> a #

peeks :: (s -> s) -> w a -> a #

seek :: s -> w a -> w a #

seeks :: (s -> s) -> w a -> w a #

experiment :: Functor f => (s -> f s) -> w a -> f a #

Instances

Instances details

ComonadStore s w => ComonadStore s (Cofree w)
Instance details Defined in Control.Comonad.Cofree 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)
Instance details Defined in Control.Comonad.Store.Class 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)
Instance details Defined in Control.Comonad.Store.Class 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)
Instance details Defined in Control.Comonad.Store.Class 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)
Instance details Defined in Control.Comonad.Store.Class 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)
Instance details Defined in Control.Lens.Internal.Context Methods pos :: Context a b a0 -> a # peek :: a -> Context a b a0 -> a0 # peeks :: (a -> a) -> Context a b a0 -> a0 # seek :: a -> Context a b a0 -> Context a b a0 # seeks :: (a -> a) -> Context a b a0 -> Context a b a0 # experiment :: Functor f => (a -> f a) -> Context a b a0 -> f a0 #
(a ~ b, Conjoined p) => ComonadStore a (Pretext p a b)
Instance details Defined in Control.Lens.Internal.Context Methods pos :: Pretext p a b a0 -> a # peek :: a -> Pretext p a b a0 -> a0 # peeks :: (a -> a) -> Pretext p a b a0 -> a0 # seek :: a -> Pretext p a b a0 -> Pretext p a b a0 # seeks :: (a -> a) -> Pretext p a b a0 -> Pretext p a b a0 # experiment :: Functor f => (a -> f a) -> Pretext p a b a0 -> f a0 #
(a ~ b, Conjoined p) => ComonadStore a (PretextT p g a b)
Instance details Defined in Control.Lens.Internal.Context Methods pos :: PretextT p g a b a0 -> a # peek :: a -> PretextT p g a b a0 -> a0 # peeks :: (a -> a) -> PretextT p g a b a0 -> a0 # seek :: a -> PretextT p g a b a0 -> PretextT p g a b a0 # seeks :: (a -> a) -> PretextT p g a b a0 -> PretextT p g a b a0 # experiment :: Functor f => (a -> f a) -> PretextT p g a b a0 -> f a0 #
Shape f => ComonadStore (f Int) (Focused f) Source #
Instance details Defined in Data.Dense.Base 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 f0 => (f Int -> f0 (f Int)) -> Focused f a -> f0 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

Instances details

Functor (Stencil f) Source #
Instance details Defined in Data.Dense.Stencil Methods fmap :: (a -> b) -> Stencil f a -> Stencil f b # (<$) :: a -> Stencil f b -> Stencil f a #
Foldable (Stencil f) Source #
Instance details Defined in Data.Dense.Stencil Methods fold :: Monoid m => Stencil f m -> m # foldMap :: Monoid m => (a -> m) -> Stencil f a -> 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 #
Instance details Defined in Data.Dense.Stencil Methods ifoldMap :: Monoid m => (f Int -> a -> m) -> Stencil f a -> m # ifolded :: IndexedFold (f Int) (Stencil f a) 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 #
Instance details Defined in Data.Dense.Stencil 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

Expand

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

Instances details

Monad V1
Instance details Defined in Linear.V1 Methods (>>=) :: V1 a -> (a -> V1 b) -> V1 b # (>>) :: V1 a -> V1 b -> V1 b # return :: a -> V1 a #
Functor V1
Instance details Defined in Linear.V1 Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
MonadFix V1
Instance details Defined in Linear.V1 Methods mfix :: (a -> V1 a) -> V1 a #
Applicative V1
Instance details Defined in Linear.V1 Methods pure :: a -> V1 a # (<>) :: V1 (a -> b) -> V1 a -> V1 b # liftA2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c # (>) :: V1 a -> V1 b -> V1 b # (<*) :: V1 a -> V1 b -> V1 a #
Foldable V1
Instance details Defined in Linear.V1 Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> 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
Instance details Defined in Linear.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) #
Distributive V1
Instance details Defined in Linear.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
Instance details Defined in Linear.V1 Associated Types type Rep V1 # Methods tabulate :: (Rep V1 -> a) -> V1 a # index :: V1 a -> Rep V1 -> a #
Eq1 V1
Instance details Defined in Linear.V1 Methods liftEq :: (a -> b -> Bool) -> V1 a -> V1 b -> Bool #
Ord1 V1
Instance details Defined in Linear.V1 Methods liftCompare :: (a -> b -> Ordering) -> V1 a -> V1 b -> Ordering #
Read1 V1
Instance details Defined in Linear.V1 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V1 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V1 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V1 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V1 a] #
Show1 V1
Instance details Defined in Linear.V1 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V1 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V1 a] -> ShowS #
MonadZip V1
Instance details Defined in Linear.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
Instance details Defined in Linear.V1 Methods serializeWith :: MonadPut m => (a -> m ()) -> V1 a -> m () # deserializeWith :: MonadGet m => m a -> m (V1 a) #
Hashable1 V1
Instance details Defined in Linear.V1 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V1 a -> Int #
Apply V1
Instance details Defined in Linear.V1 Methods (<.>) :: V1 (a -> b) -> V1 a -> V1 b # (.>) :: V1 a -> V1 b -> V1 b # (<.) :: V1 a -> V1 b -> V1 a # liftF2 :: (a -> b -> c) -> V1 a -> V1 b -> V1 c #
Traversable1 V1
Instance details Defined in Linear.V1 Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Trace V1
Instance details Defined in Linear.Trace Methods trace :: Num a => V1 (V1 a) -> a # diagonal :: V1 (V1 a) -> V1 a #
R1 V1
Instance details Defined in Linear.V1 Methods _x :: Lens' (V1 a) a #
Finite V1
Instance details Defined in Linear.V1 Associated Types type Size V1 :: Nat # Methods toV :: V1 a -> V (Size V1) a # fromV :: V (Size V1) a -> V1 a #
Metric V1
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Foldable1 V1
Instance details Defined in Linear.V1 Methods fold1 :: Semigroup m => V1 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V1 a -> m # toNonEmpty :: V1 a -> NonEmpty a #
Bind V1
Instance details Defined in Linear.V1 Methods (>>-) :: V1 a -> (a -> V1 b) -> V1 b # join :: V1 (V1 a) -> V1 a #
Shape V1 Source #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.TH Methods liftShape :: Lift a => V1 a -> Q Exp Source # liftShape' :: Lift a => V1 a -> Q Exp Source #
Lift a => Lift (V1 a :: Type)
Instance details Defined in Linear.V1 Methods lift :: V1 a -> Q Exp # liftTyped :: V1 a -> Q (TExp (V1 a)) #
Unbox a => Vector Vector (V1 a)
Instance details Defined in Linear.V1 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 #
Num r => Algebra r (E V1)
Instance details Defined in Linear.Algebra Methods mult :: (E V1 -> E V1 -> r) -> E V1 -> r # unital :: r -> E V1 -> r #
Num r => Coalgebra r (E V1)
Instance details Defined in Linear.Algebra Methods comult :: (E V1 -> r) -> E V1 -> E V1 -> r # counital :: (E V1 -> r) -> r #
Unbox a => MVector MVector (V1 a)
Instance details Defined in Linear.V1 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 #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V1 i) (Layout V1) Source #
Bounded a => Bounded (V1 a)
Instance details Defined in Linear.V1 Methods minBound :: V1 a # maxBound :: V1 a #
Eq a => Eq (V1 a)
Instance details Defined in Linear.V1 Methods (==) :: V1 a -> V1 a -> Bool # (/=) :: V1 a -> V1 a -> Bool #
Floating a => Floating (V1 a)
Instance details Defined in Linear.V1 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)
Instance details Defined in Linear.V1 Methods (/) :: V1 a -> V1 a -> V1 a # recip :: V1 a -> V1 a # fromRational :: Rational -> V1 a #
Data a => Data (V1 a)
Instance details Defined in Linear.V1 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 :: forall r r'. (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)
Instance details Defined in Linear.V1 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)
Instance details Defined in Linear.V1 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)
Instance details Defined in Linear.V1 Methods readsPrec :: Int -> ReadS (V1 a) # readList :: ReadS [V1 a] # readPrec :: ReadPrec (V1 a) # readListPrec :: ReadPrec [V1 a] #
Show a => Show (V1 a)
Instance details Defined in Linear.V1 Methods showsPrec :: Int -> V1 a -> ShowS # show :: V1 a -> String # showList :: [V1 a] -> ShowS #
Ix a => Ix (V1 a)
Instance details Defined in Linear.V1 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)
Instance details Defined in Linear.V1 Associated Types type Rep (V1 a) :: Type -> Type # Methods from :: V1 a -> Rep (V1 a) x # to :: Rep (V1 a) x -> V1 a #
Semigroup a => Semigroup (V1 a)
Instance details Defined in Linear.V1 Methods (<>) :: V1 a -> V1 a -> V1 a # sconcat :: NonEmpty (V1 a) -> V1 a # stimes :: Integral b => b -> V1 a -> V1 a #
Monoid a => Monoid (V1 a)
Instance details Defined in Linear.V1 Methods mempty :: V1 a # mappend :: V1 a -> V1 a -> V1 a # mconcat :: [V1 a] -> V1 a #
Storable a => Storable (V1 a)
Instance details Defined in Linear.V1 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)
Instance details Defined in Linear.V1 Methods put :: V1 a -> Put # get :: Get (V1 a) # putList :: [V1 a] -> Put #
Serial a => Serial (V1 a)
Instance details Defined in Linear.V1 Methods serialize :: MonadPut m => V1 a -> m () # deserialize :: MonadGet m => m (V1 a) #
Serialize a => Serialize (V1 a)
Instance details Defined in Linear.V1 Methods put :: Putter (V1 a) # get :: Get (V1 a) #
NFData a => NFData (V1 a)
Instance details Defined in Linear.V1 Methods rnf :: V1 a -> () #
Hashable a => Hashable (V1 a)
Instance details Defined in Linear.V1 Methods hashWithSalt :: Int -> V1 a -> Int # hash :: V1 a -> Int #
Unbox a => Unbox (V1 a)
Instance details Defined in Linear.V1
Ixed (V1 a)
Instance details Defined in Linear.V1 Methods ix :: Index (V1 a) -> Traversal' (V1 a) (IxValue (V1 a)) #
Epsilon a => Epsilon (V1 a)
Instance details Defined in Linear.V1 Methods nearZero :: V1 a -> Bool #
Random a => Random (V1 a)
Instance details Defined in Linear.V1 Methods randomR :: RandomGen g => (V1 a, V1 a) -> g -> (V1 a, g) # random :: RandomGen g => g -> (V1 a, g) # randomRs :: RandomGen g => (V1 a, V1 a) -> g -> [V1 a] # randoms :: RandomGen g => g -> [V1 a] # randomRIO :: (V1 a, V1 a) -> IO (V1 a) # randomIO :: IO (V1 a) #
Generic1 V1
Instance details Defined in Linear.V1 Associated Types type Rep1 V1 :: k -> Type # Methods from1 :: forall (a :: k). V1 a -> Rep1 V1 a # to1 :: forall (a :: k). Rep1 V1 a -> V1 a #
FunctorWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods imap :: (E V1 -> a -> b) -> V1 a -> V1 b # imapped :: IndexedSetter (E V1) (V1 a) (V1 b) a b #
FoldableWithIndex (E V1) V1
Instance details Defined in Linear.V1 Methods ifoldMap :: Monoid m => (E V1 -> a -> m) -> V1 a -> m # ifolded :: IndexedFold (E V1) (V1 a) 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
Instance details Defined in Linear.V1 Methods itraverse :: Applicative f => (E V1 -> a -> f b) -> V1 a -> f (V1 b) # itraversed :: IndexedTraversal (E V1) (V1 a) (V1 b) a b #
Each (V1 a) (V1 b) a b
Instance details Defined in Linear.V1 Methods each :: Traversal (V1 a) (V1 b) a b #
Field1 (V1 a) (V1 b) a b
Instance details Defined in Linear.V1 Methods _1 :: Lens (V1 a) (V1 b) a b #
type Rep V1
Instance details Defined in Linear.V1 type Rep V1 = E V1
type Size V1
Instance details Defined in Linear.V1 type Size V1 = 1
newtype MVector s (V1 a)
Instance details Defined in Linear.V1 newtype MVector s (V1 a) = MV_V1 (MVector s a)
type Rep (V1 a)
Instance details Defined in Linear.V1 type Rep (V1 a) = D1 ('MetaData "V1" "Linear.V1" "linear-1.21.1-8shKxkKQUSF4N39Qjrte3Y" 'True) (C1 ('MetaCons "V1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
newtype Vector (V1 a)
Instance details Defined in Linear.V1 newtype Vector (V1 a) = V_V1 (Vector a)
type Index (V1 a)
Instance details Defined in Linear.V1 type Index (V1 a) = E V1
type IxValue (V1 a)
Instance details Defined in Linear.V1 type IxValue (V1 a) = a
type Rep1 V1
Instance details Defined in Linear.V1 type Rep1 V1 = D1 ('MetaData "V1" "Linear.V1" "linear-1.21.1-8shKxkKQUSF4N39Qjrte3Y" 'True) (C1 ('MetaCons "V1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

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

Instances details

Monad V2
Instance details Defined in Linear.V2 Methods (>>=) :: V2 a -> (a -> V2 b) -> V2 b # (>>) :: V2 a -> V2 b -> V2 b # return :: a -> V2 a #
Functor V2
Instance details Defined in Linear.V2 Methods fmap :: (a -> b) -> V2 a -> V2 b # (<$) :: a -> V2 b -> V2 a #
MonadFix V2
Instance details Defined in Linear.V2 Methods mfix :: (a -> V2 a) -> V2 a #
Applicative V2
Instance details Defined in Linear.V2 Methods pure :: a -> V2 a # (<>) :: V2 (a -> b) -> V2 a -> V2 b # liftA2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c # (>) :: V2 a -> V2 b -> V2 b # (<*) :: V2 a -> V2 b -> V2 a #
Foldable V2
Instance details Defined in Linear.V2 Methods fold :: Monoid m => V2 m -> m # foldMap :: Monoid m => (a -> m) -> V2 a -> 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
Instance details Defined in Linear.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) #
Distributive V2
Instance details Defined in Linear.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
Instance details Defined in Linear.V2 Associated Types type Rep V2 # Methods tabulate :: (Rep V2 -> a) -> V2 a # index :: V2 a -> Rep V2 -> a #
Eq1 V2
Instance details Defined in Linear.V2 Methods liftEq :: (a -> b -> Bool) -> V2 a -> V2 b -> Bool #
Ord1 V2
Instance details Defined in Linear.V2 Methods liftCompare :: (a -> b -> Ordering) -> V2 a -> V2 b -> Ordering #
Read1 V2
Instance details Defined in Linear.V2 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V2 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V2 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V2 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V2 a] #
Show1 V2
Instance details Defined in Linear.V2 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V2 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V2 a] -> ShowS #
MonadZip V2
Instance details Defined in Linear.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
Instance details Defined in Linear.V2 Methods serializeWith :: MonadPut m => (a -> m ()) -> V2 a -> m () # deserializeWith :: MonadGet m => m a -> m (V2 a) #
Hashable1 V2
Instance details Defined in Linear.V2 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V2 a -> Int #
Apply V2
Instance details Defined in Linear.V2 Methods (<.>) :: V2 (a -> b) -> V2 a -> V2 b # (.>) :: V2 a -> V2 b -> V2 b # (<.) :: V2 a -> V2 b -> V2 a # liftF2 :: (a -> b -> c) -> V2 a -> V2 b -> V2 c #
Traversable1 V2
Instance details Defined in Linear.V2 Methods traverse1 :: Apply f => (a -> f b) -> V2 a -> f (V2 b) # sequence1 :: Apply f => V2 (f b) -> f (V2 b) #
Trace V2
Instance details Defined in Linear.Trace Methods trace :: Num a => V2 (V2 a) -> a # diagonal :: V2 (V2 a) -> V2 a #
R2 V2
Instance details Defined in Linear.V2 Methods _y :: Lens' (V2 a) a # _xy :: Lens' (V2 a) (V2 a) #
R1 V2
Instance details Defined in Linear.V2 Methods _x :: Lens' (V2 a) a #
Finite V2
Instance details Defined in Linear.V2 Associated Types type Size V2 :: Nat # Methods toV :: V2 a -> V (Size V2) a # fromV :: V (Size V2) a -> V2 a #
Metric V2
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Foldable1 V2
Instance details Defined in Linear.V2 Methods fold1 :: Semigroup m => V2 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V2 a -> m # toNonEmpty :: V2 a -> NonEmpty a #
Bind V2
Instance details Defined in Linear.V2 Methods (>>-) :: V2 a -> (a -> V2 b) -> V2 b # join :: V2 (V2 a) -> V2 a #
Shape V2 Source #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.TH Methods liftShape :: Lift a => V2 a -> Q Exp Source # liftShape' :: Lift a => V2 a -> Q Exp Source #
Lift a => Lift (V2 a :: Type)
Instance details Defined in Linear.V2 Methods lift :: V2 a -> Q Exp # liftTyped :: V2 a -> Q (TExp (V2 a)) #
Unbox a => Vector Vector (V2 a)
Instance details Defined in Linear.V2 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 #
Num r => Coalgebra r (E V2)
Instance details Defined in Linear.Algebra Methods comult :: (E V2 -> r) -> E V2 -> E V2 -> r # counital :: (E V2 -> r) -> r #
Unbox a => MVector MVector (V2 a)
Instance details Defined in Linear.V2 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 #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V2 i) (Layout V2) Source #
Bounded a => Bounded (V2 a)
Instance details Defined in Linear.V2 Methods minBound :: V2 a # maxBound :: V2 a #
Eq a => Eq (V2 a)
Instance details Defined in Linear.V2 Methods (==) :: V2 a -> V2 a -> Bool # (/=) :: V2 a -> V2 a -> Bool #
Floating a => Floating (V2 a)
Instance details Defined in Linear.V2 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)
Instance details Defined in Linear.V2 Methods (/) :: V2 a -> V2 a -> V2 a # recip :: V2 a -> V2 a # fromRational :: Rational -> V2 a #
Data a => Data (V2 a)
Instance details Defined in Linear.V2 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 :: forall r r'. (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)
Instance details Defined in Linear.V2 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)
Instance details Defined in Linear.V2 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)
Instance details Defined in Linear.V2 Methods readsPrec :: Int -> ReadS (V2 a) # readList :: ReadS [V2 a] # readPrec :: ReadPrec (V2 a) # readListPrec :: ReadPrec [V2 a] #
Show a => Show (V2 a)
Instance details Defined in Linear.V2 Methods showsPrec :: Int -> V2 a -> ShowS # show :: V2 a -> String # showList :: [V2 a] -> ShowS #
Ix a => Ix (V2 a)
Instance details Defined in Linear.V2 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)
Instance details Defined in Linear.V2 Associated Types type Rep (V2 a) :: Type -> Type # Methods from :: V2 a -> Rep (V2 a) x # to :: Rep (V2 a) x -> V2 a #
Semigroup a => Semigroup (V2 a)
Instance details Defined in Linear.V2 Methods (<>) :: V2 a -> V2 a -> V2 a # sconcat :: NonEmpty (V2 a) -> V2 a # stimes :: Integral b => b -> V2 a -> V2 a #
Monoid a => Monoid (V2 a)
Instance details Defined in Linear.V2 Methods mempty :: V2 a # mappend :: V2 a -> V2 a -> V2 a # mconcat :: [V2 a] -> V2 a #
Storable a => Storable (V2 a)
Instance details Defined in Linear.V2 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)
Instance details Defined in Linear.V2 Methods put :: V2 a -> Put # get :: Get (V2 a) # putList :: [V2 a] -> Put #
Serial a => Serial (V2 a)
Instance details Defined in Linear.V2 Methods serialize :: MonadPut m => V2 a -> m () # deserialize :: MonadGet m => m (V2 a) #
Serialize a => Serialize (V2 a)
Instance details Defined in Linear.V2 Methods put :: Putter (V2 a) # get :: Get (V2 a) #
NFData a => NFData (V2 a)
Instance details Defined in Linear.V2 Methods rnf :: V2 a -> () #
Hashable a => Hashable (V2 a)
Instance details Defined in Linear.V2 Methods hashWithSalt :: Int -> V2 a -> Int # hash :: V2 a -> Int #
Unbox a => Unbox (V2 a)
Instance details Defined in Linear.V2
Ixed (V2 a)
Instance details Defined in Linear.V2 Methods ix :: Index (V2 a) -> Traversal' (V2 a) (IxValue (V2 a)) #
Epsilon a => Epsilon (V2 a)
Instance details Defined in Linear.V2 Methods nearZero :: V2 a -> Bool #
Random a => Random (V2 a)
Instance details Defined in Linear.V2 Methods randomR :: RandomGen g => (V2 a, V2 a) -> g -> (V2 a, g) # random :: RandomGen g => g -> (V2 a, g) # randomRs :: RandomGen g => (V2 a, V2 a) -> g -> [V2 a] # randoms :: RandomGen g => g -> [V2 a] # randomRIO :: (V2 a, V2 a) -> IO (V2 a) # randomIO :: IO (V2 a) #
Generic1 V2
Instance details Defined in Linear.V2 Associated Types type Rep1 V2 :: k -> Type # Methods from1 :: forall (a :: k). V2 a -> Rep1 V2 a # to1 :: forall (a :: k). Rep1 V2 a -> V2 a #
FunctorWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods imap :: (E V2 -> a -> b) -> V2 a -> V2 b # imapped :: IndexedSetter (E V2) (V2 a) (V2 b) a b #
FoldableWithIndex (E V2) V2
Instance details Defined in Linear.V2 Methods ifoldMap :: Monoid m => (E V2 -> a -> m) -> V2 a -> m # ifolded :: IndexedFold (E V2) (V2 a) 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
Instance details Defined in Linear.V2 Methods itraverse :: Applicative f => (E V2 -> a -> f b) -> V2 a -> f (V2 b) # itraversed :: IndexedTraversal (E V2) (V2 a) (V2 b) a b #
Each (V2 a) (V2 b) a b
Instance details Defined in Linear.V2 Methods each :: Traversal (V2 a) (V2 b) a b #
Field1 (V2 a) (V2 a) a a
Instance details Defined in Linear.V2 Methods _1 :: Lens (V2 a) (V2 a) a a #
Field2 (V2 a) (V2 a) a a
Instance details Defined in Linear.V2 Methods _2 :: Lens (V2 a) (V2 a) a a #
type Rep V2
Instance details Defined in Linear.V2 type Rep V2 = E V2
type Size V2
Instance details Defined in Linear.V2 type Size V2 = 2
data MVector s (V2 a)
Instance details Defined in Linear.V2 data MVector s (V2 a) = MV_V2 !Int !(MVector s a)
type Rep (V2 a)
Instance details Defined in Linear.V2 type Rep (V2 a) = D1 ('MetaData "V2" "Linear.V2" "linear-1.21.1-8shKxkKQUSF4N39Qjrte3Y" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
data Vector (V2 a)
Instance details Defined in Linear.V2 data Vector (V2 a) = V_V2 !Int !(Vector a)
type Index (V2 a)
Instance details Defined in Linear.V2 type Index (V2 a) = E V2
type IxValue (V2 a)
Instance details Defined in Linear.V2 type IxValue (V2 a) = a
type Rep1 V2
Instance details Defined in Linear.V2 type Rep1 V2 = D1 ('MetaData "V2" "Linear.V2" "linear-1.21.1-8shKxkKQUSF4N39Qjrte3Y" 'False) (C1 ('MetaCons "V2" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))

data V3 a #

A 3-dimensional vector

Constructors

V3 !a !a !a

Instances

Instances details

Monad V3
Instance details Defined in Linear.V3 Methods (>>=) :: V3 a -> (a -> V3 b) -> V3 b # (>>) :: V3 a -> V3 b -> V3 b # return :: a -> V3 a #
Functor V3
Instance details Defined in Linear.V3 Methods fmap :: (a -> b) -> V3 a -> V3 b # (<$) :: a -> V3 b -> V3 a #
MonadFix V3
Instance details Defined in Linear.V3 Methods mfix :: (a -> V3 a) -> V3 a #
Applicative V3
Instance details Defined in Linear.V3 Methods pure :: a -> V3 a # (<>) :: V3 (a -> b) -> V3 a -> V3 b # liftA2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c # (>) :: V3 a -> V3 b -> V3 b # (<*) :: V3 a -> V3 b -> V3 a #
Foldable V3
Instance details Defined in Linear.V3 Methods fold :: Monoid m => V3 m -> m # foldMap :: Monoid m => (a -> m) -> V3 a -> 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
Instance details Defined in Linear.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) #
Distributive V3
Instance details Defined in Linear.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
Instance details Defined in Linear.V3 Associated Types type Rep V3 # Methods tabulate :: (Rep V3 -> a) -> V3 a # index :: V3 a -> Rep V3 -> a #
Eq1 V3
Instance details Defined in Linear.V3 Methods liftEq :: (a -> b -> Bool) -> V3 a -> V3 b -> Bool #
Ord1 V3
Instance details Defined in Linear.V3 Methods liftCompare :: (a -> b -> Ordering) -> V3 a -> V3 b -> Ordering #
Read1 V3
Instance details Defined in Linear.V3 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V3 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V3 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V3 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V3 a] #
Show1 V3
Instance details Defined in Linear.V3 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V3 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V3 a] -> ShowS #
MonadZip V3
Instance details Defined in Linear.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
Instance details Defined in Linear.V3 Methods serializeWith :: MonadPut m => (a -> m ()) -> V3 a -> m () # deserializeWith :: MonadGet m => m a -> m (V3 a) #
Hashable1 V3
Instance details Defined in Linear.V3 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V3 a -> Int #
Apply V3
Instance details Defined in Linear.V3 Methods (<.>) :: V3 (a -> b) -> V3 a -> V3 b # (.>) :: V3 a -> V3 b -> V3 b # (<.) :: V3 a -> V3 b -> V3 a # liftF2 :: (a -> b -> c) -> V3 a -> V3 b -> V3 c #
Traversable1 V3
Instance details Defined in Linear.V3 Methods traverse1 :: Apply f => (a -> f b) -> V3 a -> f (V3 b) # sequence1 :: Apply f => V3 (f b) -> f (V3 b) #
Trace V3
Instance details Defined in Linear.Trace Methods trace :: Num a => V3 (V3 a) -> a # diagonal :: V3 (V3 a) -> V3 a #
R3 V3
Instance details Defined in Linear.V3 Methods _z :: Lens' (V3 a) a # _xyz :: Lens' (V3 a) (V3 a) #
R2 V3
Instance details Defined in Linear.V3 Methods _y :: Lens' (V3 a) a # _xy :: Lens' (V3 a) (V2 a) #
R1 V3
Instance details Defined in Linear.V3 Methods _x :: Lens' (V3 a) a #
Finite V3
Instance details Defined in Linear.V3 Associated Types type Size V3 :: Nat # Methods toV :: V3 a -> V (Size V3) a # fromV :: V (Size V3) a -> V3 a #
Metric V3
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Foldable1 V3
Instance details Defined in Linear.V3 Methods fold1 :: Semigroup m => V3 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V3 a -> m # toNonEmpty :: V3 a -> NonEmpty a #
Bind V3
Instance details Defined in Linear.V3 Methods (>>-) :: V3 a -> (a -> V3 b) -> V3 b # join :: V3 (V3 a) -> V3 a #
Shape V3 Source #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.TH Methods liftShape :: Lift a => V3 a -> Q Exp Source # liftShape' :: Lift a => V3 a -> Q Exp Source #
Lift a => Lift (V3 a :: Type)
Instance details Defined in Linear.V3 Methods lift :: V3 a -> Q Exp # liftTyped :: V3 a -> Q (TExp (V3 a)) #
Unbox a => Vector Vector (V3 a)
Instance details Defined in Linear.V3 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 #
Num r => Coalgebra r (E V3)
Instance details Defined in Linear.Algebra Methods comult :: (E V3 -> r) -> E V3 -> E V3 -> r # counital :: (E V3 -> r) -> r #
Unbox a => MVector MVector (V3 a)
Instance details Defined in Linear.V3 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 #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V3 i) (Layout V3) Source #
Bounded a => Bounded (V3 a)
Instance details Defined in Linear.V3 Methods minBound :: V3 a # maxBound :: V3 a #
Eq a => Eq (V3 a)
Instance details Defined in Linear.V3 Methods (==) :: V3 a -> V3 a -> Bool # (/=) :: V3 a -> V3 a -> Bool #
Floating a => Floating (V3 a)
Instance details Defined in Linear.V3 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)
Instance details Defined in Linear.V3 Methods (/) :: V3 a -> V3 a -> V3 a # recip :: V3 a -> V3 a # fromRational :: Rational -> V3 a #
Data a => Data (V3 a)
Instance details Defined in Linear.V3 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 :: forall r r'. (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)
Instance details Defined in Linear.V3 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)
Instance details Defined in Linear.V3 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)
Instance details Defined in Linear.V3 Methods readsPrec :: Int -> ReadS (V3 a) # readList :: ReadS [V3 a] # readPrec :: ReadPrec (V3 a) # readListPrec :: ReadPrec [V3 a] #
Show a => Show (V3 a)
Instance details Defined in Linear.V3 Methods showsPrec :: Int -> V3 a -> ShowS # show :: V3 a -> String # showList :: [V3 a] -> ShowS #
Ix a => Ix (V3 a)
Instance details Defined in Linear.V3 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)
Instance details Defined in Linear.V3 Associated Types type Rep (V3 a) :: Type -> Type # Methods from :: V3 a -> Rep (V3 a) x # to :: Rep (V3 a) x -> V3 a #
Semigroup a => Semigroup (V3 a)
Instance details Defined in Linear.V3 Methods (<>) :: V3 a -> V3 a -> V3 a # sconcat :: NonEmpty (V3 a) -> V3 a # stimes :: Integral b => b -> V3 a -> V3 a #
Monoid a => Monoid (V3 a)
Instance details Defined in Linear.V3 Methods mempty :: V3 a # mappend :: V3 a -> V3 a -> V3 a # mconcat :: [V3 a] -> V3 a #
Storable a => Storable (V3 a)
Instance details Defined in Linear.V3 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)
Instance details Defined in Linear.V3 Methods put :: V3 a -> Put # get :: Get (V3 a) # putList :: [V3 a] -> Put #
Serial a => Serial (V3 a)
Instance details Defined in Linear.V3 Methods serialize :: MonadPut m => V3 a -> m () # deserialize :: MonadGet m => m (V3 a) #
Serialize a => Serialize (V3 a)
Instance details Defined in Linear.V3 Methods put :: Putter (V3 a) # get :: Get (V3 a) #
NFData a => NFData (V3 a)
Instance details Defined in Linear.V3 Methods rnf :: V3 a -> () #
Hashable a => Hashable (V3 a)
Instance details Defined in Linear.V3 Methods hashWithSalt :: Int -> V3 a -> Int # hash :: V3 a -> Int #
Unbox a => Unbox (V3 a)
Instance details Defined in Linear.V3
Ixed (V3 a)
Instance details Defined in Linear.V3 Methods ix :: Index (V3 a) -> Traversal' (V3 a) (IxValue (V3 a)) #
Epsilon a => Epsilon (V3 a)
Instance details Defined in Linear.V3 Methods nearZero :: V3 a -> Bool #
Random a => Random (V3 a)
Instance details Defined in Linear.V3 Methods randomR :: RandomGen g => (V3 a, V3 a) -> g -> (V3 a, g) # random :: RandomGen g => g -> (V3 a, g) # randomRs :: RandomGen g => (V3 a, V3 a) -> g -> [V3 a] # randoms :: RandomGen g => g -> [V3 a] # randomRIO :: (V3 a, V3 a) -> IO (V3 a) # randomIO :: IO (V3 a) #
Generic1 V3
Instance details Defined in Linear.V3 Associated Types type Rep1 V3 :: k -> Type # Methods from1 :: forall (a :: k). V3 a -> Rep1 V3 a # to1 :: forall (a :: k). Rep1 V3 a -> V3 a #
FunctorWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods imap :: (E V3 -> a -> b) -> V3 a -> V3 b # imapped :: IndexedSetter (E V3) (V3 a) (V3 b) a b #
FoldableWithIndex (E V3) V3
Instance details Defined in Linear.V3 Methods ifoldMap :: Monoid m => (E V3 -> a -> m) -> V3 a -> m # ifolded :: IndexedFold (E V3) (V3 a) 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
Instance details Defined in Linear.V3 Methods itraverse :: Applicative f => (E V3 -> a -> f b) -> V3 a -> f (V3 b) # itraversed :: IndexedTraversal (E V3) (V3 a) (V3 b) a b #
Each (V3 a) (V3 b) a b
Instance details Defined in Linear.V3 Methods each :: Traversal (V3 a) (V3 b) a b #
Field1 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _1 :: Lens (V3 a) (V3 a) a a #
Field2 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _2 :: Lens (V3 a) (V3 a) a a #
Field3 (V3 a) (V3 a) a a
Instance details Defined in Linear.V3 Methods _3 :: Lens (V3 a) (V3 a) a a #
type Rep V3
Instance details Defined in Linear.V3 type Rep V3 = E V3
type Size V3
Instance details Defined in Linear.V3 type Size V3 = 3
data MVector s (V3 a)
Instance details Defined in Linear.V3 data MVector s (V3 a) = MV_V3 !Int !(MVector s a)
type Rep (V3 a)
Instance details Defined in Linear.V3 type Rep (V3 a) = D1 ('MetaData "V3" "Linear.V3" "linear-1.21.1-8shKxkKQUSF4N39Qjrte3Y" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))
data Vector (V3 a)
Instance details Defined in Linear.V3 data Vector (V3 a) = V_V3 !Int !(Vector a)
type Index (V3 a)
Instance details Defined in Linear.V3 type Index (V3 a) = E V3
type IxValue (V3 a)
Instance details Defined in Linear.V3 type IxValue (V3 a) = a
type Rep1 V3
Instance details Defined in Linear.V3 type Rep1 V3 = D1 ('MetaData "V3" "Linear.V3" "linear-1.21.1-8shKxkKQUSF4N39Qjrte3Y" 'False) (C1 ('MetaCons "V3" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1)))

data V4 a #

A 4-dimensional vector.

Constructors

V4 !a !a !a !a

Instances

Instances details

Monad V4
Instance details Defined in Linear.V4 Methods (>>=) :: V4 a -> (a -> V4 b) -> V4 b # (>>) :: V4 a -> V4 b -> V4 b # return :: a -> V4 a #
Functor V4
Instance details Defined in Linear.V4 Methods fmap :: (a -> b) -> V4 a -> V4 b # (<$) :: a -> V4 b -> V4 a #
MonadFix V4
Instance details Defined in Linear.V4 Methods mfix :: (a -> V4 a) -> V4 a #
Applicative V4
Instance details Defined in Linear.V4 Methods pure :: a -> V4 a # (<>) :: V4 (a -> b) -> V4 a -> V4 b # liftA2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c # (>) :: V4 a -> V4 b -> V4 b # (<*) :: V4 a -> V4 b -> V4 a #
Foldable V4
Instance details Defined in Linear.V4 Methods fold :: Monoid m => V4 m -> m # foldMap :: Monoid m => (a -> m) -> V4 a -> 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
Instance details Defined in Linear.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) #
Distributive V4
Instance details Defined in Linear.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
Instance details Defined in Linear.V4 Associated Types type Rep V4 # Methods tabulate :: (Rep V4 -> a) -> V4 a # index :: V4 a -> Rep V4 -> a #
Eq1 V4
Instance details Defined in Linear.V4 Methods liftEq :: (a -> b -> Bool) -> V4 a -> V4 b -> Bool #
Ord1 V4
Instance details Defined in Linear.V4 Methods liftCompare :: (a -> b -> Ordering) -> V4 a -> V4 b -> Ordering #
Read1 V4
Instance details Defined in Linear.V4 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (V4 a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [V4 a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (V4 a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [V4 a] #
Show1 V4
Instance details Defined in Linear.V4 Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> V4 a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [V4 a] -> ShowS #
MonadZip V4
Instance details Defined in Linear.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
Instance details Defined in Linear.V4 Methods serializeWith :: MonadPut m => (a -> m ()) -> V4 a -> m () # deserializeWith :: MonadGet m => m a -> m (V4 a) #
Hashable1 V4
Instance details Defined in Linear.V4 Methods liftHashWithSalt :: (Int -> a -> Int) -> Int -> V4 a -> Int #
Apply V4
Instance details Defined in Linear.V4 Methods (<.>) :: V4 (a -> b) -> V4 a -> V4 b # (.>) :: V4 a -> V4 b -> V4 b # (<.) :: V4 a -> V4 b -> V4 a # liftF2 :: (a -> b -> c) -> V4 a -> V4 b -> V4 c #
Traversable1 V4
Instance details Defined in Linear.V4 Methods traverse1 :: Apply f => (a -> f b) -> V4 a -> f (V4 b) # sequence1 :: Apply f => V4 (f b) -> f (V4 b) #
Trace V4
Instance details Defined in Linear.Trace Methods trace :: Num a => V4 (V4 a) -> a # diagonal :: V4 (V4 a) -> V4 a #
R4 V4
Instance details Defined in Linear.V4 Methods _w :: Lens' (V4 a) a # _xyzw :: Lens' (V4 a) (V4 a) #
R3 V4
Instance details Defined in Linear.V4 Methods _z :: Lens' (V4 a) a # _xyz :: Lens' (V4 a) (V3 a) #
R2 V4
Instance details Defined in Linear.V4 Methods _y :: Lens' (V4 a) a # _xy :: Lens' (V4 a) (V2 a) #
R1 V4
Instance details Defined in Linear.V4 Methods _x :: Lens' (V4 a) a #
Finite V4
Instance details Defined in Linear.V4 Associated Types type Size V4 :: Nat # Methods toV :: V4 a -> V (Size V4) a # fromV :: V (Size V4) a -> V4 a #
Metric V4
Instance details Defined in Linear.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
Instance details Defined in Linear.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 #
Foldable1 V4
Instance details Defined in Linear.V4 Methods fold1 :: Semigroup m => V4 m -> m # foldMap1 :: Semigroup m => (a -> m) -> V4 a -> m # toNonEmpty :: V4 a -> NonEmpty a #
Bind V4
Instance details Defined in Linear.V4 Methods (>>-) :: V4 a -> (a -> V4 b) -> V4 b # join :: V4 (V4 a) -> V4 a #
Shape V4 Source #
Instance details Defined in Data.Dense.Index 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 #
Instance details Defined in Data.Dense.TH Methods liftShape :: Lift a => V4 a -> Q Exp Source # liftShape' :: Lift a => V4 a -> Q Exp Source #
Lift a => Lift (V4 a :: Type)
Instance details Defined in Linear.V4 Methods lift :: V4 a -> Q Exp # liftTyped :: V4 a -> Q (TExp (V4 a)) #
Unbox a => Vector Vector (V4 a)
Instance details Defined in Linear.V4 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 #
Num r => Coalgebra r (E V4)
Instance details Defined in Linear.Algebra Methods comult :: (E V4 -> r) -> E V4 -> E V4 -> r # counital :: (E V4 -> r) -> r #
Unbox a => MVector MVector (V4 a)
Instance details Defined in Linear.V4 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 #
Instance details Defined in Data.Dense.Index Methods layout :: Lens' (V4 i) (Layout V4) Source #
Bounded a => Bounded (V4 a)
Instance details Defined in Linear.V4 Methods minBound :: V4 a # maxBound :: V4 a #
Eq a => Eq (V4 a)
Instance details Defined in Linear.V4 Methods (==) :: V4 a -> V4 a -> Bool # (/=) :: V4 a -> V4 a -> Bool #
Floating a => Floating (V4 a)
Instance details Defined in Linear.V4 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)
Instance details Defined in Linear.V4 Methods (/) :: V4 a -> V4 a -> V4 a # recip :: V4 a -> V4 a # fromRational :: Rational -> V4 a #
Data a => Data (V4 a)
Instance details Defined in Linear.V4 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 :: forall r r'. (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)
Instance details Defined in Linear.V4 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)
Instance details Defined in Linear.V4 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)
Instance details Defined in Linear.V4 Methods readsPrec :: Int -> ReadS (V4 a) # readList :: ReadS [V4 a] # readPrec :: ReadPrec (V4 a) # readListPrec :: ReadPrec [V4 a] #
Show a => Show (V4 a)
Instance details Defined in Linear.V4 Methods showsPrec :: Int -> V4 a -> ShowS # show :: V4 a -> String # showList :: [V4 a] -> ShowS #
Ix a => Ix (V4 a)
Instance details Defined in Linear.V4 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)
Instance details Defined in Linear.V4 Associated Types type Rep (V4 a) :: Type -> Type # Methods from :: V4 a -> Rep (V4 a) x # to :: Rep (V4 a) x -> V4 a #
Semigroup a => Semigroup (V4 a)
Instance details Defined in Linear.V4 Methods (<>) :: V4 a -> V4 a -> V4 a # sconcat :: NonEmpty (V4 a) -> V4 a # stimes :: Integral b => b -> V4 a -> V4 a #
Monoid a => Monoid (V4 a)
Instance details Defined in Linear.V4 Methods mempty :: V4 a # mappend :: V4 a -> V4 a -> V4 a # mconcat :: [V4 a] -> V4 a #
Storable a => Storable (V4 a)
Instance details Defined in