fixed-vector-1.2.1.0: Generic vectors with statically known size.

Data.Vector.Fixed

Description

Generic API for vectors with fixed length.

For encoding of vector size library uses Peano naturals defined in the library. At come point in the future it would make sense to switch to new GHC type level numerals.

Common pitfalls

Library provide instances for tuples. But there's a catch. Tuples are monomorphic in element type. Let consider 2-tuple (Int,Int). Vector type v is (,) Int and only allowed element type is Int. Because of that we cannot change element type and following code will fail:

>>> map (== 1) ((1,2) :: (Int,Int))

<interactive>:3:1:
Couldn't match type Int' with Bool'
In the expression: F.map (== 1) ((1, 2) :: (Int, Int))
In an equation for it': it = map (== 1) ((1, 2) :: (Int, Int))

To make it work we need to change vector type as well. Functions from module Data.Vector.Fixed.Generic provide this functionality.

>>> map (== 1) ((1,2) :: (Int,Int)) :: (Bool,Bool)
(True,False)
Synopsis

# Vector type class

## Vector size

type family Dim (v :: * -> *) :: Nat Source #

Size of vector expressed as type-level natural.

#### Instances

Instances details
 type Dim Complex Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim Complex = 2 type Dim Identity Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim Identity = 1 type Dim Only Source # Instance detailsDefined in Data.Vector.Fixed type Dim Only = 1 type Dim ((,) a) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim ((,) a) = 2 type Dim (Proxy :: Type -> Type) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim (Proxy :: Type -> Type) = 0 type Dim (ContVec n) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim (ContVec n) = n type Dim (Empty :: Type -> Type) Source # Instance detailsDefined in Data.Vector.Fixed type Dim (Empty :: Type -> Type) = 0 type Dim (VecList n) Source # Instance detailsDefined in Data.Vector.Fixed type Dim (VecList n) = n type Dim (Vec n) Source # Instance detailsDefined in Data.Vector.Fixed.Boxed type Dim (Vec n) = n type Dim (Vec n) Source # Instance detailsDefined in Data.Vector.Fixed.Primitive type Dim (Vec n) = n type Dim (Vec n) Source # Instance detailsDefined in Data.Vector.Fixed.Storable type Dim (Vec n) = n type Dim (Vec n) Source # Instance detailsDefined in Data.Vector.Fixed.Unboxed type Dim (Vec n) = n type Dim ((,,) a b) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim ((,,) a b) = 3 type Dim ((,,,) a b c) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim ((,,,) a b c) = 4 type Dim ((,,,,) a b c d) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim ((,,,,) a b c d) = 5 type Dim ((,,,,,) a b c d e) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim ((,,,,,) a b c d e) = 6 type Dim ((,,,,,,) a b c d e f) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim ((,,,,,,) a b c d e f) = 7

## Type class

class Arity (Dim v) => Vector v a where Source #

Type class for vectors with fixed length. Instance should provide two functions: one to create vector and another for vector deconstruction. They must obey following law:

inspect v construct = v

For example instance for 2D vectors could be written as:

data V2 a = V2 a a

type instance V2 = 2
instance Vector V2 a where
construct                = Fun V2
inspect (V2 a b) (Fun f) = f a b

Minimal complete definition

Methods

construct :: Fun (Peano (Dim v)) a (v a) Source #

N-ary function for creation of vectors.

inspect :: v a -> Fun (Peano (Dim v)) a b -> b Source #

Deconstruction of vector.

basicIndex :: v a -> Int -> a Source #

Optional more efficient implementation of indexing. Shouldn't be used directly, use ! instead.

#### Instances

Instances details
 Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim Complex)) a (Complex a) Source #inspect :: Complex a -> Fun (Peano (Dim Complex)) a b -> b Source #basicIndex :: Complex a -> Int -> a Source # Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim Identity)) a (Identity a) Source #inspect :: Identity a -> Fun (Peano (Dim Identity)) a b -> b Source #basicIndex :: Identity a -> Int -> a Source # Source # Instance detailsDefined in Data.Vector.Fixed Methodsconstruct :: Fun (Peano (Dim Only)) a (Only a) Source #inspect :: Only a -> Fun (Peano (Dim Only)) a b -> b Source #basicIndex :: Only a -> Int -> a Source # b ~ a => Vector ((,) b) a Source # Note this instance (and other instances for tuples) is essentially monomorphic in element type. Vector type v of 2 element tuple (Int,Int) is (,) Int so it will only work with elements of type Int. Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim ((,) b))) a (b, a) Source #inspect :: (b, a) -> Fun (Peano (Dim ((,) b))) a b0 -> b0 Source #basicIndex :: (b, a) -> Int -> a Source # Vector (Proxy :: Type -> Type) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim Proxy)) a (Proxy a) Source #inspect :: Proxy a -> Fun (Peano (Dim Proxy)) a b -> b Source #basicIndex :: Proxy a -> Int -> a Source # Arity n => Vector (ContVec n) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim (ContVec n))) a (ContVec n a) Source #inspect :: ContVec n a -> Fun (Peano (Dim (ContVec n))) a b -> b Source #basicIndex :: ContVec n a -> Int -> a Source # Vector (Empty :: Type -> Type) a Source # Instance detailsDefined in Data.Vector.Fixed Methodsconstruct :: Fun (Peano (Dim Empty)) a (Empty a) Source #inspect :: Empty a -> Fun (Peano (Dim Empty)) a b -> b Source #basicIndex :: Empty a -> Int -> a Source # Arity n => Vector (VecList n) a Source # Instance detailsDefined in Data.Vector.Fixed Methodsconstruct :: Fun (Peano (Dim (VecList n))) a (VecList n a) Source #inspect :: VecList n a -> Fun (Peano (Dim (VecList n))) a b -> b Source #basicIndex :: VecList n a -> Int -> a Source # Arity n => Vector (Vec n) a Source # Instance detailsDefined in Data.Vector.Fixed.Boxed Methodsconstruct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source #inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source #basicIndex :: Vec n a -> Int -> a Source # (Arity n, Prim a) => Vector (Vec n) a Source # Instance detailsDefined in Data.Vector.Fixed.Primitive Methodsconstruct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source #inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source #basicIndex :: Vec n a -> Int -> a Source # (Arity n, Storable a) => Vector (Vec n) a Source # Instance detailsDefined in Data.Vector.Fixed.Storable Methodsconstruct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source #inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source #basicIndex :: Vec n a -> Int -> a Source # Unbox n a => Vector (Vec n) a Source # Instance detailsDefined in Data.Vector.Fixed.Unboxed Methodsconstruct :: Fun (Peano (Dim (Vec n))) a (Vec n a) Source #inspect :: Vec n a -> Fun (Peano (Dim (Vec n))) a b -> b Source #basicIndex :: Vec n a -> Int -> a Source # (b ~ a, c ~ a) => Vector ((,,) b c) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim ((,,) b c))) a (b, c, a) Source #inspect :: (b, c, a) -> Fun (Peano (Dim ((,,) b c))) a b0 -> b0 Source #basicIndex :: (b, c, a) -> Int -> a Source # (b ~ a, c ~ a, d ~ a) => Vector ((,,,) b c d) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim ((,,,) b c d))) a (b, c, d, a) Source #inspect :: (b, c, d, a) -> Fun (Peano (Dim ((,,,) b c d))) a b0 -> b0 Source #basicIndex :: (b, c, d, a) -> Int -> a Source # (b ~ a, c ~ a, d ~ a, e ~ a) => Vector ((,,,,) b c d e) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim ((,,,,) b c d e))) a (b, c, d, e, a) Source #inspect :: (b, c, d, e, a) -> Fun (Peano (Dim ((,,,,) b c d e))) a b0 -> b0 Source #basicIndex :: (b, c, d, e, a) -> Int -> a Source # (b ~ a, c ~ a, d ~ a, e ~ a, f ~ a) => Vector ((,,,,,) b c d e f) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim ((,,,,,) b c d e f))) a (b, c, d, e, f, a) Source #inspect :: (b, c, d, e, f, a) -> Fun (Peano (Dim ((,,,,,) b c d e f))) a b0 -> b0 Source #basicIndex :: (b, c, d, e, f, a) -> Int -> a Source # (b ~ a, c ~ a, d ~ a, e ~ a, f ~ a, g ~ a) => Vector ((,,,,,,) b c d e f g) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim ((,,,,,,) b c d e f g))) a (b, c, d, e, f, g, a) Source #inspect :: (b, c, d, e, f, g, a) -> Fun (Peano (Dim ((,,,,,,) b c d e f g))) a b0 -> b0 Source #basicIndex :: (b, c, d, e, f, g, a) -> Int -> a Source #

class (Vector (v n) a, Dim (v n) ~ n) => VectorN v n a Source #

Vector parametrized by length. In ideal world it should be:

forall n. (Arity n, Vector (v n) a, Dim (v n) ~ n) => VectorN v a

Alas polymorphic constraints aren't allowed in haskell.

#### Instances

Instances details
 Arity n => VectorN ContVec n a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Arity n => VectorN VecList n a Source # Instance detailsDefined in Data.Vector.Fixed Arity n => VectorN Vec n a Source # Instance detailsDefined in Data.Vector.Fixed.Boxed (Arity n, Prim a) => VectorN Vec n a Source # Instance detailsDefined in Data.Vector.Fixed.Primitive (Arity n, Storable a) => VectorN Vec n a Source # Instance detailsDefined in Data.Vector.Fixed.Storable Unbox n a => VectorN Vec n a Source # Instance detailsDefined in Data.Vector.Fixed.Unboxed

type Arity n = (ArityPeano (Peano n), KnownNat n, Peano (n + 1) ~ 'S (Peano n)) Source #

Type class for type level number for which we can defined operations over N-ary functions.

newtype Fun n a b Source #

Newtype wrapper which is used to make Fn injective. It's also a reader monad.

Constructors

 Fun FieldsunFun :: Fn n a b

#### Instances

Instances details
 ArityPeano n => Monad (Fun n a) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methods(>>=) :: Fun n a a0 -> (a0 -> Fun n a b) -> Fun n a b #(>>) :: Fun n a a0 -> Fun n a b -> Fun n a b #return :: a0 -> Fun n a a0 # ArityPeano n => Functor (Fun n a) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsfmap :: (a0 -> b) -> Fun n a a0 -> Fun n a b #(<$) :: a0 -> Fun n a b -> Fun n a a0 # ArityPeano n => Applicative (Fun n a) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodspure :: a0 -> Fun n a a0 #(<*>) :: Fun n a (a0 -> b) -> Fun n a a0 -> Fun n a b #liftA2 :: (a0 -> b -> c) -> Fun n a a0 -> Fun n a b -> Fun n a c #(*>) :: Fun n a a0 -> Fun n a b -> Fun n a b #(<*) :: Fun n a a0 -> Fun n a b -> Fun n a a0 # length :: forall v a. KnownNat (Dim v) => v a -> Int Source # Length of vector. Function doesn't evaluate its argument. # Constructors There are several ways to construct fixed vectors except using their constructor if it's available. For small ones it's possible to use functions mk1, mk2, etc. >>> mk3 'a' 'b' 'c' :: (Char,Char,Char) ('a','b','c')  Alternatively one could use mkN. See its documentation for examples. Another option is to create tuple and convert it to desired vector type. For example: v = convert (x,y,z) It will work on if type of v is know from elsewhere. Same trick could be used to pattern match on the vector with opaque representation using view patterns function :: Vec N3 Double -> ... function (convert -> (x,y,z)) = ... For small vectors pattern synonyms V2, V3$, V4@ are provided that use same trick internally.

Constructors for vectors with small dimensions.

mk0 :: (Vector v a, Dim v ~ 0) => v a Source #

mk1 :: (Vector v a, Dim v ~ 1) => a -> v a Source #

mk2 :: (Vector v a, Dim v ~ 2) => a -> a -> v a Source #

mk3 :: (Vector v a, Dim v ~ 3) => a -> a -> a -> v a Source #

mk4 :: (Vector v a, Dim v ~ 4) => a -> a -> a -> a -> v a Source #

mk5 :: (Vector v a, Dim v ~ 5) => a -> a -> a -> a -> a -> v a Source #

mk6 :: (Vector v a, Dim v ~ 6) => a -> a -> a -> a -> a -> a -> v a Source #

mk7 :: (Vector v a, Dim v ~ 7) => a -> a -> a -> a -> a -> a -> a -> v a Source #

mk8 :: (Vector v a, Dim v ~ 8) => a -> a -> a -> a -> a -> a -> a -> a -> v a Source #

mkN :: forall proxy v a. Vector v a => proxy (v a) -> Fn (Peano (Dim v)) a (v a) Source #

N-ary constructor. Despite scary signature it's just N-ary function with additional type parameter which is used to fix type of vector being constructed. It could be used as:

v = mkN (Proxy :: Proxy (Int,Int,Int)) 1 2 3

or using TypeApplications syntax:

v = mkN (Proxy @ (Int,Int,Int)) 1 2 3

or if type of v is fixed elsewhere

v = mkN [v] 1 2 3

## Pattern for low-dimension vectors

pattern V2 :: (Vector v a, Dim v ~ 2) => a -> a -> v a Source #

pattern V3 :: (Vector v a, Dim v ~ 3) => a -> a -> a -> v a Source #

pattern V4 :: (Vector v a, Dim v ~ 4) => a -> a -> a -> a -> v a Source #

## Continuation-based vectors

data ContVec n a Source #

Vector represented as continuation. Alternative wording: it's Church encoded N-element vector.

#### Instances

Instances details
 Arity n => VectorN ContVec n a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Arity n => Functor (ContVec n) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsfmap :: (a -> b) -> ContVec n a -> ContVec n b #(<) :: a -> ContVec n b -> ContVec n a # Arity n => Applicative (ContVec n) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodspure :: a -> ContVec n a #(<*>) :: ContVec n (a -> b) -> ContVec n a -> ContVec n b #liftA2 :: (a -> b -> c) -> ContVec n a -> ContVec n b -> ContVec n c #(*>) :: ContVec n a -> ContVec n b -> ContVec n b #(<*) :: ContVec n a -> ContVec n b -> ContVec n a # Arity n => Foldable (ContVec n) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsfold :: Monoid m => ContVec n m -> m #foldMap :: Monoid m => (a -> m) -> ContVec n a -> m #foldMap' :: Monoid m => (a -> m) -> ContVec n a -> m #foldr :: (a -> b -> b) -> b -> ContVec n a -> b #foldr' :: (a -> b -> b) -> b -> ContVec n a -> b #foldl :: (b -> a -> b) -> b -> ContVec n a -> b #foldl' :: (b -> a -> b) -> b -> ContVec n a -> b #foldr1 :: (a -> a -> a) -> ContVec n a -> a #foldl1 :: (a -> a -> a) -> ContVec n a -> a #toList :: ContVec n a -> [a] #null :: ContVec n a -> Bool #length :: ContVec n a -> Int #elem :: Eq a => a -> ContVec n a -> Bool #maximum :: Ord a => ContVec n a -> a #minimum :: Ord a => ContVec n a -> a #sum :: Num a => ContVec n a -> a #product :: Num a => ContVec n a -> a # Arity n => Traversable (ContVec n) Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodstraverse :: Applicative f => (a -> f b) -> ContVec n a -> f (ContVec n b) #sequenceA :: Applicative f => ContVec n (f a) -> f (ContVec n a) #mapM :: Monad m => (a -> m b) -> ContVec n a -> m (ContVec n b) #sequence :: Monad m => ContVec n (m a) -> m (ContVec n a) # Arity n => Vector (ContVec n) a Source # Instance detailsDefined in Data.Vector.Fixed.Cont Methodsconstruct :: Fun (Peano (Dim (ContVec n))) a (ContVec n a) Source #inspect :: ContVec n a -> Fun (Peano (Dim (ContVec n))) a b -> b Source #basicIndex :: ContVec n a -> Int -> a Source # type Dim (ContVec n) Source # Instance detailsDefined in Data.Vector.Fixed.Cont type Dim (ContVec n) = n empty :: ContVec 0 a Source # Create empty vector. vector :: (Vector v a, Dim v ~ n) => ContVec n a -> v a Source # Convert continuation to the vector. cvec :: (Vector v a, Dim v ~ n) => v a -> ContVec n a Source # Convert regular vector to continuation based one. ## Functions replicate :: Vector v a => a -> v a Source # Replicate value n times. Examples: >>> import Data.Vector.Fixed.Boxed (Vec2) >>> replicate 1 :: Vec2 Int fromList [1,1]  >>> replicate 2 :: (Double,Double,Double) (2.0,2.0,2.0)  >>> import Data.Vector.Fixed.Boxed (Vec4) >>> replicate "foo" :: Vec4 String fromList ["foo","foo","foo","foo"]  replicateM :: (Vector v a, Applicative f) => f a -> f (v a) Source # Execute monadic action for every element of vector. Examples: >>> import Data.Vector.Fixed.Boxed (Vec2,Vec3) >>> replicateM (Just 3) :: Maybe (Vec3 Int) Just (fromList [3,3,3]) >>> replicateM (putStrLn "Hi!") :: IO (Vec2 ()) Hi! Hi! fromList [(),()]  generate :: Vector v a => (Int -> a) -> v a Source # Generate vector from function which maps element's index to its value. Examples: >>> import Data.Vector.Fixed.Unboxed (Vec4) >>> generate (^2) :: Vec4 Int fromList [0,1,4,9]  generateM :: (Applicative f, Vector v a) => (Int -> f a) -> f (v a) Source # Generate vector from monadic function which maps element's index to its value. unfoldr :: Vector v a => (b -> (a, b)) -> b -> v a Source # Unfold vector. basis :: (Vector v a, Num a) => Int -> v a Source # Unit vector along Nth axis. If index is larger than vector dimensions returns zero vector. Examples: >>> import Data.Vector.Fixed.Boxed (Vec3) >>> basis 0 :: Vec3 Int fromList [1,0,0] >>> basis 1 :: Vec3 Int fromList [0,1,0] >>> basis 3 :: Vec3 Int fromList [0,0,0]  # Modifying vectors ## Transformations head :: (Vector v a, 1 <= Dim v) => v a -> a Source # First element of vector. Examples: >>> import Data.Vector.Fixed.Boxed (Vec3) >>> let x = mk3 1 2 3 :: Vec3 Int >>> head x 1  tail :: (Vector v a, Vector w a, Dim v ~ (Dim w + 1)) => v a -> w a Source # Tail of vector. Examples: >>> import Data.Complex >>> tail (1,2,3) :: Complex Double 2.0 :+ 3.0  cons :: (Vector v a, Vector w a, Dim w ~ (Dim v + 1)) => a -> v a -> w a Source # Cons element to the vector snoc :: (Vector v a, Vector w a, Dim w ~ (Dim v + 1)) => a -> v a -> w a Source # Append element to the vector concat :: (Vector v a, Vector u a, Vector w a, (Dim v + Dim u) ~ Dim w, Peano (Dim v + Dim u) ~ Add (Peano (Dim v)) (Peano (Dim u))) => v a -> u a -> w a Source # reverse :: Vector v a => v a -> v a Source # Reverse order of elements in the vector ## Indexing & lenses (!) :: Vector v a => v a -> Int -> a Source # Retrieve vector's element at index. Generic implementation is O(n) but more efficient one is used when possible. index :: (Vector v a, KnownNat k, (k + 1) <= Dim v) => v a -> proxy k -> a Source # Get element from vector at statically known index set :: (Vector v a, KnownNat k, (k + 1) <= Dim v) => proxy k -> a -> v a -> v a Source # Set n'th element in the vector element :: (Vector v a, Functor f) => Int -> (a -> f a) -> v a -> f (v a) Source # Twan van Laarhoven's lens for element of vector elementTy :: (Vector v a, KnownNat k, (k + 1) <= Dim v, Functor f) => proxy k -> (a -> f a) -> v a -> f (v a) Source # Twan van Laarhoven's lens for element of vector with statically known index. ## Comparison eq :: (Vector v a, Eq a) => v a -> v a -> Bool Source # Test two vectors for equality. Examples: >>> import Data.Vector.Fixed.Boxed (Vec2) >>> let v0 = basis 0 :: Vec2 Int >>> let v1 = basis 1 :: Vec2 Int >>> v0 eq v0 True >>> v0 eq v1 False  ord :: (Vector v a, Ord a) => v a -> v a -> Ordering Source # Lexicographic ordering of two vectors. ## Maps map :: (Vector v a, Vector v b) => (a -> b) -> v a -> v b Source # Map over vector mapM :: (Vector v a, Vector v b, Applicative f) => (a -> f b) -> v a -> f (v b) Source # Effectful map over vector. mapM_ :: (Vector v a, Applicative f) => (a -> f b) -> v a -> f () Source # Apply monadic action to each element of vector and ignore result. imap :: (Vector v a, Vector v b) => (Int -> a -> b) -> v a -> v b Source # Apply function to every element of the vector and its index. imapM :: (Vector v a, Vector v b, Applicative f) => (Int -> a -> f b) -> v a -> f (v b) Source # Apply monadic function to every element of the vector and its index. imapM_ :: (Vector v a, Applicative f) => (Int -> a -> f b) -> v a -> f () Source # Apply monadic function to every element of the vector and its index and discard result. scanl :: (Vector v a, Vector w b, Dim w ~ (Dim v + 1)) => (b -> a -> b) -> b -> v a -> w b Source # Left scan over vector scanl1 :: Vector v a => (a -> a -> a) -> v a -> v a Source # Left scan over vector sequence :: (Vector v a, Vector v (f a), Applicative f) => v (f a) -> f (v a) Source # Evaluate every action in the vector from left to right. sequence_ :: (Vector v (f a), Applicative f) => v (f a) -> f () Source # Evaluate every action in the vector from left to right and ignore result sequenceA :: (Vector v a, Vector v (f a), Applicative f) => v (f a) -> f (v a) Source # Analog of sequenceA from Traversable. traverse :: (Vector v a, Vector v b, Applicative f) => (a -> f b) -> v a -> f (v b) Source # Analog of traverse from Traversable. distribute :: (Vector v a, Vector v (f a), Functor f) => f (v a) -> v (f a) Source # collect :: (Vector v a, Vector v b, Vector v (f b), Functor f) => (a -> v b) -> f a -> v (f b) Source # # Folding foldl :: Vector v a => (b -> a -> b) -> b -> v a -> b Source # Left fold over vector foldr :: Vector v a => (a -> b -> b) -> b -> v a -> b Source # Right fold over vector foldl1 :: (Vector v a, 1 <= Dim v) => (a -> a -> a) -> v a -> a Source # Left fold over vector fold :: (Vector v m, Monoid m) => v m -> m Source # Combine the elements of a structure using a monoid. Similar to fold foldMap :: (Vector v a, Monoid m) => (a -> m) -> v a -> m Source # Map each element of the structure to a monoid, and combine the results. Similar to foldMap ifoldl :: Vector v a => (b -> Int -> a -> b) -> b -> v a -> b Source # Left fold over vector. Function is applied to each element and its index. ifoldr :: Vector v a => (Int -> a -> b -> b) -> b -> v a -> b Source # Right fold over vector foldM :: (Vector v a, Monad m) => (b -> a -> m b) -> b -> v a -> m b Source # Monadic fold over vector. ifoldM :: (Vector v a, Monad m) => (b -> Int -> a -> m b) -> b -> v a -> m b Source # Left monadic fold over vector. Function is applied to each element and its index. ## Special folds sum :: (Vector v a, Num a) => v a -> a Source # Sum all elements in the vector. maximum :: (Vector v a, 1 <= Dim v, Ord a) => v a -> a Source # Maximal element of vector. Examples: >>> import Data.Vector.Fixed.Boxed (Vec3) >>> let x = mk3 1 2 3 :: Vec3 Int >>> maximum x 3  minimum :: (Vector v a, 1 <= Dim v, Ord a) => v a -> a Source # Minimal element of vector. Examples: >>> import Data.Vector.Fixed.Boxed (Vec3) >>> let x = mk3 1 2 3 :: Vec3 Int >>> minimum x 1  and :: Vector v Bool => v Bool -> Bool Source # Conjunction of all elements of a vector. or :: Vector v Bool => v Bool -> Bool Source # Disjunction of all elements of a vector. all :: Vector v a => (a -> Bool) -> v a -> Bool Source # Determines whether all elements of vector satisfy predicate. any :: Vector v a => (a -> Bool) -> v a -> Bool Source # Determines whether any of element of vector satisfy predicate. find :: Vector v a => (a -> Bool) -> v a -> Maybe a Source # The find function takes a predicate and a vector and returns the leftmost element of the vector matching the predicate, or Nothing if there is no such element. # Zips zipWith :: (Vector v a, Vector v b, Vector v c) => (a -> b -> c) -> v a -> v b -> v c Source # Zip two vector together using function. Examples: >>> import Data.Vector.Fixed.Boxed (Vec3) >>> let b0 = basis 0 :: Vec3 Int >>> let b1 = basis 1 :: Vec3 Int >>> let b2 = basis 2 :: Vec3 Int >>> let vplus x y = zipWith (+) x y >>> vplus b0 b1 fromList [1,1,0] >>> vplus b0 b2 fromList [1,0,1] >>> vplus b1 b2 fromList [0,1,1]  zipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (a -> b -> c -> d) -> v a -> v b -> v c -> v d Source # Zip three vector together zipWithM :: (Vector v a, Vector v b, Vector v c, Applicative f) => (a -> b -> f c) -> v a -> v b -> f (v c) Source # Zip two vector together using monadic function. zipWithM_ :: (Vector v a, Vector v b, Applicative f) => (a -> b -> f c) -> v a -> v b -> f () Source # Zip two vector elementwise using monadic function and discard result izipWith :: (Vector v a, Vector v b, Vector v c) => (Int -> a -> b -> c) -> v a -> v b -> v c Source # Zip two vector together using function which takes element index as well. izipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (Int -> a -> b -> c -> d) -> v a -> v b -> v c -> v d Source # Zip three vector together izipWithM :: (Vector v a, Vector v b, Vector v c, Applicative f) => (Int -> a -> b -> f c) -> v a -> v b -> f (v c) Source # Zip two vector together using monadic function which takes element index as well.. izipWithM_ :: (Vector v a, Vector v b, Vector v c, Applicative f, Vector v (f c)) => (Int -> a -> b -> f c) -> v a -> v b -> f () Source # Zip two vector elementwise using monadic function and discard result # Storable methods Default implementation of methods for Storable type class assumes that individual elements of vector are stored as N-element array. defaultAlignemnt :: forall a v. Storable a => v a -> Int Source # Default implementation of alignment for Storable type class for fixed vectors. defaultSizeOf :: forall a v. (Storable a, Vector v a) => v a -> Int Source # Default implementation of sizeOf for Storable type class for fixed vectors defaultPeek :: (Storable a, Vector v a) => Ptr (v a) -> IO (v a) Source # Default implementation of peek for Storable type class for fixed vector defaultPoke :: (Storable a, Vector v a) => Ptr (v a) -> v a -> IO () Source # Default implementation of poke for Storable type class for fixed vector # NFData defaultRnf :: (NFData a, Vector v a) => v a -> () Source # Default implementation of rnf from NFData type class # Conversion convert :: (Vector v a, Vector w a, Dim v ~ Dim w) => v a -> w a Source # Convert between different vector types toList :: Vector v a => v a -> [a] Source # Convert vector to the list fromList :: Vector v a => [a] -> v a Source # Create vector form list. Will throw error if list is shorter than resulting vector. fromList' :: Vector v a => [a] -> v a Source # Create vector form list. Will throw error if list has different length from resulting vector. fromListM :: Vector v a => [a] -> Maybe (v a) Source # Create vector form list. Will return Nothing if list has different length from resulting vector. fromFoldable :: (Vector v a, Foldable f) => f a -> Maybe (v a) Source # Create vector from Foldable data type. Will return Nothing` if data type different number of elements that resulting vector. # Data types newtype VecList (n :: Nat) a Source # Type-based vector with statically known length parametrized by GHC's type naturals Constructors  VecList (VecPeano (Peano n) a) #### Instances Instances details  Arity n => VectorN VecList n a Source # Instance detailsDefined in Data.Vector.Fixed Arity n => Functor (VecList n) Source # Instance detailsDefined in Data.Vector.Fixed Methodsfmap :: (a -> b) -> VecList n a -> VecList n b #(<) :: a -> VecList n b -> VecList n a # Arity n => Applicative (VecList n) Source # Instance detailsDefined in Data.Vector.Fixed Methodspure :: a -> VecList n a #(<*>) :: VecList n (a -> b) -> VecList n a -> VecList n b #liftA2 :: (a -> b -> c) -> VecList n a -> VecList n b -> VecList n c #(*>) :: VecList n a -> VecList n b -> VecList n b #(<*) :: VecList n a -> VecList n b -> VecList n a # Arity n => Foldable (VecList n) Source # Instance detailsDefined in Data.Vector.Fixed Methodsfold :: Monoid m => VecList n m -> m #foldMap :: Monoid m => (a -> m) -> VecList n a -> m #foldMap' :: Monoid m => (a -> m) -> VecList n a -> m #foldr :: (a -> b -> b) -> b -> VecList n a -> b #foldr' :: (a -> b -> b) -> b -> VecList n a -> b #foldl :: (b -> a -> b) -> b -> VecList n a -> b #foldl' :: (b -> a -> b) -> b -> VecList n a -> b #foldr1 :: (a -> a -> a) -> VecList n a -> a #foldl1 :: (a -> a -> a) -> VecList n a -> a #toList :: VecList n a -> [a] #null :: VecList n a -> Bool #length :: VecList n a -> Int #elem :: Eq a => a -> VecList n a -> Bool #maximum :: Ord a => VecList n a -> a #minimum :: Ord a => VecList n a -> a #sum :: Num a => VecList n a -> a #product :: Num a => VecList n a -> a # Arity n => Traversable (VecList n) Source # Instance detailsDefined in Data.Vector.Fixed Methodstraverse :: Applicative f => (a -> f b) -> VecList n a -> f (VecList n b) #sequenceA :: Applicative f => VecList n (f a) -> f (VecList n a) #mapM :: Monad m => (a -> m b) -> VecList n a -> m (VecList n b) #sequence :: Monad m => VecList n (m a) -> m (VecList n a) # Arity n => Vector (VecList n) a Source # Instance detailsDefined in Data.Vector.Fixed Methodsconstruct :: Fun (Peano (Dim (VecList n))) a (VecList n a) Source #inspect :: VecList n a -> Fun (Peano (Dim (VecList n))) a b -> b Source #basicIndex :: VecList n a -> Int -> a Source # (Eq a, Arity n) => Eq (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed Methods(==) :: VecList n a -> VecList n a -> Bool #(/=) :: VecList n a -> VecList n a -> Bool # (Ord a, Arity n) => Ord (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed Methodscompare :: VecList n a -> VecList n a -> Ordering #(<) :: VecList n a -> VecList n a -> Bool #(<=) :: VecList n a -> VecList n a -> Bool #(>) :: VecList n a -> VecList n a -> Bool #(>=) :: VecList n a -> VecList n a -> Bool #max :: VecList n a -> VecList n a -> VecList n a #min :: VecList n a -> VecList n a -> VecList n a # (Show a, Arity n) => Show (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed MethodsshowsPrec :: Int -> VecList n a -> ShowS #show :: VecList n a -> String #showList :: [VecList n a] -> ShowS # (Arity n, Semigroup a) => Semigroup (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed Methods(<>) :: VecList n a -> VecList n a -> VecList n a #sconcat :: NonEmpty (VecList n a) -> VecList n a #stimes :: Integral b => b -> VecList n a -> VecList n a # (Arity n, Monoid a) => Monoid (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed Methodsmempty :: VecList n a #mappend :: VecList n a -> VecList n a -> VecList n a #mconcat :: [VecList n a] -> VecList n a # (Storable a, Arity n) => Storable (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed MethodssizeOf :: VecList n a -> Int #alignment :: VecList n a -> Int #peekElemOff :: Ptr (VecList n a) -> Int -> IO (VecList n a) #pokeElemOff :: Ptr (VecList n a) -> Int -> VecList n a -> IO () #peekByteOff :: Ptr b -> Int -> IO (VecList n a) #pokeByteOff :: Ptr b -> Int -> VecList n a -> IO () #peek :: Ptr (VecList n a) -> IO (VecList n a) #poke :: Ptr (VecList n a) -> VecList n a -> IO () # (Arity n, NFData a) => NFData (VecList n a) Source # Instance detailsDefined in Data.Vector.Fixed Methodsrnf :: VecList n a -> () # type Dim (VecList n) Source # Instance detailsDefined in Data.Vector.Fixed type Dim (VecList n) = n

data VecPeano (n :: PeanoNum) a where Source #

Standard GADT-based vector with statically known length parametrized by Peano numbers.

Constructors

 Nil :: VecPeano 'Z a Cons :: a -> VecPeano n a -> VecPeano ('S n) a

newtype Only a Source #

Single-element tuple.

Constructors

 Only a

#### Instances

Instances details

## Tuple synonyms

type Tuple2 a = (a, a) Source #

type Tuple3 a = (a, a, a) Source #

type Tuple4 a = (a, a, a, a) Source #

type Tuple5 a = (a, a, a, a, a) Source #