fixed-vector-0.5.1.2: 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.

Synopsis

# Vector type class

## Vector size

type family Dim v Source

Size of vector expressed as type-level natural.

data Z Source

Type level zero

Instances

 Typeable Z Arity Z Arity n => Index Z (S n)

data S n Source

Successor of n

Instances

 Typeable1 S Arity n => Index Z (S n) Arity n => Arity (S n) Index k n => Index (S k) (S n)

## Synonyms for small numerals

type N1 = S ZSource

type N2 = S N1Source

type N3 = S N2Source

type N4 = S N3Source

type N5 = S N4Source

type N6 = S N5Source

## Type class

class Arity (Dim v) => Vector v a whereSource

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
```

Methods

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

N-ary function for creation of vectors.

inspect :: v a -> Fun (Dim v) a b -> bSource

Deconstruction of vector.

basicIndex :: v a -> Int -> aSource

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

Instances

 RealFloat a => Vector Complex a Vector Empty a Vector Only a ~ * b a => Vector ((,) b) a 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`. Arity n => Vector (ContVec n) a Arity n => Vector (VecList n) a Arity n => Vector (Vec n) a (Arity n, Prim a) => Vector (Vec n) a Unbox n a => Vector (Vec n) a (Arity n, Storable a) => Vector (Vec n) a (~ * b a, ~ * c a) => Vector ((,,) b c) a (~ * b a, ~ * c a, ~ * d a) => Vector ((,,,) b c d) a (~ * b a, ~ * c a, ~ * d a, ~ * e a) => Vector ((,,,,) b c d e) a (~ * b a, ~ * c a, ~ * d a, ~ * e a, ~ * f a) => Vector ((,,,,,) b c d e f) a (~ * b a, ~ * c a, ~ * d a, ~ * e a, ~ * f a, ~ * g a) => Vector ((,,,,,,) b c d e f g) a

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

 Arity n => VectorN ContVec n a Arity n => VectorN VecList n a Arity n => VectorN Vec n a (Arity n, Prim a) => VectorN Vec n a Unbox n a => VectorN Vec n a (Arity n, Storable a) => VectorN Vec n a

class Arity n Source

Type class for handling n-ary functions.

Instances

 Arity Z Arity n => Arity (S n)

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

 Arity n => Monad (Fun n a) Arity n => Functor (Fun n a) Arity n => Applicative (Fun n a)

length :: forall v a. Arity (Dim v) => v a -> IntSource

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')
```

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)) = ...
```

Third way is to use variadic function `mkN`. It works similarly to `printf` except it produces result of type `ContVec` which should be converted to vector of desired type by `vector`:

````>>> ````vector \$ mkN 'a' 'b' 'c' :: (Char,Char,Char)
```('a','b','c')
```

Probably most generic way is to cons values to the `ContVec` and convert it vector of desired type using `vector`:

````>>> ````vector \$ 'a' <| 'b' <| 'c' <| empty :: (Char,Char,Char)
```('a','b','c')
```

mk0 :: (Vector v a, Dim v ~ Z) => v aSource

mk1 :: (Vector v a, Dim v ~ N1) => a -> v aSource

mk2 :: (Vector v a, Dim v ~ N2) => a -> a -> v aSource

mk3 :: (Vector v a, Dim v ~ N3) => a -> a -> a -> v aSource

mk4 :: (Vector v a, Dim v ~ N4) => a -> a -> a -> a -> v aSource

mk5 :: (Vector v a, Dim v ~ N5) => a -> a -> a -> a -> a -> v aSource

## Consing

data ContVec n a Source

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

Instances

 Arity n => VectorN ContVec n a Arity n => Make n a (ContVec n a) Arity n => Functor (ContVec n) Arity n => Applicative (ContVec n) Arity n => Foldable (ContVec n) Arity n => Traversable (ContVec n) Arity n => Vector (ContVec n) a

Create empty vector.

vector :: (Vector v a, Dim v ~ n) => ContVec n a -> v aSource

Convert continuation to the vector.

(<|) :: a -> ContVec n a -> ContVec (S n) aSource

Cons value to continuation based vector.

class Make n a r Source

Type class for variadic vector constructors.

Instances

 Arity n => Make n a (ContVec n a) (~ * a' a, Make (S n) a r) => Make n a' (a -> r)

mkN :: Make (S Z) a r => a -> rSource

Variadic vector constructor. Resulting vector should be converted from `ContVec` using `vector` function. For example:

````>>> ````vector \$ mkN 'a' 'b' 'c' :: (Char,Char,Char)
```('a','b','c')
```

## Functions

replicate :: Vector v a => a -> v aSource

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, Monad m) => m a -> m (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 aSource

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 :: (Monad m, Vector v a) => (Int -> m a) -> m (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 aSource

Unfold vector.

basis :: (Vector v a, Num a) => Int -> v aSource

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, Dim v ~ S n) => v a -> aSource

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 ~ S (Dim w)) => v a -> w aSource

Tail of vector.

Examples:

````>>> ````import Data.Complex
````>>> ````tail (1,2,3) :: Complex Double
```2.0 :+ 3.0
```

cons :: (Vector v a, Vector w a, S (Dim v) ~ Dim w) => a -> v a -> w aSource

Cons element to the vector

snoc :: (Vector v a, Vector w a, S (Dim v) ~ Dim w) => a -> v a -> w aSource

Append element to the vector

reverse :: Vector v a => v a -> v aSource

Reverse order of elements in the vector

## Indexing & lenses

class Index k n Source

Type class for indexing of vector when index value is known at compile time.

Instances

 Arity n => Index Z (S n) Index k n => Index (S k) (S n)

(!) :: Vector v a => v a -> Int -> aSource

Retrieve vector's element at index. Generic implementation is O(n) but more efficient one is used when possible.

index :: (Vector v a, Index k (Dim v)) => v a -> k -> aSource

Get element from vector at statically known index

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, Index k (Dim v), Functor f) => 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 -> BoolSource

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 -> OrderingSource

Lexicographic ordering of two vectors.

## Maps

map :: (Vector v a, Vector v b) => (a -> b) -> v a -> v bSource

Map over vector

mapM :: (Vector v a, Vector v b, Monad m) => (a -> m b) -> v a -> m (v b)Source

mapM_ :: (Vector v a, Monad m) => (a -> m b) -> v a -> m ()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 bSource

Apply function to every element of the vector and its index.

imapM :: (Vector v a, Vector v b, Monad m) => (Int -> a -> m b) -> v a -> m (v b)Source

Apply monadic function to every element of the vector and its index.

imapM_ :: (Vector v a, Monad m) => (Int -> a -> m b) -> v a -> m ()Source

Apply monadic function to every element of the vector and its index and discard result.

sequence :: (Vector v a, Vector v (m a), Monad m) => v (m a) -> m (v a)Source

Evaluate every action in the vector from left to right.

sequence_ :: (Vector v (m a), Monad m) => v (m a) -> m ()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`.

# Folding

foldl :: Vector v a => (b -> a -> b) -> b -> v a -> bSource

Left fold over vector

foldr :: Vector v a => (a -> b -> b) -> b -> v a -> bSource

Right fold over vector

foldl1 :: (Vector v a, Dim v ~ S n) => (a -> a -> a) -> v a -> aSource

Left fold over vector

fold :: (Vector v m, Monoid m) => v m -> mSource

Combine the elements of a structure using a monoid. Similar to `fold`

foldMap :: (Vector v a, Monoid m) => (a -> m) -> v a -> mSource

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 -> bSource

Left fold over vector. Function is applied to each element and its index.

ifoldr :: Vector v a => (Int -> a -> b -> b) -> b -> v a -> bSource

Left fold over vector

foldM :: (Vector v a, Monad m) => (b -> a -> m b) -> b -> v a -> m bSource

ifoldM :: (Vector v a, Monad m) => (b -> Int -> a -> m b) -> b -> v a -> m bSource

Left monadic fold over vector. Function is applied to each element and its index.

## Special folds

sum :: (Vector v a, Num a) => v a -> aSource

Sum all elements in the vector.

maximum :: (Vector v a, Dim v ~ S n, Ord a) => v a -> aSource

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, Dim v ~ S n, Ord a) => v a -> aSource

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 -> BoolSource

Conjunction of all elements of a vector.

or :: Vector v Bool => v Bool -> BoolSource

Disjunction of all elements of a vector.

all :: Vector v a => (a -> Bool) -> v a -> BoolSource

Determines whether all elements of vector satisfy predicate.

any :: Vector v a => (a -> Bool) -> v a -> BoolSource

Determines whether any of element of vector satisfy predicate.

# Zips

zipWith :: (Vector v a, Vector v b, Vector v c) => (a -> b -> c) -> v a -> v b -> v cSource

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]
```

zipWithM :: (Vector v a, Vector v b, Vector v c, Monad m) => (a -> b -> m c) -> v a -> v b -> m (v c)Source

Zip two vector together using monadic function.

izipWith :: (Vector v a, Vector v b, Vector v c) => (Int -> a -> b -> c) -> v a -> v b -> v cSource

Zip two vector together using function which takes element index as well.

izipWithM :: (Vector v a, Vector v b, Vector v c, Monad m) => (Int -> a -> b -> m c) -> v a -> v b -> m (v c)Source

Zip two vector together using monadic function which takes element index as well..

# Conversion

convert :: (Vector v a, Vector w a, Dim v ~ Dim w) => v a -> w aSource

Convert between different vector types

toList :: Vector v a => v a -> [a]Source

Convert vector to the list

fromList :: Vector v a => [a] -> v aSource

Create vector form list. Will throw error if list is shorter than resulting vector.

fromList' :: Vector v a => [a] -> v aSource

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

data VecList n a whereSource

Vector based on the lists. Not very useful by itself but is necessary for implementation.

Constructors

 Nil :: VecList Z a Cons :: a -> VecList n a -> VecList (S n) a

Instances

 Typeable2 VecList Arity n => VectorN VecList n a Arity n => Functor (VecList n) Arity n => Applicative (VecList n) Arity n => Foldable (VecList n) Arity n => Traversable (VecList n) Arity n => Vector (VecList n) a (Eq a, Arity n) => Eq (VecList n a) (Ord a, Arity n) => Ord (VecList n a) (Show a, Arity n) => Show (VecList n a)

newtype Only a Source

Single-element tuple.

Constructors

 Only a

Instances

 Functor Only Typeable1 Only Foldable Only Traversable Only Vector Only a Eq a => Eq (Only a) Data a => Data (Only a) Ord a => Ord (Only a) Show a => Show (Only a)

data Empty a Source

Empty tuple.

Constructors

 Empty

Instances

 Functor Empty Typeable1 Empty Foldable Empty Traversable Empty Vector Empty a Data a => Data (Empty a)

## 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