rio-0.1.9.2: A standard library for Haskell

RIO.Vector.Boxed

Description

Boxed Vector. Import as:

import qualified RIO.Vector.Boxed as VB
Synopsis

# Boxed vectors

data Vector a #

Boxed vectors, supporting efficient slicing.

Instances

data MVector s a #

Mutable boxed vectors keyed on the monad they live in (IO or ST s).

Instances

# Accessors

## Length information

length :: Vector a -> Int #

O(1) Yield the length of the vector

null :: Vector a -> Bool #

O(1) Test whether a vector is empty

## Indexing

(!?) :: Vector a -> Int -> Maybe a #

O(1) Safe indexing

## Extracting subvectors

Arguments

 :: Int i starting index -> Int n length -> Vector a -> Vector a

O(1) Yield a slice of the vector without copying it. The vector must contain at least i+n elements.

take :: Int -> Vector a -> Vector a #

O(1) Yield at the first n elements without copying. The vector may contain less than n elements in which case it is returned unchanged.

drop :: Int -> Vector a -> Vector a #

O(1) Yield all but the first n elements without copying. The vector may contain less than n elements in which case an empty vector is returned.

splitAt :: Int -> Vector a -> (Vector a, Vector a) #

O(1) Yield the first n elements paired with the remainder without copying.

Note that splitAt n v is equivalent to (take n v, drop n v) but slightly more efficient.

# Construction

## Initialisation

empty :: Vector a #

O(1) Empty vector

singleton :: a -> Vector a #

O(1) Vector with exactly one element

replicate :: Int -> a -> Vector a #

O(n) Vector of the given length with the same value in each position

generate :: Int -> (Int -> a) -> Vector a #

O(n) Construct a vector of the given length by applying the function to each index

iterateN :: Int -> (a -> a) -> a -> Vector a #

O(n) Apply function n times to value. Zeroth element is original value.

replicateM :: Monad m => Int -> m a -> m (Vector a) #

O(n) Execute the monadic action the given number of times and store the results in a vector.

generateM :: Monad m => Int -> (Int -> m a) -> m (Vector a) #

O(n) Construct a vector of the given length by applying the monadic action to each index

iterateNM :: Monad m => Int -> (a -> m a) -> a -> m (Vector a) #

O(n) Apply monadic function n times to value. Zeroth element is original value.

create :: (forall s. ST s (MVector s a)) -> Vector a #

Execute the monadic action and freeze the resulting vector.

create (do { v <- new 2; write v 0 'a'; write v 1 'b'; return v }) = <a,b>


createT :: Traversable f => (forall s. ST s (f (MVector s a))) -> f (Vector a) #

Execute the monadic action and freeze the resulting vectors.

## Unfolding

unfoldr :: (b -> Maybe (a, b)) -> b -> Vector a #

O(n) Construct a vector by repeatedly applying the generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

unfoldr (\n -> if n == 0 then Nothing else Just (n,n-1)) 10
= <10,9,8,7,6,5,4,3,2,1>

unfoldrN :: Int -> (b -> Maybe (a, b)) -> b -> Vector a #

O(n) Construct a vector with at most n elements by repeatedly applying the generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

unfoldrN 3 (\n -> Just (n,n-1)) 10 = <10,9,8>

unfoldrM :: Monad m => (b -> m (Maybe (a, b))) -> b -> m (Vector a) #

O(n) Construct a vector by repeatedly applying the monadic generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

unfoldrNM :: Monad m => Int -> (b -> m (Maybe (a, b))) -> b -> m (Vector a) #

O(n) Construct a vector by repeatedly applying the monadic generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

constructN :: Int -> (Vector a -> a) -> Vector a #

O(n) Construct a vector with n elements by repeatedly applying the generator function to the already constructed part of the vector.

constructN 3 f = let a = f <> ; b = f <a> ; c = f <a,b> in f <a,b,c>

constructrN :: Int -> (Vector a -> a) -> Vector a #

O(n) Construct a vector with n elements from right to left by repeatedly applying the generator function to the already constructed part of the vector.

constructrN 3 f = let a = f <> ; b = f<a> ; c = f <b,a> in f <c,b,a>

## Enumeration

enumFromN :: Num a => a -> Int -> Vector a #

O(n) Yield a vector of the given length containing the values x, x+1 etc. This operation is usually more efficient than enumFromTo.

enumFromN 5 3 = <5,6,7>

enumFromStepN :: Num a => a -> a -> Int -> Vector a #

O(n) Yield a vector of the given length containing the values x, x+y, x+y+y etc. This operations is usually more efficient than enumFromThenTo.

enumFromStepN 1 0.1 5 = <1,1.1,1.2,1.3,1.4>

enumFromTo :: Enum a => a -> a -> Vector a #

O(n) Enumerate values from x to y.

WARNING: This operation can be very inefficient. If at all possible, use enumFromN instead.

enumFromThenTo :: Enum a => a -> a -> a -> Vector a #

O(n) Enumerate values from x to y with a specific step z.

WARNING: This operation can be very inefficient. If at all possible, use enumFromStepN instead.

## Concatenation

cons :: a -> Vector a -> Vector a #

O(n) Prepend an element

snoc :: Vector a -> a -> Vector a #

O(n) Append an element

(++) :: Vector a -> Vector a -> Vector a infixr 5 #

O(m+n) Concatenate two vectors

concat :: [Vector a] -> Vector a #

O(n) Concatenate all vectors in the list

## Restricting memory usage

force :: Vector a -> Vector a #

O(n) Yield the argument but force it not to retain any extra memory, possibly by copying it.

This is especially useful when dealing with slices. For example:

force (slice 0 2 <huge vector>)

Here, the slice retains a reference to the huge vector. Forcing it creates a copy of just the elements that belong to the slice and allows the huge vector to be garbage collected.

# Modifying vectors

## Permutations

reverse :: Vector a -> Vector a #

O(n) Reverse a vector

## Safe destructive update

modify :: (forall s. MVector s a -> ST s ()) -> Vector a -> Vector a #

Apply a destructive operation to a vector. The operation will be performed in place if it is safe to do so and will modify a copy of the vector otherwise.

modify (\v -> write v 0 'x') (replicate 3 'a') = <'x','a','a'>


# Elementwise operations

## Indexing

indexed :: Vector a -> Vector (Int, a) #

O(n) Pair each element in a vector with its index

## Mapping

map :: (a -> b) -> Vector a -> Vector b #

O(n) Map a function over a vector

imap :: (Int -> a -> b) -> Vector a -> Vector b #

O(n) Apply a function to every element of a vector and its index

concatMap :: (a -> Vector b) -> Vector a -> Vector b #

Map a function over a vector and concatenate the results.

mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) #

O(n) Apply the monadic action to all elements of the vector, yielding a vector of results

imapM :: Monad m => (Int -> a -> m b) -> Vector a -> m (Vector b) #

O(n) Apply the monadic action to every element of a vector and its index, yielding a vector of results

mapM_ :: Monad m => (a -> m b) -> Vector a -> m () #

O(n) Apply the monadic action to all elements of a vector and ignore the results

imapM_ :: Monad m => (Int -> a -> m b) -> Vector a -> m () #

O(n) Apply the monadic action to every element of a vector and its index, ignoring the results

forM :: Monad m => Vector a -> (a -> m b) -> m (Vector b) #

O(n) Apply the monadic action to all elements of the vector, yielding a vector of results. Equivalent to flip mapM.

forM_ :: Monad m => Vector a -> (a -> m b) -> m () #

O(n) Apply the monadic action to all elements of a vector and ignore the results. Equivalent to flip mapM_.

## Zipping

zipWith :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #

O(min(m,n)) Zip two vectors with the given function.

zipWith3 :: (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d #

Zip three vectors with the given function.

zipWith4 :: (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e #

zipWith5 :: (a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f #

zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f -> Vector g #

izipWith :: (Int -> a -> b -> c) -> Vector a -> Vector b -> Vector c #

O(min(m,n)) Zip two vectors with a function that also takes the elements' indices.

izipWith3 :: (Int -> a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d #

Zip three vectors and their indices with the given function.

izipWith4 :: (Int -> a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e #

izipWith5 :: (Int -> a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f #

izipWith6 :: (Int -> a -> b -> c -> d -> e -> f -> g) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f -> Vector g #

zip :: Vector a -> Vector b -> Vector (a, b) #

Elementwise pairing of array elements.

zip3 :: Vector a -> Vector b -> Vector c -> Vector (a, b, c) #

zip together three vectors into a vector of triples

zip4 :: Vector a -> Vector b -> Vector c -> Vector d -> Vector (a, b, c, d) #

zip5 :: Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector (a, b, c, d, e) #

zip6 :: Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f -> Vector (a, b, c, d, e, f) #

zipWithM :: Monad m => (a -> b -> m c) -> Vector a -> Vector b -> m (Vector c) #

O(min(m,n)) Zip the two vectors with the monadic action and yield a vector of results

izipWithM :: Monad m => (Int -> a -> b -> m c) -> Vector a -> Vector b -> m (Vector c) #

O(min(m,n)) Zip the two vectors with a monadic action that also takes the element index and yield a vector of results

zipWithM_ :: Monad m => (a -> b -> m c) -> Vector a -> Vector b -> m () #

O(min(m,n)) Zip the two vectors with the monadic action and ignore the results

izipWithM_ :: Monad m => (Int -> a -> b -> m c) -> Vector a -> Vector b -> m () #

O(min(m,n)) Zip the two vectors with a monadic action that also takes the element index and ignore the results

## Unzipping

unzip :: Vector (a, b) -> (Vector a, Vector b) #

O(min(m,n)) Unzip a vector of pairs.

unzip3 :: Vector (a, b, c) -> (Vector a, Vector b, Vector c) #

unzip4 :: Vector (a, b, c, d) -> (Vector a, Vector b, Vector c, Vector d) #

unzip5 :: Vector (a, b, c, d, e) -> (Vector a, Vector b, Vector c, Vector d, Vector e) #

unzip6 :: Vector (a, b, c, d, e, f) -> (Vector a, Vector b, Vector c, Vector d, Vector e, Vector f) #

# Working with predicates

## Filtering

filter :: (a -> Bool) -> Vector a -> Vector a #

O(n) Drop elements that do not satisfy the predicate

ifilter :: (Int -> a -> Bool) -> Vector a -> Vector a #

O(n) Drop elements that do not satisfy the predicate which is applied to values and their indices

uniq :: Eq a => Vector a -> Vector a #

O(n) Drop repeated adjacent elements.

mapMaybe :: (a -> Maybe b) -> Vector a -> Vector b #

O(n) Drop elements when predicate returns Nothing

imapMaybe :: (Int -> a -> Maybe b) -> Vector a -> Vector b #

O(n) Drop elements when predicate, applied to index and value, returns Nothing

filterM :: Monad m => (a -> m Bool) -> Vector a -> m (Vector a) #

O(n) Drop elements that do not satisfy the monadic predicate

takeWhile :: (a -> Bool) -> Vector a -> Vector a #

O(n) Yield the longest prefix of elements satisfying the predicate without copying.

dropWhile :: (a -> Bool) -> Vector a -> Vector a #

O(n) Drop the longest prefix of elements that satisfy the predicate without copying.

## Partitioning

partition :: (a -> Bool) -> Vector a -> (Vector a, Vector a) #

O(n) Split the vector in two parts, the first one containing those elements that satisfy the predicate and the second one those that don't. The relative order of the elements is preserved at the cost of a sometimes reduced performance compared to unstablePartition.

unstablePartition :: (a -> Bool) -> Vector a -> (Vector a, Vector a) #

O(n) Split the vector in two parts, the first one containing those elements that satisfy the predicate and the second one those that don't. The order of the elements is not preserved but the operation is often faster than partition.

span :: (a -> Bool) -> Vector a -> (Vector a, Vector a) #

O(n) Split the vector into the longest prefix of elements that satisfy the predicate and the rest without copying.

break :: (a -> Bool) -> Vector a -> (Vector a, Vector a) #

O(n) Split the vector into the longest prefix of elements that do not satisfy the predicate and the rest without copying.

## Searching

elem :: Eq a => a -> Vector a -> Bool infix 4 #

O(n) Check if the vector contains an element

notElem :: Eq a => a -> Vector a -> Bool infix 4 #

O(n) Check if the vector does not contain an element (inverse of elem)

find :: (a -> Bool) -> Vector a -> Maybe a #

O(n) Yield Just the first element matching the predicate or Nothing if no such element exists.

findIndex :: (a -> Bool) -> Vector a -> Maybe Int #

O(n) Yield Just the index of the first element matching the predicate or Nothing if no such element exists.

findIndices :: (a -> Bool) -> Vector a -> Vector Int #

O(n) Yield the indices of elements satisfying the predicate in ascending order.

elemIndex :: Eq a => a -> Vector a -> Maybe Int #

O(n) Yield Just the index of the first occurence of the given element or Nothing if the vector does not contain the element. This is a specialised version of findIndex.

elemIndices :: Eq a => a -> Vector a -> Vector Int #

O(n) Yield the indices of all occurences of the given element in ascending order. This is a specialised version of findIndices.

# Folding

foldl :: (a -> b -> a) -> a -> Vector b -> a #

O(n) Left fold

foldl' :: (a -> b -> a) -> a -> Vector b -> a #

O(n) Left fold with strict accumulator

foldr :: (a -> b -> b) -> b -> Vector a -> b #

O(n) Right fold

foldr' :: (a -> b -> b) -> b -> Vector a -> b #

O(n) Right fold with a strict accumulator

ifoldl :: (a -> Int -> b -> a) -> a -> Vector b -> a #

O(n) Left fold (function applied to each element and its index)

ifoldl' :: (a -> Int -> b -> a) -> a -> Vector b -> a #

O(n) Left fold with strict accumulator (function applied to each element and its index)

ifoldr :: (Int -> a -> b -> b) -> b -> Vector a -> b #

O(n) Right fold (function applied to each element and its index)

ifoldr' :: (Int -> a -> b -> b) -> b -> Vector a -> b #

O(n) Right fold with strict accumulator (function applied to each element and its index)

## Specialised folds

all :: (a -> Bool) -> Vector a -> Bool #

O(n) Check if all elements satisfy the predicate.

any :: (a -> Bool) -> Vector a -> Bool #

O(n) Check if any element satisfies the predicate.

O(n) Check if all elements are True

O(n) Check if any element is True

sum :: Num a => Vector a -> a #

O(n) Compute the sum of the elements

product :: Num a => Vector a -> a #

O(n) Compute the produce of the elements

foldM :: Monad m => (a -> b -> m a) -> a -> Vector b -> m a #

ifoldM :: Monad m => (a -> Int -> b -> m a) -> a -> Vector b -> m a #

O(n) Monadic fold (action applied to each element and its index)

foldM' :: Monad m => (a -> b -> m a) -> a -> Vector b -> m a #

O(n) Monadic fold with strict accumulator

ifoldM' :: Monad m => (a -> Int -> b -> m a) -> a -> Vector b -> m a #

O(n) Monadic fold with strict accumulator (action applied to each element and its index)

foldM_ :: Monad m => (a -> b -> m a) -> a -> Vector b -> m () #

O(n) Monadic fold that discards the result

ifoldM_ :: Monad m => (a -> Int -> b -> m a) -> a -> Vector b -> m () #

O(n) Monadic fold that discards the result (action applied to each element and its index)

foldM'_ :: Monad m => (a -> b -> m a) -> a -> Vector b -> m () #

O(n) Monadic fold with strict accumulator that discards the result

ifoldM'_ :: Monad m => (a -> Int -> b -> m a) -> a -> Vector b -> m () #

O(n) Monadic fold with strict accumulator that discards the result (action applied to each element and its index)

sequence :: Monad m => Vector (m a) -> m (Vector a) #

Evaluate each action and collect the results

sequence_ :: Monad m => Vector (m a) -> m () #

Evaluate each action and discard the results

# Prefix sums (scans)

prescanl :: (a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Prescan

prescanl f z = init . scanl f z


Example: prescanl (+) 0 <1,2,3,4> = <0,1,3,6>

prescanl' :: (a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Prescan with strict accumulator

postscanl :: (a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Scan

postscanl f z = tail . scanl f z


Example: postscanl (+) 0 <1,2,3,4> = <1,3,6,10>

postscanl' :: (a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Scan with strict accumulator

scanl :: (a -> b -> a) -> a -> Vector b -> Vector a #

scanl f z <x1,...,xn> = <y1,...,y(n+1)>
where y1 = z
yi = f y(i-1) x(i-1)

Example: scanl (+) 0 <1,2,3,4> = <0,1,3,6,10>

scanl' :: (a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Haskell-style scan with strict accumulator

iscanl :: (Int -> a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Scan over a vector with its index

iscanl' :: (Int -> a -> b -> a) -> a -> Vector b -> Vector a #

O(n) Scan over a vector (strictly) with its index

prescanr :: (a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left prescan

prescanr f z = reverse . prescanl (flip f) z . reverse


prescanr' :: (a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left prescan with strict accumulator

postscanr :: (a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left scan

postscanr' :: (a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left scan with strict accumulator

scanr :: (a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left Haskell-style scan

scanr' :: (a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left Haskell-style scan with strict accumulator

iscanr :: (Int -> a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left scan over a vector with its index

iscanr' :: (Int -> a -> b -> b) -> b -> Vector a -> Vector b #

O(n) Right-to-left scan over a vector (strictly) with its index

# Conversions

## Lists

toList :: Vector a -> [a] #

O(n) Convert a vector to a list

fromList :: [a] -> Vector a #

O(n) Convert a list to a vector

fromListN :: Int -> [a] -> Vector a #

O(n) Convert the first n elements of a list to a vector

fromListN n xs = fromList (take n xs)


## Different vector types

convert :: (Vector v a, Vector w a) => v a -> w a #

O(n) Convert different vector types

## Mutable vectors

freeze :: PrimMonad m => MVector (PrimState m) a -> m (Vector a) #

O(n) Yield an immutable copy of the mutable vector.

thaw :: PrimMonad m => Vector a -> m (MVector (PrimState m) a) #

O(n) Yield a mutable copy of the immutable vector.

copy :: PrimMonad m => MVector (PrimState m) a -> Vector a -> m () #

O(n) Copy an immutable vector into a mutable one. The two vectors must have the same length.