vector-0.12.2.0: Efficient Arrays
Copyright (c) Roman Leshchinskiy 2008-2010 BSD-style Roman Leshchinskiy experimental non-portable None Haskell2010

Data.Vector

Description

A library for boxed vectors (that is, polymorphic arrays capable of holding any Haskell value). The vectors come in two flavours:

• mutable
• immutable

and support a rich interface of both list-like operations, and bulk array operations.

For unboxed arrays, use Data.Vector.Unboxed

Synopsis

# Boxed vectors

data Vector a Source #

Boxed vectors, supporting efficient slicing.

#### Instances

Instances details
 Source # Instance detailsDefined in Data.Vector Methods(>>=) :: Vector a -> (a -> Vector b) -> Vector b #(>>) :: Vector a -> Vector b -> Vector b #return :: a -> Vector a # Source # Instance detailsDefined in Data.Vector Methodsfmap :: (a -> b) -> Vector a -> Vector b #(<$) :: a -> Vector b -> Vector a # Source # Instance has same semantics as one for listsSince: 0.12.2.0 Instance detailsDefined in Data.Vector Methodsmfix :: (a -> Vector a) -> Vector a # Source # Since: 0.12.1.0 Instance detailsDefined in Data.Vector Methodsfail :: String -> Vector a # Source # Instance detailsDefined in Data.Vector Methodspure :: a -> Vector a #(<*>) :: Vector (a -> b) -> Vector a -> Vector b #liftA2 :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #(*>) :: Vector a -> Vector b -> Vector b #(<*) :: Vector a -> Vector b -> Vector a # Source # Instance detailsDefined in Data.Vector Methodsfold :: Monoid m => Vector m -> m #foldMap :: Monoid m => (a -> m) -> Vector a -> m #foldMap' :: Monoid m => (a -> m) -> Vector a -> m #foldr :: (a -> b -> b) -> b -> Vector a -> b #foldr' :: (a -> b -> b) -> b -> Vector a -> b #foldl :: (b -> a -> b) -> b -> Vector a -> b #foldl' :: (b -> a -> b) -> b -> Vector a -> b #foldr1 :: (a -> a -> a) -> Vector a -> a #foldl1 :: (a -> a -> a) -> Vector a -> a #toList :: Vector a -> [a] #null :: Vector a -> Bool #length :: Vector a -> Int #elem :: Eq a => a -> Vector a -> Bool #maximum :: Ord a => Vector a -> a #minimum :: Ord a => Vector a -> a #sum :: Num a => Vector a -> a #product :: Num a => Vector a -> a # Source # Instance detailsDefined in Data.Vector Methodstraverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) #sequenceA :: Applicative f => Vector (f a) -> f (Vector a) #mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) #sequence :: Monad m => Vector (m a) -> m (Vector a) # Source # Instance detailsDefined in Data.Vector MethodsliftEq :: (a -> b -> Bool) -> Vector a -> Vector b -> Bool # Source # Instance detailsDefined in Data.Vector MethodsliftCompare :: (a -> b -> Ordering) -> Vector a -> Vector b -> Ordering # Source # Instance detailsDefined in Data.Vector MethodsliftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Vector a) #liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Vector a] #liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Vector a) #liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Vector a] # Source # Instance detailsDefined in Data.Vector MethodsliftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Vector a -> ShowS #liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Vector a] -> ShowS # Source # Instance detailsDefined in Data.Vector Methodsmzip :: Vector a -> Vector b -> Vector (a, b) #mzipWith :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #munzip :: Vector (a, b) -> (Vector a, Vector b) # Source # Instance detailsDefined in Data.Vector Methodsempty :: Vector a #(<|>) :: Vector a -> Vector a -> Vector a #some :: Vector a -> Vector [a] #many :: Vector a -> Vector [a] # Source # Instance detailsDefined in Data.Vector Methodsmzero :: Vector a #mplus :: Vector a -> Vector a -> Vector a # Source # Since: 0.12.1.0 Instance detailsDefined in Data.Vector MethodsliftRnf :: (a -> ()) -> Vector a -> () # Source # Instance detailsDefined in Data.Vector MethodsbasicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) a -> m (Vector a) Source #basicUnsafeThaw :: PrimMonad m => Vector a -> m (Mutable Vector (PrimState m) a) Source #basicUnsafeSlice :: Int -> Int -> Vector a -> Vector a Source #basicUnsafeIndexM :: Monad m => Vector a -> Int -> m a Source #basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) a -> Vector a -> m () Source #elemseq :: Vector a -> a -> b -> b Source # IsList (Vector a) Source # Instance detailsDefined in Data.Vector Associated Typestype Item (Vector a) # MethodsfromList :: [Item (Vector a)] -> Vector a #fromListN :: Int -> [Item (Vector a)] -> Vector a #toList :: Vector a -> [Item (Vector a)] # Eq a => Eq (Vector a) Source # Instance detailsDefined in Data.Vector Methods(==) :: Vector a -> Vector a -> Bool #(/=) :: Vector a -> Vector a -> Bool # Data a => Data (Vector a) Source # Instance detailsDefined in Data.Vector Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector a -> c (Vector a) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector a) #toConstr :: Vector a -> Constr #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector a)) #gmapT :: (forall b. Data b => b -> b) -> Vector a -> Vector a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r #gmapQ :: (forall d. Data d => d -> u) -> Vector a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) # Ord a => Ord (Vector a) Source # Instance detailsDefined in Data.Vector Methodscompare :: Vector a -> Vector a -> Ordering #(<) :: Vector a -> Vector a -> Bool #(<=) :: Vector a -> Vector a -> Bool #(>) :: Vector a -> Vector a -> Bool #(>=) :: Vector a -> Vector a -> Bool #max :: Vector a -> Vector a -> Vector a #min :: Vector a -> Vector a -> Vector a # Read a => Read (Vector a) Source # Instance detailsDefined in Data.Vector MethodsreadsPrec :: Int -> ReadS (Vector a) #readList :: ReadS [Vector a] # Show a => Show (Vector a) Source # Instance detailsDefined in Data.Vector MethodsshowsPrec :: Int -> Vector a -> ShowS #show :: Vector a -> String #showList :: [Vector a] -> ShowS # Source # Instance detailsDefined in Data.Vector Methods(<>) :: Vector a -> Vector a -> Vector a #sconcat :: NonEmpty (Vector a) -> Vector a #stimes :: Integral b => b -> Vector a -> Vector a # Monoid (Vector a) Source # Instance detailsDefined in Data.Vector Methodsmappend :: Vector a -> Vector a -> Vector a #mconcat :: [Vector a] -> Vector a # NFData a => NFData (Vector a) Source # Instance detailsDefined in Data.Vector Methodsrnf :: Vector a -> () # type Mutable Vector Source # Instance detailsDefined in Data.Vector type Mutable Vector = MVector type Item (Vector a) Source # Instance detailsDefined in Data.Vector type Item (Vector a) = a data MVector s a Source # Mutable boxed vectors keyed on the monad they live in (IO or ST s). #### Instances Instances details  Source # Instance detailsDefined in Data.Vector.Mutable MethodsbasicLength :: MVector s a -> Int Source #basicUnsafeSlice :: Int -> Int -> MVector s a -> MVector s a Source #basicOverlaps :: MVector s a -> MVector s a -> Bool Source #basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) a) Source #basicInitialize :: PrimMonad m => MVector (PrimState m) a -> m () Source #basicUnsafeReplicate :: PrimMonad m => Int -> a -> m (MVector (PrimState m) a) Source #basicUnsafeRead :: PrimMonad m => MVector (PrimState m) a -> Int -> m a Source #basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) a -> Int -> a -> m () Source #basicClear :: PrimMonad m => MVector (PrimState m) a -> m () Source #basicSet :: PrimMonad m => MVector (PrimState m) a -> a -> m () Source #basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) a -> MVector (PrimState m) a -> m () Source #basicUnsafeMove :: PrimMonad m => MVector (PrimState m) a -> MVector (PrimState m) a -> m () Source #basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) a -> Int -> m (MVector (PrimState m) a) Source # # Accessors ## Length information length :: Vector a -> Int Source # O(1) Yield the length of the vector null :: Vector a -> Bool Source # O(1) Test whether a vector is empty ## Indexing (!) :: Vector a -> Int -> a Source # O(1) Indexing (!?) :: Vector a -> Int -> Maybe a Source # O(1) Safe indexing head :: Vector a -> a Source # O(1) First element last :: Vector a -> a Source # O(1) Last element unsafeIndex :: Vector a -> Int -> a Source # O(1) Unsafe indexing without bounds checking unsafeHead :: Vector a -> a Source # O(1) First element without checking if the vector is empty unsafeLast :: Vector a -> a Source # O(1) Last element without checking if the vector is empty ## Monadic indexing indexM :: Monad m => Vector a -> Int -> m a Source # O(1) Indexing in a monad. The monad allows operations to be strict in the vector when necessary. Suppose vector copying is implemented like this: copy mv v = ... write mv i (v ! i) ... For lazy vectors, v ! i would not be evaluated which means that mv would unnecessarily retain a reference to v in each element written. With indexM, copying can be implemented like this instead: copy mv v = ... do x <- indexM v i write mv i x Here, no references to v are retained because indexing (but not the elements) is evaluated eagerly. headM :: Monad m => Vector a -> m a Source # O(1) First element of a vector in a monad. See indexM for an explanation of why this is useful. lastM :: Monad m => Vector a -> m a Source # O(1) Last element of a vector in a monad. See indexM for an explanation of why this is useful. unsafeIndexM :: Monad m => Vector a -> Int -> m a Source # O(1) Indexing in a monad without bounds checks. See indexM for an explanation of why this is useful. unsafeHeadM :: Monad m => Vector a -> m a Source # O(1) First element in a monad without checking for empty vectors. See indexM for an explanation of why this is useful. unsafeLastM :: Monad m => Vector a -> m a Source # O(1) Last element in a monad without checking for empty vectors. See indexM for an explanation of why this is useful. ## Extracting subvectors (slicing) 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. init :: Vector a -> Vector a Source # O(1) Yield all but the last element without copying. The vector may not be empty. tail :: Vector a -> Vector a Source # O(1) Yield all but the first element without copying. The vector may not be empty. take :: Int -> Vector a -> Vector a Source # 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 Source # 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) Source # 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. Since: 0.7.1 uncons :: Vector a -> Maybe (a, Vector a) Source # O(1) Yield the head and tail of the vector, or Nothing if empty. Since: 0.12.2.0 unsnoc :: Vector a -> Maybe (Vector a, a) Source # O(1) Yield the last and init of the vector, or Nothing if empty. Since: 0.12.2.0 Arguments  :: Int i starting index -> Int n length -> Vector a -> Vector a O(1) Yield a slice of the vector without copying. The vector must contain at least i+n elements but this is not checked. O(1) Yield all but the last element without copying. The vector may not be empty but this is not checked. O(1) Yield all but the first element without copying. The vector may not be empty but this is not checked. unsafeTake :: Int -> Vector a -> Vector a Source # O(1) Yield the first n elements without copying. The vector must contain at least n elements but this is not checked. unsafeDrop :: Int -> Vector a -> Vector a Source # O(1) Yield all but the first n elements without copying. The vector must contain at least n elements but this is not checked. # Construction ## Initialisation O(1) Empty vector singleton :: a -> Vector a Source # O(1) Vector with exactly one element replicate :: Int -> a -> Vector a Source # O(n) Vector of the given length with the same value in each position generate :: Int -> (Int -> a) -> Vector a Source # O(n) Construct a vector of the given length by applying the function to each index iterateN :: Int -> (a -> a) -> a -> Vector a Source # O(n) Apply function $$\max(n - 1, 0)$$ times to an initial value, producing a vector of length $$\max(n, 0)$$. Zeroth element will contain the initial value, that's why there is one less function application than the number of elements in the produced vector. $$\underbrace{x, f (x), f (f (x)), \ldots}_{\max(0,n)\rm{~elements}}$$ ### Examples Expand >>> import qualified Data.Vector as V >>> V.iterateN 0 undefined undefined :: V.Vector String [] >>> V.iterateN 4 (\x -> x <> x) "Hi" ["Hi","HiHi","HiHiHiHi","HiHiHiHiHiHiHiHi"]  Since: 0.7.1 ## Monadic initialisation replicateM :: Monad m => Int -> m a -> m (Vector a) Source # 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) Source # 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) Source # O(n) Apply monadic function $$\max(n - 1, 0)$$ times to an initial value, producing a vector of length $$\max(n, 0)$$. Zeroth element will contain the initial value, that's why there is one less function application than the number of elements in the produced vector. For non-monadic version see iterateN Since: 0.12.0.0 create :: (forall s. ST s (MVector s a)) -> Vector a Source # 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) Source # Execute the monadic action and freeze the resulting vectors. ## Unfolding unfoldr :: (b -> Maybe (a, b)) -> b -> Vector a Source # 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 Source # 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> unfoldrExactN :: Int -> (b -> (a, b)) -> b -> Vector a Source # O(n) Construct a vector with exactly n elements by repeatedly applying the generator function to a seed. The generator function yields the next element and the new seed. unfoldrExactN 3 (\n -> (n,n-1)) 10 = <10,9,8> Since: 0.12.2.0 unfoldrM :: Monad m => (b -> m (Maybe (a, b))) -> b -> m (Vector a) Source # 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) Source # 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. unfoldrExactNM :: Monad m => Int -> (b -> m (a, b)) -> b -> m (Vector a) Source # O(n) Construct a vector with exactly n elements by repeatedly applying the monadic generator function to a seed. The generator function yields the next element and the new seed. Since: 0.12.2.0 constructN :: Int -> (Vector a -> a) -> Vector a Source # 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 <a,b,c> constructrN :: Int -> (Vector a -> a) -> Vector a Source # 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 <c,b,a> ## Enumeration enumFromN :: Num a => a -> Int -> Vector a Source # 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 Source # 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 Source # 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 Source # 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 Source # O(n) Prepend an element snoc :: Vector a -> a -> Vector a Source # O(n) Append an element (++) :: Vector a -> Vector a -> Vector a infixr 5 Source # O(m+n) Concatenate two vectors concat :: [Vector a] -> Vector a Source # O(n) Concatenate all vectors in the list ## Restricting memory usage force :: Vector a -> Vector a Source # 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 ## Bulk updates Arguments  :: Vector a initial vector (of length m) -> [(Int, a)] list of index/value pairs (of length n) -> Vector a O(m+n) For each pair (i,a) from the list, replace the vector element at position i by a. <5,9,2,7> // [(2,1),(0,3),(2,8)] = <3,9,8,7> Arguments  :: Vector a initial vector (of length m) -> Vector (Int, a) vector of index/value pairs (of length n) -> Vector a O(m+n) For each pair (i,a) from the vector of index/value pairs, replace the vector element at position i by a. update <5,9,2,7> <(2,1),(0,3),(2,8)> = <3,9,8,7> Arguments  :: Vector a initial vector (of length m) -> Vector Int index vector (of length n1) -> Vector a value vector (of length n2) -> Vector a O(m+min(n1,n2)) For each index i from the index vector and the corresponding value a from the value vector, replace the element of the initial vector at position i by a. update_ <5,9,2,7> <2,0,2> <1,3,8> = <3,9,8,7> The function update provides the same functionality and is usually more convenient. update_ xs is ys = update xs (zip is ys)  unsafeUpd :: Vector a -> [(Int, a)] -> Vector a Source # Same as (//) but without bounds checking. unsafeUpdate :: Vector a -> Vector (Int, a) -> Vector a Source # Same as update but without bounds checking. unsafeUpdate_ :: Vector a -> Vector Int -> Vector a -> Vector a Source # Same as update_ but without bounds checking. ## Accumulations Arguments  :: (a -> b -> a) accumulating function f -> Vector a initial vector (of length m) -> [(Int, b)] list of index/value pairs (of length n) -> Vector a O(m+n) For each pair (i,b) from the list, replace the vector element a at position i by f a b. #### Examples Expand >>> import qualified Data.Vector as V >>> V.accum (+) (V.fromList [1000.0,2000.0,3000.0]) [(2,4),(1,6),(0,3),(1,10)] [1003.0,2016.0,3004.0]  Arguments  :: (a -> b -> a) accumulating function f -> Vector a initial vector (of length m) -> Vector (Int, b) vector of index/value pairs (of length n) -> Vector a O(m+n) For each pair (i,b) from the vector of pairs, replace the vector element a at position i by f a b. #### Examples Expand >>> import qualified Data.Vector as V >>> V.accumulate (+) (V.fromList [1000.0,2000.0,3000.0]) (V.fromList [(2,4),(1,6),(0,3),(1,10)]) [1003.0,2016.0,3004.0]  Arguments  :: (a -> b -> a) accumulating function f -> Vector a initial vector (of length m) -> Vector Int index vector (of length n1) -> Vector b value vector (of length n2) -> Vector a O(m+min(n1,n2)) For each index i from the index vector and the corresponding value b from the the value vector, replace the element of the initial vector at position i by f a b. accumulate_ (+) <5,9,2> <2,1,0,1> <4,6,3,7> = <5+3, 9+6+7, 2+4> The function accumulate provides the same functionality and is usually more convenient. accumulate_ f as is bs = accumulate f as (zip is bs)  unsafeAccum :: (a -> b -> a) -> Vector a -> [(Int, b)] -> Vector a Source # Same as accum but without bounds checking. unsafeAccumulate :: (a -> b -> a) -> Vector a -> Vector (Int, b) -> Vector a Source # Same as accumulate but without bounds checking. unsafeAccumulate_ :: (a -> b -> a) -> Vector a -> Vector Int -> Vector b -> Vector a Source # Same as accumulate_ but without bounds checking. ## Permutations reverse :: Vector a -> Vector a Source # O(n) Reverse a vector O(n) Yield the vector obtained by replacing each element i of the index vector by xs!i. This is equivalent to map (xs!) is but is often much more efficient. backpermute <a,b,c,d> <0,3,2,3,1,0> = <a,d,c,d,b,a> Same as backpermute but without bounds checking. ## Safe destructive updates modify :: (forall s. MVector s a -> ST s ()) -> Vector a -> Vector a Source # 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) Source # O(n) Pair each element in a vector with its index ## Mapping map :: (a -> b) -> Vector a -> Vector b Source # O(n) Map a function over a vector imap :: (Int -> a -> b) -> Vector a -> Vector b Source # O(n) Apply a function to every element of a vector and its index concatMap :: (a -> Vector b) -> Vector a -> Vector b Source # Map a function over a vector and concatenate the results. ## Monadic mapping mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) Source # 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) Source # 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 () Source # 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 () Source # 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) Source # 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 () Source # O(n) Apply the monadic action to all elements of a vector and ignore the results. Equivalent to flip mapM_. iforM :: Monad m => Vector a -> (Int -> a -> m b) -> m (Vector b) Source # O(n) Apply the monadic action to all elements of the vector and their indices, yielding a vector of results. Equivalent to flip imapM. Since: 0.12.2.0 iforM_ :: Monad m => Vector a -> (Int -> a -> m b) -> m () Source # O(n) Apply the monadic action to all elements of the vector and their indices and ignore the results. Equivalent to flip imapM_. Since: 0.12.2.0 ## Zipping zipWith :: (a -> b -> c) -> Vector a -> Vector b -> Vector c Source # O(min(m,n)) Zip two vectors with the given function. zipWith3 :: (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d Source # Zip three vectors with the given function. zipWith4 :: (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e Source # zipWith5 :: (a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f Source # zipWith6 :: (a -> b -> c -> d -> e -> f -> g) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f -> Vector g Source # izipWith :: (Int -> a -> b -> c) -> Vector a -> Vector b -> Vector c Source # 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 Source # 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 Source # izipWith5 :: (Int -> a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f Source # izipWith6 :: (Int -> a -> b -> c -> d -> e -> f -> g) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f -> Vector g Source # zip :: Vector a -> Vector b -> Vector (a, b) Source # Elementwise pairing of array elements. zip3 :: Vector a -> Vector b -> Vector c -> Vector (a, b, c) Source # zip together three vectors into a vector of triples zip4 :: Vector a -> Vector b -> Vector c -> Vector d -> Vector (a, b, c, d) Source # zip5 :: Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector (a, b, c, d, e) Source # zip6 :: Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f -> Vector (a, b, c, d, e, f) Source # ## Monadic zipping zipWithM :: Monad m => (a -> b -> m c) -> Vector a -> Vector b -> m (Vector c) Source # 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) Source # 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 () Source # 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 () Source # 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) Source # O(min(m,n)) Unzip a vector of pairs. unzip3 :: Vector (a, b, c) -> (Vector a, Vector b, Vector c) Source # unzip4 :: Vector (a, b, c, d) -> (Vector a, Vector b, Vector c, Vector d) Source # unzip5 :: Vector (a, b, c, d, e) -> (Vector a, Vector b, Vector c, Vector d, Vector e) Source # unzip6 :: Vector (a, b, c, d, e, f) -> (Vector a, Vector b, Vector c, Vector d, Vector e, Vector f) Source # # Working with predicates ## Filtering filter :: (a -> Bool) -> Vector a -> Vector a Source # O(n) Drop elements that do not satisfy the predicate ifilter :: (Int -> a -> Bool) -> Vector a -> Vector a Source # O(n) Drop elements that do not satisfy the predicate which is applied to values and their indices filterM :: Monad m => (a -> m Bool) -> Vector a -> m (Vector a) Source # O(n) Drop elements that do not satisfy the monadic predicate uniq :: Eq a => Vector a -> Vector a Source # O(n) Drop repeated adjacent elements. mapMaybe :: (a -> Maybe b) -> Vector a -> Vector b Source # O(n) Drop elements when predicate returns Nothing imapMaybe :: (Int -> a -> Maybe b) -> Vector a -> Vector b Source # O(n) Drop elements when predicate, applied to index and value, returns Nothing mapMaybeM :: Monad m => (a -> m (Maybe b)) -> Vector a -> m (Vector b) Source # O(n) Apply monadic function to each element of vector and discard elements returning Nothing. Since: 0.12.2.0 imapMaybeM :: Monad m => (Int -> a -> m (Maybe b)) -> Vector a -> m (Vector b) Source # O(n) Apply monadic function to each element of vector and its index. Discards elements returning Nothing. Since: 0.12.2.0 catMaybes :: Vector (Maybe a) -> Vector a Source # O(n) Return a Vector of all the Just values. Since: 0.12.2.0 takeWhile :: (a -> Bool) -> Vector a -> Vector a Source # O(n) Yield the longest prefix of elements satisfying the predicate. Current implementation is not copy-free, unless the result vector is fused away. dropWhile :: (a -> Bool) -> Vector a -> Vector a Source # O(n) Drop the longest prefix of elements that satisfy the predicate without copying. ## Partitioning partition :: (a -> Bool) -> Vector a -> (Vector a, Vector a) Source # 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) Source # 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. partitionWith :: (a -> Either b c) -> Vector a -> (Vector b, Vector c) Source # O(n) Split the vector into two parts, the first one containing the Left elements and the second containing the Right elements. The relative order of the elements is preserved. Since: 0.12.1.0 span :: (a -> Bool) -> Vector a -> (Vector a, Vector a) Source # 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) Source # 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 Source # O(n) Check if the vector contains an element notElem :: Eq a => a -> Vector a -> Bool infix 4 Source # O(n) Check if the vector does not contain an element (inverse of elem) find :: (a -> Bool) -> Vector a -> Maybe a Source # O(n) Yield Just the first element matching the predicate or Nothing if no such element exists. findIndex :: (a -> Bool) -> Vector a -> Maybe Int Source # 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 Source # O(n) Yield the indices of elements satisfying the predicate in ascending order. elemIndex :: Eq a => a -> Vector a -> Maybe Int Source # 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 Source # 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 Source # O(n) Left fold foldl1 :: (a -> a -> a) -> Vector a -> a Source # O(n) Left fold on non-empty vectors foldl' :: (a -> b -> a) -> a -> Vector b -> a Source # O(n) Left fold with strict accumulator foldl1' :: (a -> a -> a) -> Vector a -> a Source # O(n) Left fold on non-empty vectors with strict accumulator foldr :: (a -> b -> b) -> b -> Vector a -> b Source # O(n) Right fold foldr1 :: (a -> a -> a) -> Vector a -> a Source # O(n) Right fold on non-empty vectors foldr' :: (a -> b -> b) -> b -> Vector a -> b Source # O(n) Right fold with a strict accumulator foldr1' :: (a -> a -> a) -> Vector a -> a Source # O(n) Right fold on non-empty vectors with strict accumulator ifoldl :: (a -> Int -> b -> a) -> a -> Vector b -> a Source # O(n) Left fold (function applied to each element and its index) ifoldl' :: (a -> Int -> b -> a) -> a -> Vector b -> a Source # O(n) Left fold with strict accumulator (function applied to each element and its index) ifoldr :: (Int -> a -> b -> b) -> b -> Vector a -> b Source # O(n) Right fold (function applied to each element and its index) ifoldr' :: (Int -> a -> b -> b) -> b -> Vector a -> b Source # O(n) Right fold with strict accumulator (function applied to each element and its index) foldMap :: Monoid m => (a -> m) -> Vector a -> m Source # O(n) Map each element of the structure to a monoid, and combine the results. It uses same implementation as corresponding method of Foldable type cless. Note it's implemented in terms of foldr and won't fuse with functions that traverse vector from left to right (map, generate, etc.). Since: 0.12.2.0 foldMap' :: Monoid m => (a -> m) -> Vector a -> m Source # O(n) foldMap which is strict in accumulator. It uses same implementation as corresponding method of Foldable type class. Note it's implemented in terms of foldl' so it fuses in most contexts. Since: 0.12.2.0 ## Specialised folds all :: (a -> Bool) -> Vector a -> Bool Source # O(n) Check if all elements satisfy the predicate. #### Examples Expand >>> import qualified Data.Vector as V >>> V.all even$ V.fromList [2, 4, 12 :: Int]
True
>>> V.all even $V.fromList [2, 4, 13 :: Int] False >>> V.all even (V.empty :: V.Vector Int) True  any :: (a -> Bool) -> Vector a -> Bool Source # O(n) Check if any element satisfies the predicate. #### Examples Expand >>> import qualified Data.Vector as V >>> V.any even$ V.fromList [1, 3, 7 :: Int]
False
>>> V.any even $V.fromList [3, 2, 13 :: Int] True >>> V.any even (V.empty :: V.Vector Int) False  O(n) Check if all elements are True #### Examples Expand >>> import qualified Data.Vector as V >>> V.and$ V.fromList [True, False]
False
>>> V.and V.empty
True


O(n) Check if any element is True

#### Examples

Expand
>>> import qualified Data.Vector as V
>>> V.or $V.fromList [True, False] True >>> V.or V.empty False  sum :: Num a => Vector a -> a Source # O(n) Compute the sum of the elements #### Examples Expand >>> import qualified Data.Vector as V >>> V.sum$ V.fromList [300,20,1 :: Int]
321
>>> V.sum (V.empty :: V.Vector Int)
0


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

O(n) Compute the produce of the elements

#### Examples

Expand
>>> import qualified Data.Vector as V
>>> V.product $V.fromList [1,2,3,4 :: Int] 24 >>> V.product (V.empty :: V.Vector Int) 1  maximum :: Ord a => Vector a -> a Source # O(n) Yield the maximum element of the vector. The vector may not be empty. #### Examples Expand >>> import qualified Data.Vector as V >>> V.maximum$ V.fromList [2.0, 1.0]
2.0


maximumBy :: (a -> a -> Ordering) -> Vector a -> a Source #

O(n) Yield the maximum element of the vector according to the given comparison function. The vector may not be empty.

minimum :: Ord a => Vector a -> a Source #

O(n) Yield the minimum element of the vector. The vector may not be empty.

#### Examples

Expand
>>> import qualified Data.Vector as V
>>> V.minimum \$ V.fromList [2.0, 1.0]
1.0


minimumBy :: (a -> a -> Ordering) -> Vector a -> a Source #

O(n) Yield the minimum element of the vector according to the given comparison function. The vector may not be empty.

minIndex :: Ord a => Vector a -> Int Source #

O(n) Yield the index of the minimum element of the vector. The vector may not be empty.

minIndexBy :: (a -> a -> Ordering) -> Vector a -> Int Source #

O(n) Yield the index of the minimum element of the vector according to the given comparison function. The vector may not be empty.

maxIndex :: Ord a => Vector a -> Int Source #

O(n) Yield the index of the maximum element of the vector. The vector may not be empty.

maxIndexBy :: (a -> a -> Ordering) -> Vector a -> Int Source #

O(n) Yield the index of the maximum element of the vector according to the given comparison function. The vector may not be empty.

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

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

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

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

O(n) Monadic fold with strict accumulator

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

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

fold1M :: Monad m => (a -> a -> m a) -> Vector a -> m a Source #

O(n) Monadic fold over non-empty vectors

fold1M' :: Monad m => (a -> a -> m a) -> Vector a -> m a Source #

O(n) Monadic fold over non-empty vectors with strict accumulator

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

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

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 () Source #

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

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

fold1M_ :: Monad m => (a -> a -> m a) -> Vector a -> m () Source #

fold1M'_ :: Monad m => (a -> a -> m a) -> Vector a -> m () Source #

O(n) Monadic fold over non-empty vectors with strict accumulator that discards the result

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

Evaluate each action and collect the results

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

Evaluate each action and discard the results

# Prefix sums (scans)

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

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 Source #

O(n) Prescan with strict accumulator

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

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 Source #

O(n) Scan with strict accumulator

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

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 Source #

O(n) Haskell-style scan with strict accumulator

scanl1 :: (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Scan over a non-empty vector

scanl f <x1,...,xn> = <y1,...,yn>
where y1 = x1
yi = f y(i-1) xi

scanl1' :: (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Scan over a non-empty vector with a strict accumulator

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

O(n) Scan over a vector with its index

Since: 0.12.0.0

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

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

Since: 0.12.0.0

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

O(n) Right-to-left prescan

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


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

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

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

O(n) Right-to-left scan

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

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

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

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

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

scanr1 :: (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Right-to-left scan over a non-empty vector

scanr1' :: (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Right-to-left scan over a non-empty vector with a strict accumulator

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

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

Since: 0.12.0.0

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

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

Since: 0.12.0.0

## Comparisons

eqBy :: (a -> b -> Bool) -> Vector a -> Vector b -> Bool Source #

O(n) Check if two vectors are equal using supplied equality predicate.

Since: 0.12.2.0

cmpBy :: (a -> b -> Ordering) -> Vector a -> Vector b -> Ordering Source #

O(n) Compare two vectors using supplied comparison function for vector elements. Comparison works same as for lists.

cmpBy compare == compare

Since: 0.12.2.0

# Conversions

## Lists

toList :: Vector a -> [a] Source #

O(n) Convert a vector to a list

fromList :: [a] -> Vector a Source #

O(n) Convert a list to a vector

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

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

fromListN n xs = fromList (take n xs)


## Arrays

fromArray :: Array a -> Vector a Source #

O(1) Convert an array to a vector.

Since: 0.12.2.0

toArray :: Vector a -> Array a Source #

O(n) Convert a vector to an array.

Since: 0.12.2.0

## Other vector types

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

O(n) Convert different vector types

## Mutable vectors

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

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

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

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

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

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

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

O(1) Unsafe convert a mutable vector to an immutable one without copying. The mutable vector may not be used after this operation.

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

O(1) Unsafely convert an immutable vector to a mutable one without copying. The immutable vector may not be used after this operation.

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

O(n) Copy an immutable vector into a mutable one. The two vectors must have the same length. This is not checked.