Portability  nonportable 

Stability  experimental 
Maintainer  Roman Leshchinskiy <rl@cse.unsw.edu.au> 
Safe Haskell  None 
Generic interface to pure vectors.
 class MVector (Mutable v) a => Vector v a where
 basicUnsafeFreeze :: PrimMonad m => Mutable v (PrimState m) a > m (v a)
 basicUnsafeThaw :: PrimMonad m => v a > m (Mutable v (PrimState m) a)
 basicLength :: v a > Int
 basicUnsafeSlice :: Int > Int > v a > v a
 basicUnsafeIndexM :: Monad m => v a > Int > m a
 basicUnsafeCopy :: PrimMonad m => Mutable v (PrimState m) a > v a > m ()
 elemseq :: v a > a > b > b
 type family Mutable v :: * > * > *
 length :: Vector v a => v a > Int
 null :: Vector v a => v a > Bool
 (!) :: Vector v a => v a > Int > a
 (!?) :: Vector v a => v a > Int > Maybe a
 head :: Vector v a => v a > a
 last :: Vector v a => v a > a
 unsafeIndex :: Vector v a => v a > Int > a
 unsafeHead :: Vector v a => v a > a
 unsafeLast :: Vector v a => v a > a
 indexM :: (Vector v a, Monad m) => v a > Int > m a
 headM :: (Vector v a, Monad m) => v a > m a
 lastM :: (Vector v a, Monad m) => v a > m a
 unsafeIndexM :: (Vector v a, Monad m) => v a > Int > m a
 unsafeHeadM :: (Vector v a, Monad m) => v a > m a
 unsafeLastM :: (Vector v a, Monad m) => v a > m a
 slice :: Vector v a => Int > Int > v a > v a
 init :: Vector v a => v a > v a
 tail :: Vector v a => v a > v a
 take :: Vector v a => Int > v a > v a
 drop :: Vector v a => Int > v a > v a
 splitAt :: Vector v a => Int > v a > (v a, v a)
 unsafeSlice :: Vector v a => Int > Int > v a > v a
 unsafeInit :: Vector v a => v a > v a
 unsafeTail :: Vector v a => v a > v a
 unsafeTake :: Vector v a => Int > v a > v a
 unsafeDrop :: Vector v a => Int > v a > v a
 empty :: Vector v a => v a
 singleton :: forall v a. Vector v a => a > v a
 replicate :: forall v a. Vector v a => Int > a > v a
 generate :: Vector v a => Int > (Int > a) > v a
 iterateN :: Vector v a => Int > (a > a) > a > v a
 replicateM :: (Monad m, Vector v a) => Int > m a > m (v a)
 generateM :: (Monad m, Vector v a) => Int > (Int > m a) > m (v a)
 create :: Vector v a => (forall s. ST s (Mutable v s a)) > v a
 unfoldr :: Vector v a => (b > Maybe (a, b)) > b > v a
 unfoldrN :: Vector v a => Int > (b > Maybe (a, b)) > b > v a
 constructN :: forall v a. Vector v a => Int > (v a > a) > v a
 constructrN :: forall v a. Vector v a => Int > (v a > a) > v a
 enumFromN :: (Vector v a, Num a) => a > Int > v a
 enumFromStepN :: forall v a. (Vector v a, Num a) => a > a > Int > v a
 enumFromTo :: (Vector v a, Enum a) => a > a > v a
 enumFromThenTo :: (Vector v a, Enum a) => a > a > a > v a
 cons :: forall v a. Vector v a => a > v a > v a
 snoc :: forall v a. Vector v a => v a > a > v a
 (++) :: Vector v a => v a > v a > v a
 concat :: Vector v a => [v a] > v a
 force :: Vector v a => v a > v a
 (//) :: Vector v a => v a > [(Int, a)] > v a
 update :: (Vector v a, Vector v (Int, a)) => v a > v (Int, a) > v a
 update_ :: (Vector v a, Vector v Int) => v a > v Int > v a > v a
 unsafeUpd :: Vector v a => v a > [(Int, a)] > v a
 unsafeUpdate :: (Vector v a, Vector v (Int, a)) => v a > v (Int, a) > v a
 unsafeUpdate_ :: (Vector v a, Vector v Int) => v a > v Int > v a > v a
 accum :: Vector v a => (a > b > a) > v a > [(Int, b)] > v a
 accumulate :: (Vector v a, Vector v (Int, b)) => (a > b > a) > v a > v (Int, b) > v a
 accumulate_ :: (Vector v a, Vector v Int, Vector v b) => (a > b > a) > v a > v Int > v b > v a
 unsafeAccum :: Vector v a => (a > b > a) > v a > [(Int, b)] > v a
 unsafeAccumulate :: (Vector v a, Vector v (Int, b)) => (a > b > a) > v a > v (Int, b) > v a
 unsafeAccumulate_ :: (Vector v a, Vector v Int, Vector v b) => (a > b > a) > v a > v Int > v b > v a
 reverse :: Vector v a => v a > v a
 backpermute :: (Vector v a, Vector v Int) => v a > v Int > v a
 unsafeBackpermute :: (Vector v a, Vector v Int) => v a > v Int > v a
 modify :: Vector v a => (forall s. Mutable v s a > ST s ()) > v a > v a
 indexed :: (Vector v a, Vector v (Int, a)) => v a > v (Int, a)
 map :: (Vector v a, Vector v b) => (a > b) > v a > v b
 imap :: (Vector v a, Vector v b) => (Int > a > b) > v a > v b
 concatMap :: (Vector v a, Vector v b) => (a > v b) > v a > v b
 mapM :: (Monad m, Vector v a, Vector v b) => (a > m b) > v a > m (v b)
 mapM_ :: (Monad m, Vector v a) => (a > m b) > v a > m ()
 forM :: (Monad m, Vector v a, Vector v b) => v a > (a > m b) > m (v b)
 forM_ :: (Monad m, Vector v a) => v a > (a > m b) > m ()
 zipWith :: (Vector v a, Vector v b, Vector v c) => (a > b > c) > v a > v b > v c
 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
 zipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (a > b > c > d > e) > v a > v b > v c > v d > v e
 zipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (a > b > c > d > e > f) > v a > v b > v c > v d > v e > v f
 zipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (a > b > c > d > e > f > g) > v a > v b > v c > v d > v e > v f > v g
 izipWith :: (Vector v a, Vector v b, Vector v c) => (Int > a > b > c) > v a > v b > v c
 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
 izipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (Int > a > b > c > d > e) > v a > v b > v c > v d > v e
 izipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (Int > a > b > c > d > e > f) > v a > v b > v c > v d > v e > v f
 izipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (Int > a > b > c > d > e > f > g) > v a > v b > v c > v d > v e > v f > v g
 zip :: (Vector v a, Vector v b, Vector v (a, b)) => v a > v b > v (a, b)
 zip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => v a > v b > v c > v (a, b, c)
 zip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => v a > v b > v c > v d > v (a, b, c, d)
 zip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => v a > v b > v c > v d > v e > v (a, b, c, d, e)
 zip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => v a > v b > v c > v d > v e > v f > v (a, b, c, d, e, f)
 zipWithM :: (Monad m, Vector v a, Vector v b, Vector v c) => (a > b > m c) > v a > v b > m (v c)
 zipWithM_ :: (Monad m, Vector v a, Vector v b) => (a > b > m c) > v a > v b > m ()
 unzip :: (Vector v a, Vector v b, Vector v (a, b)) => v (a, b) > (v a, v b)
 unzip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => v (a, b, c) > (v a, v b, v c)
 unzip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => v (a, b, c, d) > (v a, v b, v c, v d)
 unzip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => v (a, b, c, d, e) > (v a, v b, v c, v d, v e)
 unzip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => v (a, b, c, d, e, f) > (v a, v b, v c, v d, v e, v f)
 filter :: Vector v a => (a > Bool) > v a > v a
 ifilter :: Vector v a => (Int > a > Bool) > v a > v a
 filterM :: (Monad m, Vector v a) => (a > m Bool) > v a > m (v a)
 takeWhile :: Vector v a => (a > Bool) > v a > v a
 dropWhile :: Vector v a => (a > Bool) > v a > v a
 partition :: Vector v a => (a > Bool) > v a > (v a, v a)
 unstablePartition :: Vector v a => (a > Bool) > v a > (v a, v a)
 span :: Vector v a => (a > Bool) > v a > (v a, v a)
 break :: Vector v a => (a > Bool) > v a > (v a, v a)
 elem :: (Vector v a, Eq a) => a > v a > Bool
 notElem :: (Vector v a, Eq a) => a > v a > Bool
 find :: Vector v a => (a > Bool) > v a > Maybe a
 findIndex :: Vector v a => (a > Bool) > v a > Maybe Int
 findIndices :: (Vector v a, Vector v Int) => (a > Bool) > v a > v Int
 elemIndex :: (Vector v a, Eq a) => a > v a > Maybe Int
 elemIndices :: (Vector v a, Vector v Int, Eq a) => a > v a > v Int
 foldl :: Vector v b => (a > b > a) > a > v b > a
 foldl1 :: Vector v a => (a > a > a) > v a > a
 foldl' :: Vector v b => (a > b > a) > a > v b > a
 foldl1' :: Vector v a => (a > a > a) > v a > a
 foldr :: Vector v a => (a > b > b) > b > v a > b
 foldr1 :: Vector v a => (a > a > a) > v a > a
 foldr' :: Vector v a => (a > b > b) > b > v a > b
 foldr1' :: Vector v a => (a > a > a) > v a > a
 ifoldl :: Vector v b => (a > Int > b > a) > a > v b > a
 ifoldl' :: Vector v b => (a > Int > b > a) > a > v b > a
 ifoldr :: Vector v a => (Int > a > b > b) > b > v a > b
 ifoldr' :: Vector v a => (Int > a > b > b) > b > v a > b
 all :: Vector v a => (a > Bool) > v a > Bool
 any :: Vector v a => (a > Bool) > v a > Bool
 and :: Vector v Bool => v Bool > Bool
 or :: Vector v Bool => v Bool > Bool
 sum :: (Vector v a, Num a) => v a > a
 product :: (Vector v a, Num a) => v a > a
 maximum :: (Vector v a, Ord a) => v a > a
 maximumBy :: Vector v a => (a > a > Ordering) > v a > a
 minimum :: (Vector v a, Ord a) => v a > a
 minimumBy :: Vector v a => (a > a > Ordering) > v a > a
 minIndex :: (Vector v a, Ord a) => v a > Int
 minIndexBy :: Vector v a => (a > a > Ordering) > v a > Int
 maxIndex :: (Vector v a, Ord a) => v a > Int
 maxIndexBy :: Vector v a => (a > a > Ordering) > v a > Int
 foldM :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m a
 foldM' :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m a
 fold1M :: (Monad m, Vector v a) => (a > a > m a) > v a > m a
 fold1M' :: (Monad m, Vector v a) => (a > a > m a) > v a > m a
 foldM_ :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m ()
 foldM'_ :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m ()
 fold1M_ :: (Monad m, Vector v a) => (a > a > m a) > v a > m ()
 fold1M'_ :: (Monad m, Vector v a) => (a > a > m a) > v a > m ()
 sequence :: (Monad m, Vector v a, Vector v (m a)) => v (m a) > m (v a)
 sequence_ :: (Monad m, Vector v (m a)) => v (m a) > m ()
 prescanl :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v a
 prescanl' :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v a
 postscanl :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v a
 postscanl' :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v a
 scanl :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v a
 scanl' :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v a
 scanl1 :: Vector v a => (a > a > a) > v a > v a
 scanl1' :: Vector v a => (a > a > a) > v a > v a
 prescanr :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v b
 prescanr' :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v b
 postscanr :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v b
 postscanr' :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v b
 scanr :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v b
 scanr' :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v b
 scanr1 :: Vector v a => (a > a > a) > v a > v a
 scanr1' :: Vector v a => (a > a > a) > v a > v a
 toList :: Vector v a => v a > [a]
 fromList :: Vector v a => [a] > v a
 fromListN :: Vector v a => Int > [a] > v a
 convert :: (Vector v a, Vector w a) => v a > w a
 freeze :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > m (v a)
 thaw :: (PrimMonad m, Vector v a) => v a > m (Mutable v (PrimState m) a)
 copy :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > v a > m ()
 unsafeFreeze :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > m (v a)
 unsafeThaw :: (PrimMonad m, Vector v a) => v a > m (Mutable v (PrimState m) a)
 unsafeCopy :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > v a > m ()
 stream :: Vector v a => v a > Stream a
 unstream :: Vector v a => Stream a > v a
 streamR :: Vector v a => v a > Stream a
 unstreamR :: Vector v a => Stream a > v a
 new :: Vector v a => New v a > v a
 clone :: Vector v a => v a > New v a
 eq :: (Vector v a, Eq a) => v a > v a > Bool
 cmp :: (Vector v a, Ord a) => v a > v a > Ordering
 showsPrec :: (Vector v a, Show a) => Int > v a > ShowS
 readPrec :: (Vector v a, Read a) => ReadPrec (v a)
 gfoldl :: (Vector v a, Data a) => (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > v a > c (v a)
 dataCast :: (Vector v a, Data a, Typeable1 v, Typeable1 t) => (forall d. Data d => c (t d)) > Maybe (c (v a))
 mkType :: String > DataType
Immutable vectors
class MVector (Mutable v) a => Vector v a whereSource
Class of immutable vectors. Every immutable vector is associated with its
mutable version through the Mutable
type family. Methods of this class
should not be used directly. Instead, Data.Vector.Generic and other
Data.Vector modules provide safe and fusible wrappers.
Minimum complete implementation:
basicUnsafeFreeze :: PrimMonad m => Mutable v (PrimState m) a > m (v a)Source
Assumed complexity: O(1)
Unsafely convert a mutable vector to its immutable version without copying. The mutable vector may not be used after this operation.
basicUnsafeThaw :: PrimMonad m => v a > m (Mutable v (PrimState m) a)Source
Assumed complexity: O(1)
Unsafely convert an immutable vector to its mutable version without copying. The immutable vector may not be used after this operation.
basicLength :: v a > IntSource
Assumed complexity: O(1)
Yield the length of the vector.
:: Int  starting index 
> Int  length 
> v a  
> v a 
Assumed complexity: O(1)
Yield a slice of the vector without copying it. No range checks are performed.
basicUnsafeIndexM :: Monad m => v a > Int > m aSource
Assumed complexity: O(1)
Yield the element at the given position in a monad. No range checks are performed.
The monad allows us to be strict in the vector if we want. Suppose we had
unsafeIndex :: v a > Int > a
instead. Now, if we wanted to copy a vector, we'd do something like
copy mv v ... = ... unsafeWrite mv i (unsafeIndex v i) ...
For lazy vectors, the indexing would not be evaluated which means that we would retain a reference to the original vector in each element we write. This is not what we want!
With basicUnsafeIndexM
, we can do
copy mv v ... = ... case basicUnsafeIndexM v i of Box x > unsafeWrite mv i x ...
which does not have this problem because indexing (but not the returned element!) is evaluated immediately.
basicUnsafeCopy :: PrimMonad m => Mutable v (PrimState m) a > v a > m ()Source
Assumed complexity: O(n)
Copy an immutable vector into a mutable one. The two vectors must have the same length but this is not checked.
Instances of Vector
should redefine this method if they wish to support
an efficient block copy operation.
Default definition: copying basic on basicUnsafeIndexM
and
basicUnsafeWrite
.
elemseq :: v a > a > b > bSource
Evaluate a
as far as storing it in a vector would and yield b
.
The v a
argument only fixes the type and is not touched. The method is
only used for optimisation purposes. Thus, it is safe for instances of
Vector
to evaluate a
less than it would be when stored in a vector
although this might result in suboptimal code.
elemseq v x y = (singleton x `asTypeOf` v) `seq` y
Default defintion: a
is not evaluated at all
Prim a => Vector Vector a  
Storable a => Vector Vector a  
Vector Vector Bool  
Vector Vector Char  
Vector Vector Double  
Vector Vector Float  
Vector Vector Int  
Vector Vector Int8  
Vector Vector Int16  
Vector Vector Int32  
Vector Vector Int64  
Vector Vector Word  
Vector Vector Word8  
Vector Vector Word16  
Vector Vector Word32  
Vector Vector Word64  
Vector Vector ()  
Vector Vector a  
(RealFloat a, Unbox a) => Vector Vector (Complex a)  
(Unbox a, Unbox b) => Vector Vector (a, b)  
(Unbox a, Unbox b, Unbox c) => Vector Vector (a, b, c)  
(Unbox a, Unbox b, Unbox c, Unbox d) => Vector Vector (a, b, c, d)  
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Vector Vector (a, b, c, d, e)  
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Vector Vector (a, b, c, d, e, f) 
type family Mutable v :: * > * > *Source
Mutable v s a
is the mutable version of the pure vector type v a
with
the state token s
Accessors
Length information
Indexing
unsafeIndex :: Vector v a => v a > Int > aSource
O(1) Unsafe indexing without bounds checking
unsafeHead :: Vector v a => v a > aSource
O(1) First element without checking if the vector is empty
unsafeLast :: Vector v a => v a > aSource
O(1) Last element without checking if the vector is empty
Monadic indexing
indexM :: (Vector v a, Monad m) => v a > Int > m aSource
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 :: (Vector v a, Monad m) => v a > m aSource
O(1) First element of a vector in a monad. See indexM
for an
explanation of why this is useful.
lastM :: (Vector v a, Monad m) => v a > m aSource
O(1) Last element of a vector in a monad. See indexM
for an
explanation of why this is useful.
unsafeIndexM :: (Vector v a, Monad m) => v a > Int > m aSource
O(1) Indexing in a monad without bounds checks. See indexM
for an
explanation of why this is useful.
unsafeHeadM :: (Vector v a, Monad m) => v a > m aSource
O(1) First element in a monad without checking for empty vectors.
See indexM
for an explanation of why this is useful.
unsafeLastM :: (Vector v a, Monad m) => v a > m aSource
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)
:: Vector v a  
=> Int 

> Int 

> v a  
> v a 
O(1) Yield a slice of the vector without copying it. The vector must
contain at least i+n
elements.
init :: Vector v a => v a > v aSource
O(1) Yield all but the last element without copying. The vector may not be empty.
tail :: Vector v a => v a > v aSource
O(1) Yield all but the first element without copying. The vector may not be empty.
take :: Vector v a => Int > v a > v aSource
O(1) Yield the first n
elements without copying. The vector may
contain less than n
elements in which case it is returned unchanged.
drop :: Vector v a => Int > v a > v aSource
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.
:: Vector v a  
=> Int 

> Int 

> v a  
> v 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.
unsafeInit :: Vector v a => v a > v aSource
O(1) Yield all but the last element without copying. The vector may not be empty but this is not checked.
unsafeTail :: Vector v a => v a > v aSource
O(1) Yield all but the first element without copying. The vector may not be empty but this is not checked.
unsafeTake :: Vector v a => Int > v a > v aSource
O(1) Yield the first n
elements without copying. The vector must
contain at least n
elements but this is not checked.
unsafeDrop :: Vector v a => Int > v a > v aSource
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
replicate :: forall v a. Vector v a => Int > a > v aSource
O(n) Vector of the given length with the same value in each position
generate :: Vector v a => Int > (Int > a) > v aSource
O(n) Construct a vector of the given length by applying the function to each index
iterateN :: Vector v a => Int > (a > a) > a > v aSource
O(n) Apply function n times to value. Zeroth element is original value.
Monadic initialisation
replicateM :: (Monad m, Vector v a) => Int > m a > m (v a)Source
O(n) Execute the monadic action the given number of times and store the results in a vector.
generateM :: (Monad m, Vector v a) => Int > (Int > m a) > m (v a)Source
O(n) Construct a vector of the given length by applying the monadic action to each index
Unfolding
unfoldr :: Vector v a => (b > Maybe (a, b)) > b > v aSource
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,n1)) 10 = <10,9,8,7,6,5,4,3,2,1>
unfoldrN :: Vector v a => Int > (b > Maybe (a, b)) > b > v aSource
O(n) Construct a vector with at most n
by repeatedly applying the
generator function to the 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,n1)) 10 = <10,9,8>
constructN :: forall v a. Vector v a => Int > (v a > a) > v aSource
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 :: forall v a. Vector v a => Int > (v a > a) > v aSource
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 :: (Vector v a, Num a) => a > Int > v aSource
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 :: forall v a. (Vector v a, Num a) => a > a > Int > v aSource
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 :: (Vector v a, Enum a) => a > a > v aSource
O(n) Enumerate values from x
to y
.
WARNING: This operation can be very inefficient. If at all possible, use
enumFromN
instead.
enumFromThenTo :: (Vector v a, Enum a) => a > a > a > v aSource
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
Restricting memory usage
force :: Vector v a => v a > v aSource
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
:: Vector v a  
=> v a  initial vector (of length 
> [(Int, a)]  list of index/value pairs (of length 
> v 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>
:: (Vector v a, Vector v (Int, a))  
=> v a  initial vector (of length 
> v (Int, a)  vector of index/value pairs (of length 
> v 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>
:: (Vector v a, Vector v Int)  
=> v a  initial vector (of length 
> v Int  index vector (of length 
> v a  value vector (of length 
> v 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>
This function is useful for instances of Vector
that cannot store pairs.
Otherwise, update
is probably more convenient.
update_ xs is ys =update
xs (zip
is ys)
unsafeUpdate :: (Vector v a, Vector v (Int, a)) => v a > v (Int, a) > v aSource
Same as update
but without bounds checking.
unsafeUpdate_ :: (Vector v a, Vector v Int) => v a > v Int > v a > v aSource
Same as update_
but without bounds checking.
Accumulations
:: Vector v a  
=> (a > b > a)  accumulating function 
> v a  initial vector (of length 
> [(Int, b)]  list of index/value pairs (of length 
> v a 
O(m+n) For each pair (i,b)
from the list, replace the vector element
a
at position i
by f a b
.
accum (+) <5,9,2> [(2,4),(1,6),(0,3),(1,7)] = <5+3, 9+6+7, 2+4>
:: (Vector v a, Vector v (Int, b))  
=> (a > b > a)  accumulating function 
> v a  initial vector (of length 
> v (Int, b)  vector of index/value pairs (of length 
> v 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
.
accumulate (+) <5,9,2> <(2,4),(1,6),(0,3),(1,7)> = <5+3, 9+6+7, 2+4>
:: (Vector v a, Vector v Int, Vector v b)  
=> (a > b > a)  accumulating function 
> v a  initial vector (of length 
> v Int  index vector (of length 
> v b  value vector (of length 
> v 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>
This function is useful for instances of Vector
that cannot store pairs.
Otherwise, accumulate
is probably more convenient:
accumulate_ f as is bs =accumulate
f as (zip
is bs)
unsafeAccum :: Vector v a => (a > b > a) > v a > [(Int, b)] > v aSource
Same as accum
but without bounds checking.
unsafeAccumulate :: (Vector v a, Vector v (Int, b)) => (a > b > a) > v a > v (Int, b) > v aSource
Same as accumulate
but without bounds checking.
unsafeAccumulate_ :: (Vector v a, Vector v Int, Vector v b) => (a > b > a) > v a > v Int > v b > v aSource
Same as accumulate_
but without bounds checking.
Permutations
unsafeBackpermute :: (Vector v a, Vector v Int) => v a > v Int > v aSource
Same as backpermute
but without bounds checking.
Safe destructive updates
Elementwise operations
Indexing
indexed :: (Vector v a, Vector v (Int, a)) => v a > v (Int, a)Source
O(n) Pair each element in a vector with its index
Mapping
imap :: (Vector v a, Vector v b) => (Int > a > b) > v a > v bSource
O(n) Apply a function to every element of a vector and its index
concatMap :: (Vector v a, Vector v b) => (a > v b) > v a > v bSource
Map a function over a vector and concatenate the results.
Monadic mapping
mapM :: (Monad m, Vector v a, Vector v b) => (a > m b) > v a > m (v b)Source
O(n) Apply the monadic action to all elements of the vector, yielding a vector of results
mapM_ :: (Monad m, Vector v a) => (a > m b) > v a > m ()Source
O(n) Apply the monadic action to all elements of a vector and ignore the results
forM :: (Monad m, Vector v a, Vector v b) => v a > (a > m b) > m (v b)Source
O(n) Apply the monadic action to all elements of the vector, yielding a
vector of results. Equvalent to flip
.
mapM
forM_ :: (Monad m, Vector v a) => v 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_
Zipping
zipWith :: (Vector v a, Vector v b, Vector v c) => (a > b > c) > v a > v b > v cSource
O(min(m,n)) Zip two vectors with the given function.
zipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (a > b > c > d) > v a > v b > v c > v dSource
Zip three vectors with the given function.
zipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (a > b > c > d > e) > v a > v b > v c > v d > v eSource
zipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (a > b > c > d > e > f) > v a > v b > v c > v d > v e > v fSource
zipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (a > b > c > d > e > f > g) > v a > v b > v c > v d > v e > v f > v gSource
izipWith :: (Vector v a, Vector v b, Vector v c) => (Int > a > b > c) > v a > v b > v cSource
O(min(m,n)) Zip two vectors with a function that also takes the elements' indices.
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 dSource
izipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (Int > a > b > c > d > e) > v a > v b > v c > v d > v eSource
izipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (Int > a > b > c > d > e > f) > v a > v b > v c > v d > v e > v fSource
izipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (Int > a > b > c > d > e > f > g) > v a > v b > v c > v d > v e > v f > v gSource
zip :: (Vector v a, Vector v b, Vector v (a, b)) => v a > v b > v (a, b)Source
O(min(m,n)) Zip two vectors
zip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => v a > v b > v c > v (a, b, c)Source
zip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => v a > v b > v c > v d > v (a, b, c, d)Source
zip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => v a > v b > v c > v d > v e > v (a, b, c, d, e)Source
zip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => v a > v b > v c > v d > v e > v f > v (a, b, c, d, e, f)Source
Monadic zipping
zipWithM :: (Monad m, Vector v a, Vector v b, Vector v c) => (a > b > m c) > v a > v b > m (v c)Source
O(min(m,n)) Zip the two vectors with the monadic action and yield a vector of results
zipWithM_ :: (Monad m, Vector v a, Vector v b) => (a > b > m c) > v a > v b > m ()Source
O(min(m,n)) Zip the two vectors with the monadic action and ignore the results
Unzipping
unzip :: (Vector v a, Vector v b, Vector v (a, b)) => v (a, b) > (v a, v b)Source
O(min(m,n)) Unzip a vector of pairs.
unzip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => v (a, b, c) > (v a, v b, v c)Source
unzip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => v (a, b, c, d) > (v a, v b, v c, v d)Source
unzip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => v (a, b, c, d, e) > (v a, v b, v c, v d, v e)Source
unzip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => v (a, b, c, d, e, f) > (v a, v b, v c, v d, v e, v f)Source
Working with predicates
Filtering
filter :: Vector v a => (a > Bool) > v a > v aSource
O(n) Drop elements that do not satisfy the predicate
ifilter :: Vector v a => (Int > a > Bool) > v a > v aSource
O(n) Drop elements that do not satisfy the predicate which is applied to values and their indices
filterM :: (Monad m, Vector v a) => (a > m Bool) > v a > m (v a)Source
O(n) Drop elements that do not satisfy the monadic predicate
takeWhile :: Vector v a => (a > Bool) > v a > v aSource
O(n) Yield the longest prefix of elements satisfying the predicate without copying.
dropWhile :: Vector v a => (a > Bool) > v a > v aSource
O(n) Drop the longest prefix of elements that satisfy the predicate without copying.
Partitioning
partition :: Vector v a => (a > Bool) > v a > (v a, v 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 :: Vector v a => (a > Bool) > v a > (v a, v 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
.
span :: Vector v a => (a > Bool) > v a > (v a, v a)Source
O(n) Split the vector into the longest prefix of elements that satisfy the predicate and the rest without copying.
break :: Vector v a => (a > Bool) > v a > (v a, v 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
notElem :: (Vector v a, Eq a) => a > v a > BoolSource
O(n) Check if the vector does not contain an element (inverse of elem
)
find :: Vector v a => (a > Bool) > v a > Maybe aSource
O(n) Yield Just
the first element matching the predicate or Nothing
if no such element exists.
findIndex :: Vector v a => (a > Bool) > v a > Maybe IntSource
O(n) Yield Just
the index of the first element matching the predicate
or Nothing
if no such element exists.
findIndices :: (Vector v a, Vector v Int) => (a > Bool) > v a > v IntSource
O(n) Yield the indices of elements satisfying the predicate in ascending order.
elemIndex :: (Vector v a, Eq a) => a > v a > Maybe IntSource
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 :: (Vector v a, Vector v Int, Eq a) => a > v a > v IntSource
O(n) Yield the indices of all occurences of the given element in
ascending order. This is a specialised version of findIndices
.
Folding
foldl1' :: Vector v a => (a > a > a) > v a > aSource
O(n) Left fold on nonempty vectors with strict accumulator
foldr' :: Vector v a => (a > b > b) > b > v a > bSource
O(n) Right fold with a strict accumulator
foldr1' :: Vector v a => (a > a > a) > v a > aSource
O(n) Right fold on nonempty vectors with strict accumulator
ifoldl :: Vector v b => (a > Int > b > a) > a > v b > aSource
O(n) Left fold (function applied to each element and its index)
ifoldl' :: Vector v b => (a > Int > b > a) > a > v b > aSource
O(n) Left fold with strict accumulator (function applied to each element and its index)
ifoldr :: Vector v a => (Int > a > b > b) > b > v a > bSource
O(n) Right fold (function applied to each element and its index)
ifoldr' :: Vector v a => (Int > a > b > b) > b > v a > bSource
O(n) Right fold with strict accumulator (function applied to each element and its index)
Specialised folds
all :: Vector v a => (a > Bool) > v a > BoolSource
O(n) Check if all elements satisfy the predicate.
any :: Vector v a => (a > Bool) > v a > BoolSource
O(n) Check if any element satisfies the predicate.
maximum :: (Vector v a, Ord a) => v a > aSource
O(n) Yield the maximum element of the vector. The vector may not be empty.
maximumBy :: Vector v a => (a > a > Ordering) > v a > aSource
O(n) Yield the maximum element of the vector according to the given comparison function. The vector may not be empty.
minimum :: (Vector v a, Ord a) => v a > aSource
O(n) Yield the minimum element of the vector. The vector may not be empty.
minimumBy :: Vector v a => (a > a > Ordering) > v a > aSource
O(n) Yield the minimum element of the vector according to the given comparison function. The vector may not be empty.
minIndex :: (Vector v a, Ord a) => v a > IntSource
O(n) Yield the index of the minimum element of the vector. The vector may not be empty.
minIndexBy :: Vector v a => (a > a > Ordering) > v a > IntSource
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 :: (Vector v a, Ord a) => v a > IntSource
O(n) Yield the index of the maximum element of the vector. The vector may not be empty.
maxIndexBy :: Vector v a => (a > a > Ordering) > v a > IntSource
O(n) Yield the index of the maximum element of the vector according to the given comparison function. The vector may not be empty.
Monadic folds
foldM' :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m aSource
O(n) Monadic fold with strict accumulator
fold1M :: (Monad m, Vector v a) => (a > a > m a) > v a > m aSource
O(n) Monadic fold over nonempty vectors
fold1M' :: (Monad m, Vector v a) => (a > a > m a) > v a > m aSource
O(n) Monadic fold over nonempty vectors with strict accumulator
foldM_ :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m ()Source
O(n) Monadic fold that discards the result
foldM'_ :: (Monad m, Vector v b) => (a > b > m a) > a > v b > m ()Source
O(n) Monadic fold with strict accumulator that discards the result
fold1M_ :: (Monad m, Vector v a) => (a > a > m a) > v a > m ()Source
O(n) Monadic fold over nonempty vectors that discards the result
fold1M'_ :: (Monad m, Vector v a) => (a > a > m a) > v a > m ()Source
O(n) Monad fold over nonempty vectors with strict accumulator that discards the result
Monadic sequencing
sequence :: (Monad m, Vector v a, Vector v (m a)) => v (m a) > m (v a)Source
Evaluate each action and collect the results
sequence_ :: (Monad m, Vector v (m a)) => v (m a) > m ()Source
Evaluate each action and discard the results
Prefix sums (scans)
prescanl' :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v aSource
O(n) Prescan with strict accumulator
postscanl' :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v aSource
O(n) Scan with strict accumulator
scanl :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v aSource
O(n) Haskellstyle scan
scanl f z <x1,...,xn> = <y1,...,y(n+1)> where y1 = z yi = f y(i1) x(i1)
Example: scanl (+) 0 <1,2,3,4> = <0,1,3,6,10>
scanl' :: (Vector v a, Vector v b) => (a > b > a) > a > v b > v aSource
O(n) Haskellstyle scan with strict accumulator
scanl1 :: Vector v a => (a > a > a) > v a > v aSource
O(n) Scan over a nonempty vector
scanl f <x1,...,xn> = <y1,...,yn> where y1 = x1 yi = f y(i1) xi
scanl1' :: Vector v a => (a > a > a) > v a > v aSource
O(n) Scan over a nonempty vector with a strict accumulator
prescanr' :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v bSource
O(n) Righttoleft prescan with strict accumulator
postscanr :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v bSource
O(n) Righttoleft scan
postscanr' :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v bSource
O(n) Righttoleft scan with strict accumulator
scanr :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v bSource
O(n) Righttoleft Haskellstyle scan
scanr' :: (Vector v a, Vector v b) => (a > b > b) > b > v a > v bSource
O(n) Righttoleft Haskellstyle scan with strict accumulator
scanr1 :: Vector v a => (a > a > a) > v a > v aSource
O(n) Righttoleft scan over a nonempty vector
scanr1' :: Vector v a => (a > a > a) > v a > v aSource
O(n) Righttoleft scan over a nonempty vector with a strict accumulator
Conversions
Lists
Different vector types
Mutable vectors
freeze :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > m (v a)Source
O(n) Yield an immutable copy of the mutable vector.
thaw :: (PrimMonad m, Vector v a) => v a > m (Mutable v (PrimState m) a)Source
O(n) Yield a mutable copy of the immutable vector.
copy :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > v a > m ()Source
O(n) Copy an immutable vector into a mutable one. The two vectors must have the same length.
unsafeFreeze :: (PrimMonad m, Vector v a) => Mutable v (PrimState m) a > m (v 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 v a) => v a > m (Mutable v (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, Vector v a) => Mutable v (PrimState m) a > v 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.
Fusion support
Conversion to/from Streams
streamR :: Vector v a => v a > Stream aSource
O(1) Convert a vector to a Stream
, proceeding from right to left
unstreamR :: Vector v a => Stream a > v aSource
O(n) Construct a vector from a Stream
, proceeding from right to left
Recycling support
clone :: Vector v a => v a > New v aSource
Convert a vector to an initialiser which, when run, produces a copy of the vector.
Utilities
Comparisons
eq :: (Vector v a, Eq a) => v a > v a > BoolSource
O(n) Check if two vectors are equal. All Vector
instances are also
instances of Eq
and it is usually more appropriate to use those. This
function is primarily intended for implementing Eq
instances for new
vector types.
cmp :: (Vector v a, Ord a) => v a > v a > OrderingSource
O(n) Compare two vectors lexicographically. All Vector
instances are
also instances of Ord
and it is usually more appropriate to use those. This
function is primarily intended for implementing Ord
instances for new
vector types.
Show and Read
Data
and Typeable
gfoldl :: (Vector v a, Data a) => (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > v a > c (v a)Source