Copyright | (c) Roman Leshchinskiy 2008-2010 |
---|---|

License | BSD-style |

Maintainer | Roman Leshchinskiy <rl@cse.unsw.edu.au> |

Stability | experimental |

Portability | non-portable |

Safe Haskell | None |

Language | Haskell2010 |

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, Typeable v, Typeable 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 where Source

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 -> Int Source

*Assumed complexity: O(1)*

Yield the length of the vector.

*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 a Source

*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 -> b Source

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 -> a Source

*O(1)* Unsafe indexing without bounds checking

unsafeHead :: Vector v a => v a -> a Source

*O(1)* First element without checking if the vector is empty

unsafeLast :: Vector v a => v a -> a Source

*O(1)* Last element without checking if the vector is empty

## Monadic indexing

indexM :: (Vector v a, Monad m) => v 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 :: (Vector v a, Monad m) => v 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 :: (Vector v a, Monad m) => v 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 :: (Vector v a, Monad m) => v 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 :: (Vector v a, Monad m) => v 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 :: (Vector v a, Monad m) => v 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)

*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 a Source

*O(1)* Yield all but the last element without copying. The vector may not
be empty.

tail :: Vector v a => v a -> v a Source

*O(1)* Yield all but the first element without copying. The vector may not
be empty.

take :: Vector v a => Int -> v a -> v a Source

*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 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.

*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 a Source

*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 a Source

*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 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 :: Vector v a => Int -> v a -> v 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

replicate :: forall v a. Vector v a => Int -> a -> v a Source

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

generate :: Vector v a => Int -> (Int -> a) -> v a Source

*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 a Source

*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

constructN :: forall v a. Vector v a => Int -> (v a -> a) -> v 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 f <a,b,c>

constructrN :: forall v a. Vector v a => Int -> (v a -> a) -> v 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 f <c,b,a>

## Enumeration

enumFromN :: (Vector v a, Num a) => a -> Int -> v 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 :: forall v a. (Vector v a, Num a) => a -> a -> Int -> v 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 :: (Vector v a, Enum a) => a -> a -> v 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 :: (Vector v a, Enum a) => a -> a -> a -> v 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

## Restricting memory usage

force :: Vector v a => v a -> v 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

:: 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 a Source

Same as `update`

but without bounds checking.

unsafeUpdate_ :: (Vector v a, Vector v Int) => v a -> v Int -> v a -> v a Source

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 a Source

Same as `accum`

but without bounds checking.

unsafeAccumulate :: (Vector v a, Vector v (Int, b)) => (a -> b -> a) -> v a -> v (Int, b) -> v a Source

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 a Source

Same as `accumulate_`

but without bounds checking.

## Permutations

unsafeBackpermute :: (Vector v a, Vector v Int) => v a -> v Int -> v a Source

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 b Source

*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 b Source

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 c Source

*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 d Source

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 e Source

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 Source

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 Source

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

*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 d Source

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 Source

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 Source

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 Source

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 a Source

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

ifilter :: Vector v a => (Int -> a -> Bool) -> v a -> v a Source

*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 a Source

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

dropWhile :: Vector v a => (a -> Bool) -> v a -> v a Source

*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

elem :: (Vector v a, Eq a) => a -> v a -> Bool infix 4 Source

*O(n)* Check if the vector contains an element

notElem :: (Vector v a, Eq a) => a -> v a -> Bool infix 4 Source

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

)

findIndices :: (Vector v a, Vector v Int) => (a -> Bool) -> v a -> v Int Source

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

elemIndices :: (Vector v a, Vector v Int, Eq a) => a -> v a -> v 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

foldl1' :: Vector v a => (a -> a -> a) -> v a -> a Source

*O(n)* Left fold on non-empty vectors with strict accumulator

foldr' :: Vector v a => (a -> b -> b) -> b -> v a -> b Source

*O(n)* Right fold with a strict accumulator

foldr1' :: Vector v a => (a -> a -> a) -> v a -> a Source

*O(n)* Right fold on non-empty vectors with strict accumulator

ifoldl :: Vector v b => (a -> Int -> b -> a) -> a -> v b -> a Source

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

ifoldl' :: Vector v b => (a -> Int -> b -> a) -> a -> v b -> a Source

*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 -> b Source

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

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

*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 -> Bool Source

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

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

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

maximum :: (Vector v a, Ord a) => v a -> a Source

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

maximumBy :: Vector v a => (a -> a -> Ordering) -> v 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 :: (Vector v a, Ord a) => v a -> a Source

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

minimumBy :: Vector v a => (a -> a -> Ordering) -> v 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 :: (Vector v a, Ord a) => v a -> Int Source

*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 -> 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 :: (Vector v a, Ord a) => v a -> Int Source

*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 -> 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.

## Monadic folds

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

*O(n)* Monadic fold with strict accumulator

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

*O(n)* Monadic fold over non-empty vectors

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

*O(n)* Monadic fold over non-empty 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 non-empty vectors that discards the result

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

*O(n)* Monad fold over non-empty 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 a Source

*O(n)* Prescan with strict accumulator

postscanl' :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a Source

*O(n)* Scan with strict accumulator

scanl :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a Source

*O(n)* Haskell-style scan

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' :: (Vector v a, Vector v b) => (a -> b -> a) -> a -> v b -> v a Source

*O(n)* Haskell-style scan with strict accumulator

scanl1 :: Vector v a => (a -> a -> a) -> v a -> v 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' :: Vector v a => (a -> a -> a) -> v a -> v a Source

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

prescanr' :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b Source

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

postscanr :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b Source

*O(n)* Right-to-left scan

postscanr' :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b Source

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

scanr :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b Source

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

scanr' :: (Vector v a, Vector v b) => (a -> b -> b) -> b -> v a -> v b Source

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

scanr1 :: Vector v a => (a -> a -> a) -> v a -> v a Source

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

scanr1' :: Vector v a => (a -> a -> a) -> v a -> v a Source

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

*O(1)* Convert a vector to a `Stream`

, proceeding from right to left

unstreamR :: Vector v a => Stream a -> v a Source

*O(n)* Construct a vector from a `Stream`

, proceeding from right to left

## Recycling support

clone :: Vector v a => v a -> New v a Source

Convert a vector to an initialiser which, when run, produces a copy of the vector.

# Utilities

## Comparisons

## 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