vector-0.12.0.1: Efficient Arrays

Copyright(c) Roman Leshchinskiy 2008-2010
LicenseBSD-style
MaintainerRoman Leshchinskiy <rl@cse.unsw.edu.au>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Vector.Generic

Contents

Description

Generic interface to pure vectors.

Synopsis

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:

Methods

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.

basicUnsafeSlice Source #

Arguments

:: 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 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

Instances
Vector Vector a Source # 
Instance details

Defined in Data.Vector

Prim a => Vector Vector a Source # 
Instance details

Defined in Data.Vector.Primitive

Storable a => Vector Vector a Source # 
Instance details

Defined in Data.Vector.Storable

Vector Vector Bool Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Char Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Double Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Float Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Int Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Int8 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Int16 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Int32 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Int64 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Word Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Word8 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Word16 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Word32 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector Word64 Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Vector Vector () Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Unbox a => Vector Vector (Complex a) Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

(Unbox a, Unbox b) => Vector Vector (a, b) Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b) -> m (Vector (a, b)) Source #

basicUnsafeThaw :: PrimMonad m => Vector (a, b) -> m (Mutable Vector (PrimState m) (a, b)) Source #

basicLength :: Vector (a, b) -> Int Source #

basicUnsafeSlice :: Int -> Int -> Vector (a, b) -> Vector (a, b) Source #

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

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b) -> Vector (a, b) -> m () Source #

elemseq :: Vector (a, b) -> (a, b) -> b0 -> b0 Source #

(Unbox a, Unbox b, Unbox c) => Vector Vector (a, b, c) Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c) -> m (Vector (a, b, c)) Source #

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c) -> m (Mutable Vector (PrimState m) (a, b, c)) Source #

basicLength :: Vector (a, b, c) -> Int Source #

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c) -> Vector (a, b, c) Source #

basicUnsafeIndexM :: Monad m => Vector (a, b, c) -> Int -> m (a, b, c) Source #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c) -> Vector (a, b, c) -> m () Source #

elemseq :: Vector (a, b, c) -> (a, b, c) -> b0 -> b0 Source #

(Unbox a, Unbox b, Unbox c, Unbox d) => Vector Vector (a, b, c, d) Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d) -> m (Vector (a, b, c, d)) Source #

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d) -> m (Mutable Vector (PrimState m) (a, b, c, d)) Source #

basicLength :: Vector (a, b, c, d) -> Int Source #

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d) -> Vector (a, b, c, d) Source #

basicUnsafeIndexM :: Monad m => Vector (a, b, c, d) -> Int -> m (a, b, c, d) Source #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d) -> Vector (a, b, c, d) -> m () Source #

elemseq :: Vector (a, b, c, d) -> (a, b, c, d) -> b0 -> b0 Source #

(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Vector Vector (a, b, c, d, e) Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e) -> m (Vector (a, b, c, d, e)) Source #

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d, e) -> m (Mutable Vector (PrimState m) (a, b, c, d, e)) Source #

basicLength :: Vector (a, b, c, d, e) -> Int Source #

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d, e) -> Vector (a, b, c, d, e) Source #

basicUnsafeIndexM :: Monad m => Vector (a, b, c, d, e) -> Int -> m (a, b, c, d, e) Source #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e) -> Vector (a, b, c, d, e) -> m () Source #

elemseq :: Vector (a, b, c, d, e) -> (a, b, c, d, e) -> b0 -> b0 Source #

(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Vector Vector (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e, f) -> m (Vector (a, b, c, d, e, f)) Source #

basicUnsafeThaw :: PrimMonad m => Vector (a, b, c, d, e, f) -> m (Mutable Vector (PrimState m) (a, b, c, d, e, f)) Source #

basicLength :: Vector (a, b, c, d, e, f) -> Int Source #

basicUnsafeSlice :: Int -> Int -> Vector (a, b, c, d, e, f) -> Vector (a, b, c, d, e, f) Source #

basicUnsafeIndexM :: Monad m => Vector (a, b, c, d, e, f) -> Int -> m (a, b, c, d, e, f) Source #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (a, b, c, d, e, f) -> Vector (a, b, c, d, e, f) -> m () Source #

elemseq :: Vector (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> b0 -> b0 Source #

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

Instances
type Mutable Vector Source # 
Instance details

Defined in Data.Vector

type Mutable Vector Source # 
Instance details

Defined in Data.Vector.Primitive

type Mutable Vector Source # 
Instance details

Defined in Data.Vector.Storable

type Mutable Vector Source # 
Instance details

Defined in Data.Vector.Unboxed.Base

Accessors

Length information

length :: Vector v a => v a -> Int Source #

O(1) Yield the length of the vector

null :: Vector v a => v a -> Bool Source #

O(1) Test whether a vector is empty

Indexing

(!) :: Vector v a => v a -> Int -> a infixl 9 Source #

O(1) Indexing

(!?) :: Vector v a => v a -> Int -> Maybe a infixl 9 Source #

O(1) Safe indexing

head :: Vector v a => v a -> a Source #

O(1) First element

last :: Vector v a => v a -> a Source #

O(1) Last element

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)

slice Source #

Arguments

:: Vector v a 
=> Int

i starting index

-> Int

n length

-> 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 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.

splitAt :: Vector v a => Int -> v a -> (v a, v 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.

unsafeSlice Source #

Arguments

:: Vector v a 
=> Int

i starting index

-> Int

n length

-> 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 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

empty :: Vector v a => v a Source #

O(1) Empty vector

singleton :: forall v a. Vector v a => a -> v a Source #

O(1) Vector with exactly one element

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

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

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

create :: Vector v a => (forall s. ST s (Mutable v s a)) -> v 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, Vector v a) => (forall s. ST s (f (Mutable v s a))) -> f (v a) Source #

Execute the monadic action and freeze the resulting vectors.

Unfolding

unfoldr :: Vector v a => (b -> Maybe (a, b)) -> b -> v 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 :: Vector v a => Int -> (b -> Maybe (a, b)) -> b -> v 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>

unfoldrM :: (Monad m, Vector v a) => (b -> m (Maybe (a, b))) -> b -> m (v 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, Vector v a) => Int -> (b -> m (Maybe (a, b))) -> b -> m (v 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.

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

cons :: forall v a. Vector v a => a -> v a -> v a Source #

O(n) Prepend an element

snoc :: forall v a. Vector v a => v a -> a -> v a Source #

O(n) Append an element

(++) :: Vector v a => v a -> v a -> v a infixr 5 Source #

O(m+n) Concatenate two vectors

concat :: Vector v a => [v a] -> v a Source #

O(n) Concatenate all vectors in the list

concatNE :: Vector v a => NonEmpty (v a) -> v a Source #

O(n) Concatenate all vectors in the non-empty list

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

(//) Source #

Arguments

:: Vector v a 
=> v a

initial vector (of length m)

-> [(Int, a)]

list of index/value pairs (of length n)

-> 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>

update Source #

Arguments

:: (Vector v a, Vector v (Int, a)) 
=> v a

initial vector (of length m)

-> v (Int, a)

vector of index/value pairs (of length n)

-> 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>

update_ Source #

Arguments

:: (Vector v a, Vector v Int) 
=> v a

initial vector (of length m)

-> v Int

index vector (of length n1)

-> v a

value vector (of length n2)

-> 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)

unsafeUpd :: Vector v a => v a -> [(Int, a)] -> v a Source #

Same as (//) but without bounds checking.

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

accum Source #

Arguments

:: Vector v a 
=> (a -> b -> a)

accumulating function f

-> v a

initial vector (of length m)

-> [(Int, b)]

list of index/value pairs (of length n)

-> 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>

accumulate Source #

Arguments

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

accumulating function f

-> v a

initial vector (of length m)

-> v (Int, b)

vector of index/value pairs (of length n)

-> 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>

accumulate_ Source #

Arguments

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

accumulating function f

-> v a

initial vector (of length m)

-> v Int

index vector (of length n1)

-> v b

value vector (of length n2)

-> 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

reverse :: Vector v a => v a -> v a Source #

O(n) Reverse a vector

backpermute Source #

Arguments

:: (Vector v a, Vector v Int) 
=> v a

xs value vector

-> v Int

is index vector (of length n)

-> v a 

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>

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

Same as backpermute but without bounds checking.

Safe destructive updates

modify :: Vector v a => (forall s. Mutable v s a -> ST s ()) -> v a -> v 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 v a, Vector v (Int, a)) => v a -> v (Int, a) Source #

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

Mapping

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

O(n) Map a function over a vector

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

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

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

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

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

uniq :: (Vector v a, Eq a) => v a -> v a Source #

O(n) Drop repeated adjacent elements.

mapMaybe :: (Vector v a, Vector v b) => (a -> Maybe b) -> v a -> v b Source #

O(n) Drop elements when predicate returns Nothing

imapMaybe :: (Vector v a, Vector v b) => (Int -> a -> Maybe b) -> v a -> v b Source #

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

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)

find :: Vector v a => (a -> Bool) -> v a -> Maybe a Source #

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 Int Source #

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 Int Source #

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

elemIndex :: (Vector v a, Eq a) => a -> v 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 :: (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

foldl :: Vector v b => (a -> b -> a) -> a -> v b -> a Source #

O(n) Left fold

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

O(n) Left fold on non-empty vectors

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

O(n) Left fold with strict accumulator

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

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

O(n) Right fold on non-empty vectors

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.

and :: Vector v Bool => v Bool -> Bool Source #

O(n) Check if all elements are True

or :: Vector v Bool => v Bool -> Bool Source #

O(n) Check if any element is True

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

O(n) Compute the sum of the elements

product :: (Vector v a, Num a) => v a -> a Source #

O(n) Compute the produce of the elements

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

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

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

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

O(n) Monadic fold with strict accumulator

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

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

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

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

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

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

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

prescanl f z = init . scanl f z

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

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

postscanl f z = tail . scanl f z

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

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

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

O(n) Scan over a vector with its index

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

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

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

O(n) Right-to-left prescan

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

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

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

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

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

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

Conversions

Lists

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

O(n) Convert a vector to a list

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

O(n) Convert a list to a vector

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

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

fromListN n xs = fromList (take n xs)

Different vector types

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

O(n) Convert 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 Bundles

stream :: Vector v a => v a -> Bundle v a Source #

O(1) Convert a vector to a Bundle

unstream :: Vector v a => Bundle v a -> v a Source #

O(n) Construct a vector from a Bundle

streamR :: Vector v a => v a -> Bundle u a Source #

O(1) Convert a vector to a Bundle, proceeding from right to left

unstreamR :: Vector v a => Bundle v a -> v a Source #

O(n) Construct a vector from a Bundle, proceeding from right to left

Recycling support

new :: Vector v a => New v a -> v a Source #

Construct a vector from a monadic initialiser.

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

eq :: (Vector v a, Eq a) => v a -> v a -> Bool Source #

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 -> Ordering Source #

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.

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

O(n)

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

O(n)

Show and Read

showsPrec :: (Vector v a, Show a) => Int -> v a -> ShowS Source #

Generic definition of showsPrec

readPrec :: (Vector v a, Read a) => ReadPrec (v a) Source #

Generic definition of readPrec

liftShowsPrec :: Vector v a => (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> v a -> ShowS Source #

liftReadsPrec :: Vector v a => (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (v a) Source #

Note: uses ReadS

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 #

Generic definion of gfoldl that views a Vector as a list.

dataCast :: (Vector v a, Data a, Typeable v, Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (v a)) Source #