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
• basicUnsafeThaw
• basicLength
• basicUnsafeSlice
• basicUnsafeIndexM

O(1) Yield the length of the vector

O(1) Test whether a vector is empty

O(1) Safe indexing

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

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

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 the first n elements paired with the remainder without copying.

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

Since: vector-0.7.1

O(1) Empty vector

O(1) Vector with exactly one element

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

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

O(n) Apply function \(\max(n - 1, 0)\) times to an initial value, producing a vector of length \(\max(n, 0)\). Zeroth element will contain the initial value, that's why there is one less function application than the number of elements in the produced vector.

\( \underbrace{x, f (x), f (f (x)), \ldots}_{\max(0,n)\rm{~elements}} \)

Since: vector-0.7.1

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

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

O(n) Apply monadic function \(\max(n - 1, 0)\) times to an initial value, producing a vector of length \(\max(n, 0)\). Zeroth element will contain the initial value, that's why there is one less function application than the number of elements in the produced vector.

For non-monadic version see iterateN

Since: vector-0.12.0.0

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>

Execute the monadic action and freeze the resulting vectors.

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>

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>

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.

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.

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

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

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

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

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>

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>

O(n) Enumerate values from x to y.

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

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.

O(n) Prepend an element

O(n) Append an element

O(m+n) Concatenate two vectors

O(n) Concatenate all vectors in the list

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

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.

O(n) Reverse a vector

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'>

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

O(n) Map a function over a vector

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

Map a function over a vector and concatenate the results.

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

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

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

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

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

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

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

Zip three vectors with the given function.

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

O(min(m,n)) Zip two vectors

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

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

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

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

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

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

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

O(n) Drop repeated adjacent elements.

O(n) Drop elements when predicate returns Nothing

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

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

O(n) Yield the longest prefix of elements satisfying the predicate. Current implementation is not copy-free, unless the result vector is fused away.

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

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.

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.

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

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

O(n) Check if the vector contains an element

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

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

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

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

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.

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

O(n) Left fold

O(n) Left fold with strict accumulator

O(n) Right fold

O(n) Right fold with a strict accumulator

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

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

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

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

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

Examples

>>> import qualified Data.Vector as V
>>> V.all even $ V.fromList [2, 4, 12 :: Int]
True
>>> V.all even $ V.fromList [2, 4, 13 :: Int]
False
>>> V.all even (V.empty :: V.Vector Int)
True

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

Examples

>>> import qualified Data.Vector as V
>>> V.any even $ V.fromList [1, 3, 7 :: Int]
False
>>> V.any even $ V.fromList [3, 2, 13 :: Int]
True
>>> V.any even (V.empty :: V.Vector Int)
False

O(n) Check if all elements are True

Examples

>>> import qualified Data.Vector as V
>>> V.and $ V.fromList [True, False]
False
>>> V.and V.empty
True

O(n) Check if any element is True

Examples

>>> import qualified Data.Vector as V
>>> V.or $ V.fromList [True, False]
True
>>> V.or V.empty
False

O(n) Compute the sum of the elements

Examples

>>> import qualified Data.Vector as V
>>> V.sum $ V.fromList [300,20,1 :: Int]
321
>>> V.sum (V.empty :: V.Vector Int)
0

O(n) Compute the produce of the elements

Examples

>>> import qualified Data.Vector as V
>>> V.product $ V.fromList [1,2,3,4 :: Int]
24
>>> V.product (V.empty :: V.Vector Int)
1

O(n) Monadic fold

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

O(n) Monadic fold with strict accumulator

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

O(n) Monadic fold that discards the result

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

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

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

Evaluate each action and collect the results

Evaluate each action and discard the results

O(n) Prescan

prescanl f z = init . scanl f z

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

O(n) Prescan with strict accumulator

O(n) Scan

postscanl f z = tail . scanl f z

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

O(n) Scan with strict accumulator

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>

O(n) Haskell-style scan with strict accumulator

O(n) Scan over a vector with its index

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

O(n) Right-to-left prescan

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

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

O(n) Right-to-left scan

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

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

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

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

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

O(n) Convert a vector to a list

O(n) Convert a list to a vector

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

fromListN n xs = fromList (take n xs)

Examples

>>> import qualified Data.Vector as V
>>> V.fromListN 3 [1,2,3,4,5::Int]
[1,2,3]
>>> V.fromListN 3 [1::Int]
[1]

O(n) Convert different vector types

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

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

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

O(1) Convert a vector to a Bundle

O(n) Construct a vector from a Bundle

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

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

Construct a vector from a monadic initialiser.

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

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.

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.

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

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

cmpBy compare == cmp

Generic definition of showsPrec

Generic definition of readPrec

Note: uses ReadS

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