Boxed vectors, supporting efficient slicing.

Mutable boxed vectors keyed on the monad they live in (IO or ST s).

O(1) Yield the length of the vector.

O(1) Test whether a vector if empty

O(1) Indexing

O(1) Safe indexing

O(1) First element

O(1) Last element

O(1) Unsafe indexing without bounds checking

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

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

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.

O(1) First element of a vector in a monad. See indexM for an explanation of why this is useful.

O(1) Last element of a vector in a monad. See indexM for an explanation of why this is useful.

O(1) Indexing in a monad without bounds checks. See indexM for an explanation of why this is useful.

O(1) First element in a monad without checking for empty vectors. See indexM for an explanation of why this is useful.

O(1) Last element in a monad without checking for empty vectors. See indexM for an explanation of why this is useful.

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

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

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

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

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.

O(1) Yield a slice of the vector without copying. The vector must contain at least i+n elements but this is not checked.

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

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

O(1) Yield the first n elements without copying. The vector must contain at least n elements but this is not checked.

O(1) Yield all but the first n elements without copying. The vector must contain at least n elements but this is not checked.

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 n times to value. Zeroth element is original value.

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

Execute the monadic action and freeze the resulting vector.

 create (do { v <- new 2; write v 0 'a'; write v 1 'b' }) = <a,b>

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 by repeatedly applying the generator function to the a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

 unfoldrN 3 (\n -> Just (n,n-1)) 10 = <10,9,8>

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>

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>

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) 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(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>

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>

O(m+min(n1,n2)) For each index i from the index vector and the corresponding value a from the value vector, replace the element of the initial vector at position i by a.

 update_ <5,9,2,7>  <2,0,2> <1,3,8> = <3,9,8,7>

The function update provides the same functionality and is usually more convenient.

 update_ xs is ys = update xs (zip is ys)

Same as (//) but without bounds checking.

Same as update but without bounds checking.

Same as update_ but without bounds checking.

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>

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>

O(m+min(n1,n2)) For each index i from the index vector and the corresponding value b from the the value vector, replace the element of the initial vector at position i by f a b.

 accumulate_ (+) <5,9,2> <2,1,0,1> <4,6,3,7> = <5+3, 9+6+7, 2+4>

The function accumulate provides the same functionality and is usually more convenient.

 accumulate_ f as is bs = accumulate f as (zip is bs)

Same as accum but without bounds checking.

Same as accumulate but without bounds checking.

Same as accumulate_ but without bounds checking.

O(n) Reverse a vector

O(n) Yield the vector obtained by replacing each element i of the index vector by xs!i. This is equivalent to map (xs!) is but is often much more efficient.

 backpermute <a,b,c,d> <0,3,2,3,1,0> = <a,d,c,d,b,a>

Same as backpermute but without bounds checking.

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 all elements of a vector and ignore the results

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

Zip three vectors and their indices with the given function.

Elementwise pairing of array elements.

zip together three vectors into a vector of triples

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 the monadic action 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 elements that do not satisfy the monadic predicate

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

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 on non-empty vectors

O(n) Left fold with strict accumulator

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

O(n) Right fold

O(n) Right fold on non-empty vectors

O(n) Right fold with a strict accumulator

O(n) Right fold on non-empty vectors with 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.

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

O(n) Check if all elements are True

O(n) Check if any element is True

O(n) Compute the sum of the elements

O(n) Compute the produce of the elements

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

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

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

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

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

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

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

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

O(n) Monadic fold

O(n) Monadic fold with strict accumulator

O(n) Monadic fold over non-empty vectors

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

O(n) Monadic fold that discards the result

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

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

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

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 non-empty vector

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

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

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 non-empty vector

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

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)

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

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

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