RIO.Vector.Partial

Accessors

Indexing

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

O(1) Indexing

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

O(1) First element

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

O(1) Last element

Monadic indexing

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

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

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

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

Extracting subvectors

init :: Vector v a => v a -> v a

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

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

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

Modifying vectors

Bulk updates

(//)

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

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_

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)

Accumulations

accum

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

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_

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)

Permutations

backpermute

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>

Folding

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

O(n) Left fold on non-empty vectors

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

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

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

O(n) Right fold on non-empty vectors

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

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

Specialised folds

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

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

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

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

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

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

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

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

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

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

O(n) Monadic fold over non-empty vectors

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

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

fold1M_ :: (Monad m, Vector v a) => (a -> a -> m a) -> v a -> m ()

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 ()

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

Prefix sums (scans)

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

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

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

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

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

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

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