rio-0.1.22.0: A standard library for Haskell

Safe Haskell | Safe-Inferred
Language | Haskell2010

RIO.Vector.Storable.Partial

Contents

- Accessors
  - Indexing
  - Monadic indexing
  - Extracting subvectors
- Modifying vectors
  - Bulk updates
  - Accumulations
  - Permutations
- Folding
  - Specialised folds
  - Monadic folds
- Prefix sums (scans)

Description

Storable `Vector` partial functions. Import as:

    import qualified RIO.Vector.Storable.Partial as VS'

Synopsis

- (!) :: Storable a => Vector a -> Int -> a
- head :: Storable a => Vector a -> a
- last :: Storable a => Vector a -> a
- indexM :: (Storable a, Monad m) => Vector a -> Int -> m a
- headM :: (Storable a, Monad m) => Vector a -> m a
- lastM :: (Storable a, Monad m) => Vector a -> m a
- init :: Storable a => Vector a -> Vector a
- tail :: Storable a => Vector a -> Vector a
- (//) :: Storable a => Vector a -> [(Int, a)] -> Vector a
- update_ :: Storable a => Vector a -> Vector Int -> Vector a -> Vector a
- accum :: Storable a => (a -> b -> a) -> Vector a -> [(Int, b)] -> Vector a
- accumulate_ :: (Storable a, Storable b) => (a -> b -> a) -> Vector a -> Vector Int -> Vector b -> Vector a
- backpermute :: Storable a => Vector a -> Vector Int -> Vector a
- foldl1 :: Storable a => (a -> a -> a) -> Vector a -> a
- foldl1' :: Storable a => (a -> a -> a) -> Vector a -> a
- foldr1 :: Storable a => (a -> a -> a) -> Vector a -> a
- foldr1' :: Storable a => (a -> a -> a) -> Vector a -> a
- maximum :: (Storable a, Ord a) => Vector a -> a
- maximumBy :: Storable a => (a -> a -> Ordering) -> Vector a -> a
- minimum :: (Storable a, Ord a) => Vector a -> a
- minimumBy :: Storable a => (a -> a -> Ordering) -> Vector a -> a
- minIndex :: (Storable a, Ord a) => Vector a -> Int
- minIndexBy :: Storable a => (a -> a -> Ordering) -> Vector a -> Int
- maxIndex :: (Storable a, Ord a) => Vector a -> Int
- maxIndexBy :: Storable a => (a -> a -> Ordering) -> Vector a -> Int
- fold1M :: (Monad m, Storable a) => (a -> a -> m a) -> Vector a -> m a
- fold1M' :: (Monad m, Storable a) => (a -> a -> m a) -> Vector a -> m a
- fold1M_ :: (Monad m, Storable a) => (a -> a -> m a) -> Vector a -> m ()
- fold1M'_ :: (Monad m, Storable a) => (a -> a -> m a) -> Vector a -> m ()
- scanl1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a
- scanl1' :: Storable a => (a -> a -> a) -> Vector a -> Vector a
- scanr1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a
- scanr1' :: Storable a => (a -> a -> a) -> Vector a -> Vector a

# Accessors

## Indexing

(!) :: Storable a => Vector a -> Int -> a Source #

O(1) Indexing.

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

O(1) First element.

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

O(1) Last element.

## Monadic indexing

indexM :: (Storable a, Monad m) => Vector 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 element) is evaluated eagerly.

headM :: (Storable a, Monad m) => Vector 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 :: (Storable a, Monad m) => Vector a -> m a Source #

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

## Extracting subvectors

init :: Storable a => Vector a -> Vector a Source #

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

tail :: Storable a => Vector a -> Vector a Source #

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

# Modifying vectors

## Bulk updates

(//) Source #

Arguments

:: Storable a |
=> Vector a | initial vector (of length `m`)
-> [(Int, a)] | list of index/value pairs (of length `n`)
-> Vector a |

O(m+n) For each pair `(i,a)` from the list of index/value pairs, 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

:: Storable a |
=> Vector a | initial vector (of length `m`)
-> Vector Int | index vector (of length `n1`)
-> Vector a | value vector (of length `n2`)
-> Vector 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>

## Accumulations

accum Source #

Arguments

:: Storable a |
=> (a -> b -> a) | accumulating function `f`
-> Vector a | initial vector (of length `m`)
-> [(Int, b)] | list of index/value pairs (of length `n`)
-> Vector a |

O(m+n) For each pair `(i,b)` from the list, replace the vector element `a` at position `i` by `f a b`.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.accum (+) (VS.fromList [1000,2000,3000 :: Int]) [(2,4),(1,6),(0,3),(1,10)]
    [1003,2016,3004]

accumulate_ Source #

Arguments

:: (Storable a, Storable b) |
=> (a -> b -> a) | accumulating function `f`
-> Vector a | initial vector (of length `m`)
-> Vector Int | index vector (of length `n1`)
-> Vector b | value vector (of length `n2`)
-> Vector 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>

## Permutations

backpermute :: Storable a => Vector a -> Vector Int -> Vector a Source #

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 :: Storable a => (a -> a -> a) -> Vector a -> a Source #

O(n) Left fold on non-empty vectors.

foldl1' :: Storable a => (a -> a -> a) -> Vector a -> a Source #

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

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

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

foldr1' :: Storable a => (a -> a -> a) -> Vector a -> a Source #

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

## Specialised folds

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

O(n) Yield the maximum element of the vector. The vector may not be empty. In case of a tie, the first occurrence wins.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.maximum $ VS.fromList [2, 1 :: Int]
    2

maximumBy :: Storable a => (a -> a -> Ordering) -> Vector a -> a Source #

O(n) Yield the maximum element of the vector according to the given comparison function. The vector may not be empty. In case of a tie, the first occurrence wins. This behavior is different from `maximumBy` which returns the last tie.

minimum :: (Storable a, Ord a) => Vector a -> a Source #

O(n) Yield the minimum element of the vector. The vector may not be empty. In case of a tie, the first occurrence wins.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.minimum $ VS.fromList [2, 1 :: Int]
    1

minimumBy :: Storable a => (a -> a -> Ordering) -> Vector a -> a Source #

O(n) Yield the minimum element of the vector according to the given comparison function. The vector may not be empty. In case of a tie, the first occurrence wins.

minIndex :: (Storable a, Ord a) => Vector a -> Int Source #

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

minIndexBy :: Storable a => (a -> a -> Ordering) -> Vector 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 :: (Storable a, Ord a) => Vector a -> Int Source #

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

maxIndexBy :: Storable a => (a -> a -> Ordering) -> Vector 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. In case of a tie, the first occurrence wins.

## Monadic folds

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

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

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

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

fold1M_ :: (Monad m, Storable a) => (a -> a -> m a) -> Vector a -> m () Source #

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

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

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

# Prefix sums (scans)

scanl1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Initial-value free left-to-right scan over a vector.

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

Note: Since 0.13, application of this to an empty vector no longer results in an error; instead it produces an empty vector.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.scanl1 min $ VS.fromListN 5 [4,2,4,1,3 :: Int]
    [4,2,2,1,1]
    >>> VS.scanl1 max $ VS.fromListN 5 [1,3,2,5,4 :: Int]
    [1,3,3,5,5]
    >>> VS.scanl1 min (VS.empty :: VS.Vector Int)
    []

scanl1' :: Storable a => (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Initial-value free left-to-right scan over a vector with a strict accumulator.

Note: Since 0.13, application of this to an empty vector no longer results in an error; instead it produces an empty vector.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.scanl1' min $ VS.fromListN 5 [4,2,4,1,3 :: Int]
    [4,2,2,1,1]
    >>> VS.scanl1' max $ VS.fromListN 5 [1,3,2,5,4 :: Int]
    [1,3,3,5,5]
    >>> VS.scanl1' min (VS.empty :: VS.Vector Int)
    []

scanr1 :: Storable a => (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Right-to-left, initial-value free scan over a vector.

Note: Since 0.13, application of this to an empty vector no longer results in an error; instead it produces an empty vector.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.scanr1 min $ VS.fromListN 5 [3,1,4,2,4 :: Int]
    [1,1,2,2,4]
    >>> VS.scanr1 max $ VS.fromListN 5 [4,5,2,3,1 :: Int]
    [5,5,3,3,1]
    >>> VS.scanr1 min (VS.empty :: VS.Vector Int)
    []

scanr1' :: Storable a => (a -> a -> a) -> Vector a -> Vector a Source #

O(n) Right-to-left, initial-value free scan over a vector with a strict accumulator.

Note: Since 0.13, application of this to an empty vector no longer results in an error; instead it produces an empty vector.

#### Examples

Expand

    >>> import qualified Data.Vector.Storable as VS
    >>> VS.scanr1' min $ VS.fromListN 5 [3,1,4,2,4 :: Int]
    [1,1,2,2,4]
    >>> VS.scanr1' max $ VS.fromListN 5 [4,5,2,3,1 :: Int]
    [5,5,3,3,1]
    >>> VS.scanr1' min (VS.empty :: VS.Vector Int)
    []