Copyright	(c) The University of Glasgow 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	experimental
Portability	non-portable (uses Data.Array.Base)
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Array.IArray

Contents

Array classes
Immutable non-strict (boxed) arrays
Array construction
Accessing arrays
Incremental array updates
Derived arrays

Description

Immutable arrays, with an overloaded interface. For array types which can be used with this interface, see the Array type exported by this module and the Data.Array.Unboxed module. Other packages, such as diffarray, also provide arrays using this interface.

Synopsis

Array classes

class IArray a e where #

Class of immutable array types.

An array type has the form (a i e) where a is the array type constructor (kind * -> * -> *), i is the index type (a member of the class Ix), and e is the element type. The IArray class is parameterised over both a and e, so that instances specialised to certain element types can be defined.

Minimal complete definition

bounds, numElements, unsafeArray, unsafeAt

Methods

bounds :: Ix i => a i e -> (i, i) #

Extracts the bounds of an immutable array

Instances

IArray Array e #
Methods bounds :: Ix i => Array i e -> (i, i) # numElements :: Ix i => Array i e -> Int unsafeArray :: Ix i => (i, i) -> [(Int, e)] -> Array i e unsafeAt :: Ix i => Array i e -> Int -> e unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e unsafeAccum :: Ix i => (e -> e' -> e) -> Array i e -> [(Int, e')] -> Array i e unsafeAccumArray :: Ix i => (e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> Array i e
IArray UArray Bool #
Methods bounds :: Ix i => UArray i Bool -> (i, i) # numElements :: Ix i => UArray i Bool -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Bool)] -> UArray i Bool unsafeAt :: Ix i => UArray i Bool -> Int -> Bool unsafeReplace :: Ix i => UArray i Bool -> [(Int, Bool)] -> UArray i Bool unsafeAccum :: Ix i => (Bool -> e' -> Bool) -> UArray i Bool -> [(Int, e')] -> UArray i Bool unsafeAccumArray :: Ix i => (Bool -> e' -> Bool) -> Bool -> (i, i) -> [(Int, e')] -> UArray i Bool
IArray UArray Char #
Methods bounds :: Ix i => UArray i Char -> (i, i) # numElements :: Ix i => UArray i Char -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Char)] -> UArray i Char unsafeAt :: Ix i => UArray i Char -> Int -> Char unsafeReplace :: Ix i => UArray i Char -> [(Int, Char)] -> UArray i Char unsafeAccum :: Ix i => (Char -> e' -> Char) -> UArray i Char -> [(Int, e')] -> UArray i Char unsafeAccumArray :: Ix i => (Char -> e' -> Char) -> Char -> (i, i) -> [(Int, e')] -> UArray i Char
IArray UArray Double #
Methods bounds :: Ix i => UArray i Double -> (i, i) # numElements :: Ix i => UArray i Double -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Double)] -> UArray i Double unsafeAt :: Ix i => UArray i Double -> Int -> Double unsafeReplace :: Ix i => UArray i Double -> [(Int, Double)] -> UArray i Double unsafeAccum :: Ix i => (Double -> e' -> Double) -> UArray i Double -> [(Int, e')] -> UArray i Double unsafeAccumArray :: Ix i => (Double -> e' -> Double) -> Double -> (i, i) -> [(Int, e')] -> UArray i Double
IArray UArray Float #
Methods bounds :: Ix i => UArray i Float -> (i, i) # numElements :: Ix i => UArray i Float -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Float)] -> UArray i Float unsafeAt :: Ix i => UArray i Float -> Int -> Float unsafeReplace :: Ix i => UArray i Float -> [(Int, Float)] -> UArray i Float unsafeAccum :: Ix i => (Float -> e' -> Float) -> UArray i Float -> [(Int, e')] -> UArray i Float unsafeAccumArray :: Ix i => (Float -> e' -> Float) -> Float -> (i, i) -> [(Int, e')] -> UArray i Float
IArray UArray Int #
Methods bounds :: Ix i => UArray i Int -> (i, i) # numElements :: Ix i => UArray i Int -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int)] -> UArray i Int unsafeAt :: Ix i => UArray i Int -> Int -> Int unsafeReplace :: Ix i => UArray i Int -> [(Int, Int)] -> UArray i Int unsafeAccum :: Ix i => (Int -> e' -> Int) -> UArray i Int -> [(Int, e')] -> UArray i Int unsafeAccumArray :: Ix i => (Int -> e' -> Int) -> Int -> (i, i) -> [(Int, e')] -> UArray i Int
IArray UArray Int8 #
Methods bounds :: Ix i => UArray i Int8 -> (i, i) # numElements :: Ix i => UArray i Int8 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int8)] -> UArray i Int8 unsafeAt :: Ix i => UArray i Int8 -> Int -> Int8 unsafeReplace :: Ix i => UArray i Int8 -> [(Int, Int8)] -> UArray i Int8 unsafeAccum :: Ix i => (Int8 -> e' -> Int8) -> UArray i Int8 -> [(Int, e')] -> UArray i Int8 unsafeAccumArray :: Ix i => (Int8 -> e' -> Int8) -> Int8 -> (i, i) -> [(Int, e')] -> UArray i Int8
IArray UArray Int16 #
Methods bounds :: Ix i => UArray i Int16 -> (i, i) # numElements :: Ix i => UArray i Int16 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int16)] -> UArray i Int16 unsafeAt :: Ix i => UArray i Int16 -> Int -> Int16 unsafeReplace :: Ix i => UArray i Int16 -> [(Int, Int16)] -> UArray i Int16 unsafeAccum :: Ix i => (Int16 -> e' -> Int16) -> UArray i Int16 -> [(Int, e')] -> UArray i Int16 unsafeAccumArray :: Ix i => (Int16 -> e' -> Int16) -> Int16 -> (i, i) -> [(Int, e')] -> UArray i Int16
IArray UArray Int32 #
Methods bounds :: Ix i => UArray i Int32 -> (i, i) # numElements :: Ix i => UArray i Int32 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int32)] -> UArray i Int32 unsafeAt :: Ix i => UArray i Int32 -> Int -> Int32 unsafeReplace :: Ix i => UArray i Int32 -> [(Int, Int32)] -> UArray i Int32 unsafeAccum :: Ix i => (Int32 -> e' -> Int32) -> UArray i Int32 -> [(Int, e')] -> UArray i Int32 unsafeAccumArray :: Ix i => (Int32 -> e' -> Int32) -> Int32 -> (i, i) -> [(Int, e')] -> UArray i Int32
IArray UArray Int64 #
Methods bounds :: Ix i => UArray i Int64 -> (i, i) # numElements :: Ix i => UArray i Int64 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int64)] -> UArray i Int64 unsafeAt :: Ix i => UArray i Int64 -> Int -> Int64 unsafeReplace :: Ix i => UArray i Int64 -> [(Int, Int64)] -> UArray i Int64 unsafeAccum :: Ix i => (Int64 -> e' -> Int64) -> UArray i Int64 -> [(Int, e')] -> UArray i Int64 unsafeAccumArray :: Ix i => (Int64 -> e' -> Int64) -> Int64 -> (i, i) -> [(Int, e')] -> UArray i Int64
IArray UArray Word #
Methods bounds :: Ix i => UArray i Word -> (i, i) # numElements :: Ix i => UArray i Word -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word)] -> UArray i Word unsafeAt :: Ix i => UArray i Word -> Int -> Word unsafeReplace :: Ix i => UArray i Word -> [(Int, Word)] -> UArray i Word unsafeAccum :: Ix i => (Word -> e' -> Word) -> UArray i Word -> [(Int, e')] -> UArray i Word unsafeAccumArray :: Ix i => (Word -> e' -> Word) -> Word -> (i, i) -> [(Int, e')] -> UArray i Word
IArray UArray Word8 #
Methods bounds :: Ix i => UArray i Word8 -> (i, i) # numElements :: Ix i => UArray i Word8 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word8)] -> UArray i Word8 unsafeAt :: Ix i => UArray i Word8 -> Int -> Word8 unsafeReplace :: Ix i => UArray i Word8 -> [(Int, Word8)] -> UArray i Word8 unsafeAccum :: Ix i => (Word8 -> e' -> Word8) -> UArray i Word8 -> [(Int, e')] -> UArray i Word8 unsafeAccumArray :: Ix i => (Word8 -> e' -> Word8) -> Word8 -> (i, i) -> [(Int, e')] -> UArray i Word8
IArray UArray Word16 #
Methods bounds :: Ix i => UArray i Word16 -> (i, i) # numElements :: Ix i => UArray i Word16 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word16)] -> UArray i Word16 unsafeAt :: Ix i => UArray i Word16 -> Int -> Word16 unsafeReplace :: Ix i => UArray i Word16 -> [(Int, Word16)] -> UArray i Word16 unsafeAccum :: Ix i => (Word16 -> e' -> Word16) -> UArray i Word16 -> [(Int, e')] -> UArray i Word16 unsafeAccumArray :: Ix i => (Word16 -> e' -> Word16) -> Word16 -> (i, i) -> [(Int, e')] -> UArray i Word16
IArray UArray Word32 #
Methods bounds :: Ix i => UArray i Word32 -> (i, i) # numElements :: Ix i => UArray i Word32 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word32)] -> UArray i Word32 unsafeAt :: Ix i => UArray i Word32 -> Int -> Word32 unsafeReplace :: Ix i => UArray i Word32 -> [(Int, Word32)] -> UArray i Word32 unsafeAccum :: Ix i => (Word32 -> e' -> Word32) -> UArray i Word32 -> [(Int, e')] -> UArray i Word32 unsafeAccumArray :: Ix i => (Word32 -> e' -> Word32) -> Word32 -> (i, i) -> [(Int, e')] -> UArray i Word32
IArray UArray Word64 #
Methods bounds :: Ix i => UArray i Word64 -> (i, i) # numElements :: Ix i => UArray i Word64 -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word64)] -> UArray i Word64 unsafeAt :: Ix i => UArray i Word64 -> Int -> Word64 unsafeReplace :: Ix i => UArray i Word64 -> [(Int, Word64)] -> UArray i Word64 unsafeAccum :: Ix i => (Word64 -> e' -> Word64) -> UArray i Word64 -> [(Int, e')] -> UArray i Word64 unsafeAccumArray :: Ix i => (Word64 -> e' -> Word64) -> Word64 -> (i, i) -> [(Int, e')] -> UArray i Word64
IArray UArray (StablePtr a) #
Methods bounds :: Ix i => UArray i (StablePtr a) -> (i, i) # numElements :: Ix i => UArray i (StablePtr a) -> Int unsafeArray :: Ix i => (i, i) -> [(Int, StablePtr a)] -> UArray i (StablePtr a) unsafeAt :: Ix i => UArray i (StablePtr a) -> Int -> StablePtr a unsafeReplace :: Ix i => UArray i (StablePtr a) -> [(Int, StablePtr a)] -> UArray i (StablePtr a) unsafeAccum :: Ix i => (StablePtr a -> e' -> StablePtr a) -> UArray i (StablePtr a) -> [(Int, e')] -> UArray i (StablePtr a) unsafeAccumArray :: Ix i => (StablePtr a -> e' -> StablePtr a) -> StablePtr a -> (i, i) -> [(Int, e')] -> UArray i (StablePtr a)
IArray UArray (Ptr a) #
Methods bounds :: Ix i => UArray i (Ptr a) -> (i, i) # numElements :: Ix i => UArray i (Ptr a) -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Ptr a)] -> UArray i (Ptr a) unsafeAt :: Ix i => UArray i (Ptr a) -> Int -> Ptr a unsafeReplace :: Ix i => UArray i (Ptr a) -> [(Int, Ptr a)] -> UArray i (Ptr a) unsafeAccum :: Ix i => (Ptr a -> e' -> Ptr a) -> UArray i (Ptr a) -> [(Int, e')] -> UArray i (Ptr a) unsafeAccumArray :: Ix i => (Ptr a -> e' -> Ptr a) -> Ptr a -> (i, i) -> [(Int, e')] -> UArray i (Ptr a)
IArray UArray (FunPtr a) #
Methods bounds :: Ix i => UArray i (FunPtr a) -> (i, i) # numElements :: Ix i => UArray i (FunPtr a) -> Int unsafeArray :: Ix i => (i, i) -> [(Int, FunPtr a)] -> UArray i (FunPtr a) unsafeAt :: Ix i => UArray i (FunPtr a) -> Int -> FunPtr a unsafeReplace :: Ix i => UArray i (FunPtr a) -> [(Int, FunPtr a)] -> UArray i (FunPtr a) unsafeAccum :: Ix i => (FunPtr a -> e' -> FunPtr a) -> UArray i (FunPtr a) -> [(Int, e')] -> UArray i (FunPtr a) unsafeAccumArray :: Ix i => (FunPtr a -> e' -> FunPtr a) -> FunPtr a -> (i, i) -> [(Int, e')] -> UArray i (FunPtr a)

module Data.Ix

Immutable non-strict (boxed) arrays

data Array i e :: * -> * -> * Source #

The type of immutable non-strict (boxed) arrays with indices in i and elements in e.

Instances

IArray Array e #
Methods bounds :: Ix i => Array i e -> (i, i) # numElements :: Ix i => Array i e -> Int unsafeArray :: Ix i => (i, i) -> [(Int, e)] -> Array i e unsafeAt :: Ix i => Array i e -> Int -> e unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e unsafeAccum :: Ix i => (e -> e' -> e) -> Array i e -> [(Int, e')] -> Array i e unsafeAccumArray :: Ix i => (e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> Array i e
Functor (Array i)
Methods fmap :: (a -> b) -> Array i a -> Array i b Source # (<$) :: a -> Array i b -> Array i a Source #
Foldable (Array i)
Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # sum :: Num a => Array i a -> a Source # product :: Num a => Array i a -> a Source #
Ix i => Traversable (Array i)
Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) Source # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) Source # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) Source # sequence :: Monad m => Array i (m a) -> m (Array i a) Source #
(Ix i, Eq e) => Eq (Array i e)
Methods (==) :: Array i e -> Array i e -> Bool # (/=) :: Array i e -> Array i e -> Bool #
(Ix i, Ord e) => Ord (Array i e)
Methods compare :: Array i e -> Array i e -> Ordering # (<) :: Array i e -> Array i e -> Bool # (<=) :: Array i e -> Array i e -> Bool # (>) :: Array i e -> Array i e -> Bool # (>=) :: Array i e -> Array i e -> Bool # max :: Array i e -> Array i e -> Array i e # min :: Array i e -> Array i e -> Array i e #
(Ix a, Show a, Show b) => Show (Array a b)
Methods showsPrec :: Int -> Array a b -> ShowS Source # show :: Array a b -> String Source # showList :: [Array a b] -> ShowS Source #

Array construction

array #

Arguments

:: (IArray a e, Ix i)
=> (i, i)	bounds of the array: (lowest,highest)
-> [(i, e)]	list of associations
-> a i e

Constructs an immutable array from a pair of bounds and a list of initial associations.

The bounds are specified as a pair of the lowest and highest bounds in the array respectively. For example, a one-origin vector of length 10 has bounds (1,10), and a one-origin 10 by 10 matrix has bounds ((1,1),(10,10)).

An association is a pair of the form (i,x), which defines the value of the array at index i to be x. The array is undefined if any index in the list is out of bounds. If any two associations in the list have the same index, the value at that index is implementation-dependent. (In GHC, the last value specified for that index is used. Other implementations will also do this for unboxed arrays, but Haskell 98 requires that for Array the value at such indices is bottom.)

Because the indices must be checked for these errors, array is strict in the bounds argument and in the indices of the association list. Whether array is strict or non-strict in the elements depends on the array type: Array is a non-strict array type, but all of the UArray arrays are strict. Thus in a non-strict array, recurrences such as the following are possible:

a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i \<- [2..100]])

Not every index within the bounds of the array need appear in the association list, but the values associated with indices that do not appear will be undefined.

If, in any dimension, the lower bound is greater than the upper bound, then the array is legal, but empty. Indexing an empty array always gives an array-bounds error, but bounds still yields the bounds with which the array was constructed.

listArray :: (IArray a e, Ix i) => (i, i) -> [e] -> a i e #

Constructs an immutable array from a list of initial elements. The list gives the elements of the array in ascending order beginning with the lowest index.

accumArray #

Arguments

:: (IArray a e, Ix i)
=> (e -> e' -> e)	An accumulating function
-> e	A default element
-> (i, i)	The bounds of the array
-> [(i, e')]	List of associations
-> a i e	Returns: the array

Constructs an immutable array from a list of associations. Unlike array, the same index is allowed to occur multiple times in the list of associations; an accumulating function is used to combine the values of elements with the same index.

For example, given a list of values of some index type, hist produces a histogram of the number of occurrences of each index within a specified range:

hist :: (Ix a, Num b) => (a,a) -> [a] -> Array a b
hist bnds is = accumArray (+) 0 bnds [(i, 1) | i\<-is, inRange bnds i]

Accessing arrays

(!) :: (IArray a e, Ix i) => a i e -> i -> e #

Returns the element of an immutable array at the specified index.

bounds :: (IArray a e, Ix i) => a i e -> (i, i) #

Extracts the bounds of an immutable array

indices :: (IArray a e, Ix i) => a i e -> [i] #

Returns a list of all the valid indices in an array.

elems :: (IArray a e, Ix i) => a i e -> [e] #

Returns a list of all the elements of an array, in the same order as their indices.

assocs :: (IArray a e, Ix i) => a i e -> [(i, e)] #

Returns the contents of an array as a list of associations.

Incremental array updates

(//) :: (IArray a e, Ix i) => a i e -> [(i, e)] -> a i e #

Takes an array and a list of pairs and returns an array identical to the left argument except that it has been updated by the associations in the right argument. For example, if m is a 1-origin, n by n matrix, then m//[((i,i), 0) | i <- [1..n]] is the same matrix, except with the diagonal zeroed.

As with the array function, if any two associations in the list have the same index, the value at that index is implementation-dependent. (In GHC, the last value specified for that index is used. Other implementations will also do this for unboxed arrays, but Haskell 98 requires that for Array the value at such indices is bottom.)

For most array types, this operation is O(n) where n is the size of the array. However, the diffarray package provides an array type for which this operation has complexity linear in the number of updates.

accum :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(i, e')] -> a i e #

accum f takes an array and an association list and accumulates pairs from the list into the array with the accumulating function f. Thus accumArray can be defined using accum:

accumArray f z b = accum f (array b [(i, z) | i \<- range b])

Derived arrays

amap :: (IArray a e', IArray a e, Ix i) => (e' -> e) -> a i e' -> a i e #

Returns a new array derived from the original array by applying a function to each of the elements.

ixmap :: (IArray a e, Ix i, Ix j) => (i, i) -> (i -> j) -> a j e -> a i e #

Returns a new array derived from the original array by applying a function to each of the indices.