Data.Array.IArray

array-0.5.2.0: Mutable and immutable arrays

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

- class IArray a e
- module Data.Ix
- data Array i e
- array :: (IArray a e, Ix i) => (i, i) -> [(i, e)] -> a i e
- listArray :: (IArray a e, Ix i) => (i, i) -> [e] -> a i e
- accumArray :: (IArray a e, Ix i) => (e -> e' -> e) -> e -> (i, i) -> [(i, e')] -> a i e
- (!) :: (IArray a e, Ix i) => a i e -> i -> e
- bounds :: (IArray a e, Ix i) => a i e -> (i, i)
- indices :: (IArray a e, Ix i) => a i e -> [i]
- elems :: (IArray a e, Ix i) => a i e -> [e]
- assocs :: (IArray a e, Ix i) => a i e -> [(i, e)]
- (//) :: (IArray a e, Ix i) => a i e -> [(i, e)] -> a i e
- accum :: (IArray a e, Ix i) => (e -> e' -> e) -> a i e -> [(i, e')] -> a i e
- amap :: (IArray a e', IArray a e, Ix i) => (e' -> e) -> a i e' -> a i e
- ixmap :: (IArray a e, Ix i, Ix j) => (i, i) -> (i -> j) -> a j e -> a i e

# Array classes

class IArray a e #

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

Instances

IArray Array e # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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) # |
Instance details Defined in Data.Array.Base 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) # |
Instance details Defined in Data.Array.Base 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) # |
Instance details Defined in Data.Array.Base 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 # |
Instance details Defined in Data.Array.Base 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) | Since: base-2.1
Instance details Defined in GHC.Arr Methods fmap :: (a -> b) -> Array i a -> Array i b Source # (<$) :: a -> Array i b -> Array i a Source #
Foldable (Array i) | Since: base-4.8.0.0
Instance details Defined in Data.Foldable 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) | Since: base-2.1
Instance details Defined in Data.Traversable 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) | Since: base-2.1
Instance details Defined in GHC.Arr Methods (==) :: Array i e -> Array i e -> Bool # (/=) :: Array i e -> Array i e -> Bool #
(Ix i, Ord e) => Ord (Array i e) | Since: base-2.1
Instance details Defined in GHC.Arr 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, Read a, Read b) => Read (Array a b) | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Array a b) Source # readList :: ReadS [Array a b] Source # readPrec :: ReadPrec (Array a b) Source # readListPrec :: ReadPrec [Array a b] Source #
(Ix a, Show a, Show b) => Show (Array a b) | Since: base-2.1
Instance details Defined in GHC.Arr 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.