| 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
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 :: Type -> Type -> Type) 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
- genArray :: (IArray a e, Ix i) => (i, i) -> (i -> e) -> a i e
- (!) :: (IArray a e, Ix i) => a i e -> i -> e
- (!?) :: (IArray a e, Ix i) => a i e -> i -> Maybe 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)]
- foldrArray :: (IArray a e, Ix i) => (e -> b -> b) -> b -> a i e -> b
- foldlArray' :: (IArray a e, Ix i) => (b -> e -> b) -> b -> a i e -> b
- foldlArray :: (IArray a e, Ix i) => (b -> e -> b) -> b -> a i e -> b
- foldrArray' :: (IArray a e, Ix i) => (e -> b -> b) -> b -> a i e -> b
- traverseArray_ :: (IArray a e, Ix i, Applicative f) => (e -> f b) -> a i e -> f ()
- forArray_ :: (IArray a e, Ix i, Applicative f) => a i e -> (e -> f b) -> f ()
- foldlArrayM' :: (IArray a e, Ix i, Monad m) => (b -> e -> m b) -> b -> a i e -> m b
- foldrArrayM' :: (IArray a e, Ix i, Monad m) => (e -> b -> m b) -> b -> a i e -> m b
- (//) :: (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 :: Type -> Type -> Type) e Source #
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
Instances
module Data.Ix
Immutable non-strict (boxed) arrays
The type of immutable non-strict (boxed) arrays
with indices in i and elements in e.
Instances
| IArray Array e Source # | |
Defined in Data.Array.Base Methods bounds :: Ix i => Array i e -> (i, i) Source # numElements :: Ix i => Array i e -> Int Source # unsafeArray :: Ix i => (i, i) -> [(Int, e)] -> Array i e Source # unsafeAt :: Ix i => Array i e -> Int -> e Source # unsafeReplace :: Ix i => Array i e -> [(Int, e)] -> Array i e Source # unsafeAccum :: Ix i => (e -> e' -> e) -> Array i e -> [(Int, e')] -> Array i e Source # unsafeAccumArray :: Ix i => (e -> e' -> e) -> e -> (i, i) -> [(Int, e')] -> Array i e Source # | |
| Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> 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 # | |
| Ix i => Traversable (Array i) | Since: base-2.1 |
Defined in Data.Traversable | |
| Functor (Array i) | Since: base-2.1 |
| (Data a, Data b, Ix a) => Data (Array a b) | Since: base-4.8.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Array a b -> c (Array a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Array a b) Source # toConstr :: Array a b -> Constr Source # dataTypeOf :: Array a b -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Array a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Array a b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Array a b -> Array a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Array a b -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Array a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Array a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Array a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Array a b -> m (Array a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Array a b -> m (Array a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Array a b -> m (Array a b) Source # | |
| (Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
| (Ix a, Show a, Show b) => Show (Array a b) | Since: base-2.1 |
| (Ix i, Eq e) => Eq (Array i e) | Since: base-2.1 |
| (Ix i, Ord e) => Ord (Array i e) | Since: base-2.1 |
Array construction
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 Source #
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.
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]
genArray :: (IArray a e, Ix i) => (i, i) -> (i -> e) -> a i e Source #
Constructs an immutable array using a generator function.
Since: array-0.5.6.0
Accessing arrays
(!) :: (IArray a e, Ix i) => a i e -> i -> e Source #
Returns the element of an immutable array at the specified index, or throws an exception if the index is out of bounds.
indices :: (IArray a e, Ix i) => a i e -> [i] Source #
Returns a list of all the valid indices in an array.
elems :: (IArray a e, Ix i) => a i e -> [e] Source #
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)] Source #
Returns the contents of an array as a list of associations.
Array folds
foldrArray :: (IArray a e, Ix i) => (e -> b -> b) -> b -> a i e -> b Source #
Lazy right-associative fold.
Since: array-0.5.8.0
foldlArray' :: (IArray a e, Ix i) => (b -> e -> b) -> b -> a i e -> b Source #
Strict accumulating left-associative fold.
Since: array-0.5.8.0
foldlArray :: (IArray a e, Ix i) => (b -> e -> b) -> b -> a i e -> b Source #
Lazy left-associative fold.
Since: array-0.5.8.0
foldrArray' :: (IArray a e, Ix i) => (e -> b -> b) -> b -> a i e -> b Source #
Strict accumulating right-associative fold.
Since: array-0.5.8.0
traverseArray_ :: (IArray a e, Ix i, Applicative f) => (e -> f b) -> a i e -> f () Source #
Map elements to applicative actions, sequence them left-to-right, and discard the results.
Since: array-0.5.8.0
forArray_ :: (IArray a e, Ix i, Applicative f) => a i e -> (e -> f b) -> f () Source #
forArray_ is traverseArray_ with its arguments flipped.
Since: array-0.5.8.0
foldlArrayM' :: (IArray a e, Ix i, Monad m) => (b -> e -> m b) -> b -> a i e -> m b Source #
Strict accumulating left-associative monadic fold.
Since: array-0.5.8.0
foldrArrayM' :: (IArray a e, Ix i, Monad m) => (e -> b -> m b) -> b -> a i e -> m b Source #
Strict accumulating right-associative monadic fold.
Since: array-0.5.8.0
Incremental array updates
(//) :: (IArray a e, Ix i) => a i e -> [(i, e)] -> a i e Source #
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 Source #
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])