
Data.Array.IArray  Portability  nonportable (uses Data.Array.Base)  Stability  experimental  Maintainer  libraries@haskell.org 





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 and Data.Array.Diff modules.


Synopsis 

class HasBounds a where    class HasBounds a => 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 :: (HasBounds a, Ix i) => a i e > (i, i)   indices :: (HasBounds a, 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 HasBounds a where 
Class of array types with immutable bounds
(even if the array elements are mutable).
  Methods  bounds :: Ix i => a i e > (i, i)  Extracts the bounds of an array

  Instances  


class HasBounds a => 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.
  Instances  


module Data.Ix 

Immutable nonstrict (boxed) arrays


data Array i e 
The type of immutable nonstrict (boxed) arrays
with indices in i and elements in e.
 Instances  HasBounds Array  Typeable2 Array  IArray Array e  Ix i => Foldable (Array i)  Ix i => Functor (Array i)  Ix i => FunctorM (Array i)  Ix i => Traversable (Array i)  (Typeable a, Data b, Ix a) => Data (Array a b)  (Ix i, Eq e) => Eq (Array i e)  (Ix a, NFData a, NFData b) => NFData (Array a b)  (Ix i, Ord e) => Ord (Array i e)  (Ix a, Read a, Read b) => Read (Array a b)  (Ix a, Show a, Show b) => Show (Array a b) 



Array construction


array 
:: (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 oneorigin vector of length 10
has bounds (1,10), and a oneorigin 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 implementationdependent.
(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 nonstrict in the elements depends
on the array type: Array is a nonstrict array type, but
all of the UArray arrays are strict. Thus in a
nonstrict array, recurrences such as the following are possible:
a = array (1,100) ((1,1) : [(i, i * a!(i1))  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 arraybounds 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 
:: (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 :: (HasBounds a, Ix i) => a i e > (i, i) 
Extracts the bounds of an array


indices :: (HasBounds a, 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 1origin, 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 implementationdependent.
(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 type provides
this operation with 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.


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