
Data.Array.IArray  Portability  nonportable  Stability  experimental  Maintainer  libraries@haskell.org 





Description 
Immutable arrays, with an overloaded interface. For array types
which can be used with this interface, see Data.Array,
Data.Array.Unboxed, and Data.Array.Diff.


Synopsis 

class HasBounds a => IArray a e   class HasBounds a   data Array i e   module Data.Ix   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   (//) :: (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   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)] 



Class of immutable array types 

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  


Class of array types with immutable bounds 

class HasBounds a 
Class of array types with bounds   Instances  


Ordinary boxed/lazy arrays 

data Array i e 


The Ix class and operations 

module Data.Ix 

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 undefined.
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]



Indexing arrays 

(!) :: (IArray a e, Ix i) => a i e > i > e 
Returns the element of an immutable array at the specified index. 

Incremental 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. (As with the array function, the indices in the
association list must be unique for the updated elements to be
defined.) 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.
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. 

Deconstructing arrays 

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. 

Produced by Haddock version 0.6 