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.
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 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 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.
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]
(//) :: (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 1-origin, 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])
