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Array operations
Arrays are mutable data structures with a fixed size, which support fast access and modification, and are used pervasively in imperative computing. While arrays are completely supported in OCaml, it is often a good idea to investigate persistent alternatives, such as lists or hash maps.
A variant of arrays, arrays with capabilities, is provided in module BatArray.Cap. This notion of capabilities permit the transformation of a mutable array into a read-only or a write-only arrays, without loss of speed and with the possibility of distributing different capabilities to different expressions.
Return the length (number of elements) of the given array.
val get : 'a array->int ->'a
Array.get a n returns the element number n of array a. The first element has number 0. The last element has number Array.length a - 1. You can also write a.(n) instead of Array.get a n.
if n is outside the range 0 to Array.length a - 1.
val make : int ->'a->'a array
Array.make n x returns a fresh array of length n, initialized with x. All the elements of this new array are initially physically equal to x (in the sense of the == predicate). Consequently, if x is mutable, it is shared among all elements of the array, and modifying x through one of the array entries will modify all other entries at the same time.
Array.init n f returns a fresh array of length n, with element number i initialized to the result of f i. In other terms, Array.init n f tabulates the results of f applied to the integers 0 to n-1.
if n < 0 or n > Sys.max_array_length. If the return type of f is float, then the maximum size is only Sys.max_array_length / 2.
val make_matrix : int ->int ->'a->'a array array
Array.make_matrix dimx dimy e returns a two-dimensional array (an array of arrays) with first dimension dimx and second dimension dimy. All the elements of this new matrix are initially physically equal to e. The element (x,y) of a matrix m is accessed with the notation m.(x).(y).
if dimx or dimy is negative or greater than Sys.max_array_length. If the value of e is a floating-point number, then the maximum size is only Sys.max_array_length / 2.
val create_matrix : int ->int ->'a->'a array array
if ofs and len do not designate a valid subarray of a.
val blit : 'a array->int ->'a array->int ->int -> unit
Array.blit v1 o1 v2 o2 len copies len elements from array v1, starting at element number o1, to array v2, starting at element number o2. It works correctly even if v1 and v2 are the same array, and the source and destination chunks overlap.
kahan_sum l returns a numerically-accurate sum of the floats of l.
You should consider using Kahan summation when you really care about very small differences in the result, while the result or one of the intermediate sums can be very large (which usually results in loss of precision of floating-point addition).
The worst-case rounding error is constant, instead of growing with (the square root of) the length of the input array as with
fsum. On the other hand, processing each element requires four floating-point operations instead of one. See the wikipedia article on Kahan summation for more details.
since 2.2.0
val avg : int array-> float
avg l returns the average of l
since 2.1
val favg : float array-> float
favg l returns the average of l
since 2.1
val left : 'a array->int ->'a array
left r len returns the array containing the len first elements of r. If r contains less than len elements, it returns r.
tail r pos returns the array containing all but the pos first characters of r
Example: Array.tail [|1;2;3;4;5;6|] 4 = [|5;6|]
val iter : ('a-> unit)->'a array-> unit
Array.iter f a applies function f in turn to all the elements of a. It is equivalent to f a.(0); f a.(1); ...; f a.(Array.length a - 1); ().
val map : ('a->'b)->'a array->'b array
Array.map f a applies function f to all the elements of a, and builds an array with the results returned by f: [| f a.(0); f a.(1); ...; f a.(Array.length a - 1) |].
val iteri : (int ->'a-> unit)->'a array-> unit
Same as Array.iter, but the function is applied to the index of the element as first argument, and the element itself as second argument.
val mapi : (int ->'a->'b)->'a array->'b array
Same as Array.map, but the function is applied to the index of the element as first argument, and the element itself as second argument.
val fold_left : ('a->'b->'a)->'a->'b array->'a
Array.fold_left f x a computes f (... (f (f x a.(0)) a.(1)) ...) a.(n-1), where n is the length of the array a.
val fold_left_map : ('a->'b->'a * 'c)->'a->'b array->'a * 'c array
fold_left_map is a combination of fold_left and map that threads an accumulator through calls to f.
since 3.4.0
val fold_while :
('acc->'a-> bool)->('acc->'a->'acc)->'acc->'a array->'acc * int
fold_while p f init a, accumulates elements x of array a using function f, as long as the predicate p acc x holds. At the end, the accumulated value along with the first index i where p acc a.(i) does not hold is returned. If the returned index is equal to length a, the whole array was folded.
val fold : ('a->'b->'a)->'a->'b array->'a
Alias for fold_left.
val fold_right : ('b->'a->'a)->'b array->'a->'a
Array.fold_right f a x computes f a.(0) (f a.(1) ( ... (f a.(n-1) x) ...)), where n is the length of the array a.
val modify : ('a->'a)->'a array-> unit
modify f a replaces every element x of a with f x.
val modifyi : (int ->'a->'a)->'a array-> unit
Same as modify, but the function is applied to the index of the element as the first argument, and the element itself as the second argument.
val fold_lefti : ('a->int ->'b->'a)->'a->'b array->'a
As fold_left, but with the index of the element as additional argument
val fold_righti : (int ->'b->'a->'a)->'b array->'a->'a
As fold_right, but with the index of the element as additional argument
val reduce : ('a->'a->'a)->'a array->'a
Array.reduce f a is fold_left f a.(0) [|a.(1); ..; a.(n-1)|]. This is useful for merging a group of things that have no reasonable default value to return if the group is empty.
Create an array consisting of exactly one element.
since 2.1
Sorting
val sort : ('a->'a-> int)->'a array-> unit
Sort an array in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see below for a complete specification). For example, Pervasives.compare is a suitable comparison function, provided there are no floating-point NaN values in the data. After calling Array.sort, the array is sorted in place in increasing order. Array.sort is guaranteed to run in constant heap space and (at most) logarithmic stack space.
The current implementation uses Heap Sort. It runs in constant stack space.
Specification of the comparison function: Let a be the array and cmp the comparison function. The following must be true for all x, y, z in a :
cmp x y > 0 if and only if cmp y x < 0
if cmp x y >= 0 and cmp y z >= 0 then cmp x z >= 0
When Array.sort returns, a contains the same elements as before, reordered in such a way that for all i and j valid indices of a :
cmp a.(i) a.(j) >= 0 if and only if i >= j
val stable_sort : ('a->'a-> int)->'a array-> unit
Same as Array.sort, but the sorting algorithm is stable (i.e. elements that compare equal are kept in their original order) and not guaranteed to run in constant heap space.
The current implementation uses Merge Sort. It uses n/2 words of heap space, where n is the length of the array. It is usually faster than the current implementation of Array.sort.
val decorate_stable_sort : ('a->'b)->'a array->'a array
decorate_stable_sort f a returns a sorted copy of a such that if f
x < f y then x is earlier in the result than y. This function is useful when f is expensive, as it only computes f
x once for each element in the array. See Schwartzian Transform.
It is unnecessary to have an additional comparison function as argument, as the builtin Pervasives.compare is used to compare the 'b values. This is deemed sufficient.
val decorate_fast_sort : ('a->'b)->'a array->'a array
As Array.decorate_stable_sort, but uses fast_sort internally.
val bsearch :
'aBatOrd.ord->'a array->'a->[ `All_lower | `All_bigger| `Just_after of int| `Empty| `At of int ]
bsearch cmp arr x finds the index of the object x in the array arr, provided arr is sorted using cmp. If the array is not sorted, the result is not specified (may raise Invalid_argument).
Complexity: O(log n) where n is the length of the array (dichotomic search).
returns
`At i if cmp arr.(i) x = 0 (for some i)
`All_lower if all elements of arr are lower than x
`All_bigger if all elements of arr are bigger than x
val pivot_split : 'aBatOrd.ord->'a array->'a-> int * int
pivot_split cmp arr x assumes that arr is sorted w.r.t cmp. It splits an array arr of length len into three parts, by returning a couple (i,j) such as:
all elements with indices 0..i-1 (sub arr 0 i) are lower than x
all elements with indices i..j-1 (sub arr i (j-i)) are equal to x
all elements with indices j..len-1 (sub arr j (len-j)) are bigger than x
val cartesian_product : 'a array->'b array->('a * 'b) array
Cartesian product of the two arrays.
since 2.2.0
Predicates
val for_all : ('a-> bool)->'a array-> bool
for_all p [|a0; a1; ...; an|] checks if all elements of the array satisfy the predicate p. That is, it returns (p a0)
&& (p a1) && ... && (p an).
val exists : ('a-> bool)->'a array-> bool
exists p [|a0; a1; ...; an|] checks if at least one element of the array satisfies the predicate p. That is, it returns (p
a0) || (p a1) || ... || (p an).
val find : ('a-> bool)->'a array->'a
find p a returns the first element of array a that satisfies the predicate p.
if there is no value that satisfies p in the array a.
val filter : ('a-> bool)->'a array->'a array
filter p a returns all the elements of the array a that satisfy the predicate p. The order of the elements in the input array is preserved.
val filteri : (int ->'a-> bool)->'a array->'a array
As filter but with the index passed to the predicate.
val filter_map : ('a->'b option)->'a array->'b array
filter_map f e returns an array consisting of all elements x such that f y returns Some x , where y is an element of e.
val count_matching : ('a-> bool)->'a array-> int
count_matching p a returns the number of elements of a satisfying predicate p.
val find_all : ('a-> bool)->'a array->'a array
find_all is another name for Array.filter.
val partition : ('a-> bool)->'a array->'a array * 'a array
partition p a returns a pair of arrays (a1, a2), where a1 is the array of all the elements of a that satisfy the predicate p, and a2 is the array of all the elements of a that do not satisfy p. The order of the elements in the input array is preserved.
Array transformations
val rev : 'a array->'a array
Array reversal.
val rev_in_place : 'a array-> unit
In-place array reversal. The array argument is updated.
Print the contents of an array, with ~first preceding the first item (default: "[|"), ~last following the last item (default: "|]") and ~sep separating items (default: "; "). A printing function must be provided to print the items in the array.
compare c generates the lexicographical order on arrays induced by c. That is, given a comparison function for the elements of an array, this will return a comparison function for arrays of that type.
Hoist an element comparison function to compare arrays of those elements, with shorter arrays less than longer ones, and lexicographically for arrays of the same size. This is a different ordering than compare, but is often faster.
shuffle ~state:rs a randomly shuffles in place the elements of a. The optional random state rs allows to control the random numbers being used during shuffling (for reproducibility).
Shuffling is implemented using the Fisher-Yates algorithm and works in O(n), where n is the number of elements of a.
Hoist a equality test for elements to arrays. Arrays are only equal if their lengths are the same and corresponding elements test equal.
Override modules
The following modules replace functions defined in Array with functions behaving slightly differently but having the same name. This is by design: the functions are meant to override the corresponding functions of Array.