Module BatArray

module BatArray: sig .. end
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.

This module replaces Stdlib's Array module.

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.


type 'a t = 'a array 

The type of arrays.

include BatEnum.Enumerable
include BatInterfaces.Mappable
val length : 'a array -> int

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.

val set : 'a array -> int -> 'a -> unit

Array.set a n x modifies array a in place, replacing element number n with x. You can also write a.(n) <- x instead of Array.set a n x.

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.

val create_float : int -> float array
val make_float : int -> float array

Array.make_float n returns a fresh float array of length n, with uninitialized data.

val create : int -> 'a -> 'a array
Deprecated.Array.create is an alias for Array.make.
val init : int -> (int -> 'a) -> 'a array

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.

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).

val create_matrix : int -> int -> 'a -> 'a array array
Deprecated.Array.create_matrix is an alias for Array.make_matrix.
val append : 'a array -> 'a array -> 'a array

Array.append v1 v2 returns a fresh array containing the concatenation of the arrays v1 and v2.

val concat : 'a array list -> 'a array

Same as Array.append, but concatenates a list of arrays.

val sub : 'a array -> int -> int -> 'a array

Array.sub a start len returns a fresh array of length len, containing the elements number start to start + len - 1 of array a.

val copy : 'a array -> 'a array

Array.copy a returns a copy of a, that is, a fresh array containing the same elements as a.

val fill : 'a array -> int -> int -> 'a -> unit

Array.fill a ofs len x modifies the array a in place, storing x in elements number ofs to ofs + len - 1.

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.

val to_list : 'a array -> 'a list

Array.to_list a returns the list of all the elements of a.

val of_list : 'a list -> 'a array

Array.of_list l returns a fresh array containing the elements of l.

val max : 'a array -> 'a

max a returns the largest value in a as judged by Pervasives.compare

val min : 'a array -> 'a

min a returns the smallest value in a as judged by Pervasives.compare

val min_max : 'a array -> 'a * 'a

min_max a returns the (smallest, largest) pair of values from a as judged by Pervasives.compare

val sum : int array -> int

sum l returns the sum of the integers of l

val fsum : float array -> float

fsum l returns the sum of the floats of l

val kahan_sum : float array -> float

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 BatArray.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.

val avg : int array -> float

avg l returns the average of l

val favg : float array -> float

favg l returns the average of l

val left : 'a array -> int -> 'a array

left r len returns the array containing the len first characters of r. If r contains less than len characters, it returns r.

Examples: Array.left [|0;1;2;3;4;5;6|] 4 = [|0;1;2;3|] Array.left [|1;2;3|] 0 = [||] Array.left [|1;2;3|] 10 = [|1;2;3|]

val right : 'a array -> int -> 'a array

left r len returns the array containing the len last characters of r. If r contains less than len characters, it returns r.

Example: Array.right [|1;2;3;4;5;6|] 4 = [|3;4;5;6|]

val head : 'a array -> int -> 'a array

as BatArray.left

val tail : 'a array -> int -> 'a array

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_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 BatArray.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.

val singleton : 'a -> 'a array

Create an array consisting of exactly one element.

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 :

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 :

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 fast_sort : ('a -> 'a -> int) -> 'a array -> unit

Same as Array.sort or Array.stable_sort, whichever is faster on typical input.

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 : 'a BatOrd.ord ->
'a array ->
'a -> [ `All_bigger | `All_lower | `At of int | `Empty | `Just_after 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).

Operations on two arrays
val iter2 : ('a -> 'b -> unit) -> 'a array -> 'b array -> unit

Array.iter2 f [|a0; a1; ...; an|] [|b0; b1; ...; bn|] performs calls f a0 b0; f a1 b1; ...; f an bn in that order.

val iter2i : (int -> 'a -> 'b -> unit) -> 'a array -> 'b array -> unit

Array.iter2i f [|a0; a1; ...; an|] [|b0; b1; ...; bn|] performs calls f 0 a0 b0; f 1 a1 b1; ...; f n an bn in that order.

val for_all2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool

As Array.for_all but on two arrays.

val exists2 : ('a -> 'b -> bool) -> 'a array -> 'b array -> bool

As Array.exists but on two arrays.

val map2 : ('a -> 'b -> 'c) -> 'a array -> 'b array -> 'c array

As Array.map but on two arrays.

val cartesian_product : 'a array -> 'b array -> ('a * 'b) array

Cartesian product of the two arrays.

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.

val mem : 'a -> 'a array -> bool

mem m a is true if and only if m is equal to an element of a.

val memq : 'a -> 'a array -> bool

Same as Array.mem but uses physical equality instead of structural equality to compare array elements.

val findi : ('a -> bool) -> 'a array -> int

findi p a returns the index of the first element of array a that satisfies the predicate p.

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 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.

Conversions
val enum : 'a array -> 'a BatEnum.t

Returns an enumeration of the elements of an array. Behavior of the enumeration is undefined if the contents of the array changes afterwards.

val of_enum : 'a BatEnum.t -> 'a array

Build an array from an enumeration.

val backwards : 'a array -> 'a BatEnum.t

Returns an enumeration of the elements of an array, from last to first.

val of_backwards : 'a BatEnum.t -> 'a array

Build an array from an enumeration, with the first element of the enumeration as the last element of the array and vice versa.

Utilities
val range : 'a array -> int BatEnum.t

range a returns an enumeration of all valid indexes into the given array. For example, range [|2;4;6;8|] = 0--3.

val insert : 'a array -> 'a -> int -> 'a array

insert xs x i returns a copy of xs except the value x is inserted in position i (and all later indices are shifted to the right).

Boilerplate code
val print : ?first:string ->
?last:string ->
?sep:string -> ('a, 'b) BatIO.printer -> ('a t, 'b) BatIO.printer

Print the contents of an array, with ~first preceeding 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.

Example: IO.to_string (Array.print Int.print) |2;4;66| = "|2; 4; 66|"

val compare : 'a BatOrd.comp -> 'a array BatOrd.comp

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.

val ord : 'a BatOrd.ord -> 'a array BatOrd.ord

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.

val shuffle : ?state:Random.State.t -> 'a array -> unit

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.

val equal : 'a BatOrd.eq -> 'a array BatOrd.eq

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.

module Exceptionless: sig .. end

Operations on Array without exceptions.

module Labels: sig .. end

Operations on Array with labels.

module Cap: sig .. end

Capabilities for arrays.

module Incubator: sig .. end