Batteries user guide : BatArray

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.

Author(s): Xavier Leroy, Richard W.M. Jones, David Teller

Return the length (number of elements) of the given array.

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.

Raises Invalid_argument if n is outside the range 0 to (Array.length a - 1).

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.

Raises Invalid_argument if n is outside the range 0 to Array.length a - 1.

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.

Raises Invalid_argument if n < 0 or n > Sys.max_array_length. If the value of x is a floating-point number, then the maximum size is only Sys.max_array_length / 2.

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

Since 2.3.0

Deprecated. Array.create is an alias for Array.make.

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.

Raises Invalid_argument 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.

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).

Raises Invalid_argument 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.

Deprecated. Array.create_matrix is an alias for Array.make_matrix.

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

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

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

Raises Invalid_argument if start and len do not designate a valid subarray of a; that is, if start < 0, or len < 0, or start + len > Array.length a.

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

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

Raises Invalid_argument if ofs and len do not designate a valid subarray of a.

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.

Raises Invalid_argument if o1 and len do not designate a valid subarray of v1, or if o2 and len do not designate a valid subarray of v2.

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

Array.split a converts the array of pairs a into a pair of arrays.

combine [|a1; ...; an|] [|b1; ...; bn|] is [|(a1,b1); ...; (an,bn)|]. Raise Invalid_argument if the two arrays have different lengths.

Since 3.4.0

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

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

Raises Invalid_argument on empty input

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

Raises Invalid_argument on empty input

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

Raises Invalid_argument on empty input

sum l returns the sum of the integers of l

fsum l returns the sum of the floats of l

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.

Since 2.2.0

avg l returns the average of l

Since 2.1

favg l returns the average of l

Since 2.1

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|]

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|]

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|]

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); ().

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) |].

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.

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.

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.

fold_left_map is a combination of BatArray.fold_left and BatArray.map that threads an accumulator through calls to f.

Since 3.4.0

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.

Alias for fold_left.

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.

modify f a replaces every element x of a with f x.

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.

As fold_left, but with the index of the element as additional argument

As fold_right, but with the index of the element as additional argument

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.

Raises Invalid_argument on empty arrays.

Create an array consisting of exactly one element.

Since 2.1

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

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.

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

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.

As Array.decorate_stable_sort, but uses fast_sort internally.

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).

Since 2.2.0
Raises Invalid_argument if the array is found to be unsorted w.r.t cmp
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
- `Just_after i if arr.(i) < x < arr.(i+1)
- `Empty if the array is empty

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

In particular, it returns:

(0, 0) if all elements of arr are bigger than x
(len, len) if all elements are lower than x
(0, len) if all elements are equal to x

Complexity: logarithmic in the size of the array

Raises Invalid_argument if the array is found not to be sorted

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

Raises Invalid_argument if the two arrays have different lengths.

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.

Raises Invalid_argument if the two arrays have different lengths.

As Array.for_all but on two arrays.

Raises Invalid_argument if the two arrays have different lengths.

As Array.exists but on two arrays.

Raises Invalid_argument if the two arrays have different lengths.

As Array.map but on two arrays.

Raises Invalid_argument if the two arrays have different lengths.

Cartesian product of the two arrays.

Since 2.2.0

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).

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).

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

Raises Not_found if there is no value that satisfies p in the array a.

find_opt p a returns the first element of the array a that satisfies the predicate p, or None if there is no such element.

Since 3.4.0

find_map f a applies f to the elements of a in order, and returns the first result of the form Some v, or None if none exist.

Since 3.4.0

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

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

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

Raises Not_found if there is no value that satisfies p in the array a.

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.

As filter but with the index passed to the predicate.

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.

count_matching p a returns the number of elements of a satisfying predicate p.

find_all is another name for Array.filter.

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.

In-place array reversal. The array argument is updated.

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

Build an array from an enumeration.

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

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

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

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).

Raises Invalid_argument if i < 0 || i > Array.length xs.

remove_at i a returns the array a without the element at index i.

Since 3.3.0
Raises Invalid_argument if i is outside of a bounds.

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.

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

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.

Since 2.6.0

Hoist a equality test for elements to arrays. Arrays are only equal if their lengths are the same and corresponding elements test equal.

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 BatArray