Large, multi-dimensional, numerical arrays.

This module implements multi-dimensional arrays of integers and floating-point numbers, thereafter referred to as ``big arrays''. The implementation allows efficient sharing of large numerical arrays between OCaml code and C or Fortran numerical libraries.

Concerning the naming conventions, users of this module are encouraged to do `open Bigarray` in their source, then refer to array types and operations via short dot notation, e.g. `Array1.t` or `Array2.sub`.

Big arrays support all the OCaml ad-hoc polymorphic operations:

- comparisons (`=`, `<>`, `<=`, etc, as well as `Pervasives.compare`);
- hashing (module `Hash`);
- and structured input-output (`Pervasives.output_value` and `Pervasives.input_value`, as well as the functions from the `Marshal` module).

This module replaces Stdlib's Bigarray module.

- author Michel Serrano (Base library)

- author Xavier Leroy (Base library)

- author David Teller

## Element kinds

Big arrays can contain elements of the following kinds:

- IEEE single precision (32 bits) floating-point numbers (`Bigarray.float32_elt`),
- IEEE double precision (64 bits) floating-point numbers (`Bigarray.float64_elt`),
- IEEE single precision (2 * 32 bits) floating-point complex numbers (`Bigarray.complex32_elt`),
- IEEE double precision (2 * 64 bits) floating-point complex numbers (`Bigarray.complex64_elt`),
- 8-bit integers (signed or unsigned) (`Bigarray.int8_signed_elt` or `Bigarray.int8_unsigned_elt`),
- 16-bit integers (signed or unsigned) (`Bigarray.int16_signed_elt` or `Bigarray.int16_unsigned_elt`),
- OCaml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures) (`Bigarray.int_elt`),
- 32-bit signed integer (`Bigarray.int32_elt`),
- 64-bit signed integers (`Bigarray.int64_elt`),
- platform-native signed integers (32 bits on 32-bit architectures, 64 bits on 64-bit architectures) (`Bigarray.nativeint_elt`).

Each element kind is represented at the type level by one of the abstract types defined below.

`type float16_elt = Stdlib.Bigarray.float16_elt =`

1. `| Float16_elt`

`type float32_elt = Stdlib.Bigarray.float32_elt =`

1. `| Float32_elt`

`type float64_elt = Stdlib.Bigarray.float64_elt =`

1. `| Float64_elt`

`type complex32_elt = Stdlib.Bigarray.complex32_elt =`

1. `| Complex32_elt`

`type complex64_elt = Stdlib.Bigarray.complex64_elt =`

1. `| Complex64_elt`

`type int8_signed_elt = Stdlib.Bigarray.int8_signed_elt =`

1. `| Int8_signed_elt`

`type int8_unsigned_elt = Stdlib.Bigarray.int8_unsigned_elt =`

1. `| Int8_unsigned_elt`

`type int16_signed_elt = Stdlib.Bigarray.int16_signed_elt =`

1. `| Int16_signed_elt`

`type int16_unsigned_elt = Stdlib.Bigarray.int16_unsigned_elt =`

1. `| Int16_unsigned_elt`

`type int_elt = Stdlib.Bigarray.int_elt =`

1. `| Int_elt`

`type int32_elt = Stdlib.Bigarray.int32_elt =`

1. `| Int32_elt`

`type int64_elt = Stdlib.Bigarray.int64_elt =`

1. `| Int64_elt`

`type nativeint_elt = Stdlib.Bigarray.nativeint_elt =`

1. `| Nativeint_elt`

`type ('a, 'b) kind = ('a, 'b) Stdlib.Bigarray.kind =`

1. `| Float32 : (float, float32_elt) kind`
2. `| Float64 : (float, float64_elt) kind`
3. `| Int8_signed : (int, int8_signed_elt) kind`
4. `| Int8_unsigned : (int, int8_unsigned_elt) kind`
5. `| Int16_signed : (int, int16_signed_elt) kind`
6. `| Int16_unsigned : (int, int16_unsigned_elt) kind`
7. `| Int32 : (int32, int32_elt) kind`
8. `| Int64 : (int64, int64_elt) kind`
9. `| Int : (int, int_elt) kind`
10. `| Nativeint : (nativeint, nativeint_elt) kind`
11. `| Complex32 : (Stdlib.Complex.t, complex32_elt) kind`
12. `| Complex64 : (Stdlib.Complex.t, complex64_elt) kind`
13. `| Char : (char, int8_unsigned_elt) kind`
14. `| Float16 : (float, float16_elt) kind`
    (*

    To each element kind is associated an OCaml type, which is the type of OCaml values that can be stored in the big array or read back from it. This type is not necessarily the same as the type of the array elements proper: for instance, a big array whose elements are of kind `float32_elt` contains 32-bit single precision floats, but reading or writing one of its elements from OCaml uses the OCaml type `float`, which is 64-bit double precision floats.

    # 137 "src/batBigarray.mli" # 138 "src/batBigarray.mli" # 139 "src/batBigarray.mli" # 140 "src/batBigarray.mli" # 141 "src/batBigarray.mli" # 142 "src/batBigarray.mli" The GADT type `('a, 'b) kind` captures this association of an OCaml type `'a` for values read or written in the big array, and of an element kind `'b` which represents the actual contents of the big array. Its constructors list all possible associations of OCaml types with element kinds, and are re-exported below for backward-compatibility reasons.

    Using a generalized algebraic datatype (GADT) here allows to write well-typed polymorphic functions whose return type depend on the argument type, such as:

          let zero : type a b. (a, b) kind -> a = function
            | Float32 -> 0.0 | Complex32 -> Complex.zero
            | Float64 -> 0.0 | Complex64 -> Complex.zero
            | Int8_signed -> 0 | Int8_unsigned -> 0
            | Int16_signed -> 0 | Int16_unsigned -> 0
            | Int32 -> 0l | Int64 -> 0L
            | Int -> 0 | Nativeint -> 0n
            | Char -> '\000'

    *)

`val float32 : (float, float32_elt) kind`

See `Bigarray.char`.

`val float64 : (float, float64_elt) kind`

See `Bigarray.char`.

`val complex32 : (Stdlib.Complex.t, complex32_elt) kind`

See `Bigarray.char`.

`val complex64 : (Stdlib.Complex.t, complex64_elt) kind`

See `Bigarray.char`.

`val int8_signed : (int, int8_signed_elt) kind`

See `Bigarray.char`.

`val int8_unsigned : (int, int8_unsigned_elt) kind`

See `Bigarray.char`.

`val int16_signed : (int, int16_signed_elt) kind`

See `Bigarray.char`.

`val int16_unsigned : (int, int16_unsigned_elt) kind`

See `Bigarray.char`.

`val int : (int, int_elt) kind`

See `Bigarray.char`.

`val int32 : (int32, int32_elt) kind`

See `Bigarray.char`.

`val int64 : (int64, int64_elt) kind`

See `Bigarray.char`.

`val nativeint : (nativeint, nativeint_elt) kind`

See `Bigarray.char`.

`val char : (char, int8_unsigned_elt) kind`

As shown by the types of the values above, big arrays of kind `float32_elt` and `float64_elt` are accessed using the OCaml type `float`. Big arrays of complex kinds `complex32_elt`, `complex64_elt` are accessed with the OCaml type `Complex.t`. Big arrays of integer kinds are accessed using the smallest OCaml integer type large enough to represent the array elements: `int` for 8- and 16-bit integer bigarrays, as well as OCaml-integer bigarrays; `int32` for 32-bit integer bigarrays; `int64` for 64-bit integer bigarrays; and `nativeint` for platform-native integer bigarrays. Finally, big arrays of kind `int8_unsigned_elt` can also be accessed as arrays of characters instead of arrays of small integers, by using the kind value `char` instead of `int8_unsigned`.

`val kind_size_in_bytes : ('a, 'b) kind -> int`

`kind_size_in_bytes k` is the number of bytes used to store an element of type `k`.

- since 2.5.0

## Array layouts

`type c_layout = Stdlib.Bigarray.c_layout =`

1. `| C_layout_typ`

See `Bigarray.fortran_layout`.

`type fortran_layout = Stdlib.Bigarray.fortran_layout =`

1. `| Fortran_layout_typ`

To facilitate interoperability with existing C and Fortran code, this library supports two different memory layouts for big arrays, one compatible with the C conventions, the other compatible with the Fortran conventions.

In the C-style layout, array indices start at 0, and multi-dimensional arrays are laid out in row-major format. That is, for a two-dimensional array, all elements of row 0 are contiguous in memory, followed by all elements of row 1, etc. In other terms, the array elements at `(x,y)` and `(x, y+1)` are adjacent in memory.

In the Fortran-style layout, array indices start at 1, and multi-dimensional arrays are laid out in column-major format. That is, for a two-dimensional array, all elements of column 0 are contiguous in memory, followed by all elements of column 1, etc. In other terms, the array elements at `(x,y)` and `(x+1, y)` are adjacent in memory.

Each layout style is identified at the type level by the abstract types `Bigarray.c_layout` and `fortran_layout` respectively.

`type 'a layout = 'a Stdlib.Bigarray.layout =`

1. `| C_layout : c_layout layout`
2. `| Fortran_layout : fortran_layout layout`

The type `'a layout` represents one of the two supported memory layouts: C-style if `'a` is `Bigarray.c_layout`, Fortran-style if `'a` is `Bigarray.fortran_layout`.

### Supported layouts

The abstract values `c_layout` and `fortran_layout` represent the two supported layouts at the level of values.

`val c_layout : c_layout layout`
`val fortran_layout : fortran_layout layout`
`module Genarray : sig ... end`

Generic arrays (of arbitrarily many dimensions)

## Zero-dimensional arrays

`module Array0 : sig ... end`

Zero-dimensional arrays. The `Array0` structure provides operations similar to those of `Bigarray.Genarray`, but specialized to the case of zero-dimensional arrays that only contain a single scalar value. Statically knowing the number of dimensions of the array allows faster operations, and more precise static type-checking.

## One-dimensional arrays

`module Array1 : sig ... end`

One-dimensional arrays. The `Array1` structure provides operations similar to those of `Bigarray.Genarray`, but specialized to the case of one-dimensional arrays. (The `Array2` and `Array3` structures below provide operations specialized for two- and three-dimensional arrays.) Statically knowing the number of dimensions of the array allows faster operations, and more precise static type-checking.

## Two-dimensional arrays

`module Array2 : sig ... end`

Two-dimensional arrays. The `Array2` structure provides operations similar to those of `Bigarray.Genarray`, but specialized to the case of two-dimensional arrays.

## Three-dimensional arrays

`module Array3 : sig ... end`

Three-dimensional arrays. The `Array3` structure provides operations similar to those of `Bigarray.Genarray`, but specialized to the case of three-dimensional arrays.

## Coercions between generic big arrays and fixed-dimension big arrays

`val genarray_of_array0 : ('a, 'b, 'c) Array0.t -> ('a, 'b, 'c) Genarray.t`

Return the generic big array corresponding to the given zero-dimensional big array.

- since 2.7.0 and OCaml 4.05.0

`val genarray_of_array1 : ('a, 'b, 'c) Array1.t -> ('a, 'b, 'c) Genarray.t`

Return the generic big array corresponding to the given one-dimensional big array.

`val genarray_of_array2 : ('a, 'b, 'c) Array2.t -> ('a, 'b, 'c) Genarray.t`

Return the generic big array corresponding to the given two-dimensional big array.

`val genarray_of_array3 : ('a, 'b, 'c) Array3.t -> ('a, 'b, 'c) Genarray.t`

Return the generic big array corresponding to the given three-dimensional big array.

`val array0_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t`

Return the zero-dimensional big array corresponding to the given generic big array. Raise `Invalid_argument` if the generic big array does not have exactly zero dimension.

- since 2.7.0 and OCaml 4.05.0

`val array1_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array1.t`

Return the one-dimensional big array corresponding to the given generic big array.

- raises `Invalid_argument`

  if the generic big array does not have exactly one dimension.

`val array2_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array2.t`

Return the two-dimensional big array corresponding to the given generic big array.

- raises `Invalid_argument`

  if the generic big array does not have exactly two dimensions.

`val array3_of_genarray : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array3.t`

Return the three-dimensional big array corresponding to the given generic big array.

- raises `Invalid_argument`

  if the generic big array does not have exactly three dimensions.

## Re-shaping big arrays

`val reshape : ('a, 'b, 'c) Genarray.t -> int array -> ('a, 'b, 'c) Genarray.t`

`reshape b [|d1;...;dN|]` converts the big array `b` to a `N`-dimensional array of dimensions `d1`...`dN`. The returned array and the original array `b` share their data and have the same layout. For instance, assuming that `b` is a one-dimensional array of dimension 12, `reshape b [|3;4|]` returns a two-dimensional array `b'` of dimensions 3 and 4. If `b` has C layout, the element `(x,y)` of `b'` corresponds to the element `x * 3 + y` of `b`. If `b` has Fortran layout, the element `(x,y)` of `b'` corresponds to the element `x + (y - 1) * 4` of `b`. The returned big array must have exactly the same number of elements as the original big array `b`. That is, the product of the dimensions of `b` must be equal to `i1 * ... * iN`.

- raises `Invalid_argument`

  otherwise.

`val reshape_0 : ('a, 'b, 'c) Genarray.t -> ('a, 'b, 'c) Array0.t`

Specialized version of `Bigarray.reshape` for reshaping to zero-dimensional arrays.

- since 2.7.0 and OCaml 4.05.0

`val reshape_1 : ('a, 'b, 'c) Genarray.t -> int -> ('a, 'b, 'c) Array1.t`

Specialized version of `Bigarray.reshape` for reshaping to one-dimensional arrays.

`val reshape_2 : ('a, 'b, 'c) Genarray.t -> int -> int -> ('a, 'b, 'c) Array2.t`

Specialized version of `Bigarray.reshape` for reshaping to two-dimensional arrays.

`val reshape_3 : ('a, 'b, 'c) Genarray.t -> int -> int -> int -> ('a, 'b, 'c) Array3.t`

Specialized version of `Bigarray.reshape` for reshaping to three-dimensional arrays.