Module Bigarray

module Bigarray: sig .. end

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 (the functions from the Marshal module, as well as Pervasives.output_value and Pervasives.input_value).

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 *_elt types defined below (defined with a single constructor instead of abstract types for technical injectivity reasons).

type float32_elt =

`\|`	`Float32_elt`

type float64_elt =

`\|`	`Float64_elt`

type int8_signed_elt =

`\|`	`Int8_signed_elt`

type int8_unsigned_elt =

`\|`	`Int8_unsigned_elt`

type int16_signed_elt =

`\|`	`Int16_signed_elt`

type int16_unsigned_elt =

`\|`	`Int16_unsigned_elt`

type int32_elt =

`\|`	`Int32_elt`

type int64_elt =

`\|`	`Int64_elt`

type int_elt =

| Int_elt

type nativeint_elt =

`\|`	`Nativeint_elt`

type complex32_elt =

`\|`	`Complex32_elt`

type complex64_elt =

`\|`	`Complex64_elt`

type ('a, 'b) kind =

`\|`	`Float32 : (float, float32_elt) kind`
`\|`	`Float64 : (float, float64_elt) kind`
`\|`	`Int8_signed : (int, int8_signed_elt) kind`
`\|`	`Int8_unsigned : (int, int8_unsigned_elt) kind`
`\|`	`Int16_signed : (int, int16_signed_elt) kind`
`\|`	`Int16_unsigned : (int, int16_unsigned_elt) kind`
`\|`	`Int32 : (int32, int32_elt) kind`
`\|`	`Int64 : (int64, int64_elt) kind`
`\|`	`Int : (int, int_elt) kind`
`\|`	`Nativeint : (nativeint, nativeint_elt) kind`
`\|`	`Complex32 : (Complex.t, complex32_elt) kind`
`\|`	`Complex64 : (Complex.t, complex64_elt) kind`
`\|`	`Char : (char, int8_unsigned_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. 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'	`*)`

let float32: kind(float, float32_elt);

See Bigarray.char.

let float64: kind(float, float64_elt);

See Bigarray.char.

let complex32: kind(Complex.t, complex32_elt);

See Bigarray.char.

let complex64: kind(Complex.t, complex64_elt);

See Bigarray.char.

let int8_signed: kind(int, int8_signed_elt);

See Bigarray.char.

let int8_unsigned: kind(int, int8_unsigned_elt);

See Bigarray.char.

let int16_signed: kind(int, int16_signed_elt);

See Bigarray.char.

let int16_unsigned: kind(int, int16_unsigned_elt);

See Bigarray.char.

let int: kind(int, int_elt);

See Bigarray.char.

let int32: kind(int32, int32_elt);

See Bigarray.char.

let int64: kind(int64, int64_elt);

See Bigarray.char.

let nativeint: kind(nativeint, nativeint_elt);

See Bigarray.char.

let char: kind(char, int8_unsigned_elt);

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.

Array layouts

type c_layout =

|

C_layout_typ

(*

See Bigarray.fortran_layout.

*)

type fortran_layout =

|

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 phantom types Bigarray.c_layout and Bigarray.fortran_layout respectively.

*)

Supported layouts

The GADT type 'a layout represents one of the two supported memory layouts: C-style or Fortran-style. Its constructors are re-exported as values below for backward-compatibility reasons.

type 'a layout =

`\|`	`C_layout : c_layout layout`
`\|`	`Fortran_layout : fortran_layout layout`

let c_layout: layout(c_layout);

let fortran_layout: layout(fortran_layout);

Generic arrays (of arbitrarily many dimensions)

module Genarray: sig .. end

One-dimensional arrays

module Array1: sig .. end

One-dimensional arrays.

Two-dimensional arrays

module Array2: sig .. end

Two-dimensional arrays.

Three-dimensional arrays

module Array3: sig .. end

Three-dimensional arrays.

Coercions between generic big arrays and fixed-dimension big arrays

let genarray_of_array1: Array1.t('a, 'b, 'c) => Genarray.t('a, 'b, 'c);

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

let genarray_of_array2: Array2.t('a, 'b, 'c) => Genarray.t('a, 'b, 'c);

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

let genarray_of_array3: Array3.t('a, 'b, 'c) => Genarray.t('a, 'b, 'c);

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

let array1_of_genarray: Genarray.t('a, 'b, 'c) => Array1.t('a, 'b, 'c);

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

let array2_of_genarray: Genarray.t('a, 'b, 'c) => Array2.t('a, 'b, 'c);

Return the two-dimensional big array corresponding to the given generic big array. Raise Invalid_argument if the generic big array does not have exactly two dimensions.

let array3_of_genarray: Genarray.t('a, 'b, 'c) => Array3.t('a, 'b, 'c);

Return the three-dimensional big array corresponding to the given generic big array. Raise Invalid_argument if the generic big array does not have exactly three dimensions.

Re-shaping big arrays

let reshape: (Genarray.t('a, 'b, 'c), array(int)) => Genarray.t('a, 'b, 'c);

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. Otherwise, Invalid_argument is raised.

let reshape_1: (Genarray.t('a, 'b, 'c), int) => Array1.t('a, 'b, 'c);

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

let reshape_2: (Genarray.t('a, 'b, 'c), int, int) => Array2.t('a, 'b, 'c);

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

let reshape_3: (Genarray.t('a, 'b, 'c), int, int, int) => Array3.t('a, 'b, 'c);

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