Bigarray (3)
NAME
Bigarray - Large, multi-dimensional, numerical arrays.Module
Module BigarrayDocumentation
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 -> 'rs000'
val float32
:
(float, float32_elt) kind
See
Bigarray.char
.
val float64
:
(float, float64_elt) kind
See
Bigarray.char
.
val complex32
:
(Complex.t, complex32_elt) kind
See
Bigarray.char
.
val complex64
:
(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
4.03.0
===
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
val c_layout
:
c_layout layout
val fortran_layout
:
fortran_layout layout
===
Generic arrays (of arbitrarily many dimensions)
===
module Genarray :
sig end
===
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_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 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. Raise
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. Raise
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. Raise
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
.
Otherwise,
Invalid_argument
is raised.
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.