Bigarray − Large, multi-dimensional, numerical arrays.

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
’Bigarrays’, to distinguish them from the
standard OCaml arrays described in **Array** .

The implementation allows efficient sharing of large numerical arrays between OCaml code and C or Fortran numerical libraries.

The main differences between ’Bigarrays’ and standard OCaml arrays are as follows:

−Bigarrays are not limited in size, unlike OCaml arrays. (Normal float arrays are limited to 2,097,151 elements on a 32−bit platform, and normal arrays of other types to 4,194,303 elements.)

−Bigarrays are multi−dimensional. Any number of dimensions between 0 and 16 is supported. In contrast, OCaml arrays are mono−dimensional and require encoding multi−dimensional arrays as arrays of arrays.

−Bigarrays can only contain integers and floating−point numbers, while OCaml arrays can contain arbitrary OCaml data types.

−Bigarrays provide more space−efficient storage of integer and floating−point elements than normal OCaml arrays, in particular because they support ’small’ types such as single−precision floats and 8 and 16−bit integers, in addition to the standard OCaml types of double−precision floats and 32 and 64−bit integers.

−The memory layout of Bigarrays is entirely compatible with that of arrays in C and Fortran, allowing large arrays to be passed back and forth between OCaml code and C / Fortran code with no data copying at all.

−Bigarrays support interesting high−level operations that normal arrays do not provide efficiently, such as extracting sub−arrays and ’slicing’ a multi−dimensional array along certain dimensions, all without any copying.

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**
.

Bigarrays support all the OCaml ad−hoc polymorphic operations:

−comparisons
( **=** , **<>** , **<=** , etc, as well
as **compare** );

−hashing
(module **Hash** );

−and
structured input−output (the functions from the
**Marshal** module, as well as **output_value** and
**input_value** ).

**Element
kinds**

Bigarrays 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 integers ( **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 Bigarray or read back from
it. This type is not necessarily the same as the type of the
array elements proper: for instance, a Bigarray 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 Bigarray, and of an element kind **’b**
which represents the actual contents of the Bigarray. 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 writing 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* : **(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, Bigarrays of kind
**float32_elt** and **float64_elt** are accessed using
the OCaml type **float** . Bigarrays of complex kinds
**complex32_elt** , **complex64_elt** are accessed
with the OCaml type **Complex.t** . Bigarrays 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, Bigarrays 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 Bigarrays, 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**

**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.

**Since**
4.05.0

**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 **Bigarray.Array2** and **Bigarray.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 Bigarrays and fixed-dimension Bigarrays**
*
val genarray_of_array0* :

Return the generic Bigarray corresponding to the given zero−dimensional Bigarray.

**Since**
4.05.0

*val
genarray_of_array1* : **(’a, ’b, ’c)
Array1.t -> (’a, ’b, ’c)
Genarray.t**

Return the generic Bigarray corresponding to the given one−dimensional Bigarray.

*val
genarray_of_array2* : **(’a, ’b, ’c)
Array2.t -> (’a, ’b, ’c)
Genarray.t**

Return the generic Bigarray corresponding to the given two−dimensional Bigarray.

*val
genarray_of_array3* : **(’a, ’b, ’c)
Array3.t -> (’a, ’b, ’c)
Genarray.t**

Return the generic Bigarray corresponding to the given three−dimensional Bigarray.

*val
array0_of_genarray* : **(’a, ’b, ’c)
Genarray.t -> (’a, ’b, ’c)
Array0.t**

Return the zero−dimensional Bigarray corresponding to the given generic Bigarray.

**Since**
4.05.0

**Raises
Invalid_argument** if the generic Bigarray does not have
exactly zero dimension.

*val
array1_of_genarray* : **(’a, ’b, ’c)
Genarray.t -> (’a, ’b, ’c)
Array1.t**

Return the one−dimensional Bigarray corresponding to the given generic Bigarray.

**Raises
Invalid_argument** if the generic Bigarray does not have
exactly one dimension.

*val
array2_of_genarray* : **(’a, ’b, ’c)
Genarray.t -> (’a, ’b, ’c)
Array2.t**

Return the two−dimensional Bigarray corresponding to the given generic Bigarray.

**Raises
Invalid_argument** if the generic Bigarray does not have
exactly two dimensions.

*val
array3_of_genarray* : **(’a, ’b, ’c)
Genarray.t -> (’a, ’b, ’c)
Array3.t**

Return the three−dimensional Bigarray corresponding to the given generic Bigarray.

**Raises
Invalid_argument** if the generic Bigarray does not have
exactly three dimensions.

**Re-shaping
Bigarrays** *
val reshape* :

**reshape b
[|d1;...;dN|]** converts the Bigarray **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
Bigarray must have exactly the same number of elements as
the original Bigarray **b** . That is, the product of the
dimensions of **b** must be equal to **i1 * ... * iN**
. Otherwise, **Invalid_argument** is raised.

*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**
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.