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@@@(Bigarrayf&Array3!t=7'@@@@@@@@@@z{$l@@y@@*unsafe_get@(Bigarrayg&Array3!t!a@+\@!b@-\@!c@/\@@@@"@dh@@@#@ki@@@$@rj@@@%*@@&@@'@@(@@)5%caml_ba_unsafe_ref_3DA@@@@@@E@@@@*unsafe_set@(Bigarrayk&Array3!t!a@A\@0!b@C\@1!c@E\@2@@@6@l@@@7@m@@@8@n@@@9@,o@@@:@@;@@<@@=@@>@@?5%caml_ba_unsafe_set_3EA4@@@@@@@@@ @@@@Aru@@@@2genarray_of_array0@(Bigarrayp&Array0!t!a@\@F!b@\@G!c@\@H@@@L(Bigarrayq(Genarray!t@@@@@)%identityAAw@@@MN#@@L@@2genarray_of_array1@(Bigarrayr&Array1!t!a@\@!b@\@!c@\@@@@(Bigarrays(Genarray!t@@@@@Ȑ)%identityAA@@@@@@@2genarray_of_array2@(Bigarrayt&Array2!t!a@\@Ϡ!b@\@Р!c@\@@@@(Bigarrayu(Genarray!t@@@@@ڐ)%identityAA@@@MMk@@@@2genarray_of_array3@(Bigarrayv&Array3!t!a@\@}!b@\@~!c@\@@@@(Bigarrayw(Genarray!t@@@@@)%identityAA(@@@&f@@@@2array0_of_genarray@(Bigarrayx(Genarray!t!a@\@!b@\@!c@\@@@@(Bigarrayy&Array0!t@@@@@@56@@4@@2array1_of_genarray@(Bigarrayz(Genarray!t!a@\@!b@\@!c@\@@@@(Bigarray{&Array1!t@@@@@@lm @@k@@2array2_of_genarray@(Bigarray|(Genarray!t!a@\@!b@\@!c@\@@@@(Bigarray}&Array2!t@@@@@@!@@@@2array3_of_genarray@(Bigarray~(Genarray!t!a@\@Š!b@\@Ơ!c@\@@@@(Bigarray&Array3!t@@@@@@#@@@@'reshape@(Bigarray(Genarray!t!a@\@נ!b@\@ؠ!c@\@@@@@M@@@@@@(Bigarray(Genarray!t,& @@@@@@@@  O@@@@)reshape_0@(Bigarray(Genarray!t!a@\@!b@\@!c@\@@@@(Bigarray&Array0!t@@@@@@UV@@T@@)reshape_1@(Bigarray(Genarray!t!a@\@!b@\@!c@\@@@@@?@@@(Bigarray&Array1!t& @@@ @@ @@ @"99"9@@@@)reshape_2@(Bigarray(Genarray!t!a@$\@!b@&\@!c@(\@@@@@}@@@@@@@(Bigarray&Array2!t-'!@@@@@ @@!@@"@&&.@@@@)reshape_3@(Bigarray(Genarray!t!a@<\@)!b@>\@*!c@@\@+@@@/@@@@0@@@@1@@@@2(Bigarray&Array3!t4.(@@@6@@7@@8@@9@@:@$*%+@@#@@@3 +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.@ Y 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.@ SBigarrays 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!.@ B Bigarrays support all the OCaml ad-hoc polymorphic operations:-comparisons (!=", "<>", "<=2, etc, as well as .Stdlib.compare@@");@0hashing (module $Hash");@ 9and structured input-output (the functions from the 'Marshal@@4 module, as well as 3Stdlib.output_value@@* and 2Stdlib.input_value@@").@@@@@@@@@@@@@@A9../../stdlib/bigarray.mliA,elementkinds-Element kinds@@ 6Bigarrays can contain elements of the following kinds: 9IEEE half precision (16 bits) floating-point numbers (4Bigarray.float16_eltE@"),@ ;IEEE single precision (32 bits) floating-point numbers (4Bigarray.float32_eltE@"),@ ;IEEE double precision (64 bits) floating-point numbers (4Bigarray.float64_eltE@"),@ GIEEE single precision (2 * 32 bits) floating-point complex numbers (6Bigarray.complex32_eltE@"),@ GIEEE double precision (2 * 64 bits) floating-point complex numbers (6Bigarray.complex64_eltE@"),@ (8-bit integers (signed or unsigned) (8Bigarray.int8_signed_eltE@$ or :Bigarray.int8_unsigned_eltE@"),@ )16-bit integers (signed or unsigned) (9Bigarray.int16_signed_eltE@$ or ;Bigarray.int16_unsigned_eltE@"),@ ^OCaml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures) (0Bigarray.int_eltE@"),@832-bit signed integers (2Bigarray.int32_eltE@"),@864-bit signed integers (2Bigarray.int64_eltE@"),@ gplatform-native signed integers (32 bits on 32-bit architectures, 64 bits on 64-bit architectures) (6Bigarray.nativeint_eltE@").@@ H Each element kind is represented at the type level by one of the %*_elt x types defined below (defined with a single constructor instead of abstract types for technical injectivity reasons).@#@@ [@@@@A@@ V Z@@#@@ Q@@@@A@@ N Q@@#@@ I@@@@A@@ F I@@#t@@ A@@@@A@@ > A@@#w@@ 9@@@@A@@ 6 9@@#v@@ 1@@@@A@@ . 1@@#y@@ )@@@@A@@ & )@@#m@@ !@@@@A@@  !@@#l@@ @@@@A@@  @@#@@ @@@@A@@  @@#u@@ @@@@A@@  @@#@@ @@@@A@@ @@#@@@@@@A@@@@#-Bigarray.kind3 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 z 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.@2 The GADT type -('a, 'b) kind / captures this association of an OCaml type "'a G 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 | Float16 -> 0.0 | Int8_signed -> 0 | Int8_unsigned -> 0 | Int16_signed -> 0 | Int16_unsigned -> 0 | Int32 -> 0l | Int64 -> 0L | Int -> 0 | Nativeint -> 0n | Char -> '\000' @@@@ %5.2 Constructor Float16 for the GADT.@@@@@@@ ) &@ !@ @ @ @@@ȑ@@@@@@q@p@S@R@5@4@@@@@ؑ@@@@@@@A@@z@@0Bigarray.float163$See -Bigarray.charD@!.@@@@#5.2@@@@@@@@@@@q0Bigarray.float323$See D@!.@@@@@@@@@@@@x@@@@c0Bigarray.float643$See 'D@!.@@@@@@@@@@@@j@@@@U2Bigarray.complex323$See 9D@!.@@@@@@@@@@@@\@@@@B2Bigarray.complex643$See KD@!.@@@@@@@@@@@@I@@@@/4Bigarray.int8_signed3$See ]D@!.@@@@@@@@@@@@6@@@@!6Bigarray.int8_unsigned3$See oD@!.@@@@@@@@@@@@(@@@@5Bigarray.int16_signed3$See D@!.@@@@@@@@@@@@@@@@7Bigarray.int16_unsigned3$See D@!.@@@@@@@@@@@@ @@@@,Bigarray.int3$See D@% and 5Bigarray.elementkindsO@@!.@ Beware that this is a bigarray containing OCaml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures), which does not match the !C* int type.@@@@@@@@@@@@@@@@.Bigarray.int323$See ʐD@!.@@@@@@@@@@@@@@@@.Bigarray.int643$See ܐD@!.@@@@@@@@@@@@@@@@ࠕ2Bigarray.nativeint3$See D@!.@@@@@@@@@@@@@@@@Ҡ3 @As shown by the types of the values above, Bigarrays of kind +float16_elt", +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 M 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 J for platform-native integer Bigarrays. Finally, Bigarrays of kind 1int8_unsigned_elt q can also be accessed as arrays of characters instead of arrays of small integers, by using the kind value $char, instead of -int8_unsigned!.@@@@@@@@@@@@&@@@@;Bigarray.kind_size_in_bytes34kind_size_in_bytes k < is the number of bytes used to store an element of type !k!.@@@@$4.03@@@@@@@@ @@@@A@-Array layouts@@#1Bigarray.c_layout3$See 7Bigarray.fortran_layoutE@!.@@@@@@@@@@@@@@@@@A@@@@#7Bigarray.fortran_layout3 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)8 are adjacent in memory.@ 4 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)8 are adjacent in memory.@ N Each layout style is identified at the type level by the phantom types 1Bigarray.c_layoutE@% and 7Bigarray.fortran_layoutE@1 respectively.@@@@@@@@@@@@@E@@@@A@@BE@@B@1Supported layouts@@2 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.@#/Bigarray.layout@Q@L@K@5@4@@A@@$@@1Bigarray.c_layout@@@@@ 7Bigarray.fortran_layout@@@@@A@ /Generic arrays (of arbitrarily many dimensions)@@/1Bigarray.Genarray@A#3Bigarray.Genarray.t3)The type *Genarray.t is the type of Bigarrays with variable numbers of dimensions. Any number of dimensions between 0 and 16 is supported.@ # The three type parameters to *Genarray.t = identify the array element kind and layout, as follows:5the first parameter, "'a 9, is the OCaml type for accessing array elements (%float", #int", %int32", %int64", )nativeint");@6the second parameter, "'b /, is the actual kind of array elements (+float32_elt", +float64_elt", /int8_signed_elt", 1int8_unsigned_elt., etc);@5the third parameter, "'c &, identifies the array layout ((c_layout$ or .fortran_layout").@@4 For instance, /(float, float32_elt, fortran_layout) Genarray.t is the type of generic Bigarrays containing 32-bit floats in Fortran layout; reads and writes in this array use the OCaml type %float!.@@@@@@@@@@@@OO|O@@A@@sr@@8Bigarray.Genarray.create3 &Genarray.create kind layout dimensions O returns a new Bigarray whose element kind is determined by the parameter $kind. (one of 'float32", 'float64", +int8_signed <, etc) and whose layout is determined by the parameter &layout) (one of (c_layout) or .fortran_layout(). The *dimensions u parameter is an array of integers that indicate the size of the Bigarray in each dimension. The length of *dimensions : determines the number of dimensions of the Bigarray.@4 For instance, (Genarray.create int32 c_layout [|4;6;8|] returns a fresh Bigarray of 32-bit integers, in C layout, having three dimensions, the three dimensions being 4, 6 and 8 respectively.@< Bigarrays returned by /Genarray.create O are not initialized: the initial values of array elements is unspecified.@& /Genarray.create( raises 0Invalid_argument v if the number of dimensions is not in the range 0 to 16 inclusive, or if one of the dimensions is negative.@@@@@@@@@@@@@@@@@@@6Bigarray.Genarray.init3 &Genarray.init kind layout dimensions f8 returns a new Bigarray !b 9 whose element kind is determined by the parameter $kind/ (one of 'float32", 'float64", +int8_signed =, etc) and whose layout is determined by the parameter &layout) (one of (c_layout* or .fortran_layout(). The *dimensions w parameter is an array of integers that indicate the size of the Bigarray in each dimension. The length of *dimensions ; determines the number of dimensions of the Bigarray.@4 Each element 0Genarray.get b i ! is initialized to the result of #f i8. In other words, &Genarray.init kind layout dimensions f tabulates the results of !f M applied to the indices of a new Bigarray whose layout is described by $kind", &layout% and *dimensions9. The index array !i . may be shared and mutated between calls to f.@5 For instance, DGenarray.init int c_layout [|2; 1; 3|] (Array.fold_left (+) 0) returns a fresh Bigarray of integers, in C layout, having three dimensions (2, 1, 3, respectively), with the element values 0, 1, 2, 1, 2, 3.@' -Genarray.init( raises 0Invalid_argument x if the number of dimensions is not in the range 0 to 16 inclusive, or if one of the dimensions is negative.@@@@$4.12@@@@@@@"@B#@E@H@K@@@@ޠ:Bigarray.Genarray.num_dims3 6Return the number of dimensions of the given Bigarray.@@@@@@@@@@@@@Z@@@@6Bigarray.Genarray.dims3/Genarray.dims a ( returns all dimensions of the Bigarray !a ), as an array of integers of length 3Genarray.num_dims a!.@@@@@@@@@@@@@x@@@@9Bigarray.Genarray.nth_dim34Genarray.nth_dim a n- returns the !n #-th dimension of the Bigarray !a &. The first dimension corresponds to %n = 0 +; the second dimension corresponds to %n = 1>; the last dimension, to ;n = Genarray.num_dims a - 1!.@@@@@@@@0Invalid_argument#if !n . is less than 0 or greater or equal than 3Genarray.num_dims a!.@@@@@@@@@@@6Bigarray.Genarray.kind3 &Return the kind of the given Bigarray.@@@@@@@@@@@@@@@@@8Bigarray.Genarray.layout3 (Return the layout of the given Bigarray.@@@@@@@@@@@@@@@@@\?Bigarray.Genarray.change_layout3?Genarray.change_layout a layout - returns a Bigarray with the specified &layout8, sharing the data with !a 0 (and hence having the same dimensions as !a ). No copying of elements is involved: the new array and the original array share the same storage space. The dimensions are reversed, such that 0get v [| a; b |]; in C layout becomes 4get v [| b+1; a+1 |]3 in Fortran layout.@@@@$4.04@@@@@@@@ @c@@@@D?Bigarray.Genarray.size_in_bytes3/size_in_bytes a> is the number of elements in !a3 multiplied by !a#'s BD@!.@@@@$4.03@@@@@@@\@6]@@@@;5Bigarray.Genarray.get3 ,Read an element of a generic Bigarray. >Genarray.get a [|i1; ...; iN|]8 returns the element of !a< whose coordinates are "i19 in the first dimension, "i2 $ in the second dimension, ..., "iN( in the !N.-th dimension.@) If !a { has C layout, the coordinates must be greater or equal than 0 and strictly less than the corresponding dimensions of !a*. If !a has Fortran layout, the coordinates must be greater or equal than 1 and less or equal than the corresponding dimensions of !a!.@) If %N > 3 3, alternate syntax is provided: you can write 3a.{i1, i2, ..., iN}, instead of >Genarray.get a [|i1; ...; iN|]3. (The syntax 'a.{...} with one, two or three coordinates is reserved for accessing one-, two- and three-dimensional arrays as described below.)@@@@@@@@0Invalid_argument-if the array !a7 does not have exactly !N E dimensions, or if the coordinates are outside the array bounds.@@@@@@@@@@@5Bigarray.Genarray.set3 .Assign an element of a generic Bigarray. Genarray.set a [|i1; ...; iN|] v2 stores the value !v8 in the element of !a7 whose coordinates are "i1> in the first dimension, "i2? in the second dimension, ..., "iN( in the !N.-th dimension.@0 The array !a3 must have exactly !N Y dimensions, and all coordinates must lie inside the array bounds, as described for ,Genarray.get2; otherwise, 0Invalid_argument+ is raised.@) If %N > 3 3, alternate syntax is provided: you can write 8a.{i1, i2, ..., iN} <- v1 instead of Genarray.set a [|i1; ...; iN|] v3. (The syntax ,a.{...} <- v with one, two or three coordinates is reserved for updating one-, two- and three-dimensional arrays as described below.)@@@@@@@@@@@@@'@*@-@@@@:Bigarray.Genarray.sub_left3 `Extract a sub-array of the given Bigarray by restricting the first (left-most) dimension. ;Genarray.sub_left a ofs len ? returns a Bigarray with the same number of dimensions as !a ", and the same dimensions as !a E, except the first dimension, which corresponds to the interval 7[ofs ... ofs + len - 1] of the first dimension of !a . No copying of elements is involved: the sub-array and the original array share the same storage space. In other terms, the element at coordinates /[|i1; ...; iN|] B of the sub-array is identical to the element at coordinates 3[|i1+ofs; ...; iN|]< of the original array !a!.@& 1Genarray.sub_left ' applies only to Bigarrays in C layout.@@@@@@@@0Invalid_argument#if #ofs% and #len , do not designate a valid sub-array of !a., that is, if 'ofs < 0%, or 'len < 0*, or ofs + len > Genarray.nth_dim a 0!.@@@@@@@@@@@@ՠ;Bigarray.Genarray.sub_right3 `Extract a sub-array of the given Bigarray by restricting the last (right-most) dimension. Genarray.nth_dim a (Genarray.num_dims a - 1)!.@@@@@:@;@@@@@@ in the slice is identical to the element at coordinates [|i1; ...; iM; j1; ...; j(N-M)|]< in the original array !a j. No copying of elements is involved: the slice and the original array share the same storage space.@& 3Genarray.slice_left ' applies only to Bigarrays in C layout.@@@@@@@@0Invalid_argument#if &M >= N(, or if 0[|i1; ... ; iM|]? is outside the bounds of !a!.@@@@@^@_@?@@@@=Bigarray.Genarray.slice_right3 Extract a sub-array of lower dimension from the given Bigarray by fixing one or several of the last (right-most) coordinates. 'Genarray.slice_right a [|i1; ... ; iM|]= returns the 'slice' of !a> obtained by setting the last !M5 coordinates to "i1', ..., "iM&. If !a% has !N * dimensions, the slice has dimension %N - M &, and the element at coordinates 3[|j1; ...; j(N-M)|] > in the slice is identical to the element at coordinates [|j1; ...; j(N-M); i1; ...; iM|]< in the original array !a j. No copying of elements is involved: the slice and the original array share the same storage space.@& 4Genarray.slice_right - applies only to Bigarrays in Fortran layout.@@@@@@@@0Invalid_argument#if &M >= N(, or if 0[|i1; ... ; iM|]? is outside the bounds of !a!.@@@@@@@ b@@@@?6Bigarray.Genarray.blit3 :Copy all elements of a Bigarray in another Bigarray. 5Genarray.blit src dst8 copies all elements of #src+ into #dst/. Both arrays #src% and #dst \ must have the same number of dimensions and equal dimensions. Copying a sub-array of #src8 to a sub-array of #dst= can be achieved by applying -Genarray.blit to sub-array or slices of #src% and #dst!.@@@@@@@@@@@@|@V}@Y_@@@@J6Bigarray.Genarray.fill3 6Set all elements of a Bigarray to a given value. 1Genarray.fill a v2 stores the value !v & in all elements of the Bigarray !a !. Setting only some elements of !a$ to !v " can be achieved by applying -Genarray.fill # to a sub-array or a slice of !a!.@@@@@@@@@@@@u@v@o@@@@P@@NM@@@@@A@7Zero-dimensional arrays@@//Bigarray.Array0Q3=Zero-dimensional arrays. The &Array0 6 structure provides operations similar to those of @@ , 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.@@@@$4.05@@@@@@@A ͐#1Bigarray.Array0.t3 KThe type of zero-dimensional Bigarrays whose elements have OCaml type "'a6, representation kind "'b4, and memory layout "'c!.@@@@@@@@@@@@}OzOwO@@A@@on@@6Bigarray.Array0.create39Array0.create kind layout 0 returns a new Bigarray of zero dimension. $kind% and &layout M determine the array element kind and the array layout as described for ÐD@!.@@@@@@@@@@@@@@r@@@@X4Bigarray.Array0.init39Array0.init kind layout v. behaves like 9Array0.create kind layout G except that the element is additionally initialized to the value !v!.@@@@$4.12@@@@@@@j@$k@'V@*i@@@@=4Bigarray.Array0.kind3 &Return the kind of the given Bigarray.@@@@@@@@@@@@>@9?@@@@6Bigarray.Array0.layout3 (Return the layout of the given Bigarray.@@@@@@@@@@@@@H@@@@정=Bigarray.Array0.change_layout3=Array0.change_layout a layout - returns a Bigarray with the specified &layout8, sharing the data with !a t. No copying of elements is involved: the new array and the original array share the same storage space.@@@@$4.06@@@@@@@@h@k@@@@Ǡ=Bigarray.Array0.size_in_bytes3/size_in_bytes a$ is !a#'s D@!.@@@@@@@@@@@@@@@@@3Bigarray.Array0.get3,Array0.get a= returns the only element in !a!.@@@@@@@@@@@@@@@@@3Bigarray.Array0.set30Array0.set a x v2 stores the value !v$ in !a!.@@@@@@@@@@@@@@@@@@4Bigarray.Array0.blit3 9Copy the first Bigarray to the second Bigarray. See D@2 for more details.@@@@@@@@@@@@@@~@@@@i4Bigarray.Array0.fill3 7Fill the given Bigarray with the given value. See D@2 for more details.@@@@@@@@@@@@p@q@j@@@@K8Bigarray.Array0.of_value3 HBuild a zero-dimensional Bigarray initialized from the given value.@@@@@@@@@@@@L@M@8@K@@@@@@@@@@@A@6One-dimensional arrays@@//Bigarray.Array1 3 is the number of elements in !a3 multiplied by !a#'s  D@!.@@@@$4.03@@@@@@@@ t@@@@3Bigarray.Array1.get3.Array1.get a x3, or alternatively %a.{x}>, returns the element of !a* at index !x'. !x? must be greater or equal than !0= and strictly less than ,Array1.dim a$ if !a3 has C layout. If !a: has Fortran layout, !x? must be greater or equal than !1= and less or equal than ,Array1.dim a.. Otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@ @ @@@@ݠ3Bigarray.Array1.set30Array1.set a x v/, also written *a.{x} <- v8, stores the value !v* at index !x$ in !a'. !x> must be inside the bounds of !a6 as described in D@2; otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@ @ @ @@@@砕3Bigarray.Array1.sub3 DExtract a sub-array of the given one-dimensional Bigarray. See D@2 for more details.@@@@@@@@@@@@@ .@ 1@ 4@@@@5Bigarray.Array1.slice3 Extract a scalar (zero-dimensional slice) of the given one-dimensional Bigarray. The integer parameter is the index of the scalar to extract. See D@* and D@2 for more details.@@@@$4.05@@@@@@@@ Q@ T@@@@4Bigarray.Array1.blit3 9Copy the first Bigarray to the second Bigarray. See RD@2 for more details.@@@@@@@@@@@@@ i@ l@@@@n4Bigarray.Array1.fill3 7Fill the given Bigarray with the given value. See D@2 for more details.@@@@@@@@@@@@u@ v@ o@@@@P8Bigarray.Array1.of_array3 GBuild a one-dimensional Bigarray initialized from the given array.@@@@@@@@@@@@Q@ R@ =@ /@@@@:Bigarray.Array1.unsafe_get3%Like .D@ , but bounds checking is not always performed. Use with caution and only when the program logic guarantees that the access is within bounds.@@@@@@@@@@@@%@ &@ @@@@:Bigarray.Array1.unsafe_set3%Like D@ , but bounds checking is not always performed. Use with caution and only when the program logic guarantees that the access is within bounds.@@@@@@@@@@@@@ @ @ @@@@@@@@@@@A@6Two-dimensional arrays@@/ݐ3 returns a new Bigarray of two dimensions, whose size is $dim1 ! in the first dimension and $dim2; in the second dimension. $kind% and &layout R determine the array element kind and the array layout as described for  D@!.@@@@@@@@@@@@@ A@ D@ G@ J@@@@栕4Bigarray.Array2.init3 #Array2.init kind layout dim1 dim2 f8 returns a new Bigarray !b ' of two dimensions, whose size is $dim2 ! in the first dimension and $dim2; in the second dimension. $kind% and &layout R determine the array element kind and the array layout as described for  BD@!.@3 Each element 0Array2.get b i j 3 of the array is initialized to the result of %f i j!.@6 In other words, #Array2.init kind layout dim1 dim2 f? tabulates the results of !f L applied to the indices of a new Bigarray whose layout is described by $kind", &layout", $dim1% and $dim2!.@@@@$4.12@@@@@@@H@ I@ 4@ &@ "@ @@@@4Bigarray.Array2.dim13 AReturn the first dimension of the given two-dimensional Bigarray.@@@@@@@@@@@@@ @@@@᠕4Bigarray.Array2.dim23 BReturn the second dimension of the given two-dimensional Bigarray.@@@@@@@@@@@@@ @@@@4Bigarray.Array2.kind3 &Return the kind of the given Bigarray.@@@@@@@@@@@@@ @@@@6Bigarray.Array2.layout3 (Return the layout of the given Bigarray.@@@@@@@@@@@@@ @@@@l=Bigarray.Array2.change_layout3=Array2.change_layout a layout - returns a Bigarray with the specified &layout8, sharing the data with !a 0 (and hence having the same dimensions as !a ). No copying of elements is involved: the new array and the original array share the same storage space. The dimensions are reversed, such that 0get v [| a; b |]; in C layout becomes 4get v [| b+1; a+1 |]3 in Fortran layout.@@@@$4.06@@@@@@@@ 4@ 7s@@@@Y=Bigarray.Array2.size_in_bytes3/size_in_bytes a> is the number of elements in !a3 multiplied by !a#'s  iD@!.@@@@$4.03@@@@@@@q@ ]r@@@@P3Bigarray.Array2.get30Array2.get a x y/, also written 'a.{x,y}>, returns the element of !a1 at coordinates (!x", !y(). !x% and !y # must be within the bounds of !a3, as described for  ]D@2; otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@ @ m@ i@@@@`3Bigarray.Array2.set32Array2.set a x y v3, or alternatively ,a.{x,y} <- v8, stores the value !v1 at coordinates (!x", !y%) in !a'. !x% and !y> must be within the bounds of !a8, as described for  1D@2; otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@ @ @ @ @@@@q8Bigarray.Array2.sub_left3 |Extract a two-dimensional sub-array of the given two-dimensional Bigarray by restricting the first dimension. See ސD@8 for more details. /Array2.sub_left & applies only to arrays with C layout.@@@@@@@@@@@@~@ @ _@ #[@@@@=9Bigarray.Array2.sub_right3 }Extract a two-dimensional sub-array of the given two-dimensional Bigarray by restricting the second dimension. See D@8 for more details. 0Array2.sub_right , applies only to arrays with Fortran layout.@@@@@@@@@@@@J@ >K@ A+@ D'@@@@ :Bigarray.Array2.slice_left3 Extract a row (one-dimensional slice) of the given two-dimensional Bigarray. The integer parameter is the index of the row to extract. See .D@8 for more details. 1Array2.slice_left & applies only to arrays with C layout.@@@@@@@@@@@@@ _@ b@@@@ߠ;Bigarray.Array2.slice_right3 Extract a column (one-dimensional slice) of the given two-dimensional Bigarray. The integer parameter is the index of the column to extract. See ֐D@9 for more details. 2Array2.slice_right 1 applies only to arrays with Fortran layout.@@@@@@@@@@@@@ }@ @@@@4Bigarray.Array2.blit3 9Copy the first Bigarray to the second Bigarray. See ~D@2 for more details.@@@@@@@@@@@@@ @ @@@@4Bigarray.Array2.fill3 7Fill the given Bigarray with the given value. See HD@2 for more details.@@@@@@@@@@@@@ @ @@@@l8Bigarray.Array2.of_array3 QBuild a two-dimensional Bigarray initialized from the given array of arrays.@@@@@@@@@@@@m@ n@ Y@ K@@@@4:Bigarray.Array2.unsafe_get3%Like qD@ 4, but bounds checking is not always performed.@@@@@@@@@@@@;@ <@ @ @@@@:Bigarray.Array2.unsafe_set3%Like >D@ 4, but bounds checking is not always performed.@@@@@@@@@@@@@ @ @ @ @@@@@@@@@@@A@8Three-dimensional arrays@@/3>Three-dimensional arrays. The &Array3 6 structure provides operations similar to those of  }@@ =, but specialized to the case of three-dimensional arrays.@@@@@@@@@@@@A3#1Bigarray.Array3.t3 LThe type of three-dimensional Bigarrays whose elements have OCaml type "'a6, representation kind "'b4, and memory layout "'c!.@@@@@@@@@@@@OO O@@A@@@@6Bigarray.Array3.create3 (Array3.create kind layout dim1 dim2 dim3 @ returns a new Bigarray of three dimensions, whose size is $dim1> in the first dimension, $dim2> in the second dimension, and $dim34 in the third. $kind% and &layout M determine the array element kind and the array layout as described for  ;D@!.@@@@@@@@@@@@.@y/@|@ @@@@@@4Bigarray.Array3.init3 (Array3.init kind layout dim1 dim2 dim3 f8 returns a new Bigarray !b ) of three dimensions, whose size is $dim1> in the first dimension, $dim2> in the second dimension, and $dim34 in the third. $kind% and &layout M determine the array element kind and the array layout as described for  D@!.@3 Each element 2Array3.get b i j k 3 of the array is initialized to the result of 'f i j k!.@6 In other words, (Array3.init kind layout dim1 dim2 dim3 f? tabulates the results of !f L applied to the indices of a new Bigarray whose layout is described by $kind", &layout", $dim1", $dim2% and $dim3!.@@@@$4.12@@@@@@@b@c@N@@@ <@ 8@4@@@@4Bigarray.Array3.dim13 CReturn the first dimension of the given three-dimensional Bigarray.@@@@@@@@@@@@@@@@@4Bigarray.Array3.dim23 DReturn the second dimension of the given three-dimensional Bigarray.@@@@@@@@@@@@@.@@@@̠4Bigarray.Array3.dim33 CReturn the third dimension of the given three-dimensional Bigarray.@@@@@@@@@@@@@=@@@@4Bigarray.Array3.kind3 &Return the kind of the given Bigarray.@@@@@@@@@@@@@L@@@@6Bigarray.Array3.layout3 (Return the layout of the given Bigarray.@@@@@@@@@@@@@[@@@@W=Bigarray.Array3.change_layout3=Array3.change_layout a layout - returns a Bigarray with the specified &layout8, sharing the data with !a 0 (and hence having the same dimensions as !a ). No copying of elements is involved: the new array and the original array share the same storage space. The dimensions are reversed, such that 3get v [| a; b; c |]; in C layout becomes 9get v [| c+1; b+1; a+1 |]3 in Fortran layout.@@@@$4.06@@@@@@@{@|@^@@@@D=Bigarray.Array3.size_in_bytes3/size_in_bytes a> is the number of elements in !a3 multiplied by !a#'s D@!.@@@@$4.03@@@@@@@\@]@@@@;3Bigarray.Array3.get32Array3.get a x y z/, also written )a.{x,y,z}>, returns the element of !a1 at coordinates (!x", !y", !z(). !x", !y% and !z> must be within the bounds of !a8, as described for  D@2; otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@ @ d@`@\@@@@R3Bigarray.Array3.set32Array3.set a x y v3, or alternatively .a.{x,y,z} <- v8, stores the value !v1 at coordinates (!x", !y", !z%) in !a'. !x", !y% and !z> must be within the bounds of !a8, as described for  D@2; otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@m@p@s}@vy@y@@@@j8Bigarray.Array3.sub_left3 Extract a three-dimensional sub-array of the given three-dimensional Bigarray by restricting the first dimension. See  UD@4 for more details. /Array3.sub_left + applies only to arrays with C layout.@@@@@@@@@@@@w@x@X@T@@@@69Bigarray.Array3.sub_right3 Extract a three-dimensional sub-array of the given three-dimensional Bigarray by restricting the second dimension. See  D@4 for more details. 0Array3.sub_right 1 applies only to arrays with Fortran layout.@@@@@@@@@@@@C@D@$@ @@@@ 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 e. The returned Bigarray must have exactly the same number of elements as the original Bigarray !b 0. That is, the product of the dimensions of !b2 must be equal to -i1 * ... * iN0. Otherwise, 0Invalid_argument+ is raised.@@@@@@@@@@@@@@@@@@2Bigarray.reshape_037Specialized version of D@ - for reshaping to zero-dimensional arrays.@@@@$4.05@@@@@@@@@@@@2Bigarray.reshape_137Specialized version of D@ , for reshaping to one-dimensional arrays.@@@@@@@@@@@@@'@*n@@@@^2Bigarray.reshape_237Specialized version of ѐD@ , for reshaping to two-dimensional arrays.@@@@@@@@@@@@e@?f@BH@ED@@@@42Bigarray.reshape_337Specialized version of D@ / for reshaping to three-dimensional arrays.@@@@@@@@@@@@;@Z<@]@`@c@@@@A4bigarray_concurrency Bigarrays and concurrency safety@@ Care must be taken when concurrently accessing bigarrays from multiple domains: accessing a bigarray will never crash a program, but unsynchronized accesses might yield surprising (non-sequentially-consistent) results.@% B2bigarray_atomicity)Atomicity@@ Every bigarray operation that accesses more than one array element is not atomic. This includes slicing, bliting, and filling bigarrays.@ 2 For example, consider the following program: -open Bigarray let size = 100_000_000 let a = Array1.init Int C_layout size (fun _ -> 1) let update f a () = for i = 0 to size - 1 do a.{i} <- f a.{i} done let d1 = Domain.spawn (update (fun x -> x + 1) a) let d2 = Domain.spawn (update (fun x -> 2 * x + 1) a) let () = Domain.join d1; Domain.join d2 @ ; After executing this code, each field of the bigarray !a+ is either !2&, !3", !4$ or !5 k. If atomicity is required, then the user must implement their own synchronization (for example, using 'Mutex.t@@").@% B2bigarray_data_race*Data races@@ If two domains only access disjoint parts of the bigarray, then the observed behaviour is the equivalent to some sequential interleaving of the operations from the two domains.@ 1 A data race is said to occur when two domains access the same bigarray element without synchronization and at least one of the accesses is a write. In the absence of data races, the observed behaviour is equivalent to some sequential interleaving of the operations from different domains.@ Whenever possible, data races should be avoided by using synchronization to mediate the accesses to the bigarray elements.@ Indeed, in the presence of data races, programs will not crash but the observed behaviour may not be equivalent to any sequential interleaving of operations from different domains.@% B=bigarrarray_data_race_tearing'Tearing@@ C Bigarrays have a distinct caveat in the presence of data races: concurrent bigarray operations might produce surprising values due to tearing. More precisely, the interleaving of partial writes and reads might create values that would not exist with a sequential execution. For instance, at the end of let res = Array1.init Complex64 c_layout size (fun _ -> Complex.zero) let d1 = Domain.spawn (fun () -> Array1.fill res Complex.one) let d2 = Domain.spawn (fun () -> Array1.fill res Complex.i) let () = Domain.join d1; Domain.join d2 ) the #res 0 bigarray might contain values that are neither )Complex.i) nor +Complex.one/ (for instance %1 + i").@@@@@A'Complex@@@@@