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Module Owl_dense_ndarray_generic

module Owl_dense_ndarray_generic: sig .. end
N-dimensional array module: including creation, manipulation, and various vectorised mathematical operations.
type ('a, 'b) t = ('a, 'b, Bigarray.c_layout) Bigarray.Genarray.t
N-dimensional array abstract type
type ('a, 'b) kind = ('a, 'b) Bigarray.kind
Type of the ndarray, e.g., Bigarray.Float32, Bigarray.Complex64, and etc.

Create N-dimensional array

val empty : ('a, 'b) kind ->
       int array -> ('a, 'b) t
empty Bigarray.Float64 [|3;4;5|] creates a three diemensional array of type Bigarray.Float64. Each dimension has the following size: 3, 4, and 5. The elements in the array are not initialised, they can be any value. empty is faster than zeros to create a ndarray.

The module only supports the following four types of ndarray: Bigarray.Float32, Bigarray.Float64, Bigarray.Complex32, and Bigarray.Complex64.

val create : ('a, 'b) kind ->
       int array -> 'a -> ('a, 'b) t
create Bigarray.Float64 [|3;4;5|] 2. creates a three-diemensional array of type Bigarray.Float64. Each dimension has the following size: 3, 4, and 5. The elements in the array are initialised to 2.
val init : ('a, 'b) kind ->
       int array -> (int -> 'a) -> ('a, 'b) t
init Bigarray.Float64 d f creates a ndarray x of shape d, then using f to initialise the elements in x. The input of f is 1-dimensional index of the ndarray. You need to explicitly convert it if you need N-dimensional index. The function Owl_utils._index_1d_nd can help you.
val init_nd : ('a, 'b) kind ->
       int array -> (int array -> 'a) -> ('a, 'b) t
init_nd is almost the same as init but f receives n-dimensional index as input. It is more convenient since you don't have to convert the index by yourself, but this also means init_nd is slower than init.
val zeros : ('a, 'b) kind ->
       int array -> ('a, 'b) t
zeros Bigarray.Complex32 [|3;4;5|] creates a three-diemensional array of type Bigarray.Complex32. Each dimension has the following size: 3, 4, and 5. The elements in the array are initialised to "zero". Depending on the kind, zero can be 0. or Complex.zero.
val ones : ('a, 'b) kind ->
       int array -> ('a, 'b) t
ones Bigarray.Complex32 [|3;4;5|] creates a three-diemensional array of type Bigarray.Complex32. Each dimension has the following size: 3, 4, and 5. The elements in the array are initialised to "one". Depending on the kind, one can be 1. or Complex.one.
val uniform : ?scale:float ->
       ('a, 'b) kind ->
       int array -> ('a, 'b) t
uniform Bigarray.Float64 [|3;4;5|] creates a three-diemensional array of type Bigarray.Float64. Each dimension has the following size: 3, 4, and 5. The elements in the array follow a uniform distribution 0,1.
val gaussian : ?sigma:float ->
       ('a, 'b) kind ->
       int array -> ('a, 'b) t
gaussian Float64 [|3;4;5|] ...
val sequential : ('a, 'b) kind ->
       ?a:'a -> ?step:'a -> int array -> ('a, 'b) t
sequential Bigarray.Float64 [|3;4;5|] 2. creates a three-diemensional array of type Bigarray.Float64. Each dimension has the following size: 3, 4, and 5. The elements in the array are assigned sequential values.

?a specifies the starting value and the default value is zero; whilst ?step specifies the step size with default value one.

val linspace : ('a, 'b) kind ->
       'a -> 'a -> int -> ('a, 'b) t
linspace k 0. 9. 10 ...
val logspace : ('a, 'b) kind ->
       ?base:float -> 'a -> 'a -> int -> ('a, 'b) t
logspace k 0. 9. 10 ...
val bernoulli : ('a, 'b) kind ->
       ?p:float -> ?seed:int -> int array -> ('a, 'b) t
bernoulli k ~p:0.3 [|2;3;4|]

Obtain basic properties

val shape : ('a, 'b) t -> int array
shape x returns the shape of ndarray x.
val num_dims : ('a, 'b) t -> int
num_dims x returns the number of dimensions of ndarray x.
val nth_dim : ('a, 'b) t -> int -> int
nth_dim x returns the size of the nth dimension of x.
val numel : ('a, 'b) t -> int
numel x returns the number of elements in x.
val nnz : ('a, 'b) t -> int
nnz x returns the number of non-zero elements in x.
val density : ('a, 'b) t -> float
density x returns the percentage of non-zero elements in x.
val size_in_bytes : ('a, 'b) t -> int
size_in_bytes x returns the size of x in bytes in memory.
val same_shape : ('a, 'b) t ->
       ('a, 'b) t -> bool
same_shape x y checks whether x and y has the same shape or not.
val kind : ('a, 'b) t ->
       ('a, 'b) kind
kind x returns the type of ndarray x. It is one of the four possible values: Bigarray.Float32, Bigarray.Float64, Bigarray.Complex32, and Bigarray.Complex64.
val strides : ('a, 'b) t -> int array
strides x calcuates the strides of x. E.g., if x is of shape [|3;4;5|], the returned strides will be [|20;5;1|].
val slice_size : ('a, 'b) t -> int array
slice_size calculates the slice size in each dimension, E.g., if x is of shape [|3;4;5|], the returned slice size will be |60; 20; 5|.
val index_1d_nd : int -> int array -> int array
index_1d_nd i stride converts one-dimensional index i to n-dimensional index according to the passed in stride.

NOTE: you need to pass in stride, not the shape of x!

val index_nd_1d : int array -> int array -> int
index_nd_1d i shp converts n-dimensional index i to one-dimensional index according to the passed in stride.

NOTE: you need to pass in stride, not the shape of x!


Manipulate a N-dimensional array

val get : ('a, 'b) t -> int array -> 'a
get x i returns the value at i in x. E.g., get x [|0;2;1|] returns the value at [|0;2;1|] in x.
val set : ('a, 'b) t -> int array -> 'a -> unit
set x i a sets the value at i to a in x.
val sub_left : ('a, 'b) t ->
       int -> int -> ('a, 'b) t
Some as Bigarray.sub_left, please refer to Bigarray documentation.
val slice_left : ('a, 'b) t ->
       int array -> ('a, 'b) t
Same as Bigarray.slice_left, please refer to Bigarray documentation.
val slice : int list list ->
       ('a, 'b) t -> ('a, 'b) t
slice s x returns a copy of the slice in x. The slice is defined by a which is an int option array. E.g., for a ndarray x of dimension [|2; 2; 3|], slice [0] x takes the following slices of index \(0,*,*\), i.e., [|0;0;0|], [|0;0;1|], [|0;0;2|] ... Also note that if the length of s is less than the number of dimensions of x, slice function will append slice definition to higher diemensions by assuming all the elements in missing dimensions will be taken.

Basically, slice function offers very much the same semantic as that in numpy, i.e., start:stop:step grammar, so if you how to index and slice ndarray in numpy, you should not find it difficult to use this function. Please just refer to numpy documentation or my tutorial.

There are two differences between slice_left and slice: slice_left does not make a copy but simply moving the pointer; slice_left can only make a slice from left-most axis whereas slice is much more flexible and can work on arbitrary axis which need not start from left-most side.

val copy : ('a, 'b) t ->
       ('a, 'b) t -> unit
copy src dst copies the data from ndarray src to dst.
val reset : ('a, 'b) t -> unit
reset x resets all the elements in x to zero.
val fill : ('a, 'b) t -> 'a -> unit
fill x a assigns the value a to the elements in x.
val clone : ('a, 'b) t -> ('a, 'b) t
clone x makes a copy of x.
val resize : ?head:bool ->
       ('a, 'b) t ->
       int array -> ('a, 'b) t
resize ~head x d resizes the ndarray x. If there are less number of elelments in the new shape than the old one, the new ndarray shares part of the memeory with the old x. head indicates the alignment between the new and old data, either from head or from tail. Note the data is flattened before the operation.

If there are more elements in the new shape d. Then new memeory space will be allocated and the content of x will be copied to the new memory. The rest of the allocated space will be filled with zeros.

val reshape : ('a, 'b) t ->
       int array -> ('a, 'b) t
reshape x d transforms x into a new shape definted by d. Note the reshape function will not make a copy of x, the returned ndarray shares the same memory with the original x.
val flatten : ('a, 'b) t -> ('a, 'b) t
flatten x transforms x into a one-dimsonal array without making a copy. Therefore the returned value shares the same memory space with original x.
val reverse : ('a, 'b) t -> ('a, 'b) t
reverse x reverse the order of all elements in the flattened x and returns the results in a new ndarray. The original x remains intact.
val transpose : ?axis:int array ->
       ('a, 'b) t -> ('a, 'b) t
transpose ~axis x makes a copy of x, then transpose it according to ~axis. ~axis must be a valid permutation of x dimension indices. E.g., for a three-dimensional ndarray, it can be 2;1;0, 0;2;1, 1;2;0, and etc.
val swap : int ->
       int ->
       ('a, 'b) t -> ('a, 'b) t
swap i j x makes a copy of x, then swaps the data on axis i and j.
val tile : ('a, 'b) t ->
       int array -> ('a, 'b) t
tile x a tiles the data in x according the repitition specified by a. This function provides the exact behaviour as numpy.tile, please refer to the numpy's online documentation for details.
val repeat : ?axis:int ->
       ('a, 'b) t ->
       int -> ('a, 'b) t
repeat ~axis x a repeats the elements along axis for a times. The default value of ?axis is the highest dimension of x. This function is similar to numpy.repeat except that a is an integer instead of an array.
val concatenate : ?axis:int ->
       ('a, 'b) t array ->
       ('a, 'b) t
concatenate ~axis:2 x concatenates an array of ndarrays along the third dimension. For the ndarrays in x, they must have the same shape except the dimension specified by axis. The default value of axis is 0, i.e., the lowest dimension on an ndarray.
val squeeze : ?axis:int array ->
       ('a, 'b) t -> ('a, 'b) t
squeeze ~axis x removes single-dimensional entries from the shape of x.
val expand : ('a, 'b) t ->
       int -> ('a, 'b) t
expand x d reshapes x by increasing its rank from num_dims x to d. The opposite operation is squeeze x.
val pad : ?v:'a ->
       int list list ->
       ('a, 'b) t -> ('a, 'b) t
pad ~v:0. [[1;1]] x
val dropout : ?rate:float ->
       ?seed:int ->
       ('a, 'b) t -> ('a, 'b) t
dropout ~rate:0.3 x drops out 30% of the elements in x, in other words, by setting their values to zeros.
val mmap : Unix.file_descr ->
       ?pos:int64 ->
       ('a, 'b) kind ->
       bool -> int array -> ('a, 'b) t
mmap fd kind layout shared dims ...

Iterate array elements

val iteri : ?axis:int option array ->
       (int array -> 'a -> unit) -> ('a, 'b) t -> unit
iteri ~axis f x applies function f to each element in a slice defined by ~axis. If ~axis is not passed in, then iteri simply iterates all the elements in x.
val iter : ?axis:int option array ->
       ('a -> unit) -> ('a, 'b) t -> unit
iter ~axis f x is similar to iteri ~axis f x, excpet the index i of an element is not passed in f. Note that iter is much faster than iteri.
val mapi : ?axis:int option array ->
       (int array -> 'a -> 'a) ->
       ('a, 'b) t -> ('a, 'b) t
mapi ~axis f x makes a copy of x, then applies f to each element in a slice defined by ~axis. If ~axis is not passed in, then mapi simply iterates all the elements in x.
val map : ?axis:int option array ->
       ('a -> 'a) ->
       ('a, 'b) t -> ('a, 'b) t
map ~axis f x is similar to mapi ~axis f x except the index of the current element is not passed to the function f. Note that map is much faster than mapi.
val map2i : ?axis:int option array ->
       (int array -> 'a -> 'a -> 'a) ->
       ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
map2i ~axis f x y applies f to two elements of the same position in a slice defined by ~axis in both x and y. If ~axis is not passed in, then map2i simply iterates all the elements in x and y. The two matrices mush have the same shape.
val map2 : ?axis:int option array ->
       ('a -> 'a -> 'a) ->
       ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
map2 ~axis f x y is similar to map2i ~axis f x y except the index of the index of the current element is not passed to the function f.
val filteri : ?axis:int option array ->
       (int array -> 'a -> bool) ->
       ('a, 'b) t -> int array array
filteri ~axis f x uses f to filter out certain elements in a slice defined by ~axis. An element will be included if f returns true. The returned result is a list of indices of the selected elements.
val filter : ?axis:int option array ->
       ('a -> bool) -> ('a, 'b) t -> int array array
Similar to filteri, but the indices of the elements are not passed to f.
val foldi : ?axis:int option array ->
       (int array -> 'c -> 'a -> 'c) ->
       'c -> ('a, 'b) t -> 'c
foldi ~axis f a x folds all the elements in a slice defined by ~axis with the function f. If ~axis is not passed in, then foldi simply folds all the elements in x.
val fold : ?axis:int option array ->
       ('c -> 'a -> 'c) -> 'c -> ('a, 'b) t -> 'c
Similar to foldi, except that the index of an element is not passed to f.
val iteri_slice : int array ->
       (int array array -> ('a, 'b) t -> unit) ->
       ('a, 'b) t -> unit
iteri_slice s f x iterates the slices along the passed in axis indices s, and applies the function f to each of them. The order of iterating slices is based on the order of axis in s.

E.g., for a three-dimensional ndarray of shape [|2;2;2|], iteri_slice [|1;0|] f x will access the slices in the following order: [ [0]; [0]; [] ], [ [1]; [0]; [] ], [ [1]; [1]; [] ]. Also note the slice passed in f is a copy of the original data.

val iter_slice : int array ->
       (('a, 'b) t -> unit) ->
       ('a, 'b) t -> unit
Similar to iteri_slice, except that the index of a slice is not passed to f.
val iter2i : (int array -> 'a -> 'b -> unit) ->
       ('a, 'c) t ->
       ('b, 'd) t -> unit
Similar to iteri but applies to two N-dimensional arrays x and y. Both x and y must have the same shape.
val iter2 : ('a -> 'b -> unit) ->
       ('a, 'c) t ->
       ('b, 'd) t -> unit
Similar to iter2i, except that the index of a slice is not passed to f.

Examine array elements or compare two arrays 

val exists : ('a -> bool) -> ('a, 'b) t -> bool
exists f x checks all the elements in x using f. If at least one element satisfies f then the function returns true otherwise false.
val not_exists : ('a -> bool) -> ('a, 'b) t -> bool
not_exists f x checks all the elements in x, the function returns true only if all the elements fail to satisfy f : float -> bool.
val for_all : ('a -> bool) -> ('a, 'b) t -> bool
for_all f x checks all the elements in x, the function returns true if and only if all the elements pass the check of function f.
val is_zero : ('a, 'b) t -> bool
is_zero x returns true if all the elements in x are zeros.
val is_positive : ('a, 'b) t -> bool
is_positive x returns true if all the elements in x are positive.
val is_negative : ('a, 'b) t -> bool
is_negative x returns true if all the elements in x are negative.
val is_nonpositive : ('a, 'b) t -> bool
is_nonpositive returns true if all the elements in x are non-positive.
val is_nonnegative : ('a, 'b) t -> bool
is_nonnegative returns true if all the elements in x are non-negative.
val is_normal : ('a, 'b) t -> bool
is_normal x returns true if all the elelments in x are normal float numbers, i.e., not NaN, not INF, not SUBNORMAL. Please refer to

https://www.gnu.org/software/libc/manual/html_node/Floating-Point-Classes.html https://www.gnu.org/software/libc/manual/html_node/Infinity-and-NaN.html#Infinity-and-NaN

val not_nan : ('a, 'b) t -> bool
not_nan x returns false if there is any NaN element in x. Otherwise, the function returns true indicating all the numbers in x are not NaN.
val not_inf : ('a, 'b) t -> bool
not_inf x returns false if there is any positive or negative INF element in x. Otherwise, the function returns true.
val equal : ('a, 'b) t ->
       ('a, 'b) t -> bool
equal x y returns true if two ('a, 'b) trices x and y are equal.
val not_equal : ('a, 'b) t ->
       ('a, 'b) t -> bool
not_equal x y returns true if there is at least one element in x is not equal to that in y.
val greater : ('a, 'b) t ->
       ('a, 'b) t -> bool
greater x y returns true if all the elements in x are greater than the corresponding elements in y.
val less : ('a, 'b) t ->
       ('a, 'b) t -> bool
less x y returns true if all the elements in x are smaller than the corresponding elements in y.
val greater_equal : ('a, 'b) t ->
       ('a, 'b) t -> bool
greater_equal x y returns true if all the elements in x are not smaller than the corresponding elements in y.
val less_equal : ('a, 'b) t ->
       ('a, 'b) t -> bool
less_equal x y returns true if all the elements in x are not greater than the corresponding elements in y.
val elt_equal : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
elt_equal x y performs element-wise = comparison of x and y. Assume that a is from x and b is the corresponding element of a from y of the same position. The function returns another binary (0 and 1) ndarray/matrix wherein 1 indicates a = b.
val elt_not_equal : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
elt_not_equal x y performs element-wise != comparison of x and y. Assume that a is from x and b is the corresponding element of a from y of the same position. The function returns another binary (0 and 1) ndarray/matrix wherein 1 indicates a <> b.
val elt_less : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
elt_less x y performs element-wise < comparison of x and y. Assume that a is from x and b is the corresponding element of a from y of the same position. The function returns another binary (0 and 1) ndarray/matrix wherein 1 indicates a < b.
val elt_greater : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
elt_greater x y performs element-wise > comparison of x and y. Assume that a is from x and b is the corresponding element of a from y of the same position. The function returns another binary (0 and 1) ndarray/matrix wherein 1 indicates a > b.
val elt_less_equal : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
elt_less_equal x y performs element-wise <= comparison of x and y. Assume that a is from x and b is the corresponding element of a from y of the same position. The function returns another binary (0 and 1) ndarray/matrix wherein 1 indicates a <= b.
val elt_greater_equal : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
elt_greater_equal x y performs element-wise >= comparison of x and y. Assume that a is from x and b is the corresponding element of a from y of the same position. The function returns another binary (0 and 1) ndarray/matrix wherein 1 indicates a >= b.
val equal_scalar : ('a, 'b) t -> 'a -> bool
equal_scalar x a checks if all the elements in x are equal to a. The function returns true iff for every element b in x, b = a.
val not_equal_scalar : ('a, 'b) t -> 'a -> bool
not_equal_scalar x a checks if all the elements in x are not equal to a. The function returns true iff for every element b in x, b <> a.
val less_scalar : ('a, 'b) t -> 'a -> bool
less_scalar x a checks if all the elements in x are less than a. The function returns true iff for every element b in x, b < a.
val greater_scalar : ('a, 'b) t -> 'a -> bool
greater_scalar x a checks if all the elements in x are greater than a. The function returns true iff for every element b in x, b > a.
val less_equal_scalar : ('a, 'b) t -> 'a -> bool
less_equal_scalar x a checks if all the elements in x are less or equal to a. The function returns true iff for every element b in x, b <= a.
val greater_equal_scalar : ('a, 'b) t -> 'a -> bool
greater_equal_scalar x a checks if all the elements in x are greater or equal to a. The function returns true iff for every element b in x, b >= a.
val elt_equal_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
elt_equal_scalar x a performs element-wise = comparison of x and a. Assume that b is one element from x The function returns another binary (0 and 1) ndarray/matrix wherein 1 of the corresponding position indicates a = b, otherwise 0.
val elt_not_equal_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
elt_not_equal_scalar x a performs element-wise != comparison of x and a. Assume that b is one element from x The function returns another binary (0 and 1) ndarray/matrix wherein 1 of the corresponding position indicates a <> b, otherwise 0.
val elt_less_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
elt_less_scalar x a performs element-wise < comparison of x and a. Assume that b is one element from x The function returns another binary (0 and 1) ndarray/matrix wherein 1 of the corresponding position indicates a < b, otherwise 0.
val elt_greater_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
elt_greater_scalar x a performs element-wise > comparison of x and a. Assume that b is one element from x The function returns another binary (0 and 1) ndarray/matrix wherein 1 of the corresponding position indicates a > b, otherwise 0.
val elt_less_equal_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
elt_less_equal_scalar x a performs element-wise <= comparison of x and a. Assume that b is one element from x The function returns another binary (0 and 1) ndarray/matrix wherein 1 of the corresponding position indicates a <= b, otherwise 0.
val elt_greater_equal_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
elt_greater_equal_scalar x a performs element-wise >= comparison of x and a. Assume that b is one element from x The function returns another binary (0 and 1) ndarray/matrix wherein 1 of the corresponding position indicates a >= b, otherwise 0.
val approx_equal : ?eps:float ->
       ('a, 'b) t ->
       ('a, 'b) t -> bool
approx_equal ~eps x y returns true if x and y are approximately equal, i.e., for any two elements a from x and b from y, we have abs (a - b) < eps. For complex numbers, the eps applies to both real and imaginary part.

Note: the threshold check is exclusive for passed in eps.

val approx_equal_scalar : ?eps:float -> ('a, 'b) t -> 'a -> bool
approx_equal_scalar ~eps x a returns true all the elements in x are approximately equal to a, i.e., abs (x - a) < eps. For complex numbers, the eps applies to both real and imaginary part.

Note: the threshold check is exclusive for the passed in eps.

val approx_elt_equal : ?eps:float ->
       ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
approx_elt_equal ~eps x y compares the element-wise equality of x and y, then returns another binary (i.e., 0 and 1) ndarray/matrix wherein 1 indicates that two corresponding elements a from x and b from y are considered as approximately equal, namely abs (a - b) < eps.
val approx_elt_equal_scalar : ?eps:float ->
       ('a, 'b) t ->
       'a -> ('a, 'b) t
approx_elt_equal_scalar ~eps x a compares all the elements of x to a scalar value a, then returns another binary (i.e., 0 and 1) ndarray/matrix wherein 1 indicates that the element b from x is considered as approximately equal to a, namely abs (a - b) < eps.

Input/Output functions

val of_array : ('a, 'b) kind ->
       'a array -> int array -> ('a, 'b) t
of_array k x d takes an array x and converts it into an ndarray of type k and shape d.
val to_array : ('a, 'b) t -> 'a array
to_array x converts an ndarray x to OCaml's array type. Note the ndarray x is flattened before convertion.
val print : ('a, 'b) t -> unit
print x prints all the elements in x as well as their indices.
val pp_dsnda : ('a, 'b) t -> unit
pp_dsnda x prints x in OCaml toplevel. If the ndarray is too long, pp_dsnda only prints out parts of the ndarray.
val save : ('a, 'b) t -> string -> unit
save x s serialises a ndarray x to a file of name s.
val load : ('a, 'b) kind ->
       string -> ('a, 'b) t
load k s loads previously serialised ndarray from file s into memory. It is necesssary to specify the type of the ndarray with paramater k.

Unary mathematical operations 

val re_c2s : (Complex.t, Bigarray.complex32_elt) t ->
       (float, Bigarray.float32_elt) t
re_c2s x returns all the real components of x in a new ndarray of same shape.
val re_z2d : (Complex.t, Bigarray.complex64_elt) t ->
       (float, Bigarray.float64_elt) t
re_d2z x returns all the real components of x in a new ndarray of same shape.
val im_c2s : (Complex.t, Bigarray.complex32_elt) t ->
       (float, Bigarray.float32_elt) t
im_c2s x returns all the imaginary components of x in a new ndarray of same shape.
val im_z2d : (Complex.t, Bigarray.complex64_elt) t ->
       (float, Bigarray.float64_elt) t
im_d2z x returns all the imaginary components of x in a new ndarray of same shape.
val sum : ('a, 'b) t -> 'a
sum x returns the sumtion of all elements in x.
val prod : ?axis:int option array -> ('a, 'b) t -> 'a
prod x returns the product of all elements in x along passed in axises.
val min : (float, 'a) t -> float
min x returns the minimum of all elements in x.
val max : (float, 'a) t -> float
max x returns the maximum of all elements in x.
val minmax : (float, 'a) t -> float * float
minmax x returns (min_v, max_v), min_v is the minimum value in x while max_v is the maximum.
val min_i : (float, 'a) t -> float * int array
min_i x returns the minimum of all elements in x along with its index.
val max_i : (float, 'a) t -> float * int array
max_i x returns the maximum of all elements in x along with its index.
val minmax_i : (float, 'a) t ->
       (float * int array) * (float * int array)
minmax_i x returns ((min_v,min_i), (max_v,max_i)) where (min_v,min_i) is the minimum value in x along with its index while (max_v,max_i) is the maximum value along its index.
val abs : (float, 'a) t ->
       (float, 'a) t
abs x returns the absolute value of all elements in x in a new ndarray.
val abs_c2s : (Complex.t, Bigarray.complex32_elt) t ->
       (float, Bigarray.float32_elt) t
abs_c2s x is similar to abs but takes complex32 as input.
val abs_z2d : (Complex.t, Bigarray.complex64_elt) t ->
       (float, Bigarray.float64_elt) t
abs_z2d x is similar to abs but takes complex64 as input.
val abs2 : (float, 'a) t ->
       (float, 'a) t
abs2 x returns the square of absolute value of all elements in x in a new ndarray.
val abs2_c2s : (Complex.t, Bigarray.complex32_elt) t ->
       (float, Bigarray.float32_elt) t
abs2_c2s x is similar to abs2 but takes complex32 as input.
val abs2_z2d : (Complex.t, Bigarray.complex64_elt) t ->
       (float, Bigarray.float64_elt) t
abs2_z2d x is similar to abs2 but takes complex64 as input.
val conj : ('a, 'b) t -> ('a, 'b) t
conj x returns the conjugate of the complex x.
val neg : ('a, 'b) t -> ('a, 'b) t
neg x negates the elements in x and returns the result in a new ndarray.
val reci : ('a, 'b) t -> ('a, 'b) t
reci x computes the reciprocal of every elements in x and returns the result in a new ndarray.
val signum : (float, 'a) t ->
       (float, 'a) t
signum computes the sign value (-1 for negative numbers, 0 (or -0) for zero, 1 for positive numbers, nan for nan).
val sqr : (float, 'a) t ->
       (float, 'a) t
sqr x computes the square of the elements in x and returns the result in a new ndarray.
val sqrt : (float, 'a) t ->
       (float, 'a) t
sqrt x computes the square root of the elements in x and returns the result in a new ndarray.
val cbrt : (float, 'a) t ->
       (float, 'a) t
cbrt x computes the cubic root of the elements in x and returns the result in a new ndarray.
val exp : (float, 'a) t ->
       (float, 'a) t
exp x computes the exponential of the elements in x and returns the result in a new ndarray.
val exp2 : (float, 'a) t ->
       (float, 'a) t
exp2 x computes the base-2 exponential of the elements in x and returns the result in a new ndarray.
val exp10 : (float, 'a) t ->
       (float, 'a) t
exp10 x computes the base-10 exponential of the elements in x and returns the result in a new ndarray.
val expm1 : (float, 'a) t ->
       (float, 'a) t
expm1 x computes exp x -. 1. of the elements in x and returns the result in a new ndarray.
val log : (float, 'a) t ->
       (float, 'a) t
log x computes the logarithm of the elements in x and returns the result in a new ndarray.
val log10 : (float, 'a) t ->
       (float, 'a) t
log10 x computes the base-10 logarithm of the elements in x and returns the result in a new ndarray.
val log2 : (float, 'a) t ->
       (float, 'a) t
log2 x computes the base-2 logarithm of the elements in x and returns the result in a new ndarray.
val log1p : (float, 'a) t ->
       (float, 'a) t
log1p x computes log (1 + x) of the elements in x and returns the result in a new ndarray.
val sin : (float, 'a) t ->
       (float, 'a) t
sin x computes the sine of the elements in x and returns the result in a new ndarray.
val cos : (float, 'a) t ->
       (float, 'a) t
cos x computes the cosine of the elements in x and returns the result in a new ndarray.
val tan : (float, 'a) t ->
       (float, 'a) t
tan x computes the tangent of the elements in x and returns the result in a new ndarray.
val asin : (float, 'a) t ->
       (float, 'a) t
asin x computes the arc sine of the elements in x and returns the result in a new ndarray.
val acos : (float, 'a) t ->
       (float, 'a) t
acos x computes the arc cosine of the elements in x and returns the result in a new ndarray.
val atan : (float, 'a) t ->
       (float, 'a) t
atan x computes the arc tangent of the elements in x and returns the result in a new ndarray.
val sinh : (float, 'a) t ->
       (float, 'a) t
sinh x computes the hyperbolic sine of the elements in x and returns the result in a new ndarray.
val cosh : (float, 'a) t ->
       (float, 'a) t
cosh x computes the hyperbolic cosine of the elements in x and returns the result in a new ndarray.
val tanh : (float, 'a) t ->
       (float, 'a) t
tanh x computes the hyperbolic tangent of the elements in x and returns the result in a new ndarray.
val asinh : (float, 'a) t ->
       (float, 'a) t
asinh x computes the hyperbolic arc sine of the elements in x and returns the result in a new ndarray.
val acosh : (float, 'a) t ->
       (float, 'a) t
acosh x computes the hyperbolic arc cosine of the elements in x and returns the result in a new ndarray.
val atanh : (float, 'a) t ->
       (float, 'a) t
atanh x computes the hyperbolic arc tangent of the elements in x and returns the result in a new ndarray.
val floor : ('a, 'b) t -> ('a, 'b) t
floor x computes the floor of the elements in x and returns the result in a new ndarray.
val ceil : ('a, 'b) t -> ('a, 'b) t
ceil x computes the ceiling of the elements in x and returns the result in a new ndarray.
val round : ('a, 'b) t -> ('a, 'b) t
round x rounds the elements in x and returns the result in a new ndarray.
val trunc : ('a, 'b) t -> ('a, 'b) t
trunc x computes the truncation of the elements in x and returns the result in a new ndarray.
val modf : ('a, 'b) t ->
       ('a, 'b) t * ('a, 'b) t
modf x performs modf over all the elements in x, the fractal part is saved in the first element of the returned tuple whereas the integer part is saved in the second element.
val erf : (float, 'a) t ->
       (float, 'a) t
erf x computes the error function of the elements in x and returns the result in a new ndarray.
val erfc : (float, 'a) t ->
       (float, 'a) t
erfc x computes the complementary error function of the elements in x and returns the result in a new ndarray.
val logistic : (float, 'a) t ->
       (float, 'a) t
logistic x computes the logistic function 1/(1 + exp(-a) of the elements in x and returns the result in a new ndarray.
val relu : (float, 'a) t ->
       (float, 'a) t
relu x computes the rectified linear unit function max(x, 0) of the elements in x and returns the result in a new ndarray.
val elu : ?alpha:float ->
       (float, 'a) t ->
       (float, 'a) t
elu alpha x computes the exponential linear unit function x >= 0. ? x : (alpha * (exp(x) - 1)) of the elements in x and returns the result in a new ndarray.
val leaky_relu : ?alpha:float ->
       (float, 'a) t ->
       (float, 'a) t
leaky_relu alpha x computes the leaky rectified linear unit function x >= 0. ? x : (alpha * x) of the elements in x and returns the result in a new ndarray.
val softplus : (float, 'a) t ->
       (float, 'a) t
softplus x computes the softplus function log(1 + exp(x) of the elements in x and returns the result in a new ndarray.
val softsign : (float, 'a) t ->
       (float, 'a) t
softsign x computes the softsign function x / (1 + abs(x)) of the elements in x and returns the result in a new ndarray.
val softmax : (float, 'a) t ->
       (float, 'a) t
softmax x computes the softmax functions (exp x) / (sum (exp x)) of all the elements in x and returns the result in a new array.
val sigmoid : (float, 'a) t ->
       (float, 'a) t
sigmoid x computes the sigmoid function 1 / (1 + exp (-x)) for each element in x.
val log_sum_exp : (float, 'a) t -> float
log_sum_exp x computes the logarithm of the sum of exponentials of all the elements in x.
val l1norm : ('a, 'b) t -> float
l1norm x calculates the l1-norm of all the element in x.
val l2norm : ('a, 'b) t -> float
l2norm x calculates the l2-norm of all the element in x.
val l2norm_sqr : ('a, 'b) t -> float
l2norm_sqr x calculates the sum of 2-norm (or l2norm, Euclidean norm) of all elements in x. The function uses conjugate transpose in the product, hence it always returns a float number.
val cumsum : ?axis:int ->
       ('a, 'b) t -> ('a, 'b) t
cumsum ~axis x : performs cumulative sum of the elements along the given axis ~axis. If ~axis is None, then the cumsum is performed over the flattened x. The returned result however always remains the same shape.
val cumprod : ?axis:int ->
       ('a, 'b) t -> ('a, 'b) t
cumprod ~axis x : similar to cumsum but performs cumulative product of the elements along the given ~axis.

Binary mathematical operations 

val add : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
add x y adds all the elements in x and y elementwise, and returns the result in a new ndarray.
val sub : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
sub x y subtracts all the elements in x and y elementwise, and returns the result in a new ndarray.
val mul : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
mul x y multiplies all the elements in x and y elementwise, and returns the result in a new ndarray.
val div : ('a, 'b) t ->
       ('a, 'b) t -> ('a, 'b) t
div x y divides all the elements in x and y elementwise, and returns the result in a new ndarray.
val add_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
add_scalar x a adds a scalar value a to all the elements in x, and returns the result in a new ndarray.
val sub_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
sub_scalar x a subtracts a scalar value a to all the elements in x, and returns the result in a new ndarray.
val mul_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
mul_scalar x a multiplies a scalar value a to all the elements in x, and returns the result in a new ndarray.
val div_scalar : ('a, 'b) t ->
       'a -> ('a, 'b) t
div_scalar x a divides a scalar value a to all the elements in x, and returns the result in a new ndarray.
val scalar_add : 'a ->
       ('a, 'b) t -> ('a, 'b) t
scalar_add a x is similar to add_scalar but with scalar as the first parameter.
val scalar_sub : 'a ->
       ('a, 'b) t -> ('a, 'b) t
scalar_sub a x is similar to sub_scalar but with scalar as the first parameter.
val scalar_mul : 'a ->
       ('a, 'b) t -> ('a, 'b) t
scalar_mul a x is similar to mul_scalar but with scalar as the first parameter.
val scalar_div : 'a ->
       ('a, 'b) t -> ('a, 'b) t
scalar_div a x is similar to div_scalar but with scalar as the first parameter.
val pow : (float, 'a) t ->
       (float, 'a) t ->
       (float, 'a) t
pow x y computes pow(a, b) of all the elements in x and y elementwise, and returns the result in a new ndarray.
val scalar_pow : float ->
       (float, 'a) t ->
       (float, 'a) t
scalar_pow a x computes the power value of a scalar value a using the elements in a ndarray x.
val pow_scalar : (float, 'a) t ->
       float -> (float, 'a) t
pow_scalar x a computes each element in x power to a.
val atan2 : (float, 'a) t ->
       (float, 'a) t ->
       (float, 'a) t
atan2 x y computes atan2(a, b) of all the elements in x and y elementwise, and returns the result in a new ndarray.
val scalar_atan2 : float ->
       (float, 'a) t ->
       (float, 'a) t
scalar_atan2 a x
val atan2_scalar : (float, 'a) t ->
       float -> (float, 'a) t
scalar_atan2 x a
val hypot : (float, 'a) t ->
       (float, 'a) t ->
       (float, 'a) t
hypot x y computes sqrt(x*x + y*y) of all the elements in x and y elementwise, and returns the result in a new ndarray.
val min2 : (float, 'a) t ->
       (float, 'a) t ->
       (float, 'a) t
min2 x y computes the minimum of all the elements in x and y elementwise, and returns the result in a new ndarray.
val max2 : (float, 'a) t ->
       (float, 'a) t ->
       (float, 'a) t
max2 x y computes the maximum of all the elements in x and y elementwise, and returns the result in a new ndarray.
val fmod : (float, 'a) t ->
       (float, 'a) t ->
       (float, 'a) t
fmod x y performs float mod division.
val fmod_scalar : (float, 'a) t ->
       float -> (float, 'a) t
fmod_scalar x a performs mod division between x and scalar a.
val scalar_fmod : float ->
       (float, 'a) t ->
       (float, 'a) t
scalar_fmod x a performs mod division between scalar a and x.
val ssqr : ('a, 'b) t -> 'a -> 'a
ssqr x a computes the sum of squared differences of all the elements in x from constant a. This function only computes the square of each element rather than the conjugate transpose as Owl_dense_ndarray_generic.l2norm_sqr does.
val ssqr_diff : ('a, 'b) t ->
       ('a, 'b) t -> 'a
ssqr_diff x y computes the sum of squared differences of every elements in x and its corresponding element in y.
val cross_entropy : (float, 'a) t ->
       (float, 'a) t -> float
cross_entropy x y calculates the cross entropy between x and y using base e.
val clip_by_l2norm : float ->
       (float, 'a) t ->
       (float, 'a) t
clip_by_l2norm t x clips the x according to the threshold set by t.

Cast functions

val cast_s2d : (float, Bigarray.float32_elt) t ->
       (float, Bigarray.float64_elt) t
cast_s2d x casts x from float32 to float64.
val cast_d2s : (float, Bigarray.float64_elt) t ->
       (float, Bigarray.float32_elt) t
cast_d2s x casts x from float64 to float32.
val cast_c2z : (Complex.t, Bigarray.complex32_elt) t ->
       (Complex.t, Bigarray.complex64_elt) t
cast_c2z x casts x from complex32 to complex64.
val cast_z2c : (Complex.t, Bigarray.complex64_elt) t ->
       (Complex.t, Bigarray.complex32_elt) t
cast_z2c x casts x from complex64 to complex32.
val cast_s2c : (float, Bigarray.float32_elt) t ->
       (Complex.t, Bigarray.complex32_elt) t
cast_s2c x casts x from float32 to complex32.
val cast_d2z : (float, Bigarray.float64_elt) t ->
       (Complex.t, Bigarray.complex64_elt) t
cast_d2z x casts x from float64 to complex64.
val cast_s2z : (float, Bigarray.float32_elt) t ->
       (Complex.t, Bigarray.complex64_elt) t
cast_s2z x casts x from float32 to complex64.
val cast_d2c : (float, Bigarray.float64_elt) t ->
       (Complex.t, Bigarray.complex32_elt) t
cast_d2c x casts x from float64 to complex32.

Neural network related functions

type padding =
| SAME
| VALID 
val conv1d : ?padding:padding ->
       (float, 'a) t ->
       (float, 'a) t ->
       int array -> (float, 'a) t
[]
val conv2d : ?padding:padding ->
       (float, 'a) t ->
       (float, 'a) t ->
       int array -> (float, 'a) t
[]
val conv3d : ?padding:padding ->
       (float, 'a) t ->
       (float, 'a) t ->
       int array -> (float, 'a) t
[]
val max_pool1d : ?padding:padding ->
       (float, 'a) t ->
       int array -> int array -> (float, 'a) t
[]
val max_pool2d : ?padding:padding ->
       (float, 'a) t ->
       int array -> int array -> (float, 'a) t
[]
val max_pool3d : ?padding:padding ->
       (float, 'a) t ->
       int array -> int array -> (float, 'a) t
[]
val avg_pool1d : ?padding:padding ->
       (float, 'a) t ->
       int array -> int array -> (float, 'a) t
[]
val avg_pool2d : ?padding:padding ->
       (float, 'a) t ->
       int array -> int array -> (float, 'a) t
[]
val avg_pool3d : ?padding:padding ->
       (float, 'a) t ->
       int array -> int array -> (float, 'a) t
[]
val max_pool2d_argmax : ?padding:padding ->
       (float, 'a) t ->
       int array ->
       int array ->
       (float, 'a) t *
       (int64, Bigarray.int64_elt) t
[]
val conv2d_backward_input : (float, 'a) t ->
       (float, 'a) t ->
       int array ->
       (float, 'a) t ->
       (float, 'a) t
[]
val conv2d_backward_kernel : (float, 'a) t ->
       (float, 'a) t ->
       int array ->
       (float, 'a) t ->
       (float, 'a) t
[]
val conv3d_backward_input : (float, 'a) t ->
       (float, 'a) t ->
       int array ->
       (float, 'a) t ->
       (float, 'a) t
[]
val conv3d_backward_kernel : (float, 'a) t ->
       (float, 'a) t ->
       int array ->
       (float, 'a) t ->
       (float, 'a) t
[]
val max_pool2d_backward : padding ->
       (float, 'a) t ->
       int array ->
       int array ->
       (float, 'a) t ->
       (float, 'a) t
[]
val avg_pool2d_backward : padding ->
       (float, 'a) t ->
       int array ->
       int array ->
       (float, 'a) t ->
       (float, 'a) t
[]

Some helper and experimental functions


The following functions are helper functions for some other functions in both Ndarray and Ndview modules. In general, you are not supposed to use these functions directly.
val print_element : ('a, 'b) kind -> 'a -> unit
print_element kind a prints the value of a single element.
val print_index : int array -> unit
print_index i prints out the index of an element.
val _check_transpose_axis : int array -> int -> unit
_check_transpose_axis a d checks whether a is a legiti('a, 'b) te transpose index.
val sum_slices : ?axis:int ->
       ('a, 'b) t -> ('a, 'b) t
sum_slices ~axis:2 x for x of |2;3;4;5|, it returns an ndarray of shape |4;5|. Currently, the operation is done using gemm, fast but uses more memory.
val calc_conv2d_output_shape : padding ->
       int -> int -> int -> int -> int -> int -> int * int
[]
val calc_conv3d_output_shape : padding ->
       int ->
       int -> int -> int -> int -> int -> int -> int -> int -> int * int * int
[]

[]
val slice_along_dim0 : ('a, 'b) t ->
       int array -> ('a, 'b) t
val draw_along_dim0 : ('a, 'b) t ->
       int -> ('a, 'b) t * int array