Module Owl_dense_matrix_generic

Matrix module: including creation, manipulation, and various vectorised mathematical operations.

About the comparison of two complex numbers x and y, Owl uses the following conventions: 1) x and y are equal iff both real and imaginary parts are equal; 2) x is less than y if the magnitude of x is less than the magnitude of x; in case both x and y have the same magnitudes, x is less than x if the phase of x is less than the phase of y; 3) less or equal, greater, greater or equal relation can be further defined atop of the aforementioned conventions.

The generic module supports operations for the following Bigarry element types: Int8_signed, Int8_unsigned, Int16_signed, Int16_unsigned, Int32, Int64, Float32, Float64, Complex32, Complex64.

Type definition
type ('a, 'b) t = ( 'a, 'b, Stdlib.Bigarray.c_layout ) Stdlib.Bigarray.Genarray.t

N-dimensional array type, i.e. Bigarray Genarray type.

Create matrices
val empty : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> ( 'a, 'b ) t

empty m n creates an m by n matrix without initialising the values of elements in x.

val create : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> 'a -> ( 'a, 'b ) t

create m n a creates an m by n matrix and all the elements of x are initialised with the value a.

val init : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> ( int -> 'a ) -> ( 'a, 'b ) t

init m n f creates a matrix x of shape m x n, then using f to initialise the elements in x. The input of f is 1-dimensional index of the matrix. You need to explicitly convert it if you need 2D index. The function Owl_utils.ind can help you.

val init_2d : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> ( int -> int -> 'a ) -> ( 'a, 'b ) t

init_2d m n f s almost the same as init but f receives 2D index as input. It is more convenient since you don't have to convert the index by yourself, but this also means init_2d is slower than init.

val zeros : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> ( 'a, 'b ) t

zeros m n creates an m by n matrix where all the elements are initialised to zeros.

val ones : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> ( 'a, 'b ) t

ones m n creates an m by n matrix where all the elements are ones.

val eye : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> ( 'a, 'b ) t

eye m creates an m by m identity matrix.

val complex : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ( 'c, 'd ) Owl_dense_ndarray_generic.kind -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'c, 'd ) t

complex re im constructs a complex ndarray/matrix from re and im. re and im contain the real and imaginary part of x respectively.

Note that both re and im can be complex but must have same type. The real part of re will be the real part of x and the imaginary part of im will be the imaginary part of x.

val polar : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ( 'c, 'd ) Owl_dense_ndarray_generic.kind -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'c, 'd ) t

complex rho theta constructs a complex ndarray/matrix from polar coordinates rho and theta. rho contains the magnitudes and theta contains phase angles. Note that the behaviour is undefined if rho has negative elelments or theta has infinity elelments.

val unit_basis : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> int -> ( 'a, 'b ) t

unit_basis k n i returns a unit basis vector with ith element set to 1.

val sequential : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ?a:'a -> ?step:'a -> int -> int -> ( 'a, 'b ) t

sequential ~a ~step m n creates an m by n matrix. The elements in x are initialised sequentiallly from ~a and is increased by ~step.

The default value of ~a is zero whilst the default value of ~step is one.

val uniform : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ?a:'a -> ?b:'a -> int -> int -> ( 'a, 'b ) t

uniform m n creates an m by n matrix where all the elements follow a uniform distribution in (0,1) interval. uniform ~scale:a m n adjusts the interval to (0,a).

val gaussian : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ?mu:'a -> ?sigma:'a -> int -> int -> ( 'a, 'b ) t

gaussian m n creates an m by n matrix where all the elements in x follow a Gaussian distribution with specified sigma. By default sigma = 1.

val poisson : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> mu:float -> int -> int -> ( 'a, 'b ) t

poisson m n creates an m by n matrix where all the elements in x follow a Poisson distribution with specified rate mu.

val semidef : ( float, 'b ) Owl_dense_ndarray_generic.kind -> int -> ( float, 'b ) t

semidef n returns an random n by n positive semi-definite matrix.

val linspace : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> 'a -> 'a -> int -> ( 'a, 'b ) t

linspace a b n linearly divides the interval [a,b] into n pieces by creating an m by 1 row vector. E.g., linspace 0. 5. 5 will create a row vector [0;1;2;3;4;5].

val logspace : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ?base:float -> 'a -> 'a -> int -> ( 'a, 'b ) t

logspace base a b n ... the default value of base is e.

val meshgrid : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> 'a -> 'a -> 'a -> 'a -> int -> int -> ( 'a, 'b ) t * ( 'a, 'b ) t

meshgrid a1 b1 a2 b2 n1 n2 is similar to the meshgrid function in Matlab. It returns two matrices x and y where the row vectors in x are linearly spaced between [a1,b1] by n1 whilst the column vectors in y are linearly spaced between (a2,b2) by n2.

val meshup : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t * ( 'a, 'b ) t

meshup x y creates mesh grids by using two row vectors x and y.

val bernoulli : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ?p:float -> int -> int -> ( 'a, 'b ) t

bernoulli k ~p:0.3 m n

val diagm : ?k:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

diagm k v creates a diagonal matrix using the elements in v as diagonal values. k specifies the main diagonal index. If k > 0 then it is above the main diagonal, if k < 0 then it is below the main diagonal. This function is the same as the diag function in Matlab.

val triu : ?k:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

triu k x returns the element on and above the kth diagonal of x. k = 0 is the main diagonal, k > 0 is above the main diagonal, and k < 0 is below the main diagonal.

val tril : ?k:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

tril k x returns the element on and below the kth diagonal of x. k = 0 is the main diagonal, k > 0 is above the main diagonal, and k < 0 is below the main diagonal.

val symmetric : ?upper:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

symmetric ~upper x creates a symmetric matrix using either upper or lower triangular part of x. If upper is true then it uses the upper part, if upper is false, then symmetric uses the lower part. By default upper is true.

val hermitian : ?upper:bool -> ( Stdlib.Complex.t, 'a ) t -> ( Stdlib.Complex.t, 'a ) t

hermitian ~upper x creates a hermitian matrix based on x. By default, the upper triangular part is used for creating the hermitian matrix, but you use the lower part by setting upper=false

val bidiagonal : ?upper:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

bidiagonal upper dv ev creates a bidiagonal matrix using dv and ev. Both dv and ev are row vectors. dv is the main diagonal. If upper is true then ev is superdiagonal; if upper is false then ev is subdiagonal. By default, upper is true.

NOTE: because the diagonal elements in a hermitian matrix must be real, the function set the imaginary part of the diagonal elements to zero by default. In other words, if the diagonal elements of x have non-zero imaginary parts, the imaginary parts will be dropped without a warning.

val toeplitz : ?c:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

toeplitz ~c r generates a toeplitz matrix using r and c. Both r and c are row vectors of the same length. If the first elements of c is different from that of r, r's first element will be used.

Note: 1) If c is not passed in, then c = r will be used. 2) If c is not passed in and r is complex, the c = conj r will be used. 3) If r and c have different length, then the result is a rectangular matrix.

val hankel : ?r:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

hankel ~r c generates a hankel matrix using r and c. c will be the first column and r will be the last row of the returned matrix.

Note: 1) If only c is passed in, the elelments below the anti-diagnoal are zero. 2) If the last element of c is different from the first element of r then the first element of c prevails. 3) c and r can have different length, the return will be an rectangular matrix.

val hadamard : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> ( 'a, 'b ) t

hadamard k n constructs a hadamard matrix of order n. For a hadamard H, we have H'*H = n*I. Currently, this function handles only the cases where n, n/12, or n/20 is a power of 2.

val magic : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> int -> ( 'a, 'b ) t

magic k n constructs a n x n magic square matrix x. The elements in x are consecutive numbers increasing from 1 to n^2. n must n >= 3.

There are three different algorithms to deal with n is odd, singly even, and doubly even respectively.

Obtain basic properties
val shape : ( 'a, 'b ) t -> int * int

If x is an m by n matrix, shape x returns (m,n), i.e., the size of two dimensions of x.

val row_num : ( 'a, 'b ) t -> int

row_num x returns the number of rows in matrix x.

val col_num : ( 'a, 'b ) t -> int

col_num x returns the number of columns in matrix x.

val numel : ( 'a, 'b ) t -> int

numel x returns the number of elements in matrix x. It is equivalent to (row_num x) * (col_num 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 returns true if two matrics have the same shape.

val same_data : ( 'a, 'b ) t -> ( 'a, 'b ) t -> bool

Refer to :doc:`owl_dense_ndarray_generic`.

val kind : ( 'a, 'b ) t -> ( 'a, 'b ) Owl_dense_ndarray_generic.kind

kind x returns the type of matrix x.

Manipulate a matrix
val get : ( 'a, 'b ) t -> int -> int -> 'a

get x i j returns the value of element (i,j) of x. The shorthand for get x i j is x.{i,j}

val set : ( 'a, 'b ) t -> int -> int -> 'a -> unit

set x i j a sets the element (i,j) of x to value a. The shorthand for set x i j a is x.{i,j} <- a

val get_index : ( 'a, 'b ) t -> int array array -> 'a array

get_index i x returns an array of element values specified by the indices i. The length of array i equals the number of dimensions of x. The arrays in i must have the same length, and each represents the indices in that dimension.

E.g., [| [|1;2|]; [|3;4|] |] returns the value of elements at position (1,3) and (2,4) respectively.

val set_index : ( 'a, 'b ) t -> int array array -> 'a array -> unit

set_index sets the value of elements in x according to the indices specified by i. The length of array i equals the number of dimensions of x. The arrays in i must have the same length, and each represents the indices in that dimension.

val get_fancy : Owl_types.index list -> ( 'a, 'b ) t -> ( 'a, 'b ) t

get_fancy s x returns a copy of the slice in x. The slice is defined by a which is an int array. Please refer to the same function in the Owl_dense_ndarray_generic documentation for more details.

val set_fancy : Owl_types.index list -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

set_fancy axis x y set the slice defined by axis in x according to the values in y. y must have the same shape as the one defined by axis.

About the slice definition of axis, please refer to slice function.

val get_fancy_ext : Owl_types.index array -> ( 'a, 'b ) t -> ( 'a, 'b ) t

This function is used for extended indexing operator since ocaml 4.10.0. The indexing and slicing syntax become much ligher.

val set_fancy_ext : Owl_types.index array -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

This function is used for extended indexing operator since ocaml 4.10.0. The indexing and slicing syntax become much ligher.

val get_slice : int list list -> ( 'a, 'b ) t -> ( 'a, 'b ) t

get_slice axis x aims to provide a simpler version of get_fancy. This function assumes that every list element in the passed in in list list represents a range, i.e., R constructor.

E.g., [[];[0;3];[0]] is equivalent to [R []; R [0;3]; R [0]].

val set_slice : int list list -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

set_slice axis x y aims to provide a simpler version of set_slice. This function assumes that every list element in the passed in in list list represents a range, i.e., R constructor.

E.g., [[];[0;3];[0]] is equivalent to [R []; R [0;3]; R [0]].

val get_slice_ext : int list array -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Please refer to Ndarray document.

val set_slice_ext : int list array -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

Please refer to Ndarray document.

val row : ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

row x i returns row i of x. Note: Unlike col, the return value is simply a view onto the original row in x, so modifying row's value also alters x.

The function supports nagative indices.

val col : ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

col x j returns column j of x. Note: Unlike row, the return value is a copy of the original row in x.

The function supports nagative indices.

val rows : ( 'a, 'b ) t -> int array -> ( 'a, 'b ) t

rows x a returns the rows (defined in an int array a) of x. The returned rows will be combined into a new dense matrix. The order of rows in the new matrix is the same as that in the array a.

The function supports nagative indices.

val cols : ( 'a, 'b ) t -> int array -> ( 'a, 'b ) t

Similar to rows, cols x a returns the columns (specified in array a) of x in a new dense matrix.

The function supports nagative indices.

val resize : ?head:bool -> ( 'a, 'b ) t -> int array -> ( 'a, 'b ) t

resize x s please refer to the Ndarray document.

val reshape : ( 'a, 'b ) t -> int array -> ( 'a, 'b ) t

reshape x s returns a new m by n matrix from the m' by n' matrix x. Note that (m * n) must be equal to (m' * n'), and the returned matrix shares the same memory with the original x.

val flatten : ( 'a, 'b ) t -> ( 'a, 'b ) t

flatten x reshape x into a 1 by n row vector 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 matrix. The original x remains intact.

val flip : ?axis:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

flip ~axis x flips a matrix/ndarray along axis. By default axis = 0. The result is returned in a new matrix/ndarray, so the original x remains intact.

val rotate : ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

rotate x d rotates x clockwise d degrees. d must be multiple times of 90, otherwise the function will fail. If x is an n-dimensional array, then the function rotates the plane formed by the first and second dimensions.

val reset : ( 'a, 'b ) t -> unit

reset x resets all the elements of x to zero value.

val fill : ( 'a, 'b ) t -> 'a -> unit

fill x a fills the x with value a.

val copy : ( 'a, 'b ) t -> ( 'a, 'b ) t

copy x returns a copy of matrix x.

val copy_row_to : ( 'a, 'b ) t -> ( 'a, 'b ) t -> int -> unit

copy_row_to v x i copies an 1 by n row vector v to the ith row in an m by n matrix x.

val copy_col_to : ( 'a, 'b ) t -> ( 'a, 'b ) t -> int -> unit

copy_col_to v x j copies an 1 by n column vector v to the jth column in an m by n matrix x.

val concat_vertical : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

concat_vertical x y concats two matrices x and y vertically, therefore their column numbers must be the same.

The associated operator is @=, please refer to :doc:`owl_operator`.

val concat_horizontal : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

concat_horizontal x y concats two matrices x and y horizontally, therefore their row numbers must be the same.

The associated operator is @||, please refer to :doc:`owl_operator`.

val concat_vh : ( 'a, 'b ) t array array -> ( 'a, 'b ) t

concat_vh is used to assemble small parts of matrices into a bigger one. E.g. [| [|a; b; c|]; [|d; e; f|]; [|g; h; i|] |] will be concatenated into a big matrix as follows.

Please refer to :doc:`owl_dense_ndarray_generic`. for details.

val concatenate : ?axis:int -> ( 'a, 'b ) t array -> ( 'a, 'b ) t

concatenate ~axis:1 x concatenates an array of matrices along the second dimension. For the matrices 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 a marix, i.e., rows.

val split : ?axis:int -> int array -> ( 'a, 'b ) t -> ( 'a, 'b ) t array

split ~axis parts x splits an ndarray x into parts along the specified axis. This function is the inverse operation of concatenate. The elements in x must sum up to the dimension in the specified axis.

val split_vh : (int * int) array array -> ( 'a, 'b ) t -> ( 'a, 'b ) t array array

Please refer to :doc:`owl_dense_ndarray_generic`. for details.

val transpose : ( 'a, 'b ) t -> ( 'a, 'b ) t

transpose x transposes an m by n matrix to n by m one.

val ctranspose : ( 'a, 'b ) t -> ( 'a, 'b ) t

ctranspose x performs conjugate transpose of a complex matrix x. If x is a real matrix, then ctranspose x is equivalent to transpose x.

val diag : ?k:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

diag k x returns the kth diagonal elements of x. k > 0 means above the main diagonal and k < 0 means the below the main diagonal.

val swap_rows : ( 'a, 'b ) t -> int -> int -> unit

swap_rows x i i' swaps the row i with row i' of x.

val swap_cols : ( 'a, 'b ) t -> int -> int -> unit

swap_cols x j j' swaps the column j with column j' of x.

val tile : ( 'a, 'b ) t -> int array -> ( 'a, 'b ) t

tile x a provides the exact behaviour as numpy.tile function.

val repeat : ( 'a, 'b ) t -> int array -> ( 'a, 'b ) t

repeat x a repeats the elements x according the repetition specified by a.

val pad : ?v:'a -> int list list -> ( 'a, 'b ) t -> ( 'a, 'b ) t

padd ~v:0. [[1;1]] x

val dropout : ?rate:float -> ( '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 top : ( 'a, 'b ) t -> int -> int array array

top x n returns the indices of n greatest values of x. The indices are arranged according to the corresponding element values, from the greatest one to the smallest one.

val bottom : ( 'a, 'b ) t -> int -> int array array

bottom x n returns the indices of n smallest values of x. The indices are arranged according to the corresponding element values, from the smallest one to the greatest one.

val sort : ( 'a, 'b ) t -> ( 'a, 'b ) t

sort x performs quicksort of the elelments in x. A new copy is returned as result, the original x remains intact. If you want to perform in-place sorting, please use `sort_` instead.

val argsort : ( 'a, 'b ) t -> ( int64, Stdlib.Bigarray.int64_elt ) t

argsort x returns the indices with which the elements in x are sorted in increasing order. Note that the returned index ndarray has the same shape as that of x, and the indices are 1D indices.

Iteration functions
val iteri : ( int -> 'a -> unit ) -> ( 'a, 'b ) t -> unit

iteri f x iterates all the elements in x and applies the user defined function f : int -> int -> float -> 'a. f i j v takes three parameters, i and j are the coordinates of current element, and v is its value.

val iter : ( 'a -> unit ) -> ( 'a, 'b ) t -> unit

iter f x is the same as as iteri f x except the coordinates of the current element is not passed to the function f : float -> 'a

val mapi : ( int -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mapi f x maps each element in x to a new value by applying f : int -> int -> float -> float. The first two parameters are the coordinates of the element, and the third parameter is the value.

val map : ( 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

map f x is similar to mapi f x except the coordinates of the current element is not passed to the function f : float -> float

val foldi : ?axis:int -> ( int -> 'a -> 'a -> 'a ) -> 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

foldi ~axis f a x folds (or reduces) the elements in x from left along the specified axis using passed in function f. a is the initial element and in f i acc b acc is the accumulater and b is one of the elements in x along the same axis. Note that i is 1d index of b.

val fold : ?axis:int -> ( 'a -> 'a -> 'a ) -> 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Similar to foldi, except that the index of an element is not passed to f.

val scani : ?axis:int -> ( int -> 'a -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scan ~axis f x scans the x along the specified axis using passed in function f. f acc a b returns an updated acc which will be passed in the next call to f i acc a. This function can be used to implement accumulative operations such as sum and prod functions. Note that the i is 1d index of a in x.

val scan : ?axis:int -> ( 'a -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Similar to scani, except that the index of an element is not passed to f.

val filteri : ( int -> 'a -> bool ) -> ( 'a, 'b ) t -> int array

filteri f x uses f : int -> int -> float -> bool to filter out certain elements in x. An element will be included if f returns true. The returned result is a list of coordinates of the selected elements.

val filter : ( 'a -> bool ) -> ( 'a, 'b ) t -> int array

Similar to filteri, but the coordinates of the elements are not passed to the function f : float -> bool.

val iteri_2d : ( int -> int -> 'a -> unit ) -> ( 'a, 'b ) t -> unit

Similar to `iteri` but 2d indices (i,j) are passed to the user function.

val mapi_2d : ( int -> int -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Similar to `mapi` but 2d indices (i,j) are passed to the user function.

val foldi_2d : ?axis:int -> ( int -> int -> 'a -> 'a -> 'a ) -> 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Similar to `foldi` but 2d indices (i,j) are passed to the user function.

val scani_2d : ?axis:int -> ( int -> int -> 'a -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Similar to `scani` but 2d indices (i,j) are passed to the user function.

val filteri_2d : ( int -> int -> 'a -> bool ) -> ( 'a, 'b ) t -> (int * int) array

Similar to `filteri` but 2d indices (i,j) are returned.

val iter2i_2d : ( int -> int -> 'a -> 'c -> unit ) -> ( 'a, 'b ) t -> ( 'c, 'd ) t -> unit

Similar to `iter2i` but 2d indices (i,j) are passed to the user function.

val map2i_2d : ( int -> int -> 'a -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Similar to `map2i` but 2d indices (i,j) are passed to the user function.

val iter2i : ( int -> 'a -> 'b -> unit ) -> ( 'a, 'c ) t -> ( 'b, 'd ) t -> unit

Similar to iteri but applies to two matrices 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 is not passed to f.

val map2i : ( int -> 'a -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

map2i f x y applies f to two elements of the same position in both x and y. Note that 1d index is passed to function f.

val map2 : ( 'a -> 'a -> 'a ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

map2 f x y is similar to map2i f x y except the index is not passed.

val iteri_rows : ( int -> ( 'a, 'b ) t -> unit ) -> ( 'a, 'b ) t -> unit

iteri_rows f x iterates every row in x and applies function f : int -> mat -> unit to each of them.

val iter_rows : ( ( 'a, 'b ) t -> unit ) -> ( 'a, 'b ) t -> unit

Similar to iteri_rows except row number is not passed to f.

val iter2i_rows : ( int -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

iter2_rows f x y iterates rows of two matrices x and `y.

val iter2_rows : ( ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

Similar to iter2iter2i_rows but without passing in indices.

val iteri_cols : ( int -> ( 'a, 'b ) t -> unit ) -> ( 'a, 'b ) t -> unit

iteri_cols f x iterates every column in x and applies function f : int -> mat -> unit to each of them. Column number is passed to f as the first parameter.

val iter_cols : ( ( 'a, 'b ) t -> unit ) -> ( 'a, 'b ) t -> unit

Similar to iteri_cols except col number is not passed to f.

val filteri_rows : ( int -> ( 'a, 'b ) t -> bool ) -> ( 'a, 'b ) t -> int array

filteri_rows f x uses function f : int -> mat -> bool to check each row in x, then returns an int array containing the indices of those rows which satisfy the function f.

val filter_rows : ( ( 'a, 'b ) t -> bool ) -> ( 'a, 'b ) t -> int array

Similar to filteri_rows except that the row indices are not passed to f.

val filteri_cols : ( int -> ( 'a, 'b ) t -> bool ) -> ( 'a, 'b ) t -> int array

filteri_cols f x uses function f : int -> mat -> bool to check each column in x, then returns an int array containing the indices of those columns which satisfy the function f.

val filter_cols : ( ( 'a, 'b ) t -> bool ) -> ( 'a, 'b ) t -> int array

Similar to filteri_cols except that the column indices are not passed to f.

val fold_rows : ( 'c -> ( 'a, 'b ) t -> 'c ) -> 'c -> ( 'a, 'b ) t -> 'c

fold_rows f a x folds all the rows in x using function f. The order of folding is from the first row to the last one.

val fold_cols : ( 'c -> ( 'a, 'b ) t -> 'c ) -> 'c -> ( 'a, 'b ) t -> 'c

fold_cols f a x folds all the columns in x using function f. The order of folding is from the first column to the last one.

val mapi_rows : ( int -> ( 'a, 'b ) t -> 'c ) -> ( 'a, 'b ) t -> 'c array

mapi_rows f x maps every row in x to a type 'a value by applying function f : int -> mat -> 'a to each of them. The results is an array of all the returned values.

val map_rows : ( ( 'a, 'b ) t -> 'c ) -> ( 'a, 'b ) t -> 'c array

Similar to mapi_rows except row number is not passed to f.

val mapi_cols : ( int -> ( 'a, 'b ) t -> 'c ) -> ( 'a, 'b ) t -> 'c array

mapi_cols f x maps every column in x to a type 'a value by applying function f : int -> mat -> 'a.

val map_cols : ( ( 'a, 'b ) t -> 'c ) -> ( 'a, 'b ) t -> 'c array

Similar to mapi_cols except column number is not passed to f.

val mapi_by_row : int -> ( int -> ( 'a, 'b ) t -> ( 'a, 'b ) t ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mapi_by_row d f x applies f to each row of a m by n matrix x, then uses the returned d dimensional row vectors to assemble a new m by d matrix.

val map_by_row : int -> ( ( 'a, 'b ) t -> ( 'a, 'b ) t ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

map_by_row d f x is similar to mapi_by_row except that the row indices are not passed to f.

val mapi_by_col : int -> ( int -> ( 'a, 'b ) t -> ( 'a, 'b ) t ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mapi_by_col d f x applies f to each column of a m by n matrix x, then uses the returned d dimensional column vectors to assemble a new d by n matrix.

val map_by_col : int -> ( ( 'a, 'b ) t -> ( 'a, 'b ) t ) -> ( 'a, 'b ) t -> ( 'a, 'b ) t

map_by_col d f x is similar to mapi_by_col except that the column indices are not passed to f.

val mapi_at_row : ( int -> 'a -> 'a ) -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

mapi_at_row f x i creates a new matrix by applying function f only to the ith row in matrix x.

val map_at_row : ( 'a -> 'a ) -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

map_at_row f x i is similar to mapi_at_row except that the coordinates of an element is not passed to f.

val mapi_at_col : ( int -> 'a -> 'a ) -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

mapi_at_col f x j creates a new matrix by applying function f only to the jth column in matrix x.

val map_at_col : ( 'a -> 'a ) -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t

map_at_col f x i is similar to mapi_at_col except that the coordinates of an element is not passed to f.

Examination & Comparison
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 matrices 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.

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.

Randomisation functions
val draw_rows : ?replacement:bool -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t * int array

draw_rows x m draws m rows randomly from x. The row indices are also returned in an int array along with the selected rows. The parameter replacement indicates whether the drawing is by replacement or not.

val draw_cols : ?replacement:bool -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t * int array

draw_cols x m draws m cols randomly from x. The column indices are also returned in an int array along with the selected columns. The parameter replacement indicates whether the drawing is by replacement or not.

val draw_rows2 : ?replacement:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t * ( 'a, 'b ) t * int array

draw_rows2 x y c is similar to draw_rows but applies to two matrices.

val draw_cols2 : ?replacement:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> int -> ( 'a, 'b ) t * ( 'a, 'b ) t * int array

draw_col2 x y c is similar to draw_cols but applies to two matrices.

val shuffle_rows : ( 'a, 'b ) t -> ( 'a, 'b ) t

shuffle_rows x shuffles all the rows in matrix x.

val shuffle_cols : ( 'a, 'b ) t -> ( 'a, 'b ) t

shuffle_cols x shuffles all the columns in matrix x.

val shuffle : ( 'a, 'b ) t -> ( 'a, 'b ) t

shuffle x shuffles all the elements in x by first shuffling along the rows then shuffling along columns. It is equivalent to shuffle_cols (shuffle_rows x).

Input/Output functions
val to_array : ( 'a, 'b ) t -> 'a array

to_array x flattens an m by n matrix x then returns x as an float array of length (numel x).

val of_array : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> 'a array -> int -> int -> ( 'a, 'b ) t

of_array x m n converts a float array x into an m by n matrix. Note the length of x must be equal to (m * n).

Similar to reshape function, you can pass in one negative index to let Owl automatically infer its dimension.

val to_arrays : ( 'a, 'b ) t -> 'a array array

to arrays x returns an array of float arrays, wherein each row in x becomes an array in the result.

val of_arrays : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> 'a array array -> ( 'a, 'b ) t

of_arrays x converts an array of m float arrays (of length n) in to an m by n matrix.

val to_rows : ( 'a, 'b ) t -> ( 'a, 'b ) t array
val of_rows : ( 'a, 'b ) t array -> ( 'a, 'b ) t
val to_cols : ( 'a, 'b ) t -> ( 'a, 'b ) t array
val of_cols : ( 'a, 'b ) t array -> ( 'a, 'b ) t
val print : ?max_row:int -> ?max_col:int -> ?header:bool -> ?fmt:( 'a -> string ) -> ( 'a, 'b ) t -> unit

print x pretty prints matrix x without headings.

val save : out:string -> ( 'a, 'b ) t -> unit

save x ~out saves the matrix x to a file with the name out. The format is binary by using Marshal module to serialise the matrix.

val load : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> string -> ( 'a, 'b ) t

load f loads a matrix from file f. The file must be previously saved by using save function.

val save_txt : ?sep:string -> ?append:bool -> out:string -> ( 'a, 'b ) t -> unit

save_txt ~sep ~append ~out x saves the matrix x into a text file out delimited by the specified string sep (default: tab). If append is false (it is by default), an existing file will be truncated and overwritten. If append is true and the file exists, new rows will be appended to it. Files are created, if necessary, with the AND of 0o644 and the user's umask value. Note that the operation can be very time consuming.

val load_txt : ?sep:string -> ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> string -> ( 'a, 'b ) t

load_txt ~sep k f load a text file f into a matrix of type k. The delimitor is specified by sep which can be a regular expression.

val save_npy : out:string -> ( 'a, 'b ) t -> unit

save_npy ~out x saves the matrix x into a npy file out. This function is implemented using npy-ocaml https://github.com/LaurentMazare/npy-ocaml.

val load_npy : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> string -> ( 'a, 'b ) t

load_npy file load a npy file into a matrix of type k. If the matrix is in the file is not of type k, fails with [file]: incorrect format. This function is implemented using npy-ocaml https://github.com/LaurentMazare/npy-ocaml.

Unary math operators
val re_c2s : ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t -> ( float, Stdlib.Bigarray.float32_elt ) t

re_c2s x returns all the real components of x in a new ndarray of same shape.

val re_z2d : ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t -> ( float, Stdlib.Bigarray.float64_elt ) t

re_d2z x returns all the real components of x in a new ndarray of same shape.

val im_c2s : ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t -> ( float, Stdlib.Bigarray.float32_elt ) t

im_c2s x returns all the imaginary components of x in a new ndarray of same shape.

val im_z2d : ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t -> ( float, Stdlib.Bigarray.float64_elt ) t

im_d2z x returns all the imaginary components of x in a new ndarray of same shape.

val min : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

min x returns the minimum of all elements in x along specified axis. If no axis is specified, x will be flattened and the minimum of all the elements will be returned. For two complex numbers, the one with the smaller magnitude will be selected. If two magnitudes are the same, the one with the smaller phase will be selected.

val min' : ( 'a, 'b ) t -> 'a

min' x is similar to min but returns the minimum of all elements in x in scalar value.

val max : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

max x returns the maximum of all elements in x along specified axis. If no axis is specified, x will be flattened and the maximum of all the elements will be returned. For two complex numbers, the one with the greater magnitude will be selected. If two magnitudes are the same, the one with the greater phase will be selected.

val max' : ( 'a, 'b ) t -> 'a

max' x is similar to max but returns the maximum of all elements in x in scalar value.

val minmax : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t * ( 'a, 'b ) t

minmax' x returns (min_v, max_v), min_v is the minimum value in x while max_v is the maximum.

val minmax' : ( 'a, 'b ) t -> 'a * 'a

minmax' x returns (min_v, max_v), min_v is the minimum value in x while max_v is the maximum.

val min_i : ( 'a, 'b ) t -> 'a * int array

min_i x returns the minimum of all elements in x as well as its index.

val max_i : ( 'a, 'b ) t -> 'a * int array

max_i x returns the maximum of all elements in x as well as its index.

val minmax_i : ( 'a, 'b ) t -> ('a * int array) * ('a * 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 trace : ( 'a, 'b ) t -> 'a

trace x returns the sum of diagonal elements in x.

val sum : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

sum_ axis x sums the elements in x along specified axis.

val sum' : ( 'a, 'b ) t -> 'a

sum x returns the summation of all the elements in x.

val prod : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

prod_ axis x multiplies the elements in x along specified axis.

val prod' : ( 'a, 'b ) t -> 'a

prod x returns the product of all the elements in x.

val mean : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mean ~axis x calculates the mean along specified axis.

val mean' : ( 'a, 'b ) t -> 'a

mean' x calculates the mean of all the elements in x.

val var : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

var ~axis x calculates the variance along specified axis.

val var' : ( 'a, 'b ) t -> 'a

var' x calculates the variance of all the elements in x.

val std : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

std ~axis calculates the standard deviation along specified axis.

val std' : ( 'a, 'b ) t -> 'a

std' x calculates the standard deviation of all the elements in x.

val sem : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

sem ~axis calculates the standard deviation along specified axis.

val sem' : ( 'a, 'b ) t -> 'a

sem' x calculates the standard deviation of all the elements in x.

val sum_rows : ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

sum_rows x returns the summation of all the row vectors in x.

val sum_cols : ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

sum_cols returns the summation of all the column vectors in x.

val mean_rows : ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mean_rows x returns the mean value of all row vectors in x. It is equivalent to div_scalar (sum_rows x) (float_of_int (row_num x)).

val mean_cols : ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mean_cols x returns the mean value of all column vectors in x. It is equivalent to div_scalar (sum_cols x) (float_of_int (col_num x)).

val min_rows : ( float, 'b ) t -> (float * int * int) array

min_rows x returns the minimum value in each row along with their coordinates.

val min_cols : ( float, 'b ) t -> (float * int * int) array

min_cols x returns the minimum value in each column along with their coordinates.

val max_rows : ( float, 'b ) t -> (float * int * int) array

max_rows x returns the maximum value in each row along with their coordinates.

val max_cols : ( float, 'b ) t -> (float * int * int) array

max_cols x returns the maximum value in each column along with their coordinates.

val abs : ( 'a, 'b ) t -> ( 'a, 'b ) t

abs x returns the absolute value of all elements in x in a new matrix.

val abs_c2s : ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t -> ( float, Stdlib.Bigarray.float32_elt ) t

abs_c2s x is similar to abs but takes complex32 as input.

val abs_z2d : ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t -> ( float, Stdlib.Bigarray.float64_elt ) t

abs_z2d x is similar to abs but takes complex64 as input.

val abs2 : ( 'a, 'b ) t -> ( 'a, 'b ) t

abs2 x returns the square of absolute value of all elements in x in a new ndarray.

val abs2_c2s : ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t -> ( float, Stdlib.Bigarray.float32_elt ) t

abs2_c2s x is similar to abs2 but takes complex32 as input.

val abs2_z2d : ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t -> ( float, Stdlib.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 computes the conjugate of the elements in x and returns the result in a new matrix. If the passed in x is a real matrix, the function simply returns a copy of the original x.

val neg : ( 'a, 'b ) t -> ( 'a, 'b ) t

neg x negates the elements in x and returns the result in a new matrix.

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 reci_tol : ?tol:'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

reci_tol ~tol x computes the reciprocal of every element in x. Different from reci, reci_tol sets the elements whose abs value smaller than tol to zeros. If tol is not specified, the default Owl_utils.eps Float32 will be used. For complex numbers, refer to Owl's doc to see how to compare.

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 : ( 'a, 'b ) t -> ( 'a, 'b ) t

sqr x computes the square of the elements in x and returns the result in a new matrix.

val sqrt : ( 'a, 'b ) t -> ( 'a, 'b ) t

sqrt x computes the square root of the elements in x and returns the result in a new matrix.

val cbrt : ( 'a, 'b ) t -> ( 'a, 'b ) t

cbrt x computes the cubic root of the elements in x and returns the result in a new matrix.

val exp : ( 'a, 'b ) t -> ( 'a, 'b ) t

exp x computes the exponential of the elements in x and returns the result in a new matrix.

val exp2 : ( 'a, 'b ) t -> ( 'a, 'b ) t

exp2 x computes the base-2 exponential of the elements in x and returns the result in a new matrix.

val exp10 : ( 'a, 'b ) t -> ( 'a, 'b ) t

exp2 x computes the base-10 exponential of the elements in x and returns the result in a new matrix.

val expm1 : ( 'a, 'b ) t -> ( 'a, 'b ) t

expm1 x computes exp x -. 1. of the elements in x and returns the result in a new matrix.

val log : ( 'a, 'b ) t -> ( 'a, 'b ) t

log x computes the logarithm of the elements in x and returns the result in a new matrix.

val log10 : ( 'a, 'b ) t -> ( 'a, 'b ) t

log10 x computes the base-10 logarithm of the elements in x and returns the result in a new matrix.

val log2 : ( 'a, 'b ) t -> ( 'a, 'b ) t

log2 x computes the base-2 logarithm of the elements in x and returns the result in a new matrix.

val log1p : ( 'a, 'b ) t -> ( 'a, 'b ) t

log1p x computes log (1 + x) of the elements in x and returns the result in a new matrix.

val sin : ( 'a, 'b ) t -> ( 'a, 'b ) t

sin x computes the sine of the elements in x and returns the result in a new matrix.

val cos : ( 'a, 'b ) t -> ( 'a, 'b ) t

cos x computes the cosine of the elements in x and returns the result in a new matrix.

val tan : ( 'a, 'b ) t -> ( 'a, 'b ) t

tan x computes the tangent of the elements in x and returns the result in a new matrix.

val asin : ( 'a, 'b ) t -> ( 'a, 'b ) t

asin x computes the arc sine of the elements in x and returns the result in a new matrix.

val acos : ( 'a, 'b ) t -> ( 'a, 'b ) t

acos x computes the arc cosine of the elements in x and returns the result in a new matrix.

val atan : ( 'a, 'b ) t -> ( 'a, 'b ) t

atan x computes the arc tangent of the elements in x and returns the result in a new matrix.

val sinh : ( 'a, 'b ) t -> ( 'a, 'b ) t

sinh x computes the hyperbolic sine of the elements in x and returns the result in a new matrix.

val cosh : ( 'a, 'b ) t -> ( 'a, 'b ) t

cosh x computes the hyperbolic cosine of the elements in x and returns the result in a new matrix.

val tanh : ( 'a, 'b ) t -> ( 'a, 'b ) t

tanh x computes the hyperbolic tangent of the elements in x and returns the result in a new matrix.

val asinh : ( 'a, 'b ) t -> ( 'a, 'b ) t

asinh x computes the hyperbolic arc sine of the elements in x and returns the result in a new matrix.

val acosh : ( 'a, 'b ) t -> ( 'a, 'b ) t

acosh x computes the hyperbolic arc cosine of the elements in x and returns the result in a new matrix.

val atanh : ( 'a, 'b ) t -> ( 'a, 'b ) t

atanh x computes the hyperbolic arc tangent of the elements in x and returns the result in a new matrix.

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 matrix.

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 matrix.

val round : ( 'a, 'b ) t -> ( 'a, 'b ) t

round x rounds the elements in x and returns the result in a new matrix.

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 matrix.

val fix : ( 'a, 'b ) t -> ( 'a, 'b ) t

fix x rounds each element of x to the nearest integer toward zero. For positive elements, the behavior is the same as floor. For negative ones, the behavior is the same as ceil.

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 matrix.

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 matrix.

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 matrix.

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 matrix.

val elu : ?alpha:float -> ( float, 'a ) t -> ( float, 'a ) t

refer to Owl_dense_ndarray_generic.elu

val leaky_relu : ?alpha:float -> ( float, 'a ) t -> ( float, 'a ) t

refer to Owl_dense_ndarray_generic.leaky_relu

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 matrix.

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 matrix.

val softmax : ?axis:int -> ( float, 'a ) t -> ( float, 'a ) t

softmax x computes the softmax functions (exp x) / (sum (exp x)) of all the elements along the specified axis in x and returns the result in a new ndarray.

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 log_sum_exp : ?axis:int -> ?keep_dims:bool -> ( float, 'a ) t -> ( float, 'a ) t

log_sum_exp ~axis x computes the logarithm of the sum of exponentials of all the elements in x along axis axis.

val l1norm : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

l1norm x calculates the l1-norm of of x along specified axis.

val l1norm' : ( 'a, 'b ) t -> 'a

l1norm x calculates the l1-norm of all the element in x.

val l2norm : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

l2norm x calculates the l2-norm of of x along specified axis.

val l2norm' : ( 'a, 'b ) t -> 'a

l2norm x calculates the l2-norm of all the element in x.

val l2norm_sqr : ?axis:int -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

l2norm x calculates the square l2-norm of of x along specified axis.

val l2norm_sqr' : ( 'a, 'b ) t -> 'a

l2norm_sqr x calculates the square of l2-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 vecnorm : ?axis:int -> ?p:float -> ?keep_dims:bool -> ( 'a, 'b ) t -> ( 'a, 'b ) t

Refer to :doc:`owl_dense_ndarray_generic`.

val vecnorm' : ?p:float -> ( 'a, 'b ) t -> 'a

Refer to :doc:`owl_dense_ndarray_generic`.

val max_pool : ?padding:Owl_types.padding -> ( float, 'a ) t -> int array -> int array -> ( float, 'a ) t

Refer to :doc:`owl_dense_ndarray_generic`.

val avg_pool : ?padding:Owl_types.padding -> ( float, 'a ) t -> int array -> int array -> ( float, 'a ) t

Refer to :doc:`owl_dense_ndarray_generic`.

val cumsum : ?axis:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

cumsum ~axis x, refer to the documentation in Owl_dense_ndarray_generic.

val cumprod : ?axis:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

cumprod ~axis x, refer to the documentation in Owl_dense_ndarray_generic.

val cummin : ?axis:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

cummin ~axis x : performs cumulative min along axis dimension.

val cummax : ?axis:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

cummax ~axis x : performs cumulative max along axis dimension.

val diff : ?axis:int -> ?n:int -> ( 'a, 'b ) t -> ( 'a, 'b ) t

diff ~axis ~n x calculates the n-th difference of x along the specified axis.

Parameters: * axis: axis to calculate the difference. The default value is the highest dimension. * n: how many times to calculate the difference. The default value is 1.

Return: * The difference ndarray y. Note the shape of y 1 less than that of x along specified axis.

val angle : ( Stdlib.Complex.t, 'a ) t -> ( Stdlib.Complex.t, 'a ) t

angle x calculates the phase angle of all complex numbers in x.

val proj : ( Stdlib.Complex.t, 'a ) t -> ( Stdlib.Complex.t, 'a ) t

proj x computes the projection on Riemann sphere of all elelments in x.

val mat2gray : ?amin:'a -> ?amax:'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

mat2gray ~amin ~amax x converts the matrix x to the intensity image. The elements in x are clipped by amin and amax, and they will be between 0. and 1. after conversion to represents the intensity.

val lgamma : ( 'a, 'b ) t -> ( 'a, 'b ) t

lgamma x computes the loggamma of the elements in x and returns the result in a new matrix.

val dawsn : ( 'a, 'b ) t -> ( 'a, 'b ) t

dawsn x computes the Dawson function of the elements in x and returns the result in a new matrix.

val i0 : ( 'a, 'b ) t -> ( 'a, 'b ) t

i0 x computes the modified Bessel function of order 0 of the elements in x and returns the result in a new ndarray.

val i0e : ( 'a, 'b ) t -> ( 'a, 'b ) t

i0e x computes the exponentially scaled modified Bessel function of order 0 of the elements in x and returns the result in a new ndarray.

val i1 : ( 'a, 'b ) t -> ( 'a, 'b ) t

i1 x computes the modified Bessel function of order 1 of the elements in x and returns the result in a new ndarray.

val i1e : ( 'a, 'b ) t -> ( 'a, 'b ) t

i1e x computes the exponentially scaled modified Bessel function of order 1 of the elements in x and returns the result in a new ndarray.

val iv : v:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

iv v x computes modified Bessel function of x of real order v

val scalar_iv : v:'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_iv v x computes the modified Bessel function of x of real order v.

val iv_scalar : v:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

iv_scalar v x computes modified Bessel function of x of real order v

val j0 : ( 'a, 'b ) t -> ( 'a, 'b ) t

j0 x computes the Bessel function of order 0 of the elements in x and returns the result in a new ndarray.

val j1 : ( 'a, 'b ) t -> ( 'a, 'b ) t

j1 x computes the Bessel function of order 1 of the elements in x and returns the result in a new ndarray.

val jv : v:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

jv v x computes Bessel function the first kind of x of real order v

val scalar_jv : v:'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_jv v x computes the Bessel function of the first kind of x of real order v.

val jv_scalar : v:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

jv_scalar v x computes Bessel function of the first kind of x of real order v

Binary math operators
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 matrix.

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 matrix.

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 matrix.

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 matrix.

val add_scalar : ( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

add_scalar x a adds a scalar value a to each element in x, and returns the result in a new matrix.

val sub_scalar : ( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

sub_scalar x a subtracts a scalar value a from each element in x, and returns the result in a new matrix.

val mul_scalar : ( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

mul_scalar x a multiplies each element in x by a scalar value a, and returns the result in a new matrix.

val div_scalar : ( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

div_scalar x a divides each element in x by a scalar value a, and returns the result in a new matrix.

val scalar_add : 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_add a x adds a scalar value a to each element in x, and returns the result in a new matrix.

val scalar_sub : 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_sub a x subtracts each element in x from a scalar value a, and returns the result in a new matrix.

val scalar_mul : 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_mul a x multiplies each element in x by a scalar value a, and returns the result in a new matrix.

val scalar_div : 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_div a x divides a scalar value a by each element in x, and returns the result in a new matrix.

val dot : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

dot x y returns the matrix product of matrix x and y.

val add_diag : ( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

add_diag x a adds a to the diagonal elements in x. A new copy of the data is returned.

val pow : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

pow x y computes pow(a, b) of all the elements in x and y elementwise, and returns the result in a new matrix.

val scalar_pow : 'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

scalar_pow a x

val pow_scalar : ( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t

pow_scalar x 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 matrix.

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 matrix.

val min2 : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

min2 x y computes the minimum of all the elements in x and y elementwise, and returns the result in a new matrix.

val max2 : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

max2 x y computes the maximum of all the elements in x and y elementwise, and returns the result in a new matrix.

val fmod : ( float, 'a ) t -> ( float, 'a ) t -> ( float, 'a ) t

fmod x y performs float modulus 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 sqr_nrm2 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_value : ?amin:'a -> ?amax:'a -> ( 'a, 'b ) t -> ( 'a, 'b ) t

clip_by_value ~amin ~amax x clips the elements in x based on amin and amax. The elements smaller than amin will be set to amin, and the elements greater than amax will be set to amax.

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.

val cov : ?b:( 'a, 'b ) t -> a:( 'a, 'b ) t -> ( 'a, 'b ) t

cov ~a calculates the covariance matrix of a wherein each row represents one observation and each column represents one random variable. a is normalised by the number of observations-1. If there is only one observation, it is normalised by 1.

cov ~a ~b takes two matrices as inputs. The functions flatten a and b first then returns a 2 x 2 matrix, so two must have the same number of elements.

val kron : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

kron a b calculates the Kronecker product between the matrices a and b. If a is an m x n matrix and b is a p x q matrix, then kron(a,b) is an m*p x n*q matrix formed by taking all possible products between the elements of a and the matrix b.

val fma : ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t

fma x y z calculates the `fused multiply add`, i.e. (x * y) + z.

Cast functions
val cast : ( 'a, 'b ) Owl_dense_ndarray_generic.kind -> ( 'c, 'd ) t -> ( 'a, 'b ) t

cast kind x casts x of type ('c, 'd) t to type ('a, 'b) t specify by the passed in kind parameter. This function is a generalisation of the other type casting functions such as cast_s2d, cast_c2z, and etc.

val cast_s2d : ( float, Stdlib.Bigarray.float32_elt ) t -> ( float, Stdlib.Bigarray.float64_elt ) t

cast_s2d x casts x from float32 to float64.

val cast_d2s : ( float, Stdlib.Bigarray.float64_elt ) t -> ( float, Stdlib.Bigarray.float32_elt ) t

cast_d2s x casts x from float64 to float32.

val cast_c2z : ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t -> ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t

cast_c2z x casts x from complex32 to complex64.

val cast_z2c : ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t -> ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t

cast_z2c x casts x from complex64 to complex32.

val cast_s2c : ( float, Stdlib.Bigarray.float32_elt ) t -> ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t

cast_s2c x casts x from float32 to complex32.

val cast_d2z : ( float, Stdlib.Bigarray.float64_elt ) t -> ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t

cast_d2z x casts x from float64 to complex64.

val cast_s2z : ( float, Stdlib.Bigarray.float32_elt ) t -> ( Stdlib.Complex.t, Stdlib.Bigarray.complex64_elt ) t

cast_s2z x casts x from float32 to complex64.

val cast_d2c : ( float, Stdlib.Bigarray.float64_elt ) t -> ( Stdlib.Complex.t, Stdlib.Bigarray.complex32_elt ) t

cast_d2c x casts x from float64 to complex32.

In-place modification
val create_ : out:( 'a, 'b ) t -> 'a -> unit

TODO

val uniform_ : ?a:'a -> ?b:'a -> out:( 'a, 'b ) t -> unit

TODO

val bernoulli_ : ?p:float -> out:( 'a, 'b ) t -> unit

TODO

val zeros_ : out:( 'a, 'b ) t -> unit

TODO

val ones_ : out:( 'a, 'b ) t -> unit

TODO

val one_hot_ : out:( 'a, 'b ) t -> int -> ( 'a, 'b ) t -> unit

TODO

val sort_ : ( 'a, 'b ) t -> unit

sort_ x performs in-place quicksort of the elelments in x.

val copy_ : out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

copy_ ~out src copies the data from ndarray src to destination out.

val reshape_ : out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

TODO

val transpose_ : out:( 'a, 'b ) t -> ?axis:int array -> ( 'a, 'b ) t -> unit

transpose_ ~out x is similar to transpose x but the output is written to out.

val sum_ : out:( 'a, 'b ) t -> axis:int -> ( 'a, 'b ) t -> unit

TODO

val min_ : out:( 'a, 'b ) t -> axis:int -> ( 'a, 'b ) t -> unit

TODO

val max_ : out:( 'a, 'b ) t -> axis:int -> ( 'a, 'b ) t -> unit

TODO

val add_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

add_ x y is similar to add function but the output is written to out. You need to make sure out is big enough to hold the output result.

val sub_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

sub_ x y is similar to sub function but the output is written to out. You need to make sure out is big enough to hold the output result.

val mul_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

mul_ x y is similar to mul function but the output is written to out. You need to make sure out is big enough to hold the output result.

val div_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

div_ x y is similar to div function but the output is written to out. You need to make sure out is big enough to hold the output result.

val pow_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

pow_ x y is similar to pow function but the output is written to out. You need to make sure out is big enough to hold the output result.

val atan2_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

atan2_ x y is similar to atan2 function but the output is written to out. You need to make sure out is big enough to hold the output result.

val hypot_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

hypot_ x y is similar to hypot function but the output is written to out. You need to make sure out is big enough to hold the output result.

val fmod_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

fmod_ x y is similar to fmod function but the output is written to out. You need to make sure out is big enough to hold the output result.

val min2_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

min2_ x y is similar to min2 function but the output is written to out. You need to make sure out is big enough to hold the output result.

val max2_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

max2_ x y is similar to max2 function but the output is written to out. You need to make sure out is big enough to hold the output result.

val add_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

add_scalar_ x y is similar to add_scalar function but the output is written to x.

val sub_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

sub_scalar_ x y is similar to sub_scalar function but the output is written to x.

val mul_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

mul_scalar_ x y is similar to mul_scalar function but the output is written to x.

val div_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

div_scalar_ x y is similar to div_scalar function but the output is written to x.

val pow_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

pow_scalar_ x y is similar to pow_scalar function but the output is written to x.

val atan2_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

atan2_scalar_ x y is similar to atan2_scalar function but the output is written to x.

val fmod_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

fmod_scalar_ x y is similar to fmod_scalar function but the output is written to x.

val scalar_add_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_add_ a x is similar to scalar_add function but the output is written to x.

val scalar_sub_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_sub_ a x is similar to scalar_sub function but the output is written to x.

val scalar_mul_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_mul_ a x is similar to scalar_mul function but the output is written to x.

val scalar_div_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_div_ a x is similar to scalar_div function but the output is written to x.

val scalar_pow_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_pow_ a x is similar to scalar_pow function but the output is written to x.

val scalar_atan2_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_atan2_ a x is similar to scalar_atan2 function but the output is written to x.

val scalar_fmod_ : ?out:( 'a, 'b ) t -> 'a -> ( 'a, 'b ) t -> unit

scalar_fmod_ a x is similar to scalar_fmod function but the output is written to x.

val fma_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

fma_ ~out x y z is similar to fma x y z function but the output is written to out.

val dot_ : ?transa:bool -> ?transb:bool -> ?alpha:'a -> ?beta:'a -> c:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

Refer to :doc:`owl_dense_matrix_generic`

val conj_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

conj_ x is similar to conj but output is written to x

val abs_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

abs_ x is similar to abs but output is written to x

val neg_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

neg_ x is similar to neg but output is written to x

val reci_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

reci_ x is similar to reci but output is written to x

val signum_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

signum_ x is similar to signum but output is written to x

val sqr_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

sqr_ x is similar to sqr but output is written to x

val sqrt_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

sqrt_ x is similar to sqrt but output is written to x

val cbrt_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

cbrt_ x is similar to cbrt but output is written to x

val exp_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

exp_ x is similar to exp_ but output is written to x

val exp2_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

exp2_ x is similar to exp2 but output is written to x

val exp10_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

exp2_ x is similar to exp2 but output is written to x

val expm1_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

expm1_ x is similar to expm1 but output is written to x

val log_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

log_ x is similar to log but output is written to x

val log2_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

log2_ x is similar to log2 but output is written to x

val log10_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

log10_ x is similar to log10 but output is written to x

val log1p_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

log1p_ x is similar to log1p but output is written to x

val sin_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

sin_ x is similar to sin but output is written to x

val cos_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

cos_ x is similar to cos but output is written to x

val tan_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

tan_ x is similar to tan but output is written to x

val asin_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

asin_ x is similar to asin but output is written to x

val acos_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

acos_ x is similar to acos but output is written to x

val atan_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

atan_ x is similar to atan but output is written to x

val sinh_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

sinh_ x is similar to sinh but output is written to x

val cosh_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

cosh_ x is similar to cosh but output is written to x

val tanh_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

tanh_ x is similar to tanh but output is written to x

val asinh_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

asinh_ x is similar to asinh but output is written to x

val acosh_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

acosh_ x is similar to acosh but output is written to x

val atanh_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

atanh_ x is similar to atanh but output is written to x

val floor_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

floor_ x is similar to floor but output is written to x

val ceil_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

ceil_ x is similar to ceil but output is written to x

val round_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

round_ x is similar to round but output is written to x

val trunc_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

trunc_ x is similar to trunc but output is written to x

val fix_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

fix_ x is similar to fix but output is written to x

val erf_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

erf_ x is similar to erf but output is written to x

val erfc_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

erfc_ x is similar to erfc but output is written to x

val relu_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

relu_ x is similar to relu but output is written to x

val softplus_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

softplus_ x is similar to softplus but output is written to x

val softsign_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

softsign_ x is similar to softsign but output is written to x

val sigmoid_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

sigmoid_ x is similar to sigmoid but output is written to x

val softmax_ : ?out:( 'a, 'b ) t -> ?axis:int -> ( 'a, 'b ) t -> unit

softmax_ x is similar to softmax but output is written to x

val cumsum_ : ?out:( 'a, 'b ) t -> ?axis:int -> ( 'a, 'b ) t -> unit

cumsum_ x is similar to cumsum but output is written to x

val cumprod_ : ?out:( 'a, 'b ) t -> ?axis:int -> ( 'a, 'b ) t -> unit

cumprod_ x is similar to cumprod but output is written to x

val cummin_ : ?out:( 'a, 'b ) t -> ?axis:int -> ( 'a, 'b ) t -> unit

cummin_ x is similar to cummin but output is written to x

val cummax_ : ?out:( 'a, 'b ) t -> ?axis:int -> ( 'a, 'b ) t -> unit

cummax_ x is similar to cummax but output is written to x

val dropout_ : ?out:( 'a, 'b ) t -> ?rate:float -> ( 'a, 'b ) t -> unit

dropout_ x is similar to dropout but output is written to x

val elt_equal_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

elt_equal_ x y is similar to elt_equal function but the output is written to out. You need to make sure out is big enough to hold the output result.

val elt_not_equal_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

elt_not_equal_ x y is similar to elt_not_equal function but the output is written to out. You need to make sure out is big enough to hold the output result.

val elt_less_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

elt_less_ x y is similar to elt_less function but the output is written to out. You need to make sure out is big enough to hold the output result.

val elt_greater_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

elt_greater_ x y is similar to elt_greater function but the output is written to out. You need to make sure out is big enough to hold the output result.

val elt_less_equal_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

elt_less_equal_ x y is similar to elt_less_equal function but the output is written to out. You need to make sure out is big enough to hold the output result.

val elt_greater_equal_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> ( 'a, 'b ) t -> unit

elt_greater_equal_ x y is similar to elt_greater_equal function but the output is written to out. You need to make sure out is big enough to hold the output result.

val elt_equal_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

elt_equal_scalar_ x a is similar to elt_equal_scalar function but the output is written to x.

val elt_not_equal_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

elt_not_equal_scalar_ x a is similar to elt_not_equal_scalar function but the output is written to x.

val elt_less_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

elt_less_scalar_ x a is similar to elt_less_scalar function but the output is written to x.

val elt_greater_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

elt_greater_scalar_ x a is similar to elt_greater_scalar function but the output is written to x.

val elt_less_equal_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

elt_less_equal_scalar_ x a is similar to elt_less_equal_scalar function but the output is written to x.

val elt_greater_equal_scalar_ : ?out:( 'a, 'b ) t -> ( 'a, 'b ) t -> 'a -> unit

elt_greater_equal_scalar_ x a is similar to elt_greater_equal_scalar function but the output is written to x.