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Vector module: various functions of vectors

include module type of struct include M end

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.

type ('a, 'b) t = ('a, 'b, Bigarray.c_layout) Bigarray.Array2.t
type ('a, 'b) kind = ('a, 'b) Bigarray.kind
Create dense matrices
val init : ('a, 'b) 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._index_1d_nd can help you.

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

init_nd 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_nd is slower than init.

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

eye m creates an m by m identity matrix.

val complex : ('a, 'b) kind -> ('c, 'd) 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) kind -> ('c, 'd) 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 semidef : (float, 'b) kind -> int -> (float, 'b) t

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

val meshgrid : ('a, 'b) 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) kind -> ?p:float -> ?seed:int -> 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 -> (Complex.t, 'a) t -> (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) 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. Currrently, this function handles only the cases where n, n/12, or n/20 is a power of 2.

val magic : ('a, 'b) 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 the 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 kind : ('a, 'b) t -> ('a, 'b) kind

kind x returns the type of matrix x.

Manipulate a matrix
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_slice : Owl_types.index 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 array. Please refer to the same function in the Owl_dense_ndarray_generic documentation for more details.

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

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

get_slice_simple axis x aims to provide a simpler version of get_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 set_slice_simple : int list list -> ('a, 'b) t -> ('a, 'b) t -> unit

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

row x i returns the row i of x.

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

col x j returns the column j of x.

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.

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.

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

resize m n x please refer to the Ndarray document.

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

reshape m n x 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 clone : ('a, 'b) t -> ('a, 'b) t

clone x returns a copy of matrix x.

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

copy_to x y copies the elements of x to y. x and y must have the same demensions.

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.

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.

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

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

replace_row v x i uses the row vector v to replace the ith row in the matrix x.

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

replace_col v x j uses the column vector v to replace the jth column in the matrix x.

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

repeat ~axis x a repeats the elements along ~axis for a times.

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

padd ~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 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 elelment 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 elelment values, from the smallest one to the greatest one.

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

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

Iterate elements, columns, and rows.
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 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 map2i : (int -> int -> 'a -> 'a -> 'a) -> ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t
val map2 : ('a -> 'a -> 'a) -> ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t
val fold : ('c -> 'a -> 'c) -> 'c -> ('a, 'b) t -> 'c

fold f a x folds all the elements in x with the function f : 'a -> float -> 'a. For an m by n matrix x, the order of folding is from (0,0) to (m-1,n-1), row by row.

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

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

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

Examine elements and compare two matrices
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 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) 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_ndarray : ('a, 'b) t -> ('a, 'b) Owl_dense_ndarray_generic.t

to_ndarray x transforms a dense real matrix to Bigarray.Genarray.t type. No copy is made by calling this function.

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

of_ndarray x transforms a ndarray of type Bigarray.Genarray.t to a dense real matrix type. No copy is made by calling this function.

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

print x pretty prints matrix x without headings.

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

pp_spmat x pretty prints matrix x with headings. Toplevel uses this function to print out the matrices.

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

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

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

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

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

save_txt x f save the matrix x into a text file f. The operation can be very time consuming.

val load_txt : (float, 'a) kind -> string -> (float, 'a) t

load_txt f load a text file f into a matrix.

Unary mathematical operations

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

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

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

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

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

min x returns the minimum of all elements in x. 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 max : ('a, 'b) t -> 'a

max x returns the maximum of all elements in x. 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 minmax : ('a, 'b) t -> 'a * 'a

minmax x returns both the minimum and minimum values in x.

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

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

inv x returns the inverse of a square matrix x.

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

trace x returns the sum of diagonal elements in x.

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

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

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

sum_ axis x sums 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 average : ('a, 'b) t -> 'a

average x returns the average value of all the elements in x. It is equivalent to calculate sum x divided by numel x

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

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

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

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

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

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

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

average_cols x returns the average 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 : (float, 'a) t -> (float, 'a) t

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

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

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.

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

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

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

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

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

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

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

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

var x computes the variance of x along the axis dimension. By default, axis is set to the lowest dimension.

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

std x computes the standard deviation of x along the axis dimension. By default, axis is set to the lowest dimension.

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.

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 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
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 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 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.

Cast functions to different number types
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.

cast_c2z x casts x from complex32 to complex64.

cast_z2c x casts x from complex64 to complex32.

cast_s2c x casts x from float32 to complex32.

cast_d2z x casts x from float64 to complex64.

cast_s2z x casts x from float32 to complex64.

cast_d2c x casts x from float64 to complex32.

type vec_typ =
  1. | Row
  2. | Col
val empty : ?typ:vec_typ -> ('a, 'b) M.kind -> int -> ('a, 'b) M.t
val zeros : ?typ:vec_typ -> ('a, 'b) M.kind -> int -> ('a, 'b) M.t
val ones : ?typ:vec_typ -> ('a, 'b) M.kind -> int -> ('a, 'b) M.t
val create : ?typ:vec_typ -> ('a, 'b) M.kind -> int -> 'a -> ('a, 'b) M.t
val gaussian : ?typ:vec_typ -> ?sigma:float -> ('a, 'b) M.kind -> int -> ('a, 'b) M.t
val uniform : ?typ:vec_typ -> ?scale:float -> ('a, 'b) M.kind -> int -> ('a, 'b) M.t
val sequential : ?typ:vec_typ -> ?a:'a -> ?step:'a -> ('a, 'b) M.kind -> int -> ('a, 'b) M.t
val unit_basis : ?typ:vec_typ -> ('a, 'b) M.kind -> int -> int -> ('a, 'b) M.t
val linspace : ?typ:vec_typ -> ('a, 'b) M.kind -> 'a -> 'a -> int -> ('a, 'b) M.t
val logspace : ?typ:vec_typ -> ?base:float -> ('a, 'b) M.kind -> 'a -> 'a -> int -> ('a, 'b) M.t
val vec_typ : ('a, 'b) M.t -> vec_typ
val get : ('a, 'b) M.t -> int -> 'a
val set : ('a, 'b) M.t -> int -> 'a -> unit
val iteri : (int -> 'a -> unit) -> ('a, 'b) M.t -> unit
val mapi : (int -> 'a -> 'a) -> ('a, 'b) M.t -> ('a, 'b) M.t
val filteri : (int -> 'a -> bool) -> ('a, 'b) M.t -> (int * int) array
val foldi : (int -> 'a -> 'b -> 'a) -> 'a -> ('b, 'c) M.t -> 'a
val of_array : ?typ:vec_typ -> ('a, 'b) M.kind -> 'a array -> ('a, 'b) M.t
val min_i : ('a, 'b) M.t -> 'a * int
val max_i : ('a, 'b) M.t -> 'a * int
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