module Owl_dense_real: sig .. end
Real dense matrix module
type Gsl.Matrix.matrix
Type of dense matrices. It is defined as Gsl.Matrix.matrix which is
essentially a two dimensional array in Bigarray module.
Create dense matrices
val empty : int -> int -> mat
empty m n creates an m by n matrix without initialising the values of
elements in x.
val create : int -> int -> float -> mat
create m n a creates an m by n matrix and all the elements of x are
initialised with the value a.
val zeros : int -> int -> mat
zeros m n creates an m by n matrix where all the elements are
initialised to zeros.
val ones : int -> int -> mat
ones m n creates an m by n matrix where all the elements are ones.
val eye : int -> mat
eye m creates an m by m identity matrix.
val sequential : int -> int -> mat
sequential m n creates an m by n matrix. The elements in x are
initialised sequentiallly from 0 to (m * n - 1).
val uniform_int : ?a:int -> ?b:int -> int -> int -> mat
uniform ~a ~b m n creates an m by n matrix where all the elements
follow a uniform distribution in [a, b] interval. By default, a = 0 and
b = 100.
val uniform : ?scale:float -> int -> int -> mat
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 : ?sigma:float -> int -> int -> mat
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 semidef : int -> mat
semidef n returns an random n by n positive semi-definite matrix.
Dense vectors and meshgrids
val vector : int -> mat
vector m returns an 1 by m row vector x without initialising the
values in x.
val vector_zeros : int -> mat
vector_zeros m returns an 1 by m row vector x by initialising the
all values in x to zeros.
val vector_ones : int -> mat
vector_ones m returns an 1 by m row vector x by initialising the
all values in x to ones.
val vector_uniform : int -> mat
vector_zeros m returns an 1 by m row vector x and the values are
drawn from the interval (0,1) with a uniform distribution.
val linspace : float -> float -> int -> mat
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 meshgrid : float ->
float ->
float -> float -> int -> int -> mat * mat
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 : mat ->
mat -> mat * mat
meshup x y creates mesh grids by using two row vectors x and y.
Obtain the basic properties of a matrix
val shape : mat -> 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 : mat -> int
row_num x returns the number of rows in matrix x.
val col_num : mat -> int
col_num x returns the number of columns in matrix x.
val numel : mat -> int
numel x returns the number of elements in matrix x. It is equivalent
to (row_num x) * (col_num x).
val same_shape : mat -> mat -> bool
same_shape x y returns true if two matrics have the same shape.
val reshape : int -> int -> mat -> mat
reshape m n x creates a new m by n matrix from the m' by n'
matrix x. Note that (m * n) must be equal to (m' * n').
Manipulate a matrix
val get : mat -> int -> int -> float
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 : mat -> int -> int -> float -> 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 row : mat -> int -> mat
row x i returns the row i of x.
val col : mat -> int -> mat
col x j returns the column j of x.
val rows : mat -> int array -> mat
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 : mat -> int array -> mat
Similar to rows, cols x a returns the columns (specified in array a)
of x in a new dense matrix.
val clone : mat -> mat
clone x returns a copy of matrix x.
val copy_to : mat -> mat -> unit
copy_to x y copies the elements of x to y. x and y must have
the same demensions.
val copy_row_to : mat -> mat -> 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 : mat -> mat -> 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 : mat -> mat -> mat
concat_vertical x y concats two matrices x and y vertically,
therefore their column numbers must be the same.
val concat_horizontal : mat -> mat -> mat
concat_horizontal x y concats two matrices x and y horizontally,
therefore their row numbers must be the same.
val transpose : mat -> mat
transpose x transposes an m by n matrix to n by m one.
val diag : mat -> mat
diag x returns the diagonal elements of x.
val trace : mat -> float
trace x returns the sum of diagonal elements in x.
val add_diag : mat -> float -> mat
add_diag x a adds a constant a to all the diagonal elements in x.
val replace_row : mat -> mat -> int -> mat
replace_row v x i uses the row vector v to replace the ith row in
the matrix x.
val replace_col : mat -> mat -> int -> mat
replace_col v x j uses the column vector v to replace the jth column
in the matrix x.
val swap_rows : mat -> int -> int -> mat
swap_rows x i i' swaps the row i with row i' of x.
val swap_cols : mat -> int -> int -> mat
swap_cols x j j' swaps the column j with column j' of x.
Iterate elements, columns, and rows.
val iteri : (int -> int -> float -> unit) -> mat -> 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 : (float -> unit) -> mat -> 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 -> int -> float -> float) -> mat -> mat
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 : (float -> float) -> mat -> mat
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 fold : ('a -> float -> 'a) -> 'a -> mat -> 'a
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 filteri : (int -> int -> float -> bool) -> mat -> (int * 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 : (float -> bool) -> mat -> (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 -> mat -> unit) -> mat -> unit
iteri_rows f x iterates every row in x and applies function
f : int -> mat -> unit to each of them.
val iter_rows : (mat -> unit) -> mat -> unit
Similar to iteri_rows except row number is not passed to f.
val iteri_cols : (int -> mat -> unit) -> mat -> 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 : (mat -> unit) -> mat -> unit
Similar to iteri_cols except col number is not passed to f.
val filteri_rows : (int -> mat -> bool) -> mat -> 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 : (mat -> bool) -> mat -> int array
Similar to filteri_rows except that the row indices are not passed to f.
val filteri_cols : (int -> mat -> bool) -> mat -> 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 : (mat -> bool) -> mat -> int array
Similar to filteri_cols except that the column indices are not passed to f.
val fold_rows : ('a -> mat -> 'a) -> 'a -> mat -> 'a
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 : ('a -> mat -> 'a) -> 'a -> mat -> 'a
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 -> mat -> 'a) -> mat -> 'a 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 : (mat -> 'a) -> mat -> 'a array
Similar to mapi_rows except row number is not passed to f.
val mapi_cols : (int -> mat -> 'a) -> mat -> 'a 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 : (mat -> 'a) -> mat -> 'a array
Similar to mapi_cols except column number is not passed to f.
val mapi_by_row : ?d:int ->
(int -> mat -> mat) ->
mat -> mat
mapi_by_row f x applies f to each row of x, then uses the returned
row vectors to assemble a new matrix.
val map_by_row : ?d:int ->
(mat -> mat) ->
mat -> mat
map_by_row f x i is similar to mapi_by_row except that the row indices
are not passed to f.
val mapi_by_col : ?d:int ->
(int -> mat -> mat) ->
mat -> mat
mapi_by_col f x applies f to each column of x, then uses the returned
column vectors to assemble a new matrix.
val map_by_col : ?d:int ->
(mat -> mat) ->
mat -> mat
map_by_col f x i is similar to mapi_by_col except that the column
indices are not passed to f.
val mapi_at_row : (int -> int -> float -> float) ->
mat -> int -> mat
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 : (float -> float) -> mat -> int -> mat
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 -> float -> float) ->
mat -> int -> mat
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 : (float -> float) -> mat -> int -> mat
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 the elements in a matrix
val exists : (float -> bool) -> mat -> 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 : (float -> bool) -> mat -> 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 : (float -> bool) -> mat -> 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.
Compare two matrices
val is_equal : mat -> mat -> bool
is_equal x y returns true if two matrices x and y are equal.
val is_unequal : mat -> mat -> bool
is_unequal x y returns true if there is at least one element in x is
not equal to that in y.
val is_greater : mat -> mat -> bool
is_greater x y returns true if all the elements in x are greater than
the corresponding elements in y.
val is_smaller : mat -> mat -> bool
is_smaller x y returns true if all the elements in x are smaller than
the corresponding elements in y.
val equal_or_greater : mat -> mat -> bool
equal_or_greater x y returns true if all the elements in x are not
smaller than the corresponding elements in y.
val equal_or_smaller : mat -> mat -> bool
equal_or_smaller x y returns true if all the elements in x are not
greater than the corresponding elements in y.
Basic mathematical operations of matrices
val add : mat -> mat -> mat
add x y adds two matrices x and y. Both must have the same dimensions.
val sub : mat -> mat -> mat
sub x y subtracts the matrix x from y. Both must have the same dimensions.
val mul : mat -> mat -> mat
mul x y performs an element-wise multiplication, so both x and y
must have the same dimensions.
val div : mat -> mat -> mat
div x y performs an element-wise division, so both x and y
must have the same dimensions.
val dot : mat -> mat -> mat
dot x y calculates the dot product of an m by n matrix x and
another n by p matrix y.
val abs : mat -> mat
abs x returns a new matrix where each element has the absolute value of
that in the original matrix x.
val neg : mat -> mat
neg x returns a new matrix where each element has the negative value of
that in the original matrix x.
val power : mat -> float -> mat
power x a calculates the power of a of each element in x.
val add_scalar : mat -> float -> mat
add_scalar x a adds every element in x by a constant factor a.
val sub_scalar : mat -> float -> mat
sub_scalar x a subtracts every element in x by a constant factor a.
val mul_scalar : mat -> float -> mat
mul_scalar x a multiplies every element in x by a constant factor a.
val div_scalar : mat -> float -> mat
div_scalar x a divides every element in x by a constant factor a.
val sum : mat -> float
sum x returns the summation of all the elements in x.
val average : mat -> float
average x returns the average value of all the elements in x. It is
equivalent to calculate sum x divided by numel x
val min : mat -> float * int * int
min x returns the minimum value of all elements in x.
val max : mat -> float * int * int
max x returns the maximum value of all elements in x.
val minmax : mat -> float * float * int * int * int * int
minmax x returns both the minimum and minimum values in x.
val is_zero : mat -> bool
is_zero x returns true if all the elements in x are zeros.
val is_positive : mat -> bool
is_positive x returns true if all the elements in x are positive.
val is_negative : mat -> bool
is_negative x returns true if all the elements in x are negative.
val is_nonnegative : mat -> bool
is_nonnegative returns true if all the elements in x are non-negative.
val log : mat -> mat
log x applies log function to each element in matrix x.
val log10 : mat -> mat
log10 x applies log10 function to each element in matrix x.
val exp : mat -> mat
exp x applies exp function to each element in matrix x.
val sigmoid : mat -> mat
sigmoid x applies sigmoid function to each element in matrix x.
val sum_rows : mat -> mat
sum_rows x returns the summation of all the row vectors in x.
val sum_cols : mat -> mat
sum_cols returns the summation of all the column vectors in x.
val average_rows : mat -> mat
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 : mat -> mat
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 : mat -> (float * int * int) array
min_rows x returns the minimum value in each row along with their coordinates.
val min_cols : mat -> (float * int * int) array
min_cols x returns the minimum value in each column along with their coordinates.
val max_rows : mat -> (float * int * int) array
max_rows x returns the maximum value in each row along with their coordinates.
val max_cols : mat -> (float * int * int) array
min_cols x returns the minimum value in each column along with their coordinates.
Randomisation functions
val draw_rows : ?replacement:bool ->
mat -> int -> mat * 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 ->
mat -> int -> mat * 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 shuffle_rows : mat -> mat
shuffle_rows x shuffles all the rows in matrix x.
val shuffle_cols : mat -> mat
shuffle_cols x shuffles all the columns in matrix x.
val shuffle : mat -> mat
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).
val to_array : mat -> float 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 : mat -> float array array
to arrays x returns an array of float arrays, wherein each row in x
becomes an array in the result.
val of_array : float array -> int -> int -> mat
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).
val of_arrays : float array array -> mat
of_arrays x converts an array of m float arrays (of length n) in to
an m by n matrix.
val print : mat -> unit
print x pretty prints matrix x without headings.
val pp_dsmat : mat -> unit
pp_spmat x pretty prints matrix x with headings. Toplevel uses this
function to print out the matrices.
val save : mat -> 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 : string -> mat
load f loads a sparse matrix from file f. The file must be previously
saved by using save function.
val save_txt : mat -> 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 : string -> mat
load_txt f load a text file f into a matrix.
Shorhand infix operators
val (>>) : mat -> mat -> unit
Shorthand for copy_to x y, i.e., x >> y
val (<<) : mat -> mat -> unit
Shorthand for copy_to y x, i.e., x << y
val (@=) : mat -> mat -> mat
Shorthand for concat_vertical x y, i.e., x @= y
val (@||) : mat -> mat -> mat
Shorthand for concat_horizontal x y, i.e., x @|| y
val (+@) : mat -> mat -> mat
Shorthand for add x y, i.e., x +@ y
val (-@) : mat -> mat -> mat
Shorthand for sub x y, i.e., x -@ y
val ( *@ ) : mat -> mat -> mat
Shorthand for mul x y, i.e., x *@ y
val (/@) : mat -> mat -> mat
Shorthand for div x y, i.e., x /@ y
val ($@) : mat -> mat -> mat
Shorthand for dot x y, i.e., x $@ y
val ( **@ ) : mat -> float -> mat
Shorthand for power x a, i.e., x **@ a
val (+$) : mat -> float -> mat
Shorthand for add_scalar x a, i.e., x +$ a
val (-$) : mat -> float -> mat
Shorthand for sub_scalar x a, i.e., x -$ a
val ( *$ ) : mat -> float -> mat
Shorthand for mul_scalar x a, i.e., x *$ a
val (/$) : mat -> float -> mat
Shorthand for div_scalar x a, i.e., x /$ a
val ($+) : float -> mat -> mat
Shorthand for add_scalar x a, i.e., a $+ x
val ($-) : float -> mat -> mat
Shorthand for sub_scalar x a, i.e., a -$ x
val ( $* ) : float -> mat -> mat
Shorthand for mul_scalar x a, i.e., x $* a
val ($/) : float -> mat -> mat
Shorthand for div_scalar x a, i.e., x $/ a
val (=@) : mat -> mat -> bool
Shorthand for is_equal x y, i.e., x =@ y
val (>@) : mat -> mat -> bool
Shorthand for is_greater x y, i.e., x >@ y
val (<@) : mat -> mat -> bool
Shorthand for is_smaller x y, i.e., x <@ y
val (<>@) : mat -> mat -> bool
Shorthand for is_unequal x y, i.e., x <>@ y
val (>=@) : mat -> mat -> bool
Shorthand for equal_or_greater x y, i.e., x >=@ y
val (<=@) : mat -> mat -> bool
Shorthand for equal_or_smaller x y, i.e., x <=@ y
val (@@) : (float -> float) -> mat -> mat
Shorthand for map f x, i.e., f @@ x