module Dense: sig .. end
Dense matrix module
type
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 -> dsmat
empty m n creates an m by n matrix without initialising the values of
elements in x.
val create : int -> int -> float -> dsmat
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 -> dsmat
zeros m n creates an m by n matrix where all the elements are
initialised to zeros.
val ones : int -> int -> dsmat
ones m n creates an m by n matrix where all the elements are ones.
val eye : int -> dsmat
eye m creates an m by m identity matrix.
val sequential : int -> int -> dsmat
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 -> dsmat
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 -> dsmat
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 -> dsmat
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 -> dsmat
semidef n returns an random n by n positive semi-definite matrix.
Dense vectors and meshgrids
val vector : int -> dsmat
vector m returns an 1 by m row vector x without initialising the
values in x.
val vector_zeros : int -> dsmat
vector_zeros m returns an 1 by m row vector x by initialising the
all values in x to zeros.
val vector_ones : int -> dsmat
vector_ones m returns an 1 by m row vector x by initialising the
all values in x to ones.
val vector_uniform : int -> dsmat
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 -> dsmat
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 -> dsmat * dsmat
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 : dsmat -> dsmat -> dsmat * dsmat
meshup x y creates mesh grids by using two row vectors x and y.
Obtain the basic properties of a matrix
val shape : dsmat -> 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 : dsmat -> int
row_num x returns the number of rows in matrix x.
val col_num : dsmat -> int
col_num x returns the number of columns in matrix x.
val numel : dsmat -> int
numel x returns the number of elements in matrix x. It is equivalent
to (row_num x) * (col_num x).
val same_shape : dsmat -> dsmat -> bool
same_shape x y returns true if two matrics have the same shape.
val reshape : int -> int -> dsmat -> dsmat
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 : dsmat -> 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 : dsmat -> 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 : dsmat -> int -> dsmat
row x i returns the row i of x.
val col : dsmat -> int -> dsmat
col x j returns the column j of x.
val rows : dsmat -> int array -> dsmat
rows x a returns the rows (defined in an int array a) of x. The
returned rows will be combined into a new sparse matrix. The order of rows in
the new matrix is the same as that in the array a.
val cols : dsmat -> int array -> dsmat
Similar to rows, cols x a returns the columns (specified in array a)
of x in a new sparse matrix.
val clone : dsmat -> dsmat
clone x returns a copy of matrix x.
val copy_to : dsmat -> dsmat -> unit
copy_to x y copies the elements of x to y. x and y must have
the same demensions.
val copy_row_to : dsmat -> dsmat -> 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 : dsmat -> dsmat -> 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 : dsmat -> dsmat -> dsmat
concat_vertical x y concats two matrices x and y vertically,
therefore their column numbers must be the same.
val concat_horizontal : dsmat -> dsmat -> dsmat
concat_horizontal x y concats two matrices x and y horizontally,
therefore their row numbers must be the same.
val transpose : dsmat -> dsmat
transpose x transposes an m by n matrix to n by m one.
val diag : dsmat -> dsmat
diag x returns the diagonal elements of x.
val trace : dsmat -> float
trace x returns the sum of diagonal elements in x.
val add_diag : dsmat -> float -> dsmat
add_diag x a adds a constant a to all the diagonal elements in x.
val replace_row : dsmat -> dsmat -> int -> dsmat
replace_row v x i uses the row vector v to replace the ith row in
the matrix x.
val replace_col : dsmat -> dsmat -> int -> dsmat
replace_col v x j uses the column vector v to replace the jth column
in the matrix x.
Iterate elements, columns, and rows.
val iteri : (int -> int -> float -> 'a) -> dsmat -> 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 -> 'a) -> dsmat -> 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) -> dsmat -> dsmat
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) -> dsmat -> dsmat
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 -> dsmat -> '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) -> dsmat -> (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) -> dsmat -> (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 -> dsmat -> 'a) -> dsmat -> unit
iteri_rows f x iterates every row in x and applies function
f : int -> dsmat -> unit to each of them.
val iter_rows : (dsmat -> 'a) -> dsmat -> unit
Similar to iteri_rows except row number is not passed to f.
val iteri_cols : (int -> dsmat -> 'a) -> dsmat -> unit
iteri_cols f x iterates every column in x and applies function
f : int -> dsmat -> unit to each of them. Column number is passed to f as
the first parameter.
val iter_cols : (dsmat -> 'a) -> dsmat -> unit
Similar to iteri_cols except col number is not passed to f.
val filteri_rows : (int -> dsmat -> bool) -> dsmat -> int array
filteri_rows f x uses function f : int -> dsmat -> 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 : (dsmat -> bool) -> dsmat -> int array
Similar to filteri_rows except that the row indices are not passed to f.
val filteri_cols : (int -> dsmat -> bool) -> dsmat -> int array
filteri_cols f x uses function f : int -> dsmat -> 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 : (dsmat -> bool) -> dsmat -> int array
Similar to filteri_cols except that the column indices are not passed to f.
val fold_rows : ('a -> dsmat -> 'a) -> 'a -> dsmat -> '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 -> dsmat -> 'a) -> 'a -> dsmat -> '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 -> dsmat -> 'a) -> dsmat -> 'a array
mapi_rows f x maps every row in x to a type 'a value by applying
function f : int -> dsmat -> 'a to each of them. The results is an array of
all the returned values.
val map_rows : (dsmat -> 'a) -> dsmat -> 'a array
Similar to mapi_rows except row number is not passed to f.
val mapi_cols : (int -> dsmat -> 'a) -> dsmat -> 'a array
mapi_cols f x maps every column in x to a type 'a value by applying
function f : int -> dsmat -> 'a.
val map_cols : (dsmat -> 'a) -> dsmat -> 'a array
Similar to mapi_cols except column number is not passed to f.
val mapi_by_row : ?d:int -> (int -> dsmat -> dsmat) -> dsmat -> dsmat
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 -> (dsmat -> dsmat) -> dsmat -> dsmat
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 -> dsmat -> dsmat) -> dsmat -> dsmat
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 -> (dsmat -> dsmat) -> dsmat -> dsmat
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) -> dsmat -> int -> dsmat
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) -> dsmat -> int -> dsmat
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) -> dsmat -> int -> dsmat
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) -> dsmat -> int -> dsmat
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) -> dsmat -> 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) -> dsmat -> 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) -> dsmat -> 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 : dsmat -> dsmat -> bool
is_equal x y returns true if two matrices x and y are equal.
val is_unequal : dsmat -> dsmat -> 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 : dsmat -> dsmat -> bool
is_greater x y returns true if all the elements in x are greater than
the corresponding elements in y.
val is_smaller : dsmat -> dsmat -> 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 : dsmat -> dsmat -> 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 : dsmat -> dsmat -> 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 : dsmat -> dsmat -> dsmat
add x y adds two matrices x and y. Both must have the same dimensions.
val sub : dsmat -> dsmat -> dsmat
sub x y subtracts the matrix x from y. Both must have the same dimensions.
val mul : dsmat -> dsmat -> dsmat
mul x y performs an element-wise multiplication, so both x and y
must have the same dimensions.
val div : dsmat -> dsmat -> dsmat
div x y performs an element-wise division, so both x and y
must have the same dimensions.
val dot : dsmat -> dsmat -> dsmat
dot x y calculates the dot product of an m by n matrix x and
another n by p matrix y.
val abs : dsmat -> dsmat
abs x returns a new matrix where each element has the absolute value of
that in the original matrix x.
val neg : dsmat -> dsmat
neg x returns a new matrix where each element has the negative value of
that in the original matrix x.
val power : dsmat -> float -> dsmat
power x a calculates the power of a of each element in x.
val add_scalar : dsmat -> float -> dsmat
add_scalar x a adds every element in x by a constant factor a.
val sub_scalar : dsmat -> float -> dsmat
sub_scalar x a subtracts every element in x by a constant factor a.
val mul_scalar : dsmat -> float -> dsmat
mul_scalar x a multiplies every element in x by a constant factor a.
val div_scalar : dsmat -> float -> dsmat
div_scalar x a divides every element in x by a constant factor a.
val sum : dsmat -> float
sum x returns the summation of all the elements in x.
val average : dsmat -> 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 : dsmat -> float * int * int
min x returns the minimum value of all elements in x.
val max : dsmat -> float * int * int
max x returns the maximum value of all elements in x.
val minmax : dsmat -> float * float * int * int * int * int
minmax x returns both the minimum and minimum values in x.
val is_zero : dsmat -> bool
is_zero x returns true if all the elements in x are zeros.
val is_positive : dsmat -> bool
is_positive x returns true if all the elements in x are positive.
val is_negative : dsmat -> bool
is_negative x returns true if all the elements in x are negative.
val is_nonnegative : dsmat -> bool
is_nonnegative returns true if all the elements in x are non-negative.
val log : dsmat -> dsmat
log x applies log function to each element in matrix x.
val log10 : dsmat -> dsmat
log10 x applies log10 function to each element in matrix x.
val exp : dsmat -> dsmat
exp x applies exp function to each element in matrix x.
val sigmoid : dsmat -> dsmat
sigmoid x applies sigmoid function to each element in matrix x.
val sum_rows : dsmat -> dsmat
sum_rows x returns the summation of all the row vectors in x.
val sum_cols : dsmat -> dsmat
sum_cols returns the summation of all the column vectors in x.
val average_rows : dsmat -> dsmat
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 : dsmat -> dsmat
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 : dsmat -> (float * int * int) array
min_rows x returns the minimum value in each row along with their coordinates.
val min_cols : dsmat -> (float * int * int) array
min_cols x returns the minimum value in each column along with their coordinates.
val max_rows : dsmat -> (float * int * int) array
max_rows x returns the maximum value in each row along with their coordinates.
val max_cols : dsmat -> (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 -> dsmat -> int -> dsmat * 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 -> dsmat -> int -> dsmat * 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 : dsmat -> dsmat
shuffle_rows x shuffles all the rows in matrix x.
val shuffle_cols : dsmat -> dsmat
shuffle_cols x shuffles all the columns in matrix x.
val shuffle : dsmat -> dsmat
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 : dsmat -> 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 : dsmat -> 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 -> dsmat
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 -> dsmat
of_arrays x converts an array of m float arrays (of length n) in to
an m by n matrix.
val print : dsmat -> unit
print x pretty prints matrix x without headings.
val pp_dsmat : dsmat -> unit
pp_spmat x pretty prints matrix x with headings. Toplevel uses this
function to print out the matrices.
val save : dsmat -> 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 -> dsmat
load f loads a sparse matrix from file f. The file must be previously
saved by using save function.
val save_txt : dsmat -> 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 -> dsmat
load_txt f load a text file f into a matrix.
Shorhand infix operators
val (>>) : dsmat -> dsmat -> unit
Shorthand for copy_to x y, i.e., x >> y
val (<<) : dsmat -> dsmat -> unit
Shorthand for copy_to y x, i.e., x << y
val (@=) : dsmat -> dsmat -> dsmat
Shorthand for concat_vertical x y, i.e., x @= y
val (@||) : dsmat -> dsmat -> dsmat
Shorthand for concat_horizontal x y, i.e., x @|| y
val (+@) : dsmat -> dsmat -> dsmat
Shorthand for add x y, i.e., x +@ y
val (-@) : dsmat -> dsmat -> dsmat
Shorthand for sub x y, i.e., x -@ y
val ( *@ ) : dsmat -> dsmat -> dsmat
Shorthand for mul x y, i.e., x *@ y
val (/@) : dsmat -> dsmat -> dsmat
Shorthand for div x y, i.e., x /@ y
val ($@) : dsmat -> dsmat -> dsmat
Shorthand for dot x y, i.e., x $@ y
val ( **@ ) : dsmat -> float -> dsmat
Shorthand for power x a, i.e., x **@ a
val (+$) : dsmat -> float -> dsmat
Shorthand for add_scalar x a, i.e., x +$ a
val (-$) : dsmat -> float -> dsmat
Shorthand for sub_scalar x a, i.e., x -$ a
val ( *$ ) : dsmat -> float -> dsmat
Shorthand for mul_scalar x a, i.e., x *$ a
val (/$) : dsmat -> float -> dsmat
Shorthand for div_scalar x a, i.e., x /$ a
val ($+) : float -> dsmat -> dsmat
Shorthand for add_scalar x a, i.e., a $+ x
val ($-) : float -> dsmat -> dsmat
Shorthand for sub_scalar x a, i.e., a -$ x
val ( $* ) : float -> dsmat -> dsmat
Shorthand for mul_scalar x a, i.e., x $* a
val ($/) : float -> dsmat -> dsmat
Shorthand for div_scalar x a, i.e., x $/ a
val (=@) : dsmat -> dsmat -> bool
Shorthand for is_equal x y, i.e., x =@ y
val (>@) : dsmat -> dsmat -> bool
Shorthand for is_greater x y, i.e., x >@ y
val (<@) : dsmat -> dsmat -> bool
Shorthand for is_smaller x y, i.e., x <@ y
val (<>@) : dsmat -> dsmat -> bool
Shorthand for is_unequal x y, i.e., x <>@ y
val (>=@) : dsmat -> dsmat -> bool
Shorthand for equal_or_greater x y, i.e., x >=@ y
val (<=@) : dsmat -> dsmat -> bool
Shorthand for equal_or_smaller x y, i.e., x <=@ y
val (@@) : (float -> float) -> dsmat -> dsmat
Shorthand for map f x, i.e., f @@ x
val gsl_col : dsmat -> int -> dsmat