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Sparse real matrix: this module supports the operations on sparse matrices of real numbers. The module is partly built atop of GSL fucntions. Because GSL only has limited support for sparse matrices. There are some hacks and workarounds in the code.

In the future, I might use a pure OCaml implementation to replace the current solution. At the moment, use with care and let me know if you find bugs.

type ('a, 'b) t
type ('a, 'b) kind = ('a, 'b) Bigarray.kind

Type of sparse matrices. It is defined in types.ml as record type.

Create sparse matrices
val zeros : ?density:float -> ('a, 'b) kind -> int -> int -> ('a, 'b) t

zeros m n creates an m by n matrix where all the elements are zeros. This operation is very fast since it only allocates a small amount of memory. The memory will grow automatically as more elements are inserted.

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

ones m n creates an m by n matrix where all the elements are ones. This operation can be very slow if matrix size is big. You might consider to use dense matrix for better performance in this case.

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

eye m creates an m by m identity matrix.

val binary : ?density:float -> ('a, 'b) kind -> int -> int -> ('a, 'b) t

binary m n creates an m by n random matrix where 10% ~ 15% elements are 1.

val uniform : ?density:float -> ?scale:float -> ('a, 'b) kind -> int -> int -> ('a, 'b) t

uniform m n creates an m by n matrix where 10% ~ 15% elements follow a uniform distribution in (0,1) interval. uniform ~scale:a m n adjusts the interval to (0,a).

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

row_num_nz x returns the number of non-zero rows in matrix x.

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

col_num_nz x returns the number of non-zero 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 matrix x.

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

nnz_rows x returns the number of non-zero rows in matrix x. A non-zero row means there is at least one non-zero element in that row.

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

nnz_cols x returns the number of non-zero cols in matrix x.

val density : ('a, 'b) t -> float

density x returns the density of non-zero element. This operation is equivalent to nnz x divided by numel x.

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

set x i j a sets the element (i,j) of x to value a.

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

get x i j returns the value of element (i,j) of x.

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

reset x resets all the elements in x to 0.

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

clone x makes an exact copy of matrix x. Note that the clone becomes mutable no matter w is mutable or not. This is expecially useful if you want to modify certain elements in an immutable matrix from math operations.

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

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

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

diag x returns the diagonal elements of x.

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 sparse 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 sparse matrix.

val prune : ('a, 'b) t -> 'a -> float -> unit
Iterate elements, columns, and rows
val iteri : (int -> 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 -> 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 : (int -> int -> 'c -> 'a -> 'c) -> 'c -> ('a, 'b) t -> 'c
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 filteri : (int -> int -> 'a -> bool) -> ('a, 'b) t -> (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 : ('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 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 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 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 iteri_nz : (int -> int -> 'a -> unit) -> ('a, 'b) t -> unit

iteri_nz f x iterates all the non-zero elements in x by applying the function f : int -> int -> float -> 'a. It is much faster than iteri.

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

Similar to iter_nz except the coordinates of elements are not passed to f.

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

mapi_nz f x is similar to mapi f x but only applies f to non-zero elements in x. The zeros in x will remain the same in the new matrix.

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

Similar to mapi_nz except the coordinates of elements are not passed to f.

val foldi_nz : (int -> int -> 'c -> 'a -> 'c) -> 'c -> ('a, 'b) t -> 'c
val fold_nz : ('c -> 'a -> 'c) -> 'c -> ('a, 'b) t -> 'c

fold_nz f a x is similar to fold f a x but only applies to non-zero rows in x. zero rows will be simply skipped in folding.

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

filteri_nz f x is similar to filter f x but only applies f to non-zero elements in x.

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

filter_nz f x is similar to filteri_nz except that the coordinates of matrix elements are not passed to f.

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

iteri_rows_nz f x is similar to iteri_rows but only applies f to non-zero rows in x.

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

Similar to iteri_rows_nz except that row numbers are not passed to f.

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

iteri_cols_nz f x is similar to iteri_cols but only applies f to non-zero columns in x.

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

Similar to iteri_cols_nz except that column numbers are not passed to f.

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

mapi_rows_nz f x applies f only to the non-zero rows in x.

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

Similar to mapi_rows_nz, but row numbers are not passed to f.

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

mapi_cols_nz f x applies f only to the non-zero columns in x.

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

Similar to mapi_cols_nz, but columns numbers are not passed to f.

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

fold_rows_nz f a x is similar to fold_rows but only folds non-zero rows in x using function f. Zero rows will be dropped in iterating x.

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

fold_cols_nz f a x is similar to fold_cols but only folds non-zero columns in x using function f. Zero columns will be dropped in iterating x.

Examin 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 exists_nz : ('a -> bool) -> ('a, 'b) t -> bool

exists_nz f x is similar to exists but only checks non-zero elements.

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

not_exists_nz f x is similar to not_exists but only checks non-zero elements.

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

for_all_nz f x is similar to for_all_nz but only checks non-zero elements.

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 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.

Randomisation functions
val permutation_matrix : ('a, 'b) kind -> int -> ('a, 'b) t

permutation_matrix m returns an m by m permutation matrix.

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 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 and helper functions
val to_array : ('a, 'b) t -> (int array * 'a) array
val of_array : ('a, 'b) kind -> int -> int -> (int array * 'a) array -> ('a, 'b) t
val to_dense : ('a, 'b) t -> ('a, 'b) Owl_dense_matrix_generic.t

to_dense x converts x into a dense matrix.

val of_dense : ('a, 'b) Owl_dense_matrix_generic.t -> ('a, 'b) t

of_dense x returns a sparse matrix from the dense matrix x.

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

print x pretty prints matrix x without headings.

val pp_spmat : ('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 k f loads a sparse matrix from file f. The file must be previously saved by using save function.

Unary mathematical operations
val min : (float, 'a) t -> float

min x returns the minimum value of all elements in x.

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

max x returns the maximum value of all elements in x.

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

minmax x returns both the minimum and minimum values in 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 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 abs : (float, 'a) t -> (float, 'a) t

abs x returns a new matrix where each element has the absolute value of that in the original matrix x.

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

neg x returns a new matrix where each element has the negative value of that in the original matrix x.

val l1norm : (float, 'b) t -> float
val l2norm : (float, 'b) t -> float
Binary mathematical operations
val add : ('a, 'b) t -> ('a, 'b) t -> ('a, 'b) t

add x y adds two matrices x and y. Both must have the same dimensions.

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

sub x y subtracts the matrix x from y. Both must have the same dimensions.

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

mul x y performs an element-wise multiplication, so both x and y must have the same dimensions.

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

div x y performs an element-wise division, so both x and y must have the same dimensions.

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

dot x y calculates the dot product of an m by n matrix x and another n by p matrix y.

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

mul_scalar x a multiplies every element in x by a constant factor a.

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

div_scalar x a divides every element in x by a constant factor a.

val scalar_add : 'a -> ('a, 'b) t -> ('a, 'b) t
val scalar_sub : 'a -> ('a, 'b) t -> ('a, 'b) t
val scalar_mul : 'a -> ('a, 'b) t -> ('a, 'b) t
val scalar_div : 'a -> ('a, 'b) t -> ('a, 'b) t
val power_scalar : ('a, 'b) t -> 'a -> ('a, 'b) t

power x a calculates the power of a of each element in x.

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