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package owl
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.
Create sparse matrices
val zeros : int -> int -> spmatzeros 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 : int -> int -> spmatones 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 : int -> spmateye m creates an m by m identity matrix.
val binary : int -> int -> spmatbinary m n creates an m by n random matrix where 10% ~ 15% elements are 1.
val uniform : ?scale:float -> int -> int -> spmatuniform 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 uniform_int : ?a:int -> ?b:int -> int -> int -> spmatuniform ~a ~b m n creates an m by n matrix where 10% ~ 15% elements follow a uniform distribution in [a, b] interval. By default, a = 0 and b = 100.
val linspace : float -> float -> int -> spmatlinspace 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].
Obtain the basic properties of a matrix
val shape : spmat -> int * intIf x is an m by n matrix, shape x returns (m,n), i.e., the size of two dimensions of x.
val row_num : spmat -> introw_num x returns the number of rows in matrix x.
val col_num : spmat -> intcol_num x returns the number of columns in matrix x.
val row_num_nz : spmat -> introw_num_nz x returns the number of non-zero rows in matrix x.
val col_num_nz : spmat -> intcol_num_nz x returns the number of non-zero columns in matrix x.
val numel : spmat -> intnumel x returns the number of elements in matrix x. It is equivalent to (row_num x) * (col_num x).
val nnz : spmat -> intnnz x returns the number of non-zero elements in matrix x.
val nnz_rows : spmat -> int arraynnz_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 : spmat -> int arraynnz_cols x returns the number of non-zero cols in matrix x.
val density : spmat -> floatdensity x returns the density of non-zero element. This operation is equivalent to nnz x divided by numel x.
Manipulate a matrix
val get : spmat -> int -> int -> floatget x i j returns the value of element (i,j) of x.
val set : spmat -> int -> int -> float -> unitset x i j a sets the element (i,j) of x to value a.
val reset : spmat -> unitreset x resets all the elements in x to 0.
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 trace : spmat -> floattrace x returns the sum of diagonal elements in x.
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.
Similar to rows, cols x a returns the columns (specified in array a) of x in a new sparse matrix.
Iterate elements, columns, and rows
val iteri : (int -> int -> float -> unit) -> spmat -> unititeri 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) -> spmat -> unititer 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
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.
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 -> spmat -> 'afold 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) -> spmat -> (int * int) arrayfilteri 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) -> spmat -> (int * int) arraySimilar to filteri, but the coordinates of the elements are not passed to the function f : float -> bool.
iteri_rows f x iterates every row in x and applies function f : int -> spmat -> unit to each of them.
Similar to iteri_rows except row number is not passed to f.
iteri_cols f x iterates every column in x and applies function f : int -> spmat -> unit to each of them. Column number is passed to f as the first parameter.
Similar to iteri_cols except col number is not passed to f.
mapi_rows f x maps every row in x to a type 'a value by applying function f : int -> spmat -> 'a to each of them. The results is an array of all the returned values.
Similar to mapi_rows except row number is not passed to f.
mapi_cols f x maps every column in x to a type 'a value by applying function f : int -> spmat -> 'a.
Similar to mapi_cols except column number is not passed to f.
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.
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 -> float -> unit) -> spmat -> unititeri_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 : (float -> unit) -> spmat -> unitSimilar to iter_nz except the coordinates of elements are not passed to f.
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.
Similar to mapi_nz except the coordinates of elements are not passed to f.
val fold_nz : ('a -> float -> 'a) -> 'a -> spmat -> 'afold_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 -> float -> bool) -> spmat -> (int * int) arrayfilteri_nz f x is similar to filter f x but only applies f to non-zero elements in x.
val filter_nz : (float -> bool) -> spmat -> (int * int) arrayfilter_nz f x is similar to filteri_nz except that the coordinates of matrix elements are not passed to f.
iteri_rows_nz f x is similar to iteri_rows but only applies f to non-zero rows in x.
Similar to iteri_rows_nz except that row numbers are not passed to f.
iteri_cols_nz f x is similar to iteri_cols but only applies f to non-zero columns in x.
Similar to iteri_cols_nz except that column numbers are not passed to f.
mapi_rows_nz f x applies f only to the non-zero rows in x.
Similar to mapi_rows_nz, but row numbers are not passed to f.
mapi_cols_nz f x applies f only to the non-zero columns in x.
Similar to mapi_cols_nz, but columns numbers are not passed to f.
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.
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.
Examine the elements in a matrix
val exists : (float -> bool) -> spmat -> boolexists 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) -> spmat -> boolnot_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) -> spmat -> boolfor_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 : (float -> bool) -> spmat -> boolexists_nz f x is similar to exists but only checks non-zero elements.
val not_exists_nz : (float -> bool) -> spmat -> boolnot_exists_nz f x is similar to not_exists but only checks non-zero elements.
val for_all_nz : (float -> bool) -> spmat -> boolfor_all_nz f x is similar to for_all_nz but only checks non-zero elements.
Basic mathematical operations of matrices
mul_scalar x a multiplies every element in x by a constant factor a.
div_scalar x a divides every element in x by a constant factor a.
add x y adds two matrices x and y. Both must have the same dimensions.
sub x y subtracts the matrix x from y. Both must have the same dimensions.
mul x y performs an element-wise multiplication, so both x and y must have the same dimensions.
div x y performs an element-wise division, so both x and y must have the same dimensions.
dot x y calculates the dot product of an m by n matrix x and another n by p matrix y.
abs x returns a new matrix where each element has the absolute value of that in the original matrix x.
neg x returns a new matrix where each element has the negative value of that in the original matrix x.
val sum : spmat -> floatsum x returns the summation of all the elements in x.
val average : spmat -> floataverage x returns the average value of all the elements in x. It is equivalent to calculate sum x divided by numel x
val is_zero : spmat -> boolis_zero x returns true if all the elements in x are zeros.
val is_positive : spmat -> boolis_positive x returns true if all the elements in x are positive.
val is_negative : spmat -> boolis_negative x returns true if all the elements in x are negative.
val is_nonnegative : spmat -> boolis_nonnegative returns true if all the elements in x are non-negative.
val min : spmat -> floatmin x returns the minimum value of all elements in x.
val max : spmat -> floatmax x returns the maximum value of all elements in x.
val minmax : spmat -> float * floatminmax x returns both the minimum and minimum values in x.
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)).
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)).
Compare two matrices
is_unequal x y returns true if there is at least one element in x is not equal to that in y.
is_greater x y returns true if all the elements in x are greater than the corresponding elements in y.
is_smaller x y returns true if all the elements in x are smaller than the corresponding elements in y.
equal_or_greater x y returns true if all the elements in x are not smaller than the corresponding elements in y.
equal_or_smaller x y returns true if all the elements in x are not greater than the corresponding elements in y.
Randomisation functions
val permutation_matrix : int -> spmatpermutation_matrix m returns an m by m permutation matrix.
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.
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.
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_dense : spmat -> Owl_dense_real.matto_dense x converts x into a dense matrix.
val of_dense : Owl_dense_real.mat -> spmatof_dense x returns a sparse matrix from the dense matrix x.
val print : spmat -> unitprint x pretty prints matrix x without headings.
val pp_spmat : spmat -> unitpp_spmat x pretty prints matrix x with headings. Toplevel uses this function to print out the matrices.
val save : spmat -> string -> unitsave 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 -> spmatload f loads a sparse matrix from file f. The file must be previously saved by using save function.
Shorhand infix operators
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