Module Slap.Mat

module Mat: Slap_mat

Sized matrices.

type (+'m, +'n, 'num, 'prec, +'cnt_or_dsc) t

('m, 'n, 'num, 'prec) mat is the type of 'm-by-'n matrix whose elements have OCaml type 'num, representation kind 'prec and memory contiguity 'cnt_or_dsc. The internal implementation is fortran-style two-dimensional big array.

val cnt : ('m, 'n, 'num, 'prec, Slap_misc.cnt) t ->
       ('m, 'n, 'num, 'prec, 'cnt) t

Recover polymorphism of the fifth type parameter.

Creation of matrices

val create : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t -> 'n Slap_size.t -> ('m, 'n, 'num, 'prec, 'cnt) t

create kind m n
Returns a fresh m-by-n matrix (not initialized).

val make : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t -> 'num -> ('m, 'n, 'num, 'prec, 'cnt) t

make kind m n x
Returns a fresh m-by-n matrix initialized with x.

val init : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t ->
       (int -> int -> 'num) -> ('m, 'n, 'num, 'prec, 'cnt) t

An alias of init_cols.

val init_cols : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t ->
       (int -> int -> 'num) -> ('m, 'n, 'num, 'prec, 'cnt) t

init_cols kind m n f returns a fresh m-by-n matrix whose the (i,j) element is initialized by the result of calling f i j. The elements are passed column-wise.

val init_rows : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t ->
       (int -> int -> 'num) -> ('m, 'n, 'num, 'prec, 'cnt) t

init_rows kind m n f returns a fresh m-by-n matrix whose the (i,j) element is initialized by the result of calling f i j. The elements are passed row-wise.

Accessors

val kind : ('m, 'n, 'num, 'prec, 'cd) t -> ('num, 'prec) Bigarray.kind

Returns the kind of the given big array.

val dim : ('m, 'n, 'num, 'prec, 'cd) t -> 'm Slap_size.t * 'n Slap_size.t

dim a is (dim1 a, dim2 a).

val dim1 : ('m, 'n, 'num, 'prec, 'cd) t -> 'm Slap_size.t

dim1 a
Returns the number of rows in a.

val dim2 : ('m, 'n, 'num, 'prec, 'cd) t -> 'n Slap_size.t

dim1 a
Returns the number of columns in a.

val get_dyn : ('m, 'n, 'num, 'prec, 'cd) t -> int -> int -> 'num

get_dyn a i j
Returns the (i,j) element of the matrix a.

val set_dyn : ('m, 'n, 'num, 'prec, 'cd) t -> int -> int -> 'num -> unit

set_dyn a i j x assigns x to the (i,j) element of the matrix a.

val unsafe_get : ('m, 'n, 'num, 'prec, 'cd) t -> int -> int -> 'num

Like Slap_mat.get_dyn, but size checking is not always performed.

val unsafe_set : ('m, 'n, 'num, 'prec, 'cd) t -> int -> int -> 'num -> unit

Like Slap_mat.set_dyn, but size checking is not always performed.

val replace_dyn : ('m, 'n, 'num, 'prec, 'cd) t -> int -> int -> ('num -> 'num) -> unit

replace_dyn a i j f is set a i j (f (get a i j)).

val col_dyn : ('m, 'n, 'num, 'prec, 'cd) t ->
       int -> ('m, 'num, 'prec, 'cnt) Slap_vec.t

col_dyn a i
Returns the i-th column of the matrix a. The data are shared.

val row_dyn : ('m, 'n, 'num, 'prec, 'cd) t ->
       int -> ('n, 'num, 'prec, Slap_misc.dsc) Slap_vec.t

row_dyn a i
Returns the i-th row of the matrix a. The data are shared.

val diag : ('n, 'n, 'num, 'prec, 'cd) t ->
       ('n, 'num, 'prec, Slap_misc.dsc) Slap_vec.t

diag a
Returns the diagonal elements of the square matrix a. The data are shared.

val diag_rect : ('m, 'n, 'num, 'prec, 'cd) t ->
       (('m, 'n) Slap_size.min, 'num, 'prec, Slap_misc.dsc) Slap_vec.t

diag_rect a
Since 1.0.0
Returns the diagonal elements of the rectangular matrix a. The data are shared.

val as_vec : ('m, 'n, 'num, 'prec, Slap_misc.cnt) t ->
       (('m, 'n) Slap_size.mul, 'num, 'prec, 'cnt) Slap_vec.t

as_vec a
Returns the vector containing all elements of the matrix in column-major order. The data are shared.

Basic operations

val fill : ('m, 'n, 'num, 'prec, 'cd) t -> 'num -> unit

Fill the given matrix with the given value.

val copy : ?b:('m, 'n, 'num, 'prec, 'b_cd) t ->
       ('m, 'n, 'num, 'prec, 'a_cd) t ->
       ('m, 'n, 'num, 'prec, 'b_cd) t

copy ?b a copies the matrix a into the matrix b.
Returns b, which is overwritten.

b : default = a fresh matrix.

Matrix transformations

val packed : ?up:bool ->
       ?x:('n Slap_size.packed, 'num, 'prec, Slap_misc.cnt) Slap_vec.t ->
       ('n, 'n, 'num, 'prec, 'cd) t ->
       ('n Slap_size.packed, 'num, 'prec, 'cnt) Slap_vec.t

packed ?up ?x a transforms triangular matrix a into packed storage format.
Since 0.2.0
Returns vector x, which is overwritten.

up : default = true

If up = true, then the upper triangular part of a is packed;
If up = false, then the lower triangular part of a is packed.

val unpacked : ?up:bool ->
       ?fill_num:'num option ->
       ?a:('n, 'n, 'num, 'prec, 'cd) t ->
       ('n Slap_size.packed, 'num, 'prec, Slap_misc.cnt) Slap_vec.t ->
       ('n, 'n, 'num, 'prec, 'cd) t

unpacked ?up ?fill_num ?a x generates an upper or lower triangular matrix from x stored in packed storage.
Since 0.2.0
Returns matrix a, which is overwritten.

up : default = true

If up = true, then the upper triangular matrix is generated;
If up = false, then the lower triangular matrix is generated.

fill_num : default = None (Note: The default value in Slap.[SDCZ].Mat.unpacked is Some 0, not None.)

If fill_num = None, the elements in the generated matrix are not initialized;
If fill_num = Some c, the elements in the generated matrix are initialized by c.

val geband_dyn : 'kl Slap_size.t ->
       'ku Slap_size.t ->
       ?b:(('m, 'n, 'kl, 'ku) Slap_size.geband, 'n, 'num, 'prec, 'b_cd) t ->
       ('m, 'n, 'num, 'prec, 'a_cd) t ->
       (('m, 'n, 'kl, 'ku) Slap_size.geband, 'n, 'num, 'prec, 'b_cd) t

geband_dyn kl ku ?b a converts matrix a into a matrix stored in band storage.
Since 0.2.0
Raises Invalid_arg if kl >= dim1 a or ku >= dim2 a.
Returns matrix b, which is overwritten.

val ungeband : 'm Slap_size.t ->
       'kl Slap_size.t ->
       'ku Slap_size.t ->
       ?fill_num:'num option ->
       ?a:('m, 'n, 'num, 'prec, 'a_cd) t ->
       (('m, 'n, 'kl, 'ku) Slap_size.geband, 'n, 'num, 'prec, 'b_cd) t ->
       ('m, 'n, 'num, 'prec, 'a_cd) t

ungeband m kl ku ?a b converts matrix b stored in band storage into a matrix stored in the normal order.
Since 0.2.0
Returns matrix a, which is overwritten.

fill_num : default = None (Note: The default value in Slap.[SDCZ].Mat.ungeband_dyn is Some 0, not None.)

If fill_num = None, the elements in the generated matrix are not initialized;
If fill_num = Some c, the elements in the generated matrix are initialized by c.

val syband_dyn : 'kd Slap_size.t ->
       ?up:bool ->
       ?b:(('n, 'kd) Slap_size.syband, 'n, 'num, 'prec, 'b_cd) t ->
       ('n, 'n, 'num, 'prec, 'a_cd) t ->
       (('n, 'kd) Slap_size.syband, 'n, 'num, 'prec, 'b_cd) t

syband_dyn kd ?b a converts matrix a into a matrix stored in symmetric or Hermitian band storage.
Since 0.2.0
Raises Invalid_arg if kd >= dim1 a.
Returns matrix b, which is overwritten.

up : default = true

If up = true, then the upper triangular part of a is used;
If up = false, then the lower triangular part of a is used.

val unsyband : 'kd Slap_size.t ->
       ?up:bool ->
       ?fill_num:'num option ->
       ?a:('n, 'n, 'num, 'prec, 'a_cd) t ->
       (('n, 'kd) Slap_size.syband, 'n, 'num, 'prec, 'b_cd) t ->
       ('n, 'n, 'num, 'prec, 'a_cd) t

unsyband kd ?a b converts matrix b stored in symmetric or Hermitian band storage into a matrix stored in the normal order.
Since 0.2.0
Returns matrix a, which is overwritten.

up : default = true

If up = true, then b is treated as the upper triangular part of symmetric or Hermitian matrix a;
If up = false, then b is treated as the lower triangular part of symmetric or Hermitian matrix a;

fill_num : default = None (Note: The default value in Slap.[SDCZ].Mat.unsyband_dyn is Some 0, not None.)

If fill_num = None, the elements in the generated matrix are not initialized;
If fill_num = Some c, the elements in the generated matrix are initialized by c.

val luband_dyn : 'kl Slap_size.t ->
       'ku Slap_size.t ->
       ?ab:(('m, 'n, 'kl, 'ku) Slap_size.luband, 'n, 'num, 'prec, 'b_cd) t ->
       ('m, 'n, 'num, 'prec, 'a_cd) t ->
       (('m, 'n, 'kl, 'ku) Slap_size.luband, 'n, 'num, 'prec, 'b_cd) t

luband_dyn kl ku ?ab a converts matrix a into a matrix stored in band storage for LU factorization.
Since 0.2.0
Raises Invalid_arg if kl >= dim1 a or ku >= dim2 a.
Returns matrix ab, which is overwritten.

val unluband : 'm Slap_size.t ->
       'kl Slap_size.t ->
       'ku Slap_size.t ->
       ?fill_num:'num option ->
       ?a:('m, 'n, 'num, 'prec, 'a_cd) t ->
       (('m, 'n, 'kl, 'ku) Slap_size.luband, 'n, 'num, 'prec, 'b_cd) t ->
       ('m, 'n, 'num, 'prec, 'a_cd) t

unluband m kl ku ?a ab converts matrix ab stored in band storage for LU factorization into a matrix stored in the normal order.
Since 0.2.0
Returns matrix a, which is overwritten.

fill_num : default = None (Note: The default value in Slap.[SDCZ].Mat.unluband_dyn is Some 0, not None.)

If fill_num = None, the elements in the generated matrix are not initialized;
If fill_num = Some c, the elements in the generated matrix are initialized by c.

Iterators

val map : ('b_num, 'b_prec) Bigarray.kind ->
       ('a_num -> 'b_num) ->
       ?b:('m, 'n, 'b_num, 'b_prec, 'b_cd) t ->
       ('m, 'n, 'a_num, 'a_prec, 'a_cd) t ->
       ('m, 'n, 'b_num, 'b_prec, 'b_cd) t

val mapi : ('b_num, 'b_prec) Bigarray.kind ->
       (int -> int -> 'a_num -> 'b_num) ->
       ?b:('m, 'n, 'b_num, 'b_prec, 'b_cd) t ->
       ('m, 'n, 'a_num, 'a_prec, 'a_cd) t ->
       ('m, 'n, 'b_num, 'b_prec, 'b_cd) t

val fold_left : ('accum -> ('m, 'num, 'prec, 'x_cd) Slap_vec.t -> 'accum) ->
       'accum -> ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum

fold_left f init a folds column vectors of matrix a by f in the order left to right.

val fold_lefti : (int -> 'accum -> ('m, 'num, 'prec, 'x_cd) Slap_vec.t -> 'accum) ->
       'accum -> ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum

fold_lefti f init a folds column vectors of matrix a by f in the order left to right.

val fold_right : (('m, 'num, 'prec, 'x_cd) Slap_vec.t -> 'accum -> 'accum) ->
       ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum -> 'accum

fold_right f a init folds column vectors of matrix a by f in the order right to left.

val fold_righti : (int -> ('m, 'num, 'prec, 'x_cd) Slap_vec.t -> 'accum -> 'accum) ->
       ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum -> 'accum

fold_righti f a init folds column vectors of matrix a by f in the order right to left.

val fold_top : ('accum -> ('n, 'num, 'prec, Slap_misc.dsc) Slap_vec.t -> 'accum) ->
       'accum -> ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum

fold_top f init a folds row vectors of matrix a by f in the order top to bottom.

val fold_topi : (int -> 'accum -> ('n, 'num, 'prec, Slap_misc.dsc) Slap_vec.t -> 'accum) ->
       'accum -> ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum

fold_topi f init a folds row vectors of matrix a by f in the order top to bottom.

val fold_bottom : (('n, 'num, 'prec, Slap_misc.dsc) Slap_vec.t -> 'accum -> 'accum) ->
       ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum -> 'accum

fold_bottom f a init folds row vectors of matrix a by f in the order bottom to top.

val fold_bottomi : (int -> ('n, 'num, 'prec, Slap_misc.dsc) Slap_vec.t -> 'accum -> 'accum) ->
       ('m, 'n, 'num, 'prec, 'a_cd) t -> 'accum -> 'accum

fold_bottomi f a init folds row vectors of matrix a by f in the order bottom to top.

val replace_all : ('m, 'n, 'num, 'prec, 'cd) t -> ('num -> 'num) -> unit

replace_all a f modifies the matrix a in place -- the (i,j)-element aij of a will be set to f aij.

val replace_alli : ('m, 'n, 'num, 'prec, 'cd) t -> (int -> int -> 'num -> 'num) -> unit

replace_all a f modifies the matrix a in place -- the (i,j)-element aij of a will be set to f i j aij.

Type conversion

val to_array : ('m, 'n, 'num, 'prec, 'cd) t -> 'num array array

to_array a
Returns the array of arrays of all the elements of a.

val of_array_dyn : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t -> 'num array array -> ('m, 'n, 'num, 'prec, 'cnt) t

Build a matrix initialized from the given array of arrays.
Raises Invalid_argument the given array of arrays is not rectangular or its size is not m-by-n.

val unsafe_of_array : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t -> 'num array array -> ('m, 'n, 'num, 'prec, 'cnt) t

Like of_array_dyn, but size checking is not always performed.
Since 1.0.0

val to_list : ('m, 'n, 'num, 'prec, 'cd) t -> 'num list list

to_list a
Returns the list of lists of all the elements of a.

val of_list_dyn : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t -> 'num list list -> ('m, 'n, 'num, 'prec, 'cnt) t

Build a matrix initialized from the given list of lists.
Raises Invalid_argument the given list of lists is not rectangular or its size is not m-by-n.

val unsafe_of_list : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t -> 'num list list -> ('m, 'n, 'num, 'prec, 'cnt) t

Like of_list_dyn, but size checking is not always performed.
Since 1.0.0

val to_bigarray : ('m, 'n, 'num, 'prec, 'cd) t ->
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t

to_bigarray a
Since 1.0.0
Returns the big array of all the elements of the matrix a.

val of_bigarray_dyn : ?share:bool ->
       'm Slap_size.t ->
       'n Slap_size.t ->
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t ->
       ('m, 'n, 'num, 'prec, 'cnt) t

of_bigarray_dyn ?share m n ba
Since 1.0.0
Raises Invalid_argument the size of the given big array is not equal to m-by-n.
Returns a fresh matrix of all the elements of big array ba.

share : true if data are shared. (default = false)

val unsafe_of_bigarray : ?share:bool ->
       'm Slap_size.t ->
       'n Slap_size.t ->
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t ->
       ('m, 'n, 'num, 'prec, 'cnt) t

Like of_bigarray_dyn, but size checking is not always performed.
Since 1.0.0

type ('num, 'prec, 'cnt_or_dsc) dyn =

`\|`	`MAT : ('m, 'n, 'num0, 'prec0, 'cnt_or_dsc0) t -> ('num0, 'prec0, 'cnt_or_dsc0) dyn`

The type of packages of existential quantified sized type: ('num, 'prec, 'cnt_or_dsc) dyn = exists m, n. (m, n, 'num, 'prec, 'cnt_or_dsc) Vec.t.
Since 4.0.0

val of_array_c : ('num, 'prec) Bigarray.kind ->
       'num array array -> ('num, 'prec, 'cnt) dyn

let MAT n = of_array_c kind arr
Since 4.0.0
Returns a constructor MAT that has a matrix (initialized from the given array of arrays) that has the existential quantified sized type exists m, n. (n, 'num, 'prec, 'cnt_or_dsc) Mat.t. "c" of of_array_c means a "c"onstructor of GADT. This function is available in OCaml 4.00 or above.

val of_list_c : ('num, 'prec) Bigarray.kind ->
       'num list list -> ('num, 'prec, 'cnt) dyn

let MAT n = of_list_c kind lst
Since 4.0.0
Returns a constructor MAT that has a matrix (initialized from the given list of lists) that has the existential quantified sized type exists m, n. (n, 'num, 'prec, 'cnt_or_dsc) Mat.t. "c" of of_list_c means a "c"onstructor of GADT. This function is available in OCaml 4.00 or above.

val of_bigarray_c : ?share:bool ->
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t ->
       ('num, 'prec, 'cnt) dyn

let MAT n = of_bigarray_c ?share ba
Since 4.0.0
Returns a constructor MAT that has a matrix (initialized from the given big array) that has the existential quantified sized type exists m, n. (n, 'num, 'prec, 'cnt_or_dsc) Mat.t. "c" of of_bigarray_c means a "c"onstructor of GADT. This function is available in OCaml 4.00 or above.

share : true if data are shared. (default = false)

Submatrices

val submat_dyn : 'm Slap_size.t ->
       'n Slap_size.t ->
       ?ar:int ->
       ?ac:int ->
       ('a, 'b, 'num, 'prec, 'cd) t ->
       ('m, 'n, 'num, 'prec, Slap_misc.dsc) t

submat_dyn m n ?ar ?ac a
Returns a m-by-n submatrix of the matrix a. The (i,j) element of the returned matrix refers the (ar+i-1,ac+j-1) element of a. The data are shared.

ar : default = 1

ac : default = 1

Utilities

val dim_array_array : 'a array array -> (int * int) option

dim_array_array aa returns Some (n_rows, n_cols) with the number of rows n_rows and the number of columns n_cols of the given array of arrays. (0, 0) is returned if aa is an empty array. None is returned if aa is not rectangular.

val dim_list_list : 'a list list -> (int * int) option

dim_list list ll returns Some (n_rows, n_cols) with the number of rows n_rows and the number of columns n_cols of the given list of lists. (0, 0) is returned if ll is an empty list. None is returned if ll is not rectangular.

Internal functions

val check_cnt : ('m, 'n, 'num, 'prec, Slap_misc.cnt) t -> bool

val create_array2 : ('a, 'b) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t -> ('a, 'b, Bigarray.fortran_layout) Bigarray.Array2.t

val opt_mat : 'm Slap_size.t ->
       'n Slap_size.t ->
       ('m, 'n, 'num, 'prec, 'cd) t option ->
       int option * int option *
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t option

val opt_mat_alloc : ('num, 'prec) Bigarray.kind ->
       'm Slap_size.t ->
       'n Slap_size.t ->
       ('m, 'n, 'num, 'prec, 'cd) t option ->
       int * int * ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t

val __expose : ('m, 'n, 'num, 'prec, 'cnt_or_dsc) t ->
       'm Slap_size.t * 'n Slap_size.t * int * int *
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t

val __unexpose : 'm Slap_size.t ->
       'n Slap_size.t ->
       int ->
       int ->
       ('num, 'prec, Bigarray.fortran_layout) Bigarray.Array2.t ->
       ('m, 'n, 'num, 'prec, 'cnt_or_dsc) t