package slap

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Module Slap_Z.Mat

module type CNTMAT = sig ... end

The signature of modules containing dynamically-sized contiguous matrices.

module type DSCMAT = sig ... end

The signature of modules containing dynamically-sized discrete matrices.

val cnt : ('m, 'n, Slap_misc.cnt) mat -> ('m, 'n, 'cnt) mat

Recover polymorphism of the fifth type parameter.

Creation of matrices

val empty : (Slap_size.z, Slap_size.z, 'cnt) mat

An empty matrix.

val create : 'm Slap_size.t -> 'n Slap_size.t -> ('m, 'n, 'cnt) mat

create m n

  • returns

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

val make : 'm Slap_size.t -> 'n Slap_size.t -> num_type -> ('m, 'n, 'cnt) mat

make m n x

  • returns

    a fresh m-by-n matrix initialized with x.

val make0 : 'm Slap_size.t -> 'n Slap_size.t -> ('m, 'n, 'cnt) mat

make0 m n

  • returns

    a fresh m-by-n matrix initialized with 0.

val make1 : 'm Slap_size.t -> 'n Slap_size.t -> ('m, 'n, 'cnt) mat

make1 m n

  • returns

    a fresh m-by-n matrix initialized with 1.

val identity : 'n Slap_size.t -> ('n, 'n, 'cnt) mat

identity n

  • returns

    a fresh n-by-n identity matrix.

val init : 'm Slap_size.t -> 'n Slap_size.t -> (int -> int -> num_type) -> ('m, 'n, 'cnt) mat

An alias of init_cols.

val init_cols : 'm Slap_size.t -> 'n Slap_size.t -> (int -> int -> num_type) -> ('m, 'n, 'cnt) mat

init_cols 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 : 'm Slap_size.t -> 'n Slap_size.t -> (int -> int -> num_type) -> ('m, 'n, 'cnt) mat

init_rows 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 dim : ('m, 'n, 'cd) mat -> 'm Slap_size.t * 'n Slap_size.t

dim a is (dim1 a, dim2 a).

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

dim1 a

  • returns

    the number of rows in a.

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

dim1 a

  • returns

    the number of columns in a.

val get_dyn : ('m, 'n, 'cd) mat -> int -> int -> num_type

get_dyn a i j

  • returns

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

val set_dyn : ('m, 'n, 'cd) mat -> int -> int -> num_type -> unit

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

val unsafe_get : ('m, 'n, 'cd) mat -> int -> int -> num_type

Like get_dyn, but size checking is not always performed.

val unsafe_set : ('m, 'n, 'cd) mat -> int -> int -> num_type -> unit

Like set_dyn, but size checking is not always performed.

val col_dyn : ('m, 'n, 'cd) mat -> int -> ('m, 'cnt) vec

col_dyn a i

  • returns

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

val row_dyn : ('m, 'n, 'cd) mat -> int -> ('n, Slap_misc.dsc) vec

row_dyn a i

  • returns

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

val copy_row_dyn : ('m, 'n, 'cd) mat -> int -> ('n, 'cnt) vec

copy_row_dyn a i is Vec.copy (Mat.row_dyn a i).

val diag : ('n, 'n, 'cd) mat -> ('n, Slap_misc.dsc) vec

diag a

  • returns

    the diagonal elements of the matrix a. The data are shared.

val diag_rect : ('m, 'n, 'cd) mat -> (('m, 'n) Slap_size.min, Slap_misc.dsc) vec

diag_rect a

  • returns

    the diagonal elements of the rectangular matrix a. The data are shared.

  • since 1.0.0
val copy_diag : ('n, 'n, 'cd) mat -> ('n, 'cnt) vec

copy_diag a is Vec.copy (Mat.diag a).

val copy_diag_rect : ('m, 'n, 'cd) mat -> (('m, 'n) Slap_size.min, 'cnt) vec

copy_diag_rect a is Vec.copy (Mat.diag_rect a).

  • since 1.0.0
val as_vec : ('m, 'n, Slap_misc.cnt) mat -> (('m, 'n) Slap_size.mul, 'cnt) vec

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, 'cd) mat -> num_type -> unit

Fill the given matrix with the given value.

  • since 0.1.0
val copy : ?uplo:[ `L | `U ] -> ?b:('m, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> ('m, 'n, 'b_cd) mat

copy ?uplo ?b a copies the matrix a into the matrix b with the LAPACK function lacpy.

  • If uplo is omitted, all elements in a is copied.
  • If uplo is `U, the upper trapezoidal part of a is copied.
  • If uplo is `L, the lower trapezoidal part of a is copied.
  • returns

    b, which is overwritten.

  • parameter uplo

    default = all elements in a is copied.

  • parameter b

    default = a fresh matrix.

val of_col_vecs_dyn : 'm Slap_size.t -> 'n Slap_size.t -> ('m, Slap_misc.cnt) vec array -> ('m, 'n, 'cnt) mat

Type conversion

val to_array : ('m, 'n, 'cd) mat -> num_type array array

to_array a

  • returns

    the array of arrays of all the elements of a.

val of_array_dyn : 'm Slap_size.t -> 'n Slap_size.t -> num_type array array -> ('m, 'n, 'cnt) mat

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 of_array : num_type array array -> (module CNTMAT)

module M = (val of_array aa : CNTMAT)

  • returns

    module M containing the matrix M.value that has the type (M.m, M.n, 'cnt) mat with a generative phantom types M.m and M.n as a package of an existential quantified sized type like exists m, n. (m, n, 'cnt) mat.

module Of_array (X : sig ... end) : CNTMAT

A functor vesion of of_array.

val unsafe_of_array : 'm Slap_size.t -> 'n Slap_size.t -> num_type array array -> ('m, 'n, 'cnt) mat

Like of_array_dyn, but size checking is not always performed.

  • since 1.0.0
val to_list : ('m, 'n, 'cd) mat -> num_type list list

to_list a

  • returns

    the list of lists of all the elements of a.

val of_list_dyn : 'm Slap_size.t -> 'n Slap_size.t -> num_type list list -> ('m, 'n, 'cnt) mat

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 of_list : num_type list list -> (module CNTMAT)

module M = (val of_list ll : CNTMAT)

  • returns

    module M containing the matrix M.value that has the type (M.m, M.n, 'cnt) mat with a generative phantom types M.m and M.n as a package of an existential quantified sized type like exists m, n. (m, n, 'cnt) mat.

module Of_list (X : sig ... end) : CNTMAT

A functor vesion of of_list.

val unsafe_of_list : 'm Slap_size.t -> 'n Slap_size.t -> num_type list list -> ('m, 'n, 'cnt) mat

Like of_list_dyn, but size checking is not always performed.

  • since 1.0.0
val to_bigarray : ('m, 'n, 'cd) mat -> (num_type, prec, Bigarray.fortran_layout) Bigarray.Array2.t

to_bigarray a

  • returns

    the big array of all the elements of the matrix a.

  • since 1.0.0
val of_bigarray_dyn : ?share:bool -> 'm Slap_size.t -> 'n Slap_size.t -> (num_type, prec, Bigarray.fortran_layout) Bigarray.Array2.t -> ('m, 'n, 'cnt) mat

of_bigarray_dyn ?share m n ba

  • returns

    a fresh matrix of all the elements of big array ba.

  • parameter share

    true if data are shared. (default = false)

  • since 1.0.0

module M = (val of_bigarray ba : CNTMAT)

  • returns

    module M containing the matrix M.value that has the type (M.m, M.n, 'cnt) mat with a generative phantom types M.m and M.n as a package of an existential quantified sized type like exists m, n. (m, n, 'cnt) mat.

  • since 1.0.0
module Of_bigarray (X : sig ... end) : CNTMAT

A functor vesion of of_bigarray.

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

Like of_bigarray_dyn, but size checking is not always performed.

  • since 1.0.0

Iterators

val map : (num_type -> num_type) -> ?b:('m, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> ('m, 'n, 'b_cd) mat
val mapi : (int -> int -> num_type -> num_type) -> ?b:('m, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> ('m, 'n, 'b_cd) mat
val fold_left : ('accum -> ('m, 'x_cd) vec -> 'accum) -> 'accum -> ('m, 'n, 'a_cd) mat -> '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, 'x_cd) vec -> 'accum) -> 'accum -> ('m, 'n, 'a_cd) mat -> 'accum

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

val fold_right : (('m, 'x_cd) vec -> 'accum -> 'accum) -> ('m, 'n, 'a_cd) mat -> '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, 'x_cd) vec -> 'accum -> 'accum) -> ('m, 'n, 'a_cd) mat -> '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, Slap_misc.dsc) vec -> 'accum) -> 'accum -> ('m, 'n, 'a_cd) mat -> '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, Slap_misc.dsc) vec -> 'accum) -> 'accum -> ('m, 'n, 'a_cd) mat -> 'accum

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

val fold_bottom : (('n, Slap_misc.dsc) vec -> 'accum -> 'accum) -> ('m, 'n, 'a_cd) mat -> '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, Slap_misc.dsc) vec -> 'accum -> 'accum) -> ('m, 'n, 'a_cd) mat -> '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, 'cd) mat -> (num_type -> num_type) -> 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, 'cd) mat -> (int -> int -> num_type -> num_type) -> 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.

Matrix transformations

val transpose_copy : ?b:('n, 'm, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> ('n, 'm, 'b_cd) mat

transpose_copy ?b a copies the transpose of a into b.

  • returns

    the matrix b, which is overwritten.

  • since 0.1.0
val detri : ?up:bool -> ('n, 'n, 'cd) mat -> unit

detri ?up a converts triangular matrix a to a symmetric matrix, i.e., copies the upper or lower triangular part of a into another part.

  • parameter up

    default = true

  • since 0.1.0
val packed : ?up:bool -> ?x:('n Slap_size.packed, Slap_misc.cnt) vec -> ('n, 'n, 'cd) mat -> ('n Slap_size.packed, 'cnt) vec

packed ?up ?x a transforms matrix a into packed storage format.

  • returns

    vector x, which is overwritten.

  • parameter 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.
  • since 0.2.0
val unpacked : ?up:bool -> ?fill_num:num_type option -> ?a:('n, 'n, 'cd) mat -> ('n Slap_size.packed, Slap_misc.cnt) vec -> ('n, 'n, 'cd) mat

unpacked ?up ?fill_num ?a x generates an upper or lower triangular matrix from packed-storage-format vector x.

  • returns

    matrix a, which is overwritten.

  • parameter up

    default = true

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

    default = Some 0

    • If fill_num is None, the elements in the generated matrix are not initialized;
    • If fill_num is Some c, the elements in the generated matrix are initialized by c.
  • since 0.2.0
val geband_dyn : 'kl Slap_size.t -> 'ku Slap_size.t -> ?b:(('m, 'n, 'kl, 'ku) Slap_size.geband, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> (('m, 'n, 'kl, 'ku) Slap_size.geband, 'n, 'b_cd) mat

geband_dyn kl ku ?b a converts matrix a into a matrix stored in band storage.

  • returns

    matrix b, which is overwritten.

  • parameter kl

    the number of subdiagonals

  • parameter ku

    the number of superdiagonals

  • raises Invalid_arg

    if kl >= dim1 a or ku >= dim2 a.

  • since 0.2.0
val ungeband : 'm Slap_size.t -> 'kl Slap_size.t -> 'ku Slap_size.t -> ?fill_num:num_type option -> ?a:('m, 'n, 'a_cd) mat -> (('m, 'n, 'kl, 'ku) Slap_size.geband, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat

ungeband m kl ku ?a b converts matrix b stored in band storage into a matrix stored in the normal order.

  • returns

    matrix a, which is overwritten.

  • parameter m

    the number of rows in a

  • parameter kl

    the number of subdiagonals

  • parameter ku

    the number of superdiagonals

  • parameter fill_num

    default = Some 0

    • 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.
  • since 0.2.0
val syband_dyn : 'kd Slap_size.t -> ?up:bool -> ?b:(('n, 'kd) Slap_size.syband, 'n, 'b_cd) mat -> ('n, 'n, 'a_cd) mat -> (('n, 'kd) Slap_size.syband, 'n, 'b_cd) mat

syband_dyn kd ?b a converts matrix a into a matrix stored in symmetric or Hermitian band storage.

  • returns

    matrix b, which is overwritten.

  • parameter kd

    the number of subdiagonals or superdiagonals

  • parameter 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.
  • raises Invalid_arg

    if kd >= dim1 a.

  • since 0.2.0
val unsyband : 'kd Slap_size.t -> ?up:bool -> ?fill_num:num_type option -> ?a:('n, 'n, 'a_cd) mat -> (('n, 'kd) Slap_size.syband, 'n, 'b_cd) mat -> ('n, 'n, 'a_cd) mat

unsyband kd ?a b converts matrix b stored in symmetric or Hermitian band storage into a matrix stored in the normal order.

  • returns

    matrix a, which is overwritten.

  • parameter kd

    the number of subdiagonals or superdiagonals

  • parameter 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;
  • parameter fill_num

    default = Some 0

    • 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.
  • since 0.2.0
val luband_dyn : 'kl Slap_size.t -> 'ku Slap_size.t -> ?ab:(('m, 'n, 'kl, 'ku) Slap_size.luband, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> (('m, 'n, 'kl, 'ku) Slap_size.luband, 'n, 'b_cd) mat

luband_dyn kl ku ?ab a converts matrix a into a matrix stored in band storage for LU factorization.

  • returns

    matrix ab, which is overwritten.

  • parameter kl

    the number of subdiagonals

  • parameter ku

    the number of superdiagonals

  • raises Invalid_arg

    if kl >= dim1 a or ku >= dim2 a.

  • since 0.2.0
val unluband : 'm Slap_size.t -> 'kl Slap_size.t -> 'ku Slap_size.t -> ?fill_num:num_type option -> ?a:('m, 'n, 'a_cd) mat -> (('m, 'n, 'kl, 'ku) Slap_size.luband, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat

unluband m kl ku ?a ab converts matrix ab stored in band storage for LU factorization into a matrix stored in the normal order.

  • returns

    matrix a, which is overwritten.

  • parameter m

    the number of rows in a

  • parameter kl

    the number of subdiagonals

  • parameter ku

    the number of superdiagonals

  • parameter fill_num

    default = Some 0

    • 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.
  • since 0.2.0

Arithmetic operations

val add_const : num_type -> ?b:('m, 'n, 'b_cd) mat -> ('m, 'n, 'a_cd) mat -> ('m, 'n, 'b_cd) mat

add_const c ?b a adds constant value c to all elements in a.

  • returns

    the matrix b, which is overwritten.

  • since 0.1.0
val sum : ('m, 'n, 'cd) mat -> num_type

sum a returns the sum of all elements in a.

  • since 0.1.0
val trace : ('m, 'n, 'cd) mat -> num_type

trace a

  • returns

    the sum of diagonal elements of the matrix a.

val scal : num_type -> ('m, 'n, 'cd) mat -> unit

scal alpha a computes a := alpha * a with the scalar value alpha and the matrix a.

val scal_cols : ('m, 'n, 'cd) mat -> ('n, Slap_misc.cnt) vec -> unit

A column-wise scal function for matrices.

val scal_rows : ('m, Slap_misc.cnt) vec -> ('m, 'n, 'cd) mat -> unit

A row-wise scal function for matrices.

val axpy : ?alpha:num_type -> ('m, 'n, 'x_cd) mat -> ('m, 'n, 'y_cd) mat -> unit

axpy ?alpha x y computes y := alpha * x + y.

val gemm_diag : ?beta:num_type -> ?y:('n, Slap_misc.cnt) vec -> transa:(('a_n, 'a_k, 'a_cd) mat -> ('n, 'k, 'a_cd) mat) trans3 -> ?alpha:num_type -> ('a_n, 'a_k, 'a_cd) mat -> transb:(('b_k, 'b_n, 'b_cd) mat -> ('k, 'n, 'b_cd) mat) trans3 -> ('b_k, 'b_n, 'b_cd) mat -> ('n, 'cnt) vec

gemm_diag ?beta ?y ~transa ?alpha a ~transb b executes y := DIAG(alpha * OP(a) * OP(b)) + beta * y where DIAG(x) is the vector of the diagonal elements in matrix x, and OP(x) is one of OP(x) = x, OP(x) = x^T, or OP(x) = x^H (the conjugate transpose of x).

  • returns

    the vector y, which is overwritten.

  • parameter beta

    default = 0.0

  • parameter alpha

    default = 1.0

  • since 0.1.0
val syrk_diag : ?beta:num_type -> ?y:('n, Slap_misc.cnt) vec -> trans:(('a_n, 'a_k, 'a_cd) mat -> ('n, 'k, 'a_cd) mat) Slap_common.trans2 -> ?alpha:num_type -> ('a_n, 'a_k, 'a_cd) mat -> ('n, 'cnt) vec

syrk_diag ?beta ?y ~transa ?alpha a executes

where DIAG(x) is the vector of the diagonal elements in matrix x.

  • returns

    the vector y, which is overwritten.

  • parameter beta

    default = 0.0

  • parameter transa

    the transpose flag for a.

  • parameter alpha

    default = 1.0

val gemm_trace : transa:(('a_n, 'a_k, 'a_cd) mat -> ('n, 'k, 'a_cd) mat) trans3 -> ('a_n, 'a_k, 'a_cd) mat -> transb:(('b_k, 'b_n, 'b_cd) mat -> ('k, 'n, 'b_cd) mat) trans3 -> ('b_k, 'b_n, 'b_cd) mat -> num_type

gemm_trace ~transa a ~transb b

  • returns

    the trace of OP(a) * OP(b).

val syrk_trace : ('n, 'k, 'cd) mat -> num_type

syrk_trace a computes the trace of a * a^T or a^T * a.

  • since 0.1.0
val symm2_trace : ?upa:bool -> ('n, 'n, 'a_cd) mat -> ?upb:bool -> ('n, 'n, 'b_cd) mat -> num_type

symm2_trace ?upa a ?upb b computes the trace of a * b with symmetric matrices a and b.

  • parameter upa

    default = true

    • If upa = true, then the upper triangular part of a is used;
    • If upa = false, then the lower triangular part of a is used.
  • parameter upb

    default = true

    • If upb = true, then the upper triangular part of b is used;
    • If upb = false, then the lower triangular part of b is used.

Submatrices

val submat_dyn : 'm Slap_size.t -> 'n Slap_size.t -> ?ar:int -> ?ac:int -> (_, _, 'cd) mat -> ('m, 'n, Slap_misc.dsc) mat

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.

  • parameter ar

    default = 1

  • parameter ac

    default = 1

Creation of vectors

val random : ?rnd_state:Random.State.t -> ?re_from:float -> ?re_range:float -> ?im_from:float -> ?im_range:float -> 'm Slap_size.t -> 'n Slap_size.t -> ('m, 'n, 'cnt) mat

random ?rnd_state ?from ?range m n creates a m-by-n matrix randomly initialized with the uniform distribution between re_from/im_from and re_from+re_range/im_from+im_range for real and imaginary parts, respectively.

  • parameter rnd_state

    default = Random.get_state ().

  • parameter re_from

    default = -1.0.

  • parameter re_range

    default = 2.0.

  • parameter im_from

    default = -1.0.

  • parameter im_range

    default = 2.0.

  • since 0.2.0