Module Lacaml__Z.Mat

module Mat: sig .. end

type t = Lacaml__Z.mat

Matrix operations

Creation of matrices

val random : ?rnd_state:Stdlib.Random.State.t ->
       ?re_from:float ->
       ?re_range:float ->
       ?im_from:float -> ?im_range:float -> int -> int -> Lacaml__Z.mat

random ?rnd_state ?re_from ?re_range ?im_from ?im_range m n

Returns an mxn matrix initialized with random elements sampled uniformly from re_range and im_range starting at re_from and im_from for real and imaginary numbers respectively. A random state rnd_state can be passed.

rnd_state : default = Random.get_state ()

re_from : default = -1.0

re_range : default = 2.0

im_from : default = -1.0

im_range : default = 2.0

type unop = ?m:int ->
       ?n:int ->
       ?br:int ->
       ?bc:int ->
       ?b:Lacaml__Z.mat -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Lacaml__Z.mat

type binop = ?m:int ->
       ?n:int ->
       ?cr:int ->
       ?cc:int ->
       ?c:Lacaml__Z.mat ->
       ?ar:int ->
       ?ac:int ->
       Lacaml__Z.mat -> ?br:int -> ?bc:int -> Lacaml__Z.mat -> Lacaml__Z.mat

Creation of matrices and accessors

val create : int -> int -> Lacaml__Z.mat

create m n

Returns a matrix containing m rows and n columns.

val make : int -> int -> Stdlib.Complex.t -> Lacaml__Z.mat

make m n x

Returns a matrix containing m rows and n columns initialized with value x.

val make0 : int -> int -> Lacaml__Z.mat

make0 m n x

Returns a matrix containing m rows and n columns initialized with the zero element.

val of_array : Stdlib.Complex.t array array -> Lacaml__Z.mat

of_array ar

Returns a matrix initialized from the array of arrays ar. It is assumed that the OCaml matrix is in row major order (standard).

val to_array : Lacaml__Z.mat -> Stdlib.Complex.t array array

to_array mat

Returns an array of arrays initialized from matrix mat.

val of_list : Stdlib.Complex.t list list -> Lacaml__Z.mat

of_list ls

Returns a matrix initialized from the list of lists ls. Each sublist of ls represents a row of the desired matrix, and must be of the same length.

val to_list : Lacaml__Z.mat -> Stdlib.Complex.t list list

to_array mat

Returns mat in row major order as lists.

val of_col_vecs : Lacaml__Z.vec array -> Lacaml__Z.mat

of_col_vecs ar

Returns a matrix whose columns are initialized from the array of vectors ar. The vectors must be of same length.

val to_col_vecs : Lacaml__Z.mat -> Lacaml__Z.vec array

to_col_vecs mat

Returns an array of column vectors initialized from matrix mat.

val of_col_vecs_list : Lacaml__Z.vec list -> Lacaml__Z.mat

of_col_vecs_list ar

Returns a matrix whose columns are initialized from the list of vectors ar. The vectors must be of same length.

val to_col_vecs_list : Lacaml__Z.mat -> Lacaml__Z.vec list

to_col_vecs_list mat

Returns a list of column vectors initialized from matrix mat.

val as_vec : Lacaml__Z.mat -> Lacaml__Z.vec

as_vec mat

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

val init_rows : int -> int -> (int -> int -> Stdlib.Complex.t) -> Lacaml__Z.mat

init_cols m n f

Returns a matrix containing m rows and n columns, where each element at row and col is initialized by the result of calling f row col. The elements are passed row-wise.

val init_cols : int -> int -> (int -> int -> Stdlib.Complex.t) -> Lacaml__Z.mat

init_cols m n f

Returns a matrix containing m rows and n columns, where each element at row and col is initialized by the result of calling f row col. The elements are passed column-wise.

val create_mvec : int -> Lacaml__Z.mat

create_mvec m

Returns a matrix with one column containing m rows.

val make_mvec : int -> Stdlib.Complex.t -> Lacaml__Z.mat

make_mvec m x

Returns a matrix with one column containing m rows initialized with value x.

val mvec_of_array : Stdlib.Complex.t array -> Lacaml__Z.mat

mvec_of_array ar

Returns a matrix with one column initialized with values from array ar.

val mvec_to_array : Lacaml__Z.mat -> Stdlib.Complex.t array

mvec_to_array mat

Returns an array initialized with values from the first (not necessarily only) column vector of matrix mat.

val from_col_vec : Lacaml__Z.vec -> Lacaml__Z.mat

from_col_vec v

Returns a matrix with one column representing vector v. The data is shared.

val from_row_vec : Lacaml__Z.vec -> Lacaml__Z.mat

from_row_vec v

Returns a matrix with one row representing vector v. The data is shared.

val empty : Lacaml__Z.mat

empty, the empty matrix.

val identity : int -> Lacaml__Z.mat

identity n

Returns the nxn identity matrix.

val of_diag : ?n:int ->
       ?br:int ->
       ?bc:int ->
       ?b:Lacaml__Z.mat -> ?ofsx:int -> ?incx:int -> Lacaml__Z.vec -> Lacaml__Z.mat

of_diag ?n ?br ?bc ?b ?ofsx ?incx x

Returns matrix b with diagonal elements in the designated sub-matrix coming from the designated sub-vector in x.

n : default = greater n s.t. ofsx+(n-1)(abs incx) <= dim x

br : default = 1

bc : default = 1

b : default = minimal fresh matrix consistent with n, br, and bc

ofsx : default = 1

incx : default = 1

val dim1 : Lacaml__Z.mat -> int

dim1 m

Returns the first dimension of matrix m (number of rows).

val dim2 : Lacaml__Z.mat -> int

dim2 m

Returns the second dimension of matrix m (number of columns).

val has_zero_dim : Lacaml__Z.mat -> bool

has_zero_dim mat checks whether matrix mat has a dimension of size zero. In this case it cannot contain data.

val col : Lacaml__Z.mat -> int -> Lacaml__Z.vec

col m n

Returns the nth column of matrix m as a vector. The data is shared.

val copy_row : ?vec:Lacaml__Z.vec -> Lacaml__Z.mat -> int -> Lacaml__Z.vec

copy_row ?vec mat int

Returns a copy of the nth row of matrix m in vector vec.

vec : default = fresh vector of length dim2 mat

Matrix transformations

val swap : ?uplo:[ `L | `U ] ->
       ?m:int ->
       ?n:int ->
       ?ar:int ->
       ?ac:int -> Lacaml__Z.mat -> ?br:int -> ?bc:int -> Lacaml__Z.mat -> unit

swap ?m ?n ?ar ?ac a ?br ?bc b swaps the contents of (sub-matrices) a and b.

m : default = greater n s.t. ar + m - 1 <= dim1 a

n : default = greater n s.t. ac + n - 1 <= dim2 a

ar : default = 1

ac : default = 1

br : default = 1

bc : default = 1

val transpose_copy : unop

transpose_copy ?m ?n ?br ?bc ?b ?ar ?ac a

Returns the transpose of (sub-)matrix a. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. NOTE: this operations does _not_ support in-place transposes!

val detri : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> unit

detri ?up ?n ?ar ?ac a takes a triangular (sub-)matrix a, i.e. one where only the upper (iff up is true) or lower triangle is defined, and makes it a symmetric matrix by mirroring the defined triangle along the diagonal.

up : default = true

n : default = Mat.dim1 a

ar : default = 1

ac : default = 1

val packed : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Lacaml__Z.vec

packed ?up ?n ?ar ?ac a

Returns (sub-)matrix a in packed storage format.

up : default = true

n : default = Mat.dim2 a

ar : default = 1

ac : default = 1

val unpacked : ?up:bool -> ?n:int -> Lacaml__Z.vec -> Lacaml__Z.mat

unpacked ?up x

Returns an upper or lower (depending on up) triangular matrix from packed representation vec. The other triangle of the matrix will be filled with zeros.

up : default = true

n : default = Vec.dim x

Operations on one matrix

val fill : ?m:int ->
       ?n:int -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Stdlib.Complex.t -> unit

fill ?m ?n ?ar ?ac a x fills the specified sub-matrix in a with value x.

val sum : ?m:int -> ?n:int -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Stdlib.Complex.t

sum ?m ?n ?ar ?ac a computes the sum of all elements in the m-by-n submatrix starting at row ar and column ac.

val add_const : Stdlib.Complex.t -> unop

add_const c ?m ?n ?br ?bc ?b ?ar ?ac a adds constant c to the designated m by n submatrix in a and stores the result in the designated submatrix in b.

val neg : unop

neg ?m ?n ?br ?bc ?b ?ar ?ac a computes the negative of the elements in the m by n (sub-)matrix of the matrix a starting in row ar and column ac. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

val reci : unop

reci ?m ?n ?br ?bc ?b ?ar ?ac a computes the reciprocal of the elements in the m by n (sub-)matrix of the matrix a starting in row ar and column ac. If b is given, the result will be stored in there using offsets br and bc, otherwise a fresh matrix will be used. The resulting matrix is returned.

val copy_diag : ?n:int ->
       ?ofsy:int ->
       ?incy:int ->
       ?y:Lacaml__Z.vec -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Lacaml__Z.vec

copy_diag ?n ?ofsy ?incy ?y ?ar ?ac a

Returns the diagonal of the (sub-)matrix a in a (sub-)vector.

n : default = greatest n that does not exceed matrix dimensions

ofsy : default = 1

incy : default = 1

y : default = fresh vector of length n

ar : default = 1

ac : default = 1

val trace : Lacaml__Z.mat -> Stdlib.Complex.t

trace m

Returns the trace of matrix m. If m is not a square matrix, the sum of the longest possible sequence of diagonal elements will be returned.

val scal : ?m:int ->
       ?n:int -> Stdlib.Complex.t -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> unit

scal ?m ?n alpha ?ar ?ac a BLAS scal function for (sub-)matrices.

val scal_cols : ?m:int ->
       ?n:int ->
       ?ar:int -> ?ac:int -> Lacaml__Z.mat -> ?ofs:int -> Lacaml__Z.vec -> unit

scal_cols ?m ?n ?ar ?ac a ?ofs alphas column-wise scal function for matrices.

val scal_rows : ?m:int ->
       ?n:int ->
       ?ofs:int -> Lacaml__Z.vec -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> unit

scal_rows ?m ?n ?ofs alphas ?ar ?ac a row-wise scal function for matrices.

val syrk_trace : ?n:int -> ?k:int -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Stdlib.Complex.t

syrk_trace ?n ?k ?ar ?ac a computes the trace of either a' * a or a * a', whichever is more efficient (results are identical), of the (sub-)matrix a multiplied by its own transpose. This is the same as the square of the Frobenius norm of a matrix. n is the number of rows to consider in a, and k the number of columns to consider.

n : default = number of rows of a

k : default = number of columns of a

ar : default = 1

ac : default = 1

val syrk_diag : ?n:int ->
       ?k:int ->
       ?beta:Stdlib.Complex.t ->
       ?ofsy:int ->
       ?y:Lacaml__Z.vec ->
       ?trans:Lacaml__common.trans2 ->
       ?alpha:Stdlib.Complex.t ->
       ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Lacaml__Z.vec

syrk_diag ?n ?k ?beta ?ofsy ?y ?trans ?alpha ?ar ?ac a computes the diagonal of the symmetric rank-k product of the (sub-)matrix a, multiplying it with alpha and adding beta times y, storing the result in y starting at the specified offset. n elements of the diagonal will be computed, and k elements of the matrix will be part of the dot product associated with each diagonal element.

n : default = number of rows of a (or tra)

k : default = number of columns of a (or tra)

beta : default = 0

ofsy : default = 1

y : default = fresh vector of size n + ofsy - 1

trans : default = `N

alpha : default = 1

ar : default = 1

ac : default = 1

Operations on two matrices

val add : binop

add ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the sum of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

val sub : binop

sub ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the difference of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

val mul : binop

mul ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the element-wise product of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

NOTE: please do not confuse this function with matrix multiplication! The LAPACK-function for matrix multiplication is called gemm, e.g. Lacaml.D.gemm.

val div : binop

div ?m ?n ?cr ?cc ?c ?ar ?ac a ?br ?bc b computes the division of the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc. If c is given, the result will be stored in there starting in row cr and column cc, otherwise a fresh matrix will be used. The resulting matrix is returned.

val axpy : ?alpha:Stdlib.Complex.t ->
       ?m:int ->
       ?n:int ->
       ?xr:int ->
       ?xc:int -> Lacaml__Z.mat -> ?yr:int -> ?yc:int -> Lacaml__Z.mat -> unit

axpy ?alpha ?m ?n ?xr ?xc x ?yr ?yc y BLAS axpy function for matrices.

val gemm_diag : ?n:int ->
       ?k:int ->
       ?beta:Stdlib.Complex.t ->
       ?ofsy:int ->
       ?y:Lacaml__Z.vec ->
       ?transa:Lacaml__Z.trans3 ->
       ?alpha:Stdlib.Complex.t ->
       ?ar:int ->
       ?ac:int ->
       Lacaml__Z.mat ->
       ?transb:Lacaml__Z.trans3 ->
       ?br:int -> ?bc:int -> Lacaml__Z.mat -> Lacaml__Z.vec

gemm_diag ?n ?k ?beta ?ofsy ?y ?transa ?transb ?alpha ?ar ?ac a ?br ?bc b computes the diagonal of the product of the (sub-)matrices a and b (taking into account potential transposing), multiplying it with alpha and adding beta times y, storing the result in y starting at the specified offset. n elements of the diagonal will be computed, and k elements of the matrices will be part of the dot product associated with each diagonal element.

n : default = number of rows of a (or tr a) and number of columns of b (or tr b)

k : default = number of columns of a (or tr a) and number of rows of b (or tr b)

beta : default = 0

ofsy : default = 1

y : default = fresh vector of size n + ofsy - 1

transa : default = `N

alpha : default = 1

ar : default = 1

ac : default = 1

transb : default = `N

br : default = 1

bc : default = 1

val gemm_trace : ?n:int ->
       ?k:int ->
       ?transa:Lacaml__Z.trans3 ->
       ?ar:int ->
       ?ac:int ->
       Lacaml__Z.mat ->
       ?transb:Lacaml__Z.trans3 ->
       ?br:int -> ?bc:int -> Lacaml__Z.mat -> Stdlib.Complex.t

gemm_trace ?n ?k ?transa ?ar ?ac a ?transb ?br ?bc b computes the trace of the product of the (sub-)matrices a and b (taking into account potential transposing). When transposing a, this yields the so-called Frobenius product of a and b. n is the number of rows (columns) to consider in a and the number of columns (rows) in b. k is the inner dimension to use for the product.

n : default = number of rows of a (or tr a) and number of columns of b (or tr b)

k : default = number of columns of a (or tr a) and number of rows of b (or tr b)

transa : default = `N

ar : default = 1

ac : default = 1

transb : default = `N

br : default = 1

bc : default = 1

val symm2_trace : ?n:int ->
       ?upa:bool ->
       ?ar:int ->
       ?ac:int ->
       Lacaml__Z.mat ->
       ?upb:bool -> ?br:int -> ?bc:int -> Lacaml__Z.mat -> Stdlib.Complex.t

symm2_trace ?n ?upa ?ar ?ac a ?upb ?br ?bc b computes the trace of the product of the symmetric (sub-)matrices a and b. n is the number of rows and columns to consider in a and b.

n : default = dimensions of a and b

upa : default = true (upper triangular portion of a is accessed)

ar : default = 1

ac : default = 1

upb : default = true (upper triangular portion of b is accessed)

br : default = 1

bc : default = 1

val ssqr_diff : ?m:int ->
       ?n:int ->
       ?ar:int ->
       ?ac:int ->
       Lacaml__Z.mat -> ?br:int -> ?bc:int -> Lacaml__Z.mat -> Stdlib.Complex.t

ssqr_diff ?m ?n ?ar ?ac a ?br ?bc b

Returns the sum of squared differences between the m by n sub-matrix of the matrix a starting in row ar and column ac with the corresponding sub-matrix of the matrix b starting in row br and column bc.

m : default = greater n s.t. ar + m - 1 <= dim1 a

n : default = greater n s.t. ac + n - 1 <= dim2 a

ar : default = 1

ac : default = 1

br : default = 1

bc : default = 1

Iterators over matrices

val map : (Stdlib.Complex.t -> Stdlib.Complex.t) ->
       ?m:int ->
       ?n:int ->
       ?br:int ->
       ?bc:int ->
       ?b:Lacaml__Z.mat -> ?ar:int -> ?ac:int -> Lacaml__Z.mat -> Lacaml__Z.mat

map f ?m ?n ?br ?bc ?b ?ar ?ac a

Returns matrix with f applied to each element of a.

m : default = number of rows of a

n : default = number of columns of a

b : default = fresh matrix of size m by n

val fold_cols : ('a -> Lacaml__Z.vec -> 'a) -> ?n:int -> ?ac:int -> 'a -> Lacaml__Z.mat -> 'a

fold_cols f ?n ?ac acc a

Returns accumulator resulting from folding over each column vector.

n : default = number of columns of a

ac : default = 1