Module Lacaml_D.Mat

module Mat: sig .. end

Matrix operations

Creation of matrices

val hilbert : int -> Lacaml_float64.mat

hilbert n

Returns an nxn Hilbert matrix.

val hankel : int -> Lacaml_float64.mat

hankel n

Returns an nxn Hankel matrix.

val pascal : int -> Lacaml_float64.mat

pascal n

Returns an nxn Pascal matrix.

val rosser : unit -> Lacaml_float64.mat

rosser n

Returns 8x8 Rosser matrix.

val toeplitz : Lacaml_float64.vec -> Lacaml_float64.mat

toeplitz v

Raises Invalid_argument if the length of v is not an odd number.
Returns the Toeplitz matrix associated with v. The constant diagonals are read from left to right from v.

val vandermonde : Lacaml_float64.vec -> Lacaml_float64.mat

vandermonde v

Returns the Vandermonde matrix associated with v.

val wilkinson : int -> Lacaml_float64.mat

wilkinson n

Raises Invalid_argument if n is not an odd number >= 3.
Returns the nxn Wilkinson matrix.

val random : ?rnd_state:Stdlib.Random.State.t ->
       ?from:float -> ?range:float -> int -> int -> Lacaml_float64.mat

random ?rnd_state ?from ?range m n

Returns an mxn matrix initialized with random elements sampled uniformly from range starting at from. A random state rnd_state can be passed.

rnd_state : default = Random.get_state ()

from : default = -1.0

range : default = 2.0

Creation of matrices and accessors

val create : int -> int -> Lacaml_float64.mat

create m n

Returns a matrix containing m rows and n columns.

val make : int -> int -> Lacaml_float64.num_type -> Lacaml_float64.mat

make m n x

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

val make0 : int -> int -> Lacaml_float64.mat

make0 m n x

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

val of_array : Lacaml_float64.num_type array array -> Lacaml_float64.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_float64.mat -> Lacaml_float64.num_type array array

to_array mat

Returns an array of arrays initialized from matrix mat.

val of_col_vecs : Lacaml_float64.vec array -> Lacaml_float64.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_float64.mat -> Lacaml_float64.vec array

to_col_vecs mat

Returns an array of column vectors initialized from matrix mat.

val as_vec : Lacaml_float64.mat -> Lacaml_float64.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 -> Lacaml_float64.num_type) -> Lacaml_float64.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 -> Lacaml_float64.num_type) -> Lacaml_float64.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_float64.mat

create_mvec m

Returns a matrix with one column containing m rows.

val make_mvec : int -> Lacaml_float64.num_type -> Lacaml_float64.mat

make_mvec m x

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

val mvec_of_array : Lacaml_float64.num_type array -> Lacaml_float64.mat

mvec_of_array ar

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

val mvec_to_array : Lacaml_float64.mat -> Lacaml_float64.num_type 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_float64.vec -> Lacaml_float64.mat

from_col_vec v

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

val from_row_vec : Lacaml_float64.vec -> Lacaml_float64.mat

from_row_vec v

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

val empty : Lacaml_float64.mat

empty, the empty matrix.

val identity : int -> Lacaml_float64.mat

identity n

Returns the nxn identity matrix.

val of_diag : Lacaml_float64.vec -> Lacaml_float64.mat

of_diag v

Returns the diagonal matrix with diagonals elements from v.

val dim1 : Lacaml_float64.mat -> int

dim1 m

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

val dim2 : Lacaml_float64.mat -> int

dim2 m

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

val col : Lacaml_float64.mat -> int -> Lacaml_float64.vec

col m n

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

val copy_row : ?vec:Lacaml_float64.vec -> Lacaml_float64.mat -> int -> Lacaml_float64.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 transpose_copy : ?m:int ->
       ?n:int ->
       ?ar:int ->
       ?ac:int ->
       Lacaml_float64.mat -> ?br:int -> ?bc:int -> Lacaml_float64.mat -> unit

transpose_copy ?m ?n ?ar ?ac a ?br ?bc b copy the transpose of (sub-)matrix a into (sub-)matrix b.

m : default = Mat.dim1 a

n : default = Mat.dim2 a

ar : default = 1

ac : default = 1

br : default = 1

bc : default = 1

val transpose : ?m:int ->
       ?n:int -> ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.mat

transpose ?m ?n ?ar ?ac aa

Returns the transpose of (sub-)matrix a.

m : default = Mat.dim1 a

n : default = Mat.dim2 a

ar : default = 1

ac : default = 1

val detri : ?up:bool -> ?n:int -> ?ar:int -> ?ac:int -> Lacaml_float64.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_float64.mat -> Lacaml_float64.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_float64.vec -> Lacaml_float64.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

Arithmetic and other matrix operations

val add_const : Lacaml_float64.num_type ->
       ?m:int ->
       ?n:int ->
       ?br:int ->
       ?bc:int ->
       ?b:Lacaml_float64.mat ->
       ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.mat

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.

m : default = Mat.dim1 a

n : default = Mat.dim2 a

br : default = 1

bc : default = 1

b : default = fresh matrix of size m by n

ar : default = 1

ac : default = 1

val sum : ?m:int ->
       ?n:int -> ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.num_type

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 fill : ?m:int ->
       ?n:int ->
       ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.num_type -> unit

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

val copy_diag : Lacaml_float64.mat -> Lacaml_float64.vec

copy_diag m

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

val trace : Lacaml_float64.mat -> Lacaml_float64.num_type

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 ->
       Lacaml_float64.num_type -> ?ar:int -> ?ac:int -> Lacaml_float64.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_float64.mat -> ?ofs:int -> Lacaml_float64.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_float64.vec -> ?ar:int -> ?ac:int -> Lacaml_float64.mat -> unit

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

val axpy : ?alpha:Lacaml_float64.num_type ->
       ?m:int ->
       ?n:int ->
       ?xr:int ->
       ?xc:int ->
       Lacaml_float64.mat -> ?yr:int -> ?yc:int -> Lacaml_float64.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:Lacaml_float64.num_type ->
       ?ofsy:int ->
       ?y:Lacaml_float64.vec ->
       ?transa:Lacaml_float64.trans3 ->
       ?alpha:Lacaml_float64.num_type ->
       ?ar:int ->
       ?ac:int ->
       Lacaml_float64.mat ->
       ?transb:Lacaml_float64.trans3 ->
       ?br:int -> ?bc:int -> Lacaml_float64.mat -> Lacaml_float64.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 syrk_diag : ?n:int ->
       ?k:int ->
       ?beta:Lacaml_float64.num_type ->
       ?ofsy:int ->
       ?y:Lacaml_float64.vec ->
       ?trans:Lacaml_common.trans2 ->
       ?alpha:Lacaml_float64.num_type ->
       ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.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

val gemm_trace : ?n:int ->
       ?k:int ->
       ?transa:Lacaml_float64.trans3 ->
       ?ar:int ->
       ?ac:int ->
       Lacaml_float64.mat ->
       ?transb:Lacaml_float64.trans3 ->
       ?br:int -> ?bc:int -> Lacaml_float64.mat -> Lacaml_float64.num_type

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). This is also sometimes referred to as the Frobenius product. n is the number of rows (columns) to consider in a, and k the number of columns (rows) in b.

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 syrk_trace : ?n:int ->
       ?k:int -> ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.num_type

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 symm2_trace : ?n:int ->
       ?upa:bool ->
       ?ar:int ->
       ?ac:int ->
       Lacaml_float64.mat ->
       ?upb:bool ->
       ?br:int -> ?bc:int -> Lacaml_float64.mat -> Lacaml_float64.num_type

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

Iterators over matrices

val map : (Lacaml_float64.num_type -> Lacaml_float64.num_type) ->
       ?m:int ->
       ?n:int ->
       ?br:int ->
       ?bc:int ->
       ?b:Lacaml_float64.mat ->
       ?ar:int -> ?ac:int -> Lacaml_float64.mat -> Lacaml_float64.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_float64.vec -> 'a) ->
       ?n:int -> ?ac:int -> 'a -> Lacaml_float64.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