lacaml 7.2.1 · OCaml Package

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

returns
the Toeplitz matrix associated with v. The constant diagonals are read from left to right from v.

raises Invalid_argument
if the length of v is not an odd number.

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

returns
the nxn Wilkinson matrix.

raises Invalid_argument
if n is not an odd number >= 3.

val random : 
  ?rnd_state: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.

parameter rnd_state
default = Random.get_state ()

parameter from
default = -1.0

parameter 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.

parameter 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.

parameter m
default = Mat.dim1 a

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter 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.

parameter m
default = Mat.dim1 a

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter 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.

parameter up
default = true

parameter n
default = Mat.dim1 a

parameter ar
default = 1

parameter 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.

parameter up
default = true

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter 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.

parameter up
default = true

parameter 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.

parameter m
default = Mat.dim1 a

parameter n
default = Mat.dim2 a

parameter ar
default = 1

parameter ac
default = 1

parameter br
default = 1

parameter bc
default = 1

parameter b
default = fresh matrix of size m by n

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 : 
  ?m:int ->
  ?n:int ->
  ?alpha:Lacaml_float64.num_type ->
  ?xr:int ->
  ?xc:int ->
  x:Lacaml_float64.mat ->
  ?yr:int ->
  ?yc:int ->
  Lacaml_float64.mat ->
  unit

axpy ?m ?n ?alpha ?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.

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

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

parameter beta
default = 0

parameter ofsy
default = 1

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

parameter transa
default = `N

parameter alpha
default = 1

parameter ar
default = 1

parameter ac
default = 1

parameter transb
default = `N

parameter br
default = 1

parameter 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.

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

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

parameter beta
default = 0

parameter ofsy
default = 1

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

parameter trans
default = `N

parameter alpha
default = 1

parameter ar
default = 1

parameter 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.

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

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

parameter transa
default = `N

parameter ar
default = 1

parameter ac
default = 1

parameter transb
default = `N

parameter br
default = 1

parameter 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.

parameter n
default = number of rows of a

parameter k
default = number of columns of a

parameter ar
default = 1

parameter 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.

parameter n
default = dimensions of a and b

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

parameter ar
default = 1

parameter ac
default = 1

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

parameter br
default = 1

parameter 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.

parameter m
default = number of rows of a

parameter n
default = number of columns of a

parameter 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.

parameter ac
default = 1

parameter n
default = number of columns of a