mirror of
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348 lines
13 KiB
OCaml
348 lines
13 KiB
OCaml
(** Type for matrices. The ['a] and ['b] types are labels for the rows and columns. *)
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type ('a,'b) t
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val dim1: ('a,'b) t -> int
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(** First dimension of the matrix *)
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val dim2: ('a,'b) t -> int
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(** Second dimension of the matrix *)
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val make : int -> int -> float -> ('a,'b) t
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(** Creates a matrix initialized with the given value.
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@param m: First dimension
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@param n: Seconfd dimension
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@param f: Value used to initialize the matrix elements
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*)
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val make0 : int -> int -> ('a,'b) t
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(** Creates a zero-initialized matrix. *)
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val create : int -> int -> ('a,'b) t
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(** Creates an uninitialized matrix. *)
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val reshape_inplace : int -> int -> ('a,'b) t -> ('c,'d) t
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(** Changes the dimensions of the matrix *)
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val reshape_vec_inplace : int -> int -> ('a*'b) Vector.t -> ('a,'b) t
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(** Reshapres a vector into a matrix *)
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val init_cols : int -> int -> (int -> int -> float) -> ('a,'b) t
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(** Creates an uninitialized matrix. *)
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val identity: int -> ('a,'b) t
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(** Creates an identity matrix. *)
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val of_diag: 'a Vector.t -> ('a,'a) t
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(** Creates a diagonal matrix. *)
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val diag: ('a,'a) t -> 'a Vector.t
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(** Returns the diagonal of a matrix. *)
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val fill_inplace: ('a,'b) t -> float -> unit
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(** Fills the matrix with the give value. *)
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val add_const_diag : float -> ('a,'b) t -> ('a,'b) t
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(** Adds a constant to the diagonal *)
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val add_const_diag_inplace : float -> ('a,'b) t -> unit
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(** Adds a constant to the diagonal *)
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val add_const_inplace : float -> ('a,'b) t -> unit
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(** Adds a constant to the diagonal *)
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val add_const : float -> ('a,'b) t -> ('a,'b) t
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(** Adds a constant to the diagonal *)
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val add : ('a,'b) t -> ('a,'b) t -> ('a,'b) t
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(** Adds two matrices *)
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val sub : ('a,'b) t -> ('a,'b) t -> ('a,'b) t
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(** Subtracts two matrices *)
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val mul : ('a,'b) t -> ('a,'b) t -> ('a,'b) t
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(** Multiplies two matrices element-wise *)
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val div : ('a,'b) t -> ('a,'b) t -> ('a,'b) t
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(** Divides two matrices element-wise *)
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val amax : ('a,'b) t -> float
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(** Maximum of the absolute values of the elements of the matrix. *)
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val add_inplace : c:('a,'b) t -> ('a,'b) t -> ('a,'b) t -> unit
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(** [add_inplace c a b] : performs [c = a+b] in-place. *)
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val sub_inplace : c:('a,'b) t -> ('a,'b) t -> ('a,'b) t -> unit
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(** [sub_inplace c a b] : performs [c = a+b] in-place. *)
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val mul_inplace : c:('a,'b) t -> ('a,'b) t -> ('a,'b) t -> unit
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(** [mul_inplace c a b] : performs [c = a*b] element-wise in-place. *)
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val div_inplace : c:('a,'b) t -> ('a,'b) t -> ('a,'b) t -> unit
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(** [div_inplace c a b] : performs [c = a/b] element-wise in-place. *)
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(*
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val to_bigarray : ('a,'b) t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t
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(** Converts the matrix into a Bigarray in Fortran layout *)
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val of_bigarray : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> ('a,'b) t
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(** Converts a [Bigarray.Array2] in Fortran layout into a matrix *)
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*)
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val to_bigarray_inplace :
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('a,'b) t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t
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(** Converts the matrix into a Bigarray in Fortran layout in place*)
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val of_bigarray_inplace :
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(float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> ('a,'b) t
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(** Converts a [Bigarray.Array2] in Fortran layout into a matrix in place*)
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val to_col_vecs : ('a,'b) t -> 'a Vector.t array
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(** Converts the matrix into an array of vectors *)
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val to_col_vecs_list : ('a,'b) t -> 'a Vector.t list
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(** Converts the matrix into a list of vectors *)
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val of_col_vecs : 'a Vector.t array -> ('a,'b) t
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(** Converts an array of vectors into a matrix *)
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val of_col_vecs_list : 'a Vector.t list -> ('a,'b) t
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(** Converts a list of vectors into a matrix *)
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val to_array : ('a,'b) t -> float array array
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(** Converts the matrix into an array of arrays *)
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val of_array : float array array -> ('a,'b) t
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(** Converts an array of arrays into a matrix *)
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val copy: ?m:int -> ?n:int -> ?br:int -> ?bc:int -> ?ar:int -> ?ac:int -> ('a,'b) t -> ('a,'b) t
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(** Copies all or part of a two-dimensional matrix A to a new matrix B *)
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val copy_inplace: ?m:int -> ?n:int -> ?br:int -> ?bc:int -> b:('a,'b) t -> ?ar:int -> ?ac:int -> ('a,'b) t -> unit
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(** Copies all or part of a two-dimensional matrix A to an existing matrix B *)
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(*
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val col: ('a,'b) t -> int -> 'a Vector.t
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(** Returns a column of the matrix as a vector *)
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*)
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val col_inplace: ('a,'b) t -> int -> 'a Vector.t
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(** Returns a column of the matrix as a vector *)
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val transpose: ('a,'b) t -> ('b,'a) t
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(** Returns the transposed matrix *)
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val transpose_inplace: ('a,'a) t -> unit
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(** Transposes the matrix in place. *)
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val detri: ('a,'b) t -> ('a,'b) t
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(** Takes an upper-triangular matrix, and makes it a symmetric matrix
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by mirroring the defined triangle along the diagonal. *)
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val detri_inplace: ('a,'b) t -> unit
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(** Takes an upper-triangular matrix, and makes it a symmetric matrix
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by mirroring the defined triangle along the diagonal. *)
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val as_vec_inplace: ('a,'b) t -> ('a*'b) Vector.t
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(** Interpret the matrix as a vector (reshape). *)
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val as_vec: ('a,'b) t -> ('a*'b) Vector.t
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(** Return a copy of the reshaped matrix into a vector *)
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val random: ?rnd_state:Random.State.t -> ?from:float -> ?range:float -> int -> int -> ('a,'b) t
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(** Creates a random matrix, similarly to [Vector.random] *)
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val map: (float -> float) -> ('a,'b) t -> ('a,'b) t
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(** Apply the function to all elements of the matrix *)
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val map_inplace: (float -> float) -> b:('a,'b) t -> ('a,'b) t -> unit
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(** [map_inplace f b a] : Apply the function to all elements of the
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matrix [a] and store the results in [b] *)
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val scale: float -> ('a,'b) t -> ('a,'b) t
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(** Multiplies the matrix by a constant *)
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val scale_inplace: float -> ('a,'b) t -> unit
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(** Multiplies the matrix by a constant *)
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val scale_cols: ('a,'b) t -> 'b Vector.t -> ('a,'b) t
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(** Multiplies the matrix by a constant *)
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val scale_cols_inplace: ('a,'b) t -> 'b Vector.t -> unit
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(** Multiplies the matrix by a constant *)
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val scale_rows: 'a Vector.t -> ('a,'b) t -> ('a,'b) t
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(** Multiplies the matrix by a constant *)
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val scale_rows_inplace: 'a Vector.t -> ('a,'b) t -> unit
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(** Multiplies the matrix by a constant *)
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val sycon: ('a,'b) t -> float
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(** Returns the condition number of a matrix *)
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val outer_product : ?alpha:float -> 'a Vector.t -> 'b Vector.t -> ('a,'b) t
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(** Computes M = %{ $\alpha u.v^t$ %} *)
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val outer_product_inplace : ('a,'b) t -> ?alpha:float -> 'a Vector.t -> 'b Vector.t -> unit
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(** Computes M = %{ $\alpha u.v^t$ %} *)
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val gemv_n_inplace : ?m:int -> ?n:int -> ?beta:float -> 'a Vector.t ->
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?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'b Vector.t ->
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unit
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(** Performs the Lapack GEMV operation. Default values:
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[beta=0.] [alpha=1.0].
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[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M V$
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The vector Y is updated in-place.
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*)
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val gemv_t_inplace : ?m:int -> ?n:int -> ?beta:float -> 'b Vector.t ->
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?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'a Vector.t ->
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unit
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(** Performs the Lapack GEMV operation. Default values:
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[beta=0.] [alpha=1.0].
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[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M^\dagger V$
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The vector Y is updated in-place.
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*)
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val gemv_n : ?m:int -> ?n:int -> ?beta:float -> ?y:'a Vector.t ->
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?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'b Vector.t ->
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'a Vector.t
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(** Performs the Lapack GEMV operation. Default values:
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[beta=0.] [alpha=1.0].
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[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M^\dagger V$ *)
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val gemv_t : ?m:int -> ?n:int -> ?beta:float -> ?y:'b Vector.t ->
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?alpha:float -> ?ar:int -> ?ac:int -> ('a,'b) t -> 'a Vector.t ->
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'b Vector.t
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(** Performs the Lapack GEMV operation. Default values:
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[beta=0.] [alpha=1.0].
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[gemv ~beta y ~alpha m v]: %{ $Y = \beta Y + \alpha M^\dagger V$
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*)
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val gemm_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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c:('a,'b) t -> ?transa:[`N | `T] -> ?alpha:float ->
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('c,'d) t -> ?transb:[`N | `T] -> ('e,'f) t -> unit
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(** Performs the Lapack GEMM operation. Default values:
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[beta=0.] [transa=`N] [alpha=1.0] [transb=`N].
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[gemm ~beta c ~alpha a b]: %{ $C = \beta C + \alpha A B$ *)
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val gemm_nn_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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c:('a,'c) t -> ?alpha:float -> ('a,'b) t -> ('b,'c) t -> unit
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(** Performs gemm with [~transa=`N] and [~transb=`N]. *)
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val gemm_nt_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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c:('a,'c) t -> ?alpha:float -> ('a,'b) t -> ('c,'b) t -> unit
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(** Performs gemm with [~transa=`N] and [~transb=`T]. *)
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val gemm_tt_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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c:('a,'c) t -> ?alpha:float -> ('b,'a) t -> ('c,'b) t -> unit
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(** Performs gemm with [~transa=`T] and [~transb=`T]. *)
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val gemm_tn_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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c:('a,'c) t -> ?alpha:float -> ('b,'a) t -> ('b,'c) t -> unit
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(** Performs gemm with [~transa=`T] and [~transb=`N]. *)
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val gemm: ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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?c:('a,'b) t -> ?transa:[`N | `T] -> ?alpha:float ->
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('c,'d) t -> ?transb:[`N | `T] -> ('e,'f) t -> ('a,'b) t
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(** Performs the Lapack GEMM operation. Default values:
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[beta=0.] [transa=`N] [alpha=1.0] [transb=`N]
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[gemm ~beta ~alpha a b]: %{ $C = \beta C + \alpha A B$ *)
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val gemm_nn: ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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?c:('a,'c) t -> ?alpha:float -> ('a,'b) t -> ('b,'c) t -> ('a,'c) t
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(** Performs gemm with [~transa=`N] and [~transb=`N]. *)
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val gemm_nt: ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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?c:('a,'c) t -> ?alpha:float -> ('a,'b) t -> ('c,'b) t -> ('a,'c) t
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(** Performs gemm with [~transa=`N] and [~transb=`T]. *)
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val gemm_tn: ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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?c:('a,'c) t -> ?alpha:float -> ('b,'a) t -> ('b,'c) t -> ('a,'c) t
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(** Performs gemm with [~transa=`T] and [~transb=`N]. *)
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val gemm_tt: ?m:int -> ?n:int -> ?k:int -> ?beta:float ->
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?c:('a,'c) t -> ?alpha:float -> ('b,'a) t -> ('c,'b) t -> ('a,'c) t
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(** Performs gemm with [~transa=`T] and [~transb=`T]. *)
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val gemm_trace: ?transa:[`N | `T] -> ('a,'b) t -> ?transb:[`N | `T] -> ('c,'d) t -> float
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(** Computes the trace of a GEMM. Default values:
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[transa=`N] [transb=`N]
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[gemm_trace a b]: %{ $C = Tr(A B)$ *)
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val gemm_nn_trace: ('a,'b) t -> ('b,'c) t -> float
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(** Computes the trace of a GEMM with [~transa=`N] and [~transb=`N]. *)
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val gemm_nt_trace: ('a,'b) t -> ('c,'b) t -> float
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(** Computes the trace of a GEMM with [~transa=`N] and [~transb=`T]. *)
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val gemm_tn_trace: ('b,'a) t -> ('b,'c) t -> float
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(** Computes the trace of a GEMM with [~transa=`T] and [~transb=`N]. *)
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val gemm_tt_trace: ('b,'a) t -> ('c,'b) t -> float
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(** Computes the trace of a GEMM with [~transa=`T] and [~transb=`T]. *)
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val svd: ('a,'b) t -> ('a,'b) t * 'b Vector.t * ('b,'b) t
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(** Singular value decomposition of A(m,n) when m >= n. *)
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val svd': ('a,'b) t -> ('a,'a) t * 'a Vector.t * ('a,'b) t
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(** Singular value decomposition of A(m,n) when m < n. *)
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val qr: ('a,'b) t -> ('a,'b) t * ('b,'b) t
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(** QR factorization *)
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val normalize_mat : ('a,'b) t -> ('a,'b) t
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(** Returns the matrix with all the column vectors normalized *)
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val normalize_mat_inplace : ('a,'b) t -> unit
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(** Returns the matrix with all the column vectors normalized *)
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val diagonalize_symm : ('a,'a) t -> ('a,'a) t * 'a Vector.t
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(** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *)
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val exponential : ('a,'a) t -> ('a,'a) t
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(** Computes the exponential of a square matrix. *)
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val exponential_iterative : ('a,'a) t -> ('a,'a) t
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(** Computes the exponential of a square matrix with an iteratve algorithm. *)
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val xt_o_x : o:('a,'a) t -> x:('a,'b) t -> ('b,'b) t
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(** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *)
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val x_o_xt : o:('b,'b) t -> x:('a,'b) t -> ('a,'a) t
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(** Computes {% $\mathbf{X\, O\, X^\dag}$ %} *)
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val debug_matrix: string -> ('a,'b) t -> unit
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(** Prints a matrix in stdout for debug *)
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val of_file : string -> ('a,'b) t
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(** Reads a matrix from a file with format "%d %d %f" corresponding to
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[i, j, A.{i,j}]. *)
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val relabel : ('a,'b) t -> ('c,'d) t
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val sym_of_file : string -> ('a,'b) t
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(** Reads a symmetric matrix from a file with format "%d %d %f" corresponding to
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[i, j, A.{i,j}]. *)
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val sysv_inplace : b:('a,'b) t -> ('a,'a) t -> unit
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(** Solves %{ $AX=B$ %} when A is symmetric, and stores the result in B. *)
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val sysv : b:('a,'b) t -> ('a,'a) t -> ('a,'b) t
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(** Solves %{ $AX=B$ %} when A is symmetric *)
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val (%:) : ('a,'b) t -> (int*int) -> float
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(** [t%.(i,j)] returns the element at i,j. *)
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val set : ('a,'b) t -> int -> int -> float -> unit
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(** [set t i j v] sets the (i,j)-th element to v *)
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val to_file : filename:string -> ?sym:bool -> ?cutoff:float -> ('a,'b) t -> unit
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(** Write the matrix to a file. *)
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val pp : Format.formatter -> ('a,'b) t -> unit
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