(* File: impl_SDCZ.mli

   Copyright (C) 2001-

     Markus Mottl
     email: markus.mottl@gmail.com
     WWW: http://www.ocaml.info

     Liam Stewart
     email: liam@cs.toronto.edu
     WWW: http://www.cs.toronto.edu/~liam

     Christophe Troestler
     email: Christophe.Troestler@umh.ac.be
     WWW: http://math.umh.ac.be/an/

   This library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2 of the License, or (at your option) any later version.

   This library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with this library; if not, write to the Free Software
   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*)

(** Interface to BLAS/LAPACK *)

open Bigarray
open Common
open Numberxx

(** {6 BLAS-1 interface} *)

val swap :
  ?n : int ->
  ?ofsx : int ->
  ?incx : int ->
  x : vec ->
  ?ofsy : int ->
  ?incy : int ->
  vec
  -> unit
(** [swap ?n ?ofsx ?incx ~x ?ofsy ?incy y] see BLAS documentation!
    @param n default = 1
    @param ofsx default = 1
    @param incx default = 1
    @param ofsy default = 1
    @param incy default = 1 *)

val scal : ?n : int -> num_type -> ?ofsx : int -> ?incx : int -> vec -> unit
(** [scal ?n alpha ?ofsx ?incx x] see BLAS documentation!
    @param n default = greater n s.t. [ofsx+(n-1)(abs incx) <= dim x]
    @param ofsx default = 1
    @param incx default = 1 *)

val copy :
  ?n : int ->
  ?ofsy : int ->
  ?incy : int ->
  ?y : vec ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> vec
(** [copy ?n ?ofsy ?incy ?y ?ofsx ?incx x] see BLAS documentation!
    @return vector [y], which is overwritten.
    @param n default = greater n s.t. [ofsx+(n-1)(abs incx) <= dim x]
    @param ofsy default = 1
    @param incy default = 1
    @param y default = new vector with [ofsy+(n-1)(abs incy)] rows
    @param ofsx default = 1
    @param incx default = 1 *)

val axpy :
  ?n : int ->
  ?alpha : num_type ->
  ?ofsx : int ->
  ?incx : int ->
  x : vec ->
  ?ofsy : int ->
  ?incy : int ->
  vec
  -> unit
(** [axpy ?n ?alpha ?ofsx ?incx ~x ?ofsy ?incy y] see BLAS documentation!
    @param n default = greater n s.t. [ofsx+(n-1)(abs incx) <= dim x]
    @param alpha default = 1.0
    @param ofsx default = 1
    @param incx default = 1
    @param ofsy default = 1
    @param incy default = 1 *)

val iamax : ?n : int -> ?ofsx : int -> ?incx : int -> vec -> int
(** [iamax ?n ?ofsx ?incx x] see BLAS documentation!
    @param n default = greater n s.t. [ofsx+(n-1)(abs incx) <= dim x]
    @param ofsx default = 1
    @param incx default = 1 *)

val amax :
  ?n : int ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> num_type
(** [amax ?n ?ofsx ?incx x] @return the greater of the absolute
    values of the elements of the vector [x].
    @param n default = greater n s.t. [ofsx+(n-1)(abs incx) <= dim x]
    @param ofsx default = 1
    @param incx default = 1 *)


(** {6 BLAS-2 interface} *)

val gemv :
  ?m : int ->
  ?n : int ->
  ?beta : float  ->
  ?ofsy : int ->
  ?incy : int ->
  ?y : vec ->
  ?trans : trans3 ->
  ?alpha : float ->
  ?ar : int ->
  ?ac : int ->
  mat ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> vec
(** [gemv ?m ?n ?beta ?ofsy ?incy ?y ?trans ?alpha ?ar ?ac a ?ofsx ?incx x]
    see BLAS documentation!
    @return vector [y], which is overwritten.
    @param m default = number of available rows in matrix [a]
    @param n default = available columns in matrix [a]
    @param beta default = 0.0
    @param ofsy default = 1
    @param incy default = 1
    @param y default = vec with minimal required length (see BLAS)
    @param trans default = `N
    @param alpha default = 1.0
    @param ar default = 1
    @param ac default = 1
    @param ofsx default = 1
    @param incx default = 1 *)

val gbmv :
  ?m : int ->
  ?n : int ->
  ?beta : float ->
  ?ofsy : int ->
  ?incy : int ->
  ?y : vec ->
  ?trans : trans3 ->
  ?alpha : float ->
  ?ar : int ->
  ?ac : int ->
  mat ->
  int ->
  int ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> vec
(** [gbmv
      ?m ?n ?beta ?ofsy ?incy ?y ?trans ?alpha ?ar ?ac a kl ku ?ofsx ?incx x]
    see BLAS documentation!
    @return vector [y], which is overwritten.
    @param m default = same as [n] (i.e., [a] is a square matrix)
    @param n default = available number of columns in matrix [a]
    @param beta default = 0.0
    @param ofsy default = 1
    @param incy default = 1
    @param y default = vector with minimal required length (see BLAS)
    @param trans default = `N
    @param alpha default = 1.0
    @param ar default = 1
    @param ac default = 1
    @param ofsx default = 1
    @param incx default = 1 *)

val symv :
  ?n : int ->
  ?beta : float ->
  ?ofsy : int ->
  ?incy : int ->
  ?y : vec ->
  ?up : bool ->
  ?alpha : float ->
  ?ar : int ->
  ?ac : int ->
  mat ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> vec
(** [symv ?n ?beta ?ofsy ?incy ?y ?up ?alpha ?ar ?ac a ?ofsx ?incx x]
    see BLAS documentation!
    @return vector [y], which is overwritten.
    @param n default = dimension of symmetric matrix [a]
    @param beta default = 0.0
    @param ofsy default = 1
    @param incy default = 1
    @param y default = vector with minimal required length (see BLAS)
    @param up default = true (upper triangular portion of [a] is accessed)
    @param alpha default = 1.0
    @param ar default = 1
    @param ac default = 1
    @param ofsx default = 1
    @param incx default = 1 *)

val trmv :
  ?n : int ->
  ?trans : trans3 ->
  ?diag : diag ->
  ?up : bool ->
  ?ar : int ->
  ?ac : int ->
  mat ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> unit
(** [trmv ?n ?trans ?diag ?up ?ar ?ac a ?ofsx ?incx x]
    see BLAS documentation!
    @param n default = dimension of triangular matrix [a]
    @param trans default = `N
    @param diag default = false (not a unit triangular matrix)
    @param up default = true (upper triangular portion of [a] is accessed)
    @param ar default = 1
    @param ac default = 1
    @param ofsx default = 1
    @param incx default = 1 *)

val trsv :
  ?n : int ->
  ?trans : trans3 ->
  ?diag : diag ->
  ?up : bool ->
  ?ar : int ->
  ?ac : int ->
  mat ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> unit
(** [trsv ?n ?trans ?diag ?up ?ar ?ac a ?ofsx ?incx x]
    see BLAS documentation!
    @param n default = dimension of triangular matrix [a]
    @param trans default = `N
    @param diag default = false (not a unit triangular matrix)
    @param up default = true (upper triangular portion of [a] is accessed)
    @param ar default = 1
    @param ac default = 1
    @param ofsx default = 1
    @param incx default = 1 *)

val tpmv :
  ?n : int ->
  ?trans : trans3 ->
  ?diag : diag ->
  ?up : bool ->
  ?ofsap : int ->
  vec ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> unit
(** [tpmv ?n ?trans ?diag ?up ?ofsap ap ?ofsx ?incx x]
    see BLAS documentation!
    @param n default = dimension of packed triangular matrix [ap]
    @param trans default = `N
    @param diag default = false (not a unit triangular matrix)
    @param up default = true (upper triangular portion of [ap] is accessed)
    @param ofsap default = 1
    @param ofsx default = 1
    @param incx default = 1 *)

val tpsv :
  ?n : int ->
  ?trans : trans3 ->
  ?diag : diag ->
  ?up : bool ->
  ?ofsap : int ->
  vec ->
  ?ofsx : int ->
  ?incx : int ->
  vec
  -> unit
(** [tpsv ?n ?trans ?diag ?up ?ofsap ap ?ofsx ?incx x]
    see BLAS documentation!
    @param n default = dimension of packed triangular matrix [ap]
    @param trans default = `N
    @param diag default = false (not a unit triangular matrix)
    @param up default = true (upper triangular portion of [ap] is accessed)
    @param ofsap default = 1
    @param ofsx default = 1
    @param incx def