(* File: impl_SD.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/
Oleg Trott
email: ot14@columbia.edu
WWW: http://www.columbia.edu/~ot14
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
*)
open Bigarray
open Common
open Floatxx
(** {6 BLAS-1 interface} *)
val dot :
?n : int ->
?ofsx : int ->
?incx : int ->
x : vec ->
?ofsy : int ->
?incy : int ->
vec
-> float
(** [dot ?n ?ofsy ?incy y ?ofsx ?incx x] see BLAS documentation!
@param n default = greater n s.t. [ofsx+(n-1)(abs incx) <= dim x]
@param ofsy default = 1
@param incy default = 1
@param ofsx default = 1
@param incx default = 1 *)
val nrm2 : ?n : int -> ?ofsx : int -> ?incx : int -> vec -> float
(** [nrm2 ?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 asum : ?n : int -> ?ofsx : int -> ?incx : int -> vec -> float
(** [asum ?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 *)
(** {6 BLAS-2 interface} *)
val sbmv :
?ofsy : int ->
?incy : int ->
?y : vec ->
?ar : int ->
?ac : int ->
mat ->
?n : int ->
?k : int ->
?up : bool ->
?alpha : float ->
?beta : float ->
?ofsx : int ->
?incx : int ->
vec
-> vec
(** [sbmv ?ofsy ?incy ?y ?ar ?ac a ?n ?k ?up ?alpha ?beta ?ofsx ?incx x] see
BLAS documentation!
@return vector [y], which is overwritten.
@param ofsy default = 1
@param incy default = 1
@param ar default = 1
@param ac default = 1
@param y default = uninitialized vector of minimal length (see BLAS)
@param n default = number of available columns to the right of [ac].
@param k default = number of available rows in matrix [a] - 1
@param up default = true i.e., upper band of [a] is supplied
@param alpha default = 1.0
@param beta default = 0.0
@param ofsx default = 1
@param incx default = 1 *)
val syr :
?alpha : float ->
?up : bool ->
?ofsx : int ->
?incx : int ->
vec ->
?n : int ->
?ar : int ->
?ac : int ->
mat
-> mat
(** [syr ?alpha ?up ?ofsx ?incx x ?n ?ar ?ac a] see BLAS documentation!
@return vector [a], which is overwritten
@param alpha default = 1.0
@param up default = true i.e., upper triangle of [a] is supplied
@param ofsx default = 1
@param incx default = 1
@param ar default = 1
@param ac default = 1
@param n default = number of rows of [a] *)
(** {6 LAPACK interface} *)
(** Auxiliary routines *)
val lansy_min_lwork : int -> norm4 -> int
(** [lansy_min_lwork m norm]
@return the minimum length of the work array used by the [lansy]-function.
@param norm type of norm that will be computed by [lansy]
@param n the number of columns (and rows) in the matrix *)
val lansy :
?n : int ->
?up : bool ->
?norm : norm4 ->
?work : vec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [lansy ?norm ?up ?n ?ar ?ac ?work a] see LAPACK documentation!
@param norm default = `O
@param up default = true (reference upper triangular part of [a])
@param n default = number of columns of matrix [a]
@param work default = allocated work space for norm `I *)
val lamch : [ `E | `S | `B | `P | `N | `R | `M | `U | `L | `O ] -> float
(** [lamch cmach] see LAPACK documentation! *)
(** Linear equations (computational routines) *)
(* GECON *)
val gecon_min_lwork : int -> int
(** [gecon_min_lwork n] @return the minimum length of the work array
used by the [gecon]-function.
@param n the logical dimensions of the matrix given to
the [gecon]-function *)
val gecon_min_liwork : int -> int
(** [gecon_min_liwork n] @return the minimum length of the iwork array
used by the [gecon]-function.
@param n the logical dimensions of the matrix given to [gecon]-function *)
val gecon :
?n : int ->
?norm : norm2 ->
?anorm : float ->
?work : vec ->
?iwork : int_vec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [gecon ?n ?norm ?anorm ?work ?rwork ?ar ?ac a]
@return estimate of the reciprocal of the condition number of matrix [a]
@param n default = available number of columns of matrix [a]
@param norm default = 1-norm
@param anorm default = norm of the matrix [a] as returned by [lange]
@param work default = automatically allocated workspace
@param iwork default = automatically allocated workspace
@param ar default = 1
@param ac default = 1 *)
(* SYCON *)
val sycon_min_lwork : int -> int
(** [sycon_min_lwork n] @return the minimum length of the work array
used by the [sycon]-function.
@param n the logical dimensions of the matrix given to
the [sycon]-function *)
val sycon_min_liwork : int -> int
(** [sycon_min_liwork n] @return the minimum length of the iwork array
used by the [sycon]-function.
@param n the logical dimensions of the matrix given to [sycon]-function *)
val sycon :
?n : int ->
?up : bool ->
?ipiv : int_vec ->
?anorm : float ->
?work : vec ->
?iwork : int_vec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [sycon ?n ?up ?ipiv ?anorm ?work ?iwork ?ar ?ac a]
@return estimate of the reciprocal of the condition number
of symmetric matrix [a]
@param n default = available number of columns of matrix [a]
@param up default = upper triangle of the factorization of [a] is stored
@param ipiv default = vec of length [n]
@param anorm default = 1-norm of the matrix [a] as returned by [lange]
@param work default = automatically allocated workspace
@param iwork default = automatically allocated workspace *)
(* POCON *)
val pocon_min_lwork : int -> int
(** [pocon_min_lwork n] @return the minimum length of the work array
used by the [pocon]-function.
@param n the logical dimensions of the matrix given to
the [pocon]-function *)
val pocon_min_liwork : int -> int
(** [pocon_min_liwork n] @return the minimum length of the iwork array
used by the [pocon]-function.
@param n the logical dimensions of the matrix given to [pocon]-function *)
val pocon :
?n : int ->
?up : bool ->
?anorm : float ->
?work : vec ->
?iwork : int_vec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [pocon ?n ?up ?anorm ?work ?iwork ?ar ?ac a]
@return estimate of the reciprocal of the condition number of
symmetric positive definite matrix [a]
@param n default = available number of columns of matrix [a]
@param up default = upper triangle of Cholesky factorization
of [a] is stored
@param work default = automatically allocated workspace
@param iwork default = automatically allocated workspace
@param anorm default = 1-norm of the matrix [a] as returned by [lange] *)
(** Least squares (expert drivers) *)
val gelsy_min_lwork : m : int -> n : int -> nrhs : int -> int
(** [gelsy_min_lwork ~m ~n ~nrhs] @return the minimum length of the
work-array used by the [gelsy]-function if the logical dimensions
of the matrix are [m] rows and [n] columns and if there are [nrhs]
right hand side vectors. *)
val gelsy_opt_lwork :
?m : int ->
?n : int ->
?ar : int ->
?ac : int ->
mat ->
?nrhs : int ->
?br : int ->
?bc : int ->
mat
-> int
(** [gelsy_opt_lwork ?m ?n ?ar ?ac a ?nrhs ?br ?bc b] @return the optimum
length of the work-array used by the [gelsy]-function given matrix
[a], optionally its logical dimensions [m] and [n] and given right
hand side matrix [b] with an optional number [nrhs] of < 
