(* File: impl_CZ.mli
Copyright (C) 2005-
Egbert Ammicht
email: eammicht@lucent.com
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
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 Complexxx
(* LANSY *)
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 : rvec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [lansy ?n ?up ?norm ?work ?ar ?ac 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 *)
(* 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_lrwork : int -> int
(** [gecon_min_lrwork n] @return the minimum length of the rwork 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 ->
?rwork : rvec ->
?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 rwork 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 :
?n : int ->
?up : bool ->
?ipiv : int_vec ->
?anorm : float ->
?work : vec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [sycon ?n ?up ?ipiv ?anorm ?work ?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 *)
(* 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_lrwork : int -> int
(** [pocon_min_lrwork n] @return the minimum length of the rwork 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 ->
?rwork : rvec ->
?ar : int ->
?ac : int ->
mat
-> float
(** [pocon ?n ?up ?anorm ?work ?rwork ?ar ?ac a]
@return estimate of the reciprocal of the condition number of
complex Hermitian 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 rwork default = automatically allocated workspace
@param anorm default = 1-norm of the matrix [a] as returned by [lange] *)
(** General SVD routines *)
val gesvd_min_lwork : m : int -> n : int -> int
(** [gesvd_min_lwork ~m ~n] @return the minimum length of the work array
used by the [gesvd]-function for matrices with [m] rows and [n]
columns. *)
val gesvd_lrwork : m : int -> n : int -> int
(** [gesvd_lrwork m n] @return the (minimum) length of the rwork array
used by the [gesvd]-function. *)
val gesvd_opt_lwork :
?m : int -> ?n : int ->
?jobu : svd_job ->
?jobvt : svd_job ->
?s : rvec ->
?ur : int -> ?uc : int -> ?u : mat ->
?vtr : int -> ?vtc : int -> ?vt : mat ->
?ar : int -> ?ac : int -> mat
-> int
val gesvd :
?m : int -> ?n : int ->
?jobu : svd_job ->
?jobvt : svd_job ->
?s : rvec ->
?ur : int -> ?uc : int -> ?u : mat ->
?vtr : int -> ?vtc : int -> ?vt : mat ->
?work : vec ->
?rwork : rvec ->
?ar : int -> ?ac : int -> mat
-> rvec * mat * mat
(** General eigenvalue problem (simple drivers) *)
val geev_min_lwork : int -> int
(** [geev_min_lwork n] @return the minimum length of the work array
used by the [geev]-function.
@param n the logical dimensions of the matrix given to [geev]-function *)
val geev_min_lrwork : int -> int
(** [geev_min_lrwork n] @return the minimum length of the rwork array
used by the [geev]-function.
@param n the logical dimensions of the matrix given to [geev]-function *)
val geev_opt_lwork :
?n : int ->
?leftr : int -> ?leftc : int -> ?left : mat option ->
?rightr : int -> ?rightc : int -> ?right : mat option ->
?ofsw : int -> ?w : vec ->
?ar : int -> ?ac : int -> mat ->
int
(** [geev ?work ?rwork ?n ?leftr ?leftc ?left
?rightr ?rightc ?right ?ofsw w ?ar ?ac a]
See [geev]-function for details about arguments.
@return "optimal" work size *)
val geev :
?n : int ->
?work : vec ->
?rwork : vec ->
?leftr : int -> ?leftc : int -> ?left : mat option ->
?rightr : int -> ?rightc : int -> ?right : mat option ->
?ofsw : int -> ?w : vec ->
?ar : int -> ?ac : int -> mat ->
mat * vec * mat
(** [geev ?work ?rwork ?n
?leftr ?leftc ?left
?rightr ?rightc ?right
?ofsw w
?ar ?ac a]
@return [(lv, w, rv)], where [lv] and [rv] correspond to the left and
right eigenvectors respectively, [w] to the eigenvalues. [lv] ([rv])
is the empty matrix if [left] ([right]) is set to [None].
@raise Failure if the function fails to converge
@param n default = available number of columns of matrix [a]
@param work default = automatically allocated workspace
@param rwork default = automatically allocated workspace
@param left default = Automatically allocated left eigenvectors.
Pass [None] if you do not want to compute them,
[Some lv] if you want to provide the storage.
You can set [leftr], [leftc] in the last case.
(See LAPACK GEEV docs for details about storage of complex eigenvectors)
@param right default = Automatically allocated right eigenvectors.
Pass [None] if you do not want to compute them,
[Some rv] if you want to provide the storage.
You can set [rightr], [rightc] in the last case.
@param w default = automatically allocate eigenvalues
@param a the matrix whose eigensystem is computed *)
