# NAG AD Libraryf11be (real_gen_basic_solver)

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## 1Purpose

f11be is the AD Library version of the primal routine f11bef. Based (in the C++ interface) on overload resolution, f11be can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine f11be_AD_f ( ad_handle, irevcm, u, v, wgt, work, lwork, ifail)
 Integer, Intent (In) :: lwork Integer, Intent (Inout) :: irevcm, ifail ADTYPE, Intent (In) :: wgt(*) ADTYPE, Intent (Inout) :: u(*), v(*), work(lwork) Type (c_ptr), Intent (Inout) :: ad_handle
Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:
#include <dco.hpp>
namespace nag {
 void f11be ( void *&ad_handle, Integer &irevcm, ADTYPE u[], ADTYPE v[], const ADTYPE wgt[], ADTYPE work[], const Integer &lwork, Integer &ifail)
}
}
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
double,
dco::ga1s<double>::type,
dco::gt1s<double>::type
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

## 3Description

f11be is the AD Library version of the primal routine f11bef.
f11bef is an iterative solver for a real general (nonsymmetric) system of simultaneous linear equations; f11bef is the second in a suite of three routines, where the first routine, f11bdf, must be called prior to f11bef to set up the suite, and the third routine in the suite, f11bff, can be used to return additional information about the computation.
These routines are suitable for the solution of large sparse general (nonsymmetric) systems of equations. For further information see Section 3 in the documentation for f11bef.

## 4References

Freund R W (1993) A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems SIAM J. Sci. Comput. 14 470–482
Freund R W and Nachtigal N (1991) QMR: a Quasi-Minimal Residual Method for Non-Hermitian Linear Systems Numer. Math. 60 315–339
Higham N J (1988) FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation ACM Trans. Math. Software 14 381–396
Saad Y and Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 7 856–869
Sleijpen G L G and Fokkema D R (1993) BiCGSTAB$\left(\ell \right)$ for linear equations involving matrices with complex spectrum ETNA 1 11–32
Sonneveld P (1989) CGS, a fast Lanczos-type solver for nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 10 36–52
Van der Vorst H (1989) Bi-CGSTAB, a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems SIAM J. Sci. Statist. Comput. 13 631–644

## 5Arguments

In addition to the arguments present in the interface of the primal routine, f11be includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine. A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
1: ad_handle – Pointer to AD Data Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa.
2: irevcm – Integer Input/Output
3: u($*$) – ADTYPE array Input/Output
4: v($*$) – ADTYPE array Input/Output
5: wgt($*$) – ADTYPE array Input
6: work(lwork) – ADTYPE array Communication Array
7: lwork – Integer Input
8: ifail – Integer Input/Output

## 6Error Indicators and Warnings

f11be preserves all error codes from f11bef and in addition can return:
${\mathbf{ifail}}=-89$
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

f11be is not threaded in any implementation.