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## 1Purpose

f11bf is the AD Library version of the primal routine f11bff. Based (in the C++ interface) on overload resolution, f11bf can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine f11bf_AD_f ( ad_handle, itn, stplhs, stprhs, anorm, sigmax, work, lwork, ifail)
 Integer, Intent (In) :: lwork Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: itn ADTYPE, Intent (In) :: work(lwork) ADTYPE, Intent (Out) :: stplhs, stprhs, anorm, sigmax 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 {
}
}
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

## 3Description

f11bf is the AD Library version of the primal routine f11bff.
f11bff is the third in a suite of three routines for the iterative solution of a real general (nonsymmetric) system of simultaneous linear equations (see Golub and Van Loan (1996)). f11bff returns information about the computations during an iteration and/or after this has been completed. The first routine of the suite, f11bdf, is a setup routine; the second routine, f11bef, is the iterative solver itself.
These three routines are suitable for the solution of large sparse general (nonsymmetric) systems of equations. For further information see Section 3 in the documentation for f11bff.

## 4References

Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

## 5Arguments

In addition to the arguments present in the interface of the primal routine, f11bf 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.
On entry: a handle to the AD configuration data object, as created by x10aa.
2: itn – Integer Output
3: Output
4: Output
5: Output
6: Output
7: work(lwork) – ADTYPE array Communication Array
8: lwork – Integer Input
9: ifail – Integer Input/Output

## 6Error Indicators and Warnings

f11bf preserves all error codes from f11bff 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.
${\mathbf{ifail}}=-443$
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

f11bf is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for f11bff, modified to demonstrate calling the NAG AD Library.

Language Source File Data Results
Fortran f11bf_a1w_fe.f90 f11bf_a1w_fe.d f11bf_a1w_fe.r
C++ f11bf_a1w_hcppe.cpp f11bf_a1w_hcppe.d f11bf_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran f11bf_t1w_fe.f90 f11bf_t1w_fe.d f11bf_t1w_fe.r
C++ f11bf_t1w_hcppe.cpp f11bf_t1w_hcppe.d f11bf_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran f11bf_p0w_fe.f90 f11bf_p0w_fe.d f11bf_p0w_fe.r
C++ f11bf_p0w_hcppe.cpp f11bf_p0w_hcppe.d f11bf_p0w_hcppe.r