NAG AD Library
f11bd_a1w_f (real_gen_basic_setup_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
Settings help

AD Name Style:

AD Specification Language:

1 Purpose

f11bd_a1w_f is the adjoint version of the primal routine f11bdf.

2 Specification

Fortran Interface
Subroutine f11bd_a1w_f ( ad_handle, method, precon, norm, weight, iterm, n, m, tol, maxitn, anorm, sigmax, monit, lwreq, work, lwork, ifail)
Integer, Intent (In) :: iterm, n, m, maxitn, monit, lwork
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: lwreq
Type (nagad_a1w_w_rtype), Intent (In) :: tol, anorm, sigmax
Type (nagad_a1w_w_rtype), Intent (Out) :: work(lwork)
Character (*), Intent (In) :: method
Character (1), Intent (In) :: precon, norm, weight
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void f11bd_a1w_f_ ( void *&ad_handle, const char *method, const char *precon, const char *norm, const char *weight, const Integer &iterm, const Integer &n, const Integer &m, const nagad_a1w_w_rtype &tol, const Integer &maxitn, const nagad_a1w_w_rtype &anorm, const nagad_a1w_w_rtype &sigmax, const Integer &monit, Integer &lwreq, nagad_a1w_w_rtype work[], const Integer &lwork, Integer &ifail, const Charlen length_method, const Charlen length_precon, const Charlen length_norm, const Charlen length_weight)
The routine may be called by the names f11bd_a1w_f or nagf_sparse_real_gen_basic_setup_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f11bd_a1w_f is the adjoint version of the primal routine f11bdf.
f11bdf is a setup routine, the first in a suite of three routines for the iterative solution of a real general (nonsymmetric) system of simultaneous linear equations. f11bdf must be called before f11bef, the iterative solver. 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 f11bdf.

4 References

Arnoldi W (1951) The principle of minimized iterations in the solution of the matrix eigenvalue problem Quart. Appl. Math. 9 17–29
Barrett R, Berry M, Chan T F, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C and Van der Vorst H (1994) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods SIAM, Philadelphia
Dias da Cunha R and Hopkins T (1994) PIM 1.1 — the parallel iterative method package for systems of linear equations user's guide — Fortran 77 version Technical Report Computing Laboratory, University of Kent at Canterbury, Kent, UK
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
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
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() 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

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11bd_a1w_f 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 – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: method – character Input
3: precon – character Input
4: norm – character Input
5: weight – character Input
6: iterm – Integer Input
7: n – Integer Input
8: m – Integer Input
9: tolType (nagad_a1w_w_rtype) Input
10: maxitn – Integer Input
11: anormType (nagad_a1w_w_rtype) Input
12: sigmaxType (nagad_a1w_w_rtype) Input
13: monit – Integer Input
14: lwreq – Integer Output
15: work(lwork) – Type (nagad_a1w_w_rtype) array Communication Array
16: lwork – Integer Input
17: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11bd_a1w_f preserves all error codes from f11bdf and in addition can return:
An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f11bd_a1w_f is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for f11bdf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

LanguageSource FileDataResults

10.2 Tangent mode (t1w)

LanguageSource FileDataResults

10.3 Passive mode (p0w)

LanguageSource FileDataResults