f11be: FL CL CPP AD

NAG AD Library
f11be_a1w_f (real_gen_basic_solver_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.

Keyword Search:

NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F11 (Sparse) Chapter Contents

F11 (Sparse) Chapter Introduction (FL)

f11be: FL CL CPP AD

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1 Purpose

f11be_a1w_f is the adjoint version of the primal routine f11bef.

2 Specification

Fortran Interface

Subroutine f11be_a1w_f (

ad_handle, irevcm, u, v, wgt, work, lwork, ifail)

Integer, Intent (In)	::	lwork
Integer, Intent (Inout)	::	irevcm, ifail
Type (nagad_a1w_w_rtype), Intent (In)	::	wgt(*)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	u(), v(), work(lwork)
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void f11be_a1w_f_ (

void *&ad_handle, Integer &irevcm, nagad_a1w_w_rtype u[], nagad_a1w_w_rtype v[], const nagad_a1w_w_rtype wgt[], nagad_a1w_w_rtype work[], const Integer &lwork, Integer &ifail)

The routine may be called by the names f11be_a1w_f or nagf_sparse_real_gen_basic_solver_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f11be_a1w_f is the adjoint 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.

4 References

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

(ℓ)

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, f11be_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: irevcm – Integer Input/Output
3: u( $*$ ) – Type (nagad_a1w_w_rtype) array Input/Output
4: v( $*$ ) – Type (nagad_a1w_w_rtype) array Input/Output
5: wgt( $*$ ) – Type (nagad_a1w_w_rtype) array Input
6: work(lwork) – Type (nagad_a1w_w_rtype) array Communication Array
7: lwork – Integer Input
8: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11be_a1w_f preserves all error codes from f11bef and in addition can return:

$ifail = - 89$: 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.