NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
F08 (Lapackeig) Chapter Contents
F08 (Lapackeig) Chapter Introduction (FL)
f08fa:  FL   CL   CPP   AD 

NAG AD Library
f08fa_a1w_f (dsyev_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.
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
F08 (Lapackeig) Chapter Contents
F08 (Lapackeig) Chapter Introduction (FL)
f08fa:  FL   CL   CPP   AD 

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© The Numerical Algorithms Group Ltd. 2020
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1 Purpose

f08fa_a1w_f is the adjoint version of the primal routine f08faf (dsyev).

2 Specification

Fortran Interface
Subroutine f08fa_a1w_f ( ad_handle, jobz, uplo, n, a, lda, w, work, lwork, ifail)
Integer, Intent (In) :: n, lda, lwork
Integer, Intent (Inout) :: ifail
Type (nagad_a1w_w_rtype), Intent (Inout) :: a(lda,*)
Type (nagad_a1w_w_rtype), Intent (Out) :: w(n), work(max(1,lwork))
Character (1), Intent (In) :: jobz, uplo
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void f08fa_a1w_f_ ( void *&ad_handle, const char *jobz, const char *uplo, const Integer &n, nagad_a1w_w_rtype a[], const Integer &lda, nagad_a1w_w_rtype w[], nagad_a1w_w_rtype work[], const Integer &lwork, Integer &ifail, const Charlen length_jobz, const Charlen length_uplo)
The routine may be called by the names f08fa_a1w_f or nagf_lapackeig_dsyev_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f08fa_a1w_f is the adjoint version of the primal routine f08faf (dsyev).
f08faf (dsyev) computes all the eigenvalues and, optionally, all the eigenvectors of a real n×n symmetric matrix A. For further information see Section 3 in the documentation for f08faf (dsyev).

4 References

Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia https://www.netlib.org/lapack/lug
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore

5 Arguments

In addition to the arguments present in the interface of the primal routine, f08fa_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: jobz – character Input
3: uplo – character Input
4: n – Integer Input
5: a(lda, *) – Type (nagad_a1w_w_rtype) array Input/Output
6: lda – Integer Input
7: w(n) – Type (nagad_a1w_w_rtype) array Output
8: work(max(1,lwork)) – Type (nagad_a1w_w_rtype) array Workspace
9: lwork – Integer Input
10: ifail – Integer Input/Output
On entry: must be set to 0, -1  or  1.
On exit: any errors are indicated as described in Section 6.

6 Error Indicators and Warnings

f08fa_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f08faf may be indicated with the same value returned by ifail. In addition, this routine may 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.
ifail=-899
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

f08fa_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

A NAG AD Library example is not yet available, please refer to the NAG AD Library Introduction for information on calling routines from the AD Library.
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
F08 (Lapackeig) Chapter Contents
F08 (Lapackeig) Chapter Introduction (FL)
f08fa:  FL   CL   CPP   AD 
© The Numerical Algorithms Group Ltd. 2020