f08kp: FL CL CPP AD

NAG AD Library
f08kp_a1w_f (zgesvd_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

F08 (Lapackeig) Chapter Contents

F08 (Lapackeig) Chapter Introduction (FL)

f08kp: 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

10.1 Adjoint mode (a1w)

10.2 Tangent mode (t1w)

10.3 Passive mode (p0w)

1 Purpose

f08kp_a1w_f is the adjoint version of the primal routine f08kpf (zgesvd).

2 Specification

Fortran Interface

Subroutine f08kp_a1w_f (

ad_handle, jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, ifail)

Integer, Intent (In)	::	m, n, lda, ldu, ldvt, lwork
Integer, Intent (Inout)	::	ifail
Type (nagad_a1w_w_rtype), Intent (Inout)	::	s(), rwork()
Type (nagad_a1w_w_ctype), Intent (Inout)	::	a(lda,), u(ldu,), vt(ldvt,*)
Type (nagad_a1w_w_ctype), Intent (Out)	::	work(max(1,lwork))
Character (1), Intent (In)	::	jobu, jobvt
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void f08kp_a1w_f_ (

void *&ad_handle, const char *jobu, const char *jobvt, const Integer &m, const Integer &n, nagad_w_rcype a[], const Integer &lda, nagad_a1w_w_rtype s[], nagad_w_rcype u[], const Integer &ldu, nagad_w_rcype vt[], const Integer &ldvt, nagad_w_rcype work[], const Integer &lwork, nagad_a1w_w_rtype rwork[], Integer &ifail, const Charlen length_jobu, const Charlen length_jobvt)

The routine may be called by the names f08kp_a1w_f or nagf_lapackeig_zgesvd_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f08kp_a1w_f is the adjoint version of the primal routine f08kpf (zgesvd).

f08kpf (zgesvd) computes the singular value decomposition (SVD) of a complex

m \times n

matrix

A

, optionally computing the left and/or right singular vectors. For further information see Section 3 in the documentation for f08kpf (zgesvd).

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, f08kp_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: jobu – character Input
3: jobvt – character Input
4: m – Integer Input
5: n – Integer Input
6: a(lda, $*$ ) – Type (nagad_a1w_w_ctype) array Input/Output
7: lda – Integer Input
8: s( $*$ ) – Type (nagad_a1w_w_rtype) array Output
9: u(ldu, $*$ ) – Type (nagad_a1w_w_ctype) array Output
10: ldu – Integer Input
11: vt(ldvt, $*$ ) – Type (nagad_a1w_w_ctype) array Output
12: ldvt – Integer Input
13: work( $\max (1, lwork)$ ) – Type (nagad_a1w_w_ctype) array Workspace
14: lwork – Integer Input
15: rwork( $*$ ) – Type (nagad_a1w_w_rtype) array Workspace
16: 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

f08kp_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f08kpf 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

f08kp_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f08kpf (zgesvd), modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	f08kp_a1w_fe.f90	f08kp_a1w_fe.d	f08kp_a1w_fe.r
C++	f08kp_a1w_hcppe.cpp	f08kp_a1w_hcppe.d	f08kp_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	f08kp_t1w_fe.f90	f08kp_t1w_fe.d	f08kp_t1w_fe.r
C++	f08kp_t1w_hcppe.cpp	f08kp_t1w_hcppe.d	f08kp_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	f08kp_p0w_fe.f90	f08kp_p0w_fe.d	f08kp_p0w_fe.r
C++	f08kp_p0w_hcppe.cpp	f08kp_p0w_hcppe.d	f08kp_p0w_hcppe.r