NAG AD Library
f08me_a1w_f (dbdsqr_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.
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1 Purpose

f08me_a1w_f is the adjoint version of the primal routine f08mef (dbdsqr).

2 Specification

Fortran Interface
Subroutine f08me_a1w_f ( ad_handle, uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, ifail)
Integer, Intent (In) :: n, ncvt, nru, ncc, ldvt, ldu, ldc
Integer, Intent (Inout) :: ifail
Type (nagad_a1w_w_rtype), Intent (Inout) :: d(*), e(*), vt(ldvt,*), u(ldu,*), c(ldc,*), work(*)
Character (1), Intent (In) :: uplo
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void f08me_a1w_f_ ( void *&ad_handle, const char *uplo, const Integer &n, const Integer &ncvt, const Integer &nru, const Integer &ncc, nagad_a1w_w_rtype d[], nagad_a1w_w_rtype e[], nagad_a1w_w_rtype vt[], const Integer &ldvt, nagad_a1w_w_rtype u[], const Integer &ldu, nagad_a1w_w_rtype c[], const Integer &ldc, nagad_a1w_w_rtype work[], Integer &ifail, const Charlen length_uplo)
The routine may be called by the names f08me_a1w_f or nagf_lapackeig_dbdsqr_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f08me_a1w_f is the adjoint version of the primal routine f08mef (dbdsqr).
f08mef (dbdsqr) computes the singular value decomposition of a real upper or lower bidiagonal matrix, or of a real general matrix which has been reduced to bidiagonal form. For further information see Section 3 in the documentation for f08mef (dbdsqr).

4 References

Demmel J W and Kahan W (1990) Accurate singular values of bidiagonal matrices SIAM J. Sci. Statist. Comput. 11 873–912
Fernando K V and Parlett B N (1994) Accurate singular values and differential qd algorithms Numer. Math. 67 191–229
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, f08me_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: uplo – character Input
3: n – Integer Input
4: ncvt – Integer Input
5: nru – Integer Input
6: ncc – Integer Input
7: d(*) – Type (nagad_a1w_w_rtype) array Input/Output
8: e(*) – Type (nagad_a1w_w_rtype) array Input/Output
9: vt(ldvt, *) – Type (nagad_a1w_w_rtype) array Input/Output
10: ldvt – Integer Input
11: u(ldu, *) – Type (nagad_a1w_w_rtype) array Input/Output
12: ldu – Integer Input
13: c(ldc, *) – Type (nagad_a1w_w_rtype) array Input/Output
14: ldc – Integer Input
15: work(*) – 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

f08me_a1w_f uses the standard NAG ifail mechanism. Any errors indicated via info values returned by f08mef may be indicated with the same value returned by ifail. In addition, this routine may 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

f08me_a1w_f is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for f08mef (dbdsqr), modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

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10.2 Tangent mode (t1w)

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10.3 Passive mode (p0w)

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