f08me is the AD Library version of the primal routine f08mef (dbdsqr). Based (in the C++ interface) on overload resolution, f08me can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f08me_AD_f (

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
ADTYPE, Intent (Inout)	::	d(), e(), vt(ldvt,), u(ldu,), c(ldc,), work()
Character (1), Intent (In)	::	uplo
Type (c_ptr), Intent (Inout)	::	ad_handle

Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:

when ADTYPE is	Real(kind=nag_wp)	then AD is p0w
when ADTYPE is	Type(nagad_a1w_w_rtype)	then AD is a1w
when ADTYPE is	Type(nagad_t1w_w_rtype)	then AD is t1w

C++ Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void f08me (

handle_t &ad_handle, const char *uplo, const Integer &n, const Integer &ncvt, const Integer &nru, const Integer &ncc, ADTYPE d[], ADTYPE e[], ADTYPE vt[], const Integer &ldvt, ADTYPE u[], const Integer &ldu, ADTYPE c[], const Integer &ldc, ADTYPE work[], Integer &ifail)

}
}

The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
double,
dco::ga1s<double>::type,
dco::gt1s<double>::type

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

f08me is the AD Library 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 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 – nag::ad::handle_t Input/Output: On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
2: uplo – character Input
3: n – Integer Input
4: ncvt – Integer Input
5: nru – Integer Input
6: ncc – Integer Input
7: d( $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
8: e( $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
9: vt(ldvt, $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
10: ldvt – Integer Input
11: u(ldu, $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
12: ldu – Integer Input
13: c(ldc, $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
14: ldc – Integer Input
15: work( $*$ ) – ADTYPE 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 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:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Error Handling in the NAG AD Library Introduction for further information.

$ifail = - 199$: The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f08me is not threaded in any implementation.

9 Further Comments

None.

10 Example

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

Description of the primal example.

This example computes the singular value decomposition of the upper bidiagonal matrix

B

, where

B = (\begin{array}{r} 3.62 & 1.26 & 0.00 & 0.00 \\ 0.00 & - 2.41 & - 1.53 & 0.00 \\ 0.00 & 0.00 & 1.92 & 1.19 \\ 0.00 & 0.00 & 0.00 & - 1.43 \end{array}) .

See also the example for f08kf, which illustrates the use of the routine to compute the singular value decomposition of a general matrix.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f08me_a1w_fe.f90	f08me_a1w_fe.d	f08me_a1w_fe.r
C++	f08me_a1w_hcppe.cpp	f08me_a1w_hcppe.d	f08me_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f08me_t1w_fe.f90	f08me_t1w_fe.d	f08me_t1w_fe.r
C++	f08me_t1w_hcppe.cpp	f08me_t1w_hcppe.d	f08me_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f08me_p0w_fe.f90	f08me_p0w_fe.d	f08me_p0w_fe.r
C++	f08me_p0w_hcppe.cpp	f08me_p0w_hcppe.d	f08me_p0w_hcppe.r

NAG Library Manual, Mark 28.3

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F08 (Lapackeig) Chapter Contents

F08 (Lapackeig) Chapter Introduction (FL)

f08me: FL CL CPP AD

NAG AD Libraryf08me (dbdsqr)

▸▿ Contents

1 Purpose