NAG AD Library
f11xe (real_symm_matvec)

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1 Purpose

f11xe is the AD Library version of the primal routine f11xef. Based (in the C++ interface) on overload resolution, f11xe can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface
Subroutine f11xe_AD_f ( n, nnz, a, irow, icol, check, x, y, ifail)
Integer, Intent (In) :: n, nnz, irow(nnz), icol(nnz)
Integer, Intent (Inout) :: ifail
ADTYPE, Intent (In) :: a(nnz), x(n)
ADTYPE, Intent (Out) :: y(n)
Character (1), Intent (In) :: check
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 f11xe ( handle_t &ad_handle, const Integer &n, const Integer &nnz, const ADTYPE a[], const Integer irow[], const Integer icol[], const char *check, const ADTYPE x[], ADTYPE y[], Integer &ifail)
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

f11xe is the AD Library version of the primal routine f11xef.
f11xef computes a matrix-vector product involving a real sparse symmetric matrix stored in symmetric coordinate storage format. For further information see Section 3 in the documentation for f11xef.

4 References

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11xe 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_handlenag::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: n – Integer Input
3: nnz – Integer Input
4: a(nnz) – ADTYPE array Input
5: irow(nnz) – Integer array Input
6: icol(nnz) – Integer array Input
7: check – character Input
8: x(n) – ADTYPE array Input
9: y(n) – ADTYPE array Output
10: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11xe preserves all error codes from f11xef and in addition can return:
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.
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.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
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

f11xe is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for f11xef, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example reads in a symmetric positive definite sparse matrix A and a vector x. It then calls f11xe to compute the matrix-vector product y=Ax.

10.1 Adjoint modes

Language Source File Data Results
Fortran f11xe_a1w_fe.f90 f11xe_a1w_fe.d f11xe_a1w_fe.r
C++ f11xe_a1w_hcppe.cpp f11xe_a1w_hcppe.d f11xe_a1w_hcppe.r

10.2 Tangent modes

Language Source File Data Results
Fortran f11xe_t1w_fe.f90 f11xe_t1w_fe.d f11xe_t1w_fe.r
C++ f11xe_t1w_hcppe.cpp f11xe_t1w_hcppe.d f11xe_t1w_hcppe.r

10.3 Passive mode

Language Source File Data Results
Fortran f11xe_p0w_fe.f90 f11xe_p0w_fe.d f11xe_p0w_fe.r
C++ f11xe_p0w_hcppe.cpp f11xe_p0w_hcppe.d f11xe_p0w_hcppe.r