f06ya is the AD Library version of the primal routine f06yaf (dgemm). Based (in the C++ interface) on overload resolution, f06ya can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f06ya_AD_f (

ad_handle, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc, ifail)

Integer, Intent (In)	::	m, n, k, lda, ldb, ldc
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	alpha, a(lda,), b(ldb,), beta
ADTYPE, Intent (Inout)	::	c(ldc,*)
Character (1), Intent (In)	::	transa, transb
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 f06ya (

handle_t &ad_handle, const char *transa, const char *transb, const Integer &m, const Integer &n, const Integer &k, const ADTYPE &alpha, const ADTYPE a[], const Integer &lda, const ADTYPE b[], const Integer &ldb, const ADTYPE &beta, ADTYPE c[], const Integer &ldc, 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

f06ya is the AD Library version of the primal routine f06yaf (dgemm).

f06yaf (dgemm) performs one of the matrix-matrix operations

\begin{array}{l} C \leftarrow α A B + β C, & C \leftarrow α A^{T} B + β C, \\ C \leftarrow α A B^{T} + β C or & C \leftarrow α A^{T} B^{T} + β C, \end{array}

where

A

B

and

C

are real matrices, and

α

and

β

are real scalars;

C

is always

m \times n

. For further information see Section 3 in the documentation for f06yaf (dgemm).

4 References

5 Arguments

In addition to the arguments present in the interface of the primal routine, f06ya 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: transa – character Input
3: transb – character Input
4: m – Integer Input
5: n – Integer Input
6: k – Integer Input
7: alpha – ADTYPE Input
8: a(lda, $*$ ) – ADTYPE array Input
9: lda – Integer Input
10: b(ldb, $*$ ) – ADTYPE array Input
11: ldb – Integer Input
12: beta – ADTYPE Input
13: c(ldc, $*$ ) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
14: ldc – Integer Input
15: 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

There are no specific error codes from f06yaf (dgemm), however f06ya can 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

f06ya is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f06yaf (dgemm), modified to demonstrate calling the NAG AD Library.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f06ya_a1w_fe.f90	f06ya_a1w_fe.d	f06ya_a1w_fe.r
C++	f06ya_a1w_hcppe.cpp	f06ya_a1w_hcppe.d	f06ya_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f06ya_t1w_fe.f90	f06ya_t1w_fe.d	f06ya_t1w_fe.r
C++	f06ya_t1w_hcppe.cpp	f06ya_t1w_hcppe.d	f06ya_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f06ya_p0w_fe.f90	f06ya_p0w_fe.d	f06ya_p0w_fe.r
C++	f06ya_p0w_hcppe.cpp	f06ya_p0w_hcppe.d	f06ya_p0w_hcppe.r

NAG Library Manual, Mark 30

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction (FL)

f06ya: FL CL CPP AD

NAG AD Libraryf06ya (dgemm)

▸▿ Contents

1 Purpose