f03bf is the AD Library version of the primal routine f03bff. Based (in the C++ interface) on overload resolution, f03bf can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f03bf_AD_f (

ad_handle, n, a, lda, d, id, ifail)

Integer, Intent (In)	::	n, lda
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	id
ADTYPE, Intent (In)	::	a(lda,*)
ADTYPE, Intent (Out)	::	d
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 f03bf (

handle_t &ad_handle, const Integer &n, const ADTYPE a[], const Integer &lda, ADTYPE &d, Integer &id, 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

f03bf is the AD Library version of the primal routine f03bff.

f03bff computes the determinant of a real

n \times n

symmetric positive definite matrix

A

. f07fdf must be called first to supply the symmetric matrix

A

in Cholesky factorized form. The storage (upper or lower triangular) used by f07fdf is not relevant to f03bff since only the diagonal elements of the factorized

A

are referenced. For further information see Section 3 in the documentation for f03bff.

4 References

Wilkinson J H and Reinsch C (1971) Handbook for Automatic Computation II, Linear Algebra Springer–Verlag

5 Arguments

In addition to the arguments present in the interface of the primal routine, f03bf 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: n – Integer Input
3: a(lda, $*$ ) – ADTYPE array Input
4: lda – Integer Input
5: d – ADTYPE Output
6: id – Integer Output
7: ifail – Integer Input/Output

6 Error Indicators and Warnings

f03bf preserves all error codes from f03bff and in addition 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

f03bf is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for f03bff, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example computes a Cholesky factorization and calculates the determinant of the real symmetric positive definite matrix

(\begin{array}{r} 6 & 7 & 6 & 5 \\ 7 & 11 & 8 & 7 \\ 6 & 8 & 11 & 9 \\ 5 & 7 & 9 & 11 \end{array}) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	f03bf_a1w_fe.f90	f03bf_a1w_fe.d	f03bf_a1w_fe.r
C++	f03bf_a1w_hcppe.cpp	f03bf_a1w_hcppe.d	f03bf_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	f03bf_t1w_fe.f90	f03bf_t1w_fe.d	f03bf_t1w_fe.r
C++	f03bf_t1w_hcppe.cpp	f03bf_t1w_hcppe.d	f03bf_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	f03bf_p0w_fe.f90	f03bf_p0w_fe.d	f03bf_p0w_fe.r
C++	f03bf_p0w_hcppe.cpp	f03bf_p0w_hcppe.d	f03bf_p0w_hcppe.r

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F03 (Det) Chapter Contents

F03 (Det) Chapter Introduction (FL)

f03bf: FL CL CPP AD

NAG AD Libraryf03bf (real_sym)

▸▿ Contents

1 Purpose