d01ga is the AD Library version of the primal routine d01gaf. Based (in the C++ interface) on overload resolution, d01ga can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine d01ga_AD_f (

ad_handle, x, y, n, ans, er, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x(n), y(n)
ADTYPE, Intent (Out)	::	ans, er
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++ Header Interface

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

void d01ga (

void *&ad_handle, const ADTYPE x[], const ADTYPE y[], const Integer &n, ADTYPE &ans, ADTYPE &er, 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

d01ga is the AD Library version of the primal routine d01gaf.

d01gaf integrates a function which is specified numerically at four or more points, over the whole of its specified range, using third-order finite difference formulae with error estimates, according to a method due to Gill and Miller (1972). For further information see Section 3 in the documentation for d01gaf.

4 References

Gill P E and Miller G F (1972) An algorithm for the integration of unequally spaced data Comput. J. 15 80–83

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01ga 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 – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: x(n) – ADTYPE array Input
3: y(n) – ADTYPE array Input
4: n – Integer Input
5: ans – ADTYPE Output
6: er – ADTYPE Output
7: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01ga preserves all error codes from d01gaf and in addition can return:

$ifail = - 89$: 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.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

d01ga is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01gaf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example evaluates the integral

\int_{0}^{1} \frac{4}{1 + x^{2}} d x = π

reading in the function values at

21

unequally spaced points.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	d01ga_a1w_fe.f90	d01ga_a1w_fe.d	d01ga_a1w_fe.r
C++	d01ga_a1w_hcppe.cpp	None	d01ga_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	d01ga_t1w_fe.f90	d01ga_t1w_fe.d	d01ga_t1w_fe.r
C++	d01ga_t1w_hcppe.cpp	None	d01ga_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	d01ga_p0w_fe.f90	d01ga_p0w_fe.d	d01ga_p0w_fe.r
C++	d01ga_p0w_hcppe.cpp	None	d01ga_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01ga: FL CL CPP AD

NAG AD Libraryd01ga (dim1_data)

▸▿ Contents

1 Purpose