d01rg is the AD Library version of the primal routine d01rgf. Based (in the C++ interface) on overload resolution, d01rg can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine d01rg_AD_f (

a, b, f, epsabs, epsrel, dinest, errest, nevals, iuser, ruser, ifail)

Integer, Intent (Inout)	::	iuser(*), ifail
Integer, Intent (Out)	::	nevals
ADTYPE, Intent (In)	::	a, b, epsabs, epsrel
ADTYPE, Intent (Inout)	::	ruser(*)
ADTYPE, Intent (Out)	::	dinest, errest
Type (c_ptr), Intent (Inout)	::	ad_handle
External	::	f

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 {
template <typename F_T>

void d01rg (

handle_t &ad_handle, const ADTYPE &a, const ADTYPE &b, F_T &&f, const ADTYPE &epsabs, const ADTYPE &epsrel, ADTYPE &dinest, ADTYPE &errest, Integer &nevals, 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

d01rg is the AD Library version of the primal routine d01rgf.

d01rgf is a general purpose integrator which calculates an approximation to the integral of a function

f (x)

over a finite interval

[a, b]

I = \int_{a}^{b} f (x) d x .

The routine is suitable as a general purpose integrator, and can be used when the integrand has singularities and infinities. In particular, the routine can continue if the subroutine f explicitly returns a quiet or signalling NaN or a signed infinity. For further information see Section 3 in the documentation for d01rgf.

4 References

Gonnet P (2010) Increasing the reliability of adaptive quadrature using explicit interpolants ACM Trans. Math. software 37 26

Piessens R, de Doncker–Kapenga E, Überhuber C and Kahaner D (1983) QUADPACK, A Subroutine Package for Automatic Integration Springer–Verlag

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01rg 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: a – ADTYPE Input

3: b – ADTYPE Input

4: f – Callable Input

f needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of f is:

Fortran Interface

Subroutine f (

x, nx, fv, iflag, iuser, ruser)

Integer, Intent (In)	::	nx
Integer, Intent (Inout)	::	iflag, iuser(*)
ADTYPE, Intent (In)	::	x(nx)
ADTYPE, Intent (Inout)	::	ruser(*)
ADTYPE, Intent (Out)	::	fv(nx)
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Interface

auto f = [&](

const handle_t &ad_handle, const ADTYPE x[], const Integer &nx, ADTYPE fv[], Integer &iflag)

1: ad_handle – nag::ad::handle_t Input/Output: On entry: a handle to the AD handle object.
2: x – ADTYPE array Input
3: nx – Integer Input
4: fv – ADTYPE array Output
5: iflag – Integer Input/Output
*: iuser – Integer array User Workspace
*: ruser – ADTYPE array User Workspace

5: epsabs – ADTYPE Input

6: epsrel – ADTYPE Input

7: dinest – ADTYPE Output

8: errest – ADTYPE Output

9: nevals – Integer Output

*: iuser( $*$ ) – Integer array User Workspace

*: ruser( $*$ ) – ADTYPE array User Workspace

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

10: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01rg preserves all error codes from d01rgf 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

d01rg is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01rgf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example computes

\int_{−1}^{1} \frac{\sin (x)}{x} \ln (10 (1 - x)) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	d01rg_a1w_fe.f90	d01rg_a1w_fe.d	d01rg_a1w_fe.r
C++	d01rg_a1w_hcppe.cpp	d01rg_a1w_hcppe.d	d01rg_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	d01rg_t1w_fe.f90	d01rg_t1w_fe.d	d01rg_t1w_fe.r
C++	d01rg_t1w_hcppe.cpp	d01rg_t1w_hcppe.d	d01rg_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	d01rg_p0w_fe.f90	d01rg_p0w_fe.d	d01rg_p0w_fe.r
C++	d01rg_p0w_hcppe.cpp	d01rg_p0w_hcppe.d	d01rg_p0w_hcppe.r

NAG Library Manual, Mark 28.4

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01rg: FL CL CPP AD

NAG AD Libraryd01rg (dim1_fin_gonnet_vec)

▸▿ Contents

1 Purpose