NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
D01 (Quad) Chapter Contents
D01 (Quad) Chapter Introduction (FL)
d01bd:  FL   CL   CPP   AD 

NAG AD Library
d01bd_a1w_f (dim1_fin_smooth_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
D01 (Quad) Chapter Contents
D01 (Quad) Chapter Introduction (FL)
d01bd:  FL   CL   CPP   AD 

▸▿ Contents

© The Numerical Algorithms Group Ltd. 2020
Settings help

AD Name Style:


AD Specification Language:

1 Purpose

d01bd_a1w_f is the adjoint version of the primal routine d01bdf.

2 Specification

Fortran Interface
Subroutine d01bd_a1w_f ( ad_handle, f, a, b, epsabs, epsrel, result, abserr, iuser, ruser, ifail)
Integer, Intent (Inout) :: iuser(*), ifail
External :: f
Type (nagad_a1w_w_rtype), Intent (In) :: a, b, epsabs, epsrel
Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out) :: result, abserr
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void d01bd_a1w_f_ ( void *&ad_handle,
void (NAG_CALL f)(void *&ad_handle, const nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[]),
const nagad_a1w_w_rtype &a, const nagad_a1w_w_rtype &b, const nagad_a1w_w_rtype &epsabs, const nagad_a1w_w_rtype &epsrel, nagad_a1w_w_rtype &result, nagad_a1w_w_rtype &abserr, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)
The routine may be called by the names d01bd_a1w_f or nagf_quad_dim1_fin_smooth_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01bd_a1w_f is the adjoint version of the primal routine d01bdf.
d01bdf calculates an approximation to the integral of a function over a finite interval [a,b]:
I= ∫ab f(x) dx .  
It is non-adaptive and as such is recommended for the integration of ‘smooth’ functions. These exclude integrands with singularities, derivative singularities or high peaks on [a,b], or which oscillate too strongly on [a,b]. For further information see Section 3 in the documentation for d01bdf.

4 References

Patterson T N L (1968) The Optimum addition of points to quadrature formulae Math. Comput. 22 847–856
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, d01bd_a1w_f 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 – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: f – Subroutine External Procedure
Note that f is a subroutine in this interface, returning the function value via the additional output parameter retval.
The specification of f is:
Fortran Interface
Subroutine f ( ad_handle, x, retval, iuser, ruser)
Integer, Intent (Inout) :: iuser(*)
Type (nagad_a1w_w_rtype), Intent (In) :: x
Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out) :: retval
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void f ( void *&ad_handle, const nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[])
1: ad_handle – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object.
2: x – Type (nagad_a1w_w_rtype) Input
3: retval – Type (nagad_a1w_w_rtype) Output
On exit: the value of f(x) evaluated at x.
4: iuser(*) – Integer array User Workspace
5: ruser(*) – Type (nagad_a1w_w_rtype) array User Workspace
3: a – Type (nagad_a1w_w_rtype) Input
4: b – Type (nagad_a1w_w_rtype) Input
5: epsabs – Type (nagad_a1w_w_rtype) Input
6: epsrel – Type (nagad_a1w_w_rtype) Input
7: result – Type (nagad_a1w_w_rtype) Output
8: abserr – Type (nagad_a1w_w_rtype) Output
9: iuser(*) – Integer array User Workspace
User workspace.
10: ruser(*) – Type (nagad_a1w_w_rtype) array User Workspace
User workspace.
11: 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 d01bdf, however d01bd_a1w_f 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=-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

d01bd_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01bdf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

LanguageSource FileDataResults
Fortrand01bd_a1w_fe.f90Noned01bd_a1w_fe.r
C++d01bd_a1w_hcppe.cppd01bd_a1w_hcppe.dd01bd_a1w_hcppe.r

10.2 Tangent mode (t1w)

LanguageSource FileDataResults
Fortrand01bd_t1w_fe.f90Noned01bd_t1w_fe.r
C++d01bd_t1w_hcppe.cppd01bd_t1w_hcppe.dd01bd_t1w_hcppe.r

10.3 Passive mode (p0w)

LanguageSource FileDataResults
Fortrand01bd_p0w_fe.f90Noned01bd_p0w_fe.r
C++d01bd_p0w_hcppe.cppd01bd_p0w_hcppe.dd01bd_p0w_hcppe.r
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
D01 (Quad) Chapter Contents
D01 (Quad) Chapter Introduction (FL)
d01bd:  FL   CL   CPP   AD 
© The Numerical Algorithms Group Ltd. 2020