NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01rl: FL CL CPP AD

NAG AD Library
d01rl_a1w_f (dim1_fin_brkpts_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.

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NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01rl: FL CL CPP AD

▸▿ Contents

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Adjoint mode (a1w)

10.2 Tangent mode (t1w)

10.3 Passive mode (p0w)

© The Numerical Algorithms Group Ltd. 2020

1 Purpose

d01rl_a1w_f is the adjoint version of the primal routine d01rlf.

2 Specification

Fortran Interface

Subroutine d01rl_a1w_f (

ad_handle, f, a, b, npts, points, epsabs, epsrel, maxsub, result, abserr, rinfo, iinfo, iuser, ruser, cpuser, ifail)

Integer, Intent (In)	::	npts, maxsub
Integer, Intent (Inout)	::	iuser(*), ifail
Integer, Intent (Out)	::	iinfo(2*max(maxsub,npts)+npts+4)
Type (nagad_a1w_w_rtype), Intent (In)	::	a, b, points(npts), epsabs, epsrel
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	result, abserr, rinfo(4*max(maxsub,npts)+npts+6)
Type (c_ptr), Intent (Inout)	::	ad_handle
Type (c_ptr), Intent (In)	::	cpuser
External	::	f

C++ Header Interface

#include <nagad.h>

void d01rl_a1w_f_ (

void *&ad_handle,
void (NAG_CALL f)(void *&ad_handle, const nagad_a1w_w_rtype x[], const Integer &nx, nagad_a1w_w_rtype fv[], Integer &iflag, Integer iuser[], nagad_a1w_w_rtype ruser[], void *cpuser),
const nagad_a1w_w_rtype &a, const nagad_a1w_w_rtype &b, const Integer &npts, const nagad_a1w_w_rtype points[], const nagad_a1w_w_rtype &epsabs, const nagad_a1w_w_rtype &epsrel, const Integer &maxsub, nagad_a1w_w_rtype &result, nagad_a1w_w_rtype &abserr, nagad_a1w_w_rtype rinfo[], Integer iinfo[], Integer iuser[], nagad_a1w_w_rtype ruser[], void *cpuser, Integer &ifail)

The routine may be called by the names d01rl_a1w_f or nagf_quad_dim1_fin_brkpts_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01rl_a1w_f is the adjoint version of the primal routine d01rlf.

d01rlf 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,

where the integrand may have local singular behaviour at a finite number of points within the integration interval. For further information see Section 3 in the documentation for d01rlf.

4 References

de Doncker E (1978) An adaptive extrapolation algorithm for automatic integration ACM SIGNUM Newsl. 13(2) 12–18

Malcolm M A and Simpson R B (1976) Local versus global strategies for adaptive quadrature ACM Trans. Math. Software 1 129–146

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

Wynn P (1956) On a device for computing the

e_{m} (S_{n})

transformation Math. Tables Aids Comput. 10 91–96

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01rl_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

The specification of f is:

Fortran Interface

Subroutine f (

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

Integer, Intent (In)	::	nx
Integer, Intent (Inout)	::	iflag, iuser(*)
Type (nagad_a1w_w_rtype), Intent (In)	::	x(nx)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	fv(nx)
Type (c_ptr), Intent (Inout)	::	ad_handle
Type (c_ptr), Intent (In)	::	cpuser

C++ Header Interface

#include <nagad.h>

void f (

void *&ad_handle, const nagad_a1w_w_rtype x[], const Integer &nx, nagad_a1w_w_rtype fv[], Integer &iflag, Integer iuser[], nagad_a1w_w_rtype ruser[], void *cpuser)

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) array Input
3: nx – Integer Input
4: fv – Type (nagad_a1w_w_rtype) array Output
5: iflag – Integer Input/Output
6: iuser – Integer array User Workspace
7: ruser – Type (nagad_a1w_w_rtype) array User Workspace
8: cpuser – Type(c_ptr) User Workspace

3: a – Type (nagad_a1w_w_rtype) Input

4: b – Type (nagad_a1w_w_rtype) Input

5: npts – Integer Input

6: points(npts) – Type (nagad_a1w_w_rtype) array Input

7: epsabs – Type (nagad_a1w_w_rtype) Input

8: epsrel – Type (nagad_a1w_w_rtype) Input

9: maxsub – Integer Input

10: result – Type (nagad_a1w_w_rtype) Output

11: abserr – Type (nagad_a1w_w_rtype) Output

12: rinfo( $4 \times \max (maxsub, npts) + npts + 6$ ) – Type (nagad_a1w_w_rtype) array Output

13: iinfo( $2 \times \max (maxsub, npts) + npts + 4$ ) – Integer array Output

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

15: ruser( $*$ ) – Type (nagad_a1w_w_rtype) array User Workspace

16: cpuser – Type(c_ptr) User Workspace

17: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01rl_a1w_f preserves all error codes from d01rlf 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.

$ifail = - 899$: 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

d01rl_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01rlf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	d01rl_a1w_fe.f90	None	d01rl_a1w_fe.r
C++	d01rl_a1w_hcppe.cpp	None	d01rl_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	d01rl_t1w_fe.f90	None	d01rl_t1w_fe.r
C++	d01rl_t1w_hcppe.cpp	None	d01rl_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	d01rl_p0w_fe.f90	None	d01rl_p0w_fe.r
C++	d01rl_p0w_hcppe.cpp	None	d01rl_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)

d01rl: FL CL CPP AD

© The Numerical Algorithms Group Ltd. 2020