NAG AD Library
d01fb_a1w_f (md_gauss_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.

Keyword Search:

NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01fb: FL CL CPP AD

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Adjoint mode (a1w)

10.2 Tangent mode (t1w)

10.3 Passive mode (p0w)

1 Purpose

d01fb_a1w_f is the adjoint version of the primal routine d01fbf.

2 Specification

Fortran Interface

Subroutine d01fb_a1w_f (

ad_handle, ndim, nptvec, lwa, weight, abscis, f, mdint, iuser, ruser, ifail)

Integer, Intent (In)	::	ndim, nptvec(ndim), lwa
Integer, Intent (Inout)	::	iuser(*), ifail
External	::	f
Type (nagad_a1w_w_rtype), Intent (In)	::	weight(lwa), abscis(lwa)
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	mdint
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void d01fb_a1w_f_ (

void *&ad_handle, const Integer &ndim, const Integer nptvec[], const Integer &lwa, const nagad_a1w_w_rtype weight[], const nagad_a1w_w_rtype abscis[],
void (NAG_CALL f)(void *&ad_handle, const Integer &ndim, const nagad_a1w_w_rtype x[], nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[]),
nagad_a1w_w_rtype &mdint, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

The routine may be called by the names d01fb_a1w_f or nagf_quad_md_gauss_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01fb_a1w_f is the adjoint version of the primal routine d01fbf.

d01fbf computes an estimate of a multidimensional integral (from

1

20

dimensions), given the analytic form of the integrand and suitable Gaussian weights and abscissae. For further information see Section 3 in the documentation for d01fbf.

4 References

Davis P J and Rabinowitz P (1975) Methods of Numerical Integration Academic Press

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01fb_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.

Note that the primal routine is a function whereas d01fb_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, mdint.

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: ndim – Integer Input

3: nptvec(ndim) – Integer array Input

4: lwa – Integer Input

5: weight(lwa) – Type (nagad_a1w_w_rtype) array Input

6: abscis(lwa) – Type (nagad_a1w_w_rtype) array Input

7: 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, ndim, x, retval, iuser, ruser)

Integer, Intent (In)	::	ndim
Integer, Intent (Inout)	::	iuser(*)
Type (nagad_a1w_w_rtype), Intent (In)	::	x(ndim)
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 Integer &ndim, 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: ndim – Integer Input
3: x – Type (nagad_a1w_w_rtype) array Input
4: retval – Type (nagad_a1w_w_rtype) Output: On exit: the value of $f (x)$ evaluated at x.
5: iuser( $*$ ) – Integer array User Workspace
6: ruser( $*$ ) – Type (nagad_a1w_w_rtype) array User Workspace

8: mdint – Type (nagad_a1w_w_rtype) Output

On exit: the estimate of the integral.

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

6 Error Indicators and Warnings

d01fb_a1w_f preserves all error codes from d01fbf 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.