d01fc: FL CL CPP AD

NAG AD Library
d01fc_a1w_f (md_adapt_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)

d01fc: 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

d01fc_a1w_f is the adjoint version of the primal routine d01fcf.

2 Specification

Fortran Interface

Subroutine d01fc_a1w_f (

ad_handle, ndim, a, b, minpts, maxpts, f, eps, acc, lenwrk, wrkstr, finval, iuser, ruser, ifail)

Integer, Intent (In)	::	ndim, maxpts, lenwrk
Integer, Intent (Inout)	::	minpts, iuser(*), ifail
External	::	f
Type (nagad_a1w_w_rtype), Intent (In)	::	a(ndim), b(ndim), eps
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	acc, wrkstr(lenwrk), finval
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void d01fc_a1w_f_ (

void *&ad_handle, const Integer &ndim, const nagad_a1w_w_rtype a[], const nagad_a1w_w_rtype b[], Integer &minpts, const Integer &maxpts,
void (NAG_CALL f)(void *&ad_handle, const Integer &ndim, const nagad_a1w_w_rtype z[], nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[]),
const nagad_a1w_w_rtype &eps, nagad_a1w_w_rtype &acc, const Integer &lenwrk, nagad_a1w_w_rtype wrkstr[], nagad_a1w_w_rtype &finval, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

The routine may be called by the names d01fc_a1w_f or nagf_quad_md_adapt_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01fc_a1w_f is the adjoint version of the primal routine d01fcf.

d01fcf attempts to evaluate a multidimensional integral (up to

15

dimensions), with constant and finite limits, to a specified relative accuracy, using an adaptive subdivision strategy. For further information see Section 3 in the documentation for d01fcf.

4 References

Genz A C and Malik A A (1980) An adaptive algorithm for numerical integration over an N-dimensional rectangular region J. Comput. Appl. Math. 6 295–302

van Dooren P and de Ridder L (1976) An adaptive algorithm for numerical integration over an N-dimensional cube J. Comput. Appl. Math. 2 207–217

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01fc_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: ndim – Integer Input

3: a(ndim) – Type (nagad_a1w_w_rtype) array Input

4: b(ndim) – Type (nagad_a1w_w_rtype) array Input

5: minpts – Integer Input/Output

6: maxpts – Integer 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, z, retval, iuser, ruser)

Integer, Intent (In)	::	ndim
Integer, Intent (Inout)	::	iuser(*)
Type (nagad_a1w_w_rtype), Intent (In)	::	z(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 z[], 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: z – Type (nagad_a1w_w_rtype) array Input
4: retval – Type (nagad_a1w_w_rtype) Output: On exit: the value of the integrand $f$ at the given point.
5: iuser( $*$ ) – Integer array User Workspace
6: ruser( $*$ ) – Type (nagad_a1w_w_rtype) array User Workspace

8: eps – Type (nagad_a1w_w_rtype) Input

9: acc – Type (nagad_a1w_w_rtype) Output

10: lenwrk – Integer Input

11: wrkstr(lenwrk) – Type (nagad_a1w_w_rtype) array Workspace

12: finval – Type (nagad_a1w_w_rtype) Output

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

User workspace.

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

User workspace.

15: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01fc_a1w_f preserves all error codes from d01fcf 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

d01fc_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01fcf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	d01fc_a1w_fe.f90	None	d01fc_a1w_fe.r
C++	d01fc_a1w_hcppe.cpp	None	d01fc_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	d01fc_t1w_fe.f90	None	d01fc_t1w_fe.r
C++	d01fc_t1w_hcppe.cpp	None	d01fc_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	d01fc_p0w_fe.f90	None	d01fc_p0w_fe.r
C++	d01fc_p0w_hcppe.cpp	None	d01fc_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)

d01fc: FL CL CPP AD

NAG AD Libraryd01fc_a1w_f (md_adapt_a1w)

▸▿ 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)

NAG AD Library
d01fc_a1w_f (md_adapt_a1w)