d01pa: FL CL CPP AD

NAG AD Library
d01pa_a1w_f (md_simplex_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)

d01pa: 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

d01pa_a1w_f is the adjoint version of the primal routine d01paf.

2 Specification

Fortran Interface

Subroutine d01pa_a1w_f (

ad_handle, ndim, vert, ldvert, sdvert, f, minord, maxord, finvls, esterr, iuser, ruser, ifail)

Integer, Intent (In)	::	ndim, ldvert, sdvert, maxord
Integer, Intent (Inout)	::	minord, iuser(*), ifail
External	::	f
Type (nagad_a1w_w_rtype), Intent (Inout)	::	vert(ldvert,sdvert), finvls(maxord), ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	esterr
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void d01pa_a1w_f_ (

void *&ad_handle, const Integer &ndim, nagad_a1w_w_rtype vert[], const Integer &ldvert, const Integer &sdvert,
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[]),
Integer &minord, const Integer &maxord, nagad_a1w_w_rtype finvls[], nagad_a1w_w_rtype &esterr, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

The routine may be called by the names d01pa_a1w_f or nagf_quad_md_simplex_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01pa_a1w_f is the adjoint version of the primal routine d01paf.

d01paf returns a sequence of approximations to the integral of a function over a multidimensional simplex, together with an error estimate for the last approximation. For further information see Section 3 in the documentation for d01paf.

4 References

de Doncker E (1979) New Euler–Maclaurin Expansions and their application to quadrature over the

s

-dimensional simplex Math. Comput. 33 1003–1018

Grundmann A and Moller H M (1978) Invariant integration formulas for the

n

-simplex by combinatorial methods SIAM J. Numer. Anal. 15 282–290

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01pa_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: vert(ldvert, sdvert) – Type (nagad_a1w_w_rtype) array Input/Output

4: ldvert – Integer Input

5: sdvert – Integer Input

6: 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 the integrand $f$ at the given point.
5: iuser( $*$ ) – Integer array User Workspace
6: ruser( $*$ ) – Type (nagad_a1w_w_rtype) array User Workspace

7: minord – Integer Input/Output

8: maxord – Integer Input

9: finvls(maxord) – Type (nagad_a1w_w_rtype) array Input/Output

10: esterr – Type (nagad_a1w_w_rtype) Output

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

User workspace.

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

User workspace.

13: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01pa_a1w_f preserves all error codes from d01paf 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

d01pa_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01paf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	d01pa_a1w_fe.f90	None	d01pa_a1w_fe.r
C++	d01pa_a1w_hcppe.cpp	None	d01pa_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	d01pa_t1w_fe.f90	None	d01pa_t1w_fe.r
C++	d01pa_t1w_hcppe.cpp	None	d01pa_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	d01pa_p0w_fe.f90	None	d01pa_p0w_fe.r
C++	d01pa_p0w_hcppe.cpp	None	d01pa_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)

d01pa: FL CL CPP AD

NAG AD Libraryd01pa_a1w_f (md_simplex_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
d01pa_a1w_f (md_simplex_a1w)