d01rg: FL CL CPP AD

NAG AD Library
d01rg_a1w_f (dim1_fin_gonnet_vec_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)

d01rg: 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

d01rg_a1w_f is the adjoint version of the primal routine d01rgf.

2 Specification

Fortran Interface

Subroutine d01rg_a1w_f (

ad_handle, a, b, f, epsabs, epsrel, dinest, errest, nevals, iuser, ruser, ifail)

Integer, Intent (Inout)	::	iuser(*), ifail
Integer, Intent (Out)	::	nevals
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)	::	dinest, errest
Type (c_ptr), Intent (Inout)	::	ad_handle
External	::	f

C++ Header Interface

#include <nagad.h>

void d01rg_a1w_f_ (

void *&ad_handle, const nagad_a1w_w_rtype &a, const nagad_a1w_w_rtype &b,
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[]),
const nagad_a1w_w_rtype &epsabs, const nagad_a1w_w_rtype &epsrel, nagad_a1w_w_rtype &dinest, nagad_a1w_w_rtype &errest, Integer &nevals, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

The routine may be called by the names d01rg_a1w_f or nagf_quad_dim1_fin_gonnet_vec_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

d01rg_a1w_f is the adjoint version of the primal routine d01rgf.

d01rgf 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 .

The routine is suitable as a general purpose integrator, and can be used when the integrand has singularities and infinities. In particular, the routine can continue if the subroutine f explicitly returns a quiet or signalling NaN or a signed infinity. For further information see Section 3 in the documentation for d01rgf.

4 References

Gonnet P (2010) Increasing the reliability of adaptive quadrature using explicit interpolants ACM Trans. Math. software 37 26

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, d01rg_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: a – Type (nagad_a1w_w_rtype) Input

3: b – Type (nagad_a1w_w_rtype) Input

4: f – Subroutine External Procedure

The specification of f is:

Fortran Interface

Subroutine f (

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

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

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[])

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

5: epsabs – Type (nagad_a1w_w_rtype) Input

6: epsrel – Type (nagad_a1w_w_rtype) Input

7: dinest – Type (nagad_a1w_w_rtype) Output

8: errest – Type (nagad_a1w_w_rtype) Output

9: nevals – Integer Output

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

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

12: ifail – Integer Input/Output

6 Error Indicators and Warnings

d01rg_a1w_f preserves all error codes from d01rgf 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

d01rg_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d01rgf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

Language	Source File	Data	Results
Fortran	d01rg_a1w_fe.f90	d01rg_a1w_fe.d	d01rg_a1w_fe.r
C++	d01rg_a1w_hcppe.cpp	d01rg_a1w_hcppe.d	d01rg_a1w_hcppe.r

10.2 Tangent mode (t1w)

Language	Source File	Data	Results
Fortran	d01rg_t1w_fe.f90	d01rg_t1w_fe.d	d01rg_t1w_fe.r
C++	d01rg_t1w_hcppe.cpp	d01rg_t1w_hcppe.d	d01rg_t1w_hcppe.r

10.3 Passive mode (p0w)

Language	Source File	Data	Results
Fortran	d01rg_p0w_fe.f90	d01rg_p0w_fe.d	d01rg_p0w_fe.r
C++	d01rg_p0w_hcppe.cpp	d01rg_p0w_hcppe.d	d01rg_p0w_hcppe.r