d01bd: FL CL CPP AD

NAG AD Library
d01bd_a1w_f (dim1_fin_smooth_a1w)

Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. 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

Interfaces: FL CL CPP AD

NAG AD Library Introduction

D01 (Quad) Chapter Contents

D01 (Quad) Chapter Introduction (FL)

d01bd: 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

1 Purpose

d01bd_a1w_f is the adjoint version of the primal routine d01bdf.

2 Specification

Fortran Interface

Subroutine d01bd_a1w_f (

ad_handle, f, a, b, epsabs, epsrel, result, abserr, iuser, ruser, ifail)

Integer, Intent (Inout)	::	iuser(*), ifail
External	::	f
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)	::	result, abserr
Type (c_ptr), Intent (In)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void d01bd_a1w_f_ (

void *&ad_handle,
void (NAG_CALL f)(void *&ad_handle, nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[]),
const nagad_a1w_w_rtype &a, const nagad_a1w_w_rtype &b, const nagad_a1w_w_rtype &epsabs, const nagad_a1w_w_rtype &epsrel, nagad_a1w_w_rtype &result, nagad_a1w_w_rtype &abserr, Integer iuser[], nagad_a1w_w_rtype ruser[], Integer &ifail)

The routine may be called by the names d01bd_a1w_f or nagf_quad_dim1_fin_smooth_a1w.

3 Description

d01bd_a1w_f is the adjoint version of the primal routine d01bdf.

d01bdf calculates an approximation to the integral of a function over a finite interval

[a, b]

I = \int_{a}^{b} f (x) d x .

It is non-adaptive and as such is recommended for the integration of ‘smooth’ functions. These exclude integrands with singularities, derivative singularities or high peaks on

[a, b]

, or which oscillate too strongly on

[a, b]

. For further information see Section 3 in the documentation for d01bdf.

4 References

None.

5 Arguments

In addition to the arguments present in the interface of the primal routine, d01bd_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

On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.

2: 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, x, retval, iuser, ruser)

Integer, Intent (Inout)	::	iuser(*)
Type (nagad_a1w_w_rtype), Intent (In)	::	x
Type (nagad_a1w_w_rtype), Intent (Inout)	::	ruser(*)
Type (nagad_a1w_w_rtype), Intent (Out)	::	retval
Type (c_ptr), Intent (In)	::	ad_handle

C++ Interface

#include <nagad.h>

void f (

void *&ad_handle, nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &retval, Integer iuser[], nagad_a1w_w_rtype ruser[])

1: ad_handle – Type (c_ptr) Input: On entry: a handle to the AD configuration data object.
2: x – Type (nagad_a1w_w_rtype) Input
3: retval – Type (nagad_a1w_w_rtype) Output: On exit: the value of $f (x)$ evaluated at x.
4: iuser( $*$ ) – Integer array User Workspace
5: ruser( $*$ ) – Type (nagad_a1w_w_rtype) array User Workspace

3: a – Type (nagad_a1w_w_rtype) Input

4: b – Type (nagad_a1w_w_rtype) Input

5: epsabs – Type (nagad_a1w_w_rtype) Input

6: epsrel – Type (nagad_a1w_w_rtype) Input

7: result – Type (nagad_a1w_w_rtype) Output

8: abserr – Type (nagad_a1w_w_rtype) Output

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

On entry: must be set to

0

- 1 or 1

. On exit: any errors are indicated as described in Section 6.

6 Error Indicators and Warnings

There are no specific error codes from d01bdf, however d01bd_a1w_f can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.5.2 in the NAG AD Library Introduction for further information.