e04ab is the AD Library version of the primal routine e04abf. Based (in the C++ interface) on overload resolution, e04ab can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e04ab_AD_f (

ad_handle, funct, e1, e2, a, b, maxcal, x, f, iuser, ruser, ifail)

Integer, Intent (Inout)	::	maxcal, iuser(*), ifail
ADTYPE, Intent (Inout)	::	e1, e2, a, b, ruser(*)
ADTYPE, Intent (Out)	::	x, f
Type (c_ptr), Intent (Inout)	::	ad_handle
External	::	funct

Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:

when ADTYPE is	Real(kind=nag_wp)	then AD is p0w
when ADTYPE is	Type(nagad_a1w_w_rtype)	then AD is a1w
when ADTYPE is	Type(nagad_t1w_w_rtype)	then AD is t1w

C++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void e04ab (

void *&ad_handle,
void (NAG_CALL funct)(void *&ad_handle, const ADTYPE &xc, ADTYPE &fc, Integer iuser[], ADTYPE ruser[]),
ADTYPE &e1, ADTYPE &e2, ADTYPE &a, ADTYPE &b, Integer &maxcal, ADTYPE &x, ADTYPE &f, const Integer &liuser, Integer iuser[], const Integer &lruser, ADTYPE ruser[], Integer &ifail)

}
}

The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
double,
dco::ga1s<double>::type,
dco::gt1s<double>::type

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

e04ab is the AD Library version of the primal routine e04abf.

e04abf searches for a minimum, in a given finite interval, of a continuous function of a single variable, using function values only. The method (based on quadratic interpolation) is intended for functions which have a continuous first derivative (although it will usually work if the derivative has occasional discontinuities). For further information see Section 3 in the documentation for e04abf.

4 References

Gill P E and Murray W (1973) Safeguarded steplength algorithms for optimization using descent methods NPL Report NAC 37 National Physical Laboratory

5 Arguments

In addition to the arguments present in the interface of the primal routine, e04ab 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 – Pointer to AD Data Input/Output

On entry: a handle to the AD configuration data object, as created by x10aa.

2: funct – Subroutine External Procedure

The specification of funct is:

Fortran Interface

Subroutine funct (

ad_handle, xc, fc, iuser, ruser)

Integer, Intent (Inout)	::	iuser(*)
ADTYPE, Intent (In)	::	xc
ADTYPE, Intent (Inout)	::	ruser(*)
ADTYPE, Intent (Out)	::	fc
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

void funct (

void *&ad_handle, const ADTYPE &xc, ADTYPE &fc, Integer iuser[], ADTYPE ruser[])

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object.
2: xc – ADTYPE Input
3: fc – ADTYPE Output
4: iuser( $*$ ) – Integer array User Workspace
5: ruser( $*$ ) – ADTYPE array User Workspace

3: e1 – ADTYPE Input/Output

4: e2 – ADTYPE Input/Output

5: a – ADTYPE Input/Output

6: b – ADTYPE Input/Output

7: maxcal – Integer Input/Output

8: x – ADTYPE Output

9: f – ADTYPE Output

10: liuser Input

User workspace dimension (C++ only), see x10af to specify the dimension from Fortran.

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

User workspace.

12: lruser Input

User workspace dimension (C++ only), see x10ae to specify the dimension from Fortran.

13: ruser( $*$ ) – ADTYPE array User Workspace

User workspace.

14: ifail – Integer Input/Output

6 Error Indicators and Warnings

e04ab preserves all error codes from e04abf 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.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: 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

e04ab is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e04abf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

A sketch of the function

F (x) = \frac{\sin x}{x}

shows that it has a minimum somewhere in the range

[3.5, 5.0]

. The following program shows how e04ab can be used to obtain a good approximation to the position of a minimum.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	e04ab_a1w_fe.f90	None	e04ab_a1w_fe.r
C++	e04ab_a1w_hcppe.cpp	None	e04ab_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	e04ab_t1w_fe.f90	None	e04ab_t1w_fe.r
C++	e04ab_t1w_hcppe.cpp	None	e04ab_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	e04ab_p0w_fe.f90	None	e04ab_p0w_fe.r
C++	e04ab_p0w_hcppe.cpp	None	e04ab_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E04 (Opt) Chapter Contents

E04 (Opt) Chapter Introduction (FL)

e04ab: FL CL CPP AD

NAG AD Librarye04ab (one_var_func)

▸▿ Contents

1 Purpose