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 (

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++ Interface

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

void e04ab (

handle_t &ad_handle, FUNCT_T &&funct, ADTYPE &e1, ADTYPE &e2, ADTYPE &a, ADTYPE &b, Integer &maxcal, ADTYPE &x, ADTYPE &f, 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 – nag::ad::handle_t Input/Output

On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.

2: funct – Callable Input

funct needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of funct is:

Fortran Interface

Subroutine funct (

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++ Interface

auto funct = [&](

const handle_t &ad_handle, const ADTYPE &xc, ADTYPE &fc)

1: ad_handle – nag::ad::handle_t Input/Output: On entry: a handle to the AD handle object.
2: xc – ADTYPE Input
3: fc – ADTYPE Output
*: iuser( $*$ ) – Integer array User Workspace
*: ruser( $*$ ) – ADTYPE array User Workspace

3: e1 – ADTYPE Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

4: e2 – ADTYPE Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

5: a – ADTYPE Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

6: b – ADTYPE Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

7: maxcal – Integer Input/Output

8: x – ADTYPE Output

9: f – ADTYPE Output

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

User workspace.

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

User workspace.

10: 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 Error Handling in the NAG AD Library Introduction for further information.

$ifail = - 199$: The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.

$ifail = - 444$: 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 Error Handling 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 28.6

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

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 modes

10.2 Tangent modes

10.3 Passive mode

NAG AD Library
e04ab (one_var_func)