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

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:

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 27.3

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E04 (Opt) Chapter Contents

E04 (Opt) Chapter Introduction (FL)

e04ab: FL CL CPP AD

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

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)