e04dg is the AD Library version of the primal routine e04dgf. Based (in the C++ interface) on overload resolution, e04dg can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e04dg_AD_f (

ad_handle, n, objfun, iter, objf, objgrd, x, iwork, work, iuser, ruser, lwsav, iwsav, rwsav, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	iuser(*), iwsav(610), ifail
Integer, Intent (Out)	::	iter, iwork(n+1)
ADTYPE, Intent (Inout)	::	x(n), ruser(*), rwsav(475)
ADTYPE, Intent (Out)	::	objf, objgrd(n), work(13*n)
Logical, Intent (Inout)	::	lwsav(120)
Type (c_ptr), Intent (Inout)	::	ad_handle
External	::	objfun

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 OBJFUN_T>

void e04dg (

handle_t &ad_handle, const Integer &n, OBJFUN_T &&objfun, Integer &iter, ADTYPE &objf, ADTYPE objgrd[], ADTYPE x[], Integer iwork[], ADTYPE work[], logical lwsav[], Integer iwsav[], ADTYPE rwsav[], 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

e04dg is the AD Library version of the primal routine e04dgf.

e04dgf minimizes an unconstrained nonlinear function of several variables using a pre-conditioned, limited memory quasi-Newton conjugate gradient method. First derivatives (or an ‘acceptable’ finite difference approximation to them) are required. It is intended for use on large scale problems. For further information see Section 3 in the documentation for e04dgf.

4 References

Gill P E and Murray W (1979) Conjugate-gradient methods for large-scale nonlinear optimization Technical Report SOL 79-15 Department of Operations Research, Stanford University

Gill P E, Murray W and Wright M H (1981) Practical Optimization Academic Press

5 Arguments

In addition to the arguments present in the interface of the primal routine, e04dg 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: n – Integer Input

3: objfun – Callable Input

objfun 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 objfun is:

Fortran Interface

Subroutine objfun (

ad_handle, mode, n, x, objf, objgrd, nstate, iuser, ruser)

Integer, Intent (In)	::	n, nstate
Integer, Intent (Inout)	::	mode, iuser(*)
ADTYPE, Intent (In)	::	x(n)
ADTYPE, Intent (Inout)	::	ruser(*)
ADTYPE, Intent (Out)	::	objf, objgrd(n)
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Interface

auto objfun = [&](

const handle_t &ad_handle, Integer &mode, const Integer &n, const ADTYPE x[], ADTYPE &objf, ADTYPE objgrd[], const Integer &nstate)

1: ad_handle – nag::ad::handle_t Input/Output: On entry: a handle to the AD handle object.
2: mode – Integer Input/Output
3: n – Integer Input
4: x – ADTYPE array Input
5: objf – ADTYPE Output
6: objgrd – ADTYPE array Output
7: nstate – Integer Input
*: iuser – Integer array User Workspace
*: ruser – ADTYPE array User Workspace

4: iter – Integer Output

5: objf – ADTYPE Output

6: objgrd(n) – ADTYPE array Output

7: x(n) – ADTYPE array Input/Output

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

8: iwork( $n + 1$ ) – Integer array Workspace

9: work( $13 \times n$ ) – ADTYPE array Workspace

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

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

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

10: lwsav( $120$ ) – logical array Communication Array

The arrays lwsav, iwsav and rwsav must not be altered between calls to any of the routines routine, routine, routine or routine.

11: iwsav( $610$ ) – Integer array Communication Array

The arrays lwsav, iwsav and rwsav must not be altered between calls to any of the routines routine, routine, routine or routine.

12: rwsav( $475$ ) – ADTYPE array Communication Array

The arrays lwsav, iwsav and rwsav must not be altered between calls to any of the routines routine, routine, routine or routine.

13: ifail – Integer Input/Output

6 Error Indicators and Warnings

e04dg preserves all error codes from e04dgf 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

e04dg is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e04dgf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example finds a minimum of the function

F = e^{x_{1}} (4 x_{1}^{2} + 2 x_{2}^{2} + 4 x_{1} x_{2} + 2 x_{2} + 1) .

The initial point is

x_{0} = {(- 1.0, 1.0)}^{T},

and

F (x_{0}) = 1.8394

(to five figures).

The optimal solution is

x^{*} = {(0.5, - 1.0)}^{T},

and

F (x^{*}) = 0

The document for e04dj includes an example program to solve the same problem using some of the optional parameters described in Section 12.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	e04dg_a1w_fe.f90	e04dg_a1w_fe.d	e04dg_a1w_fe.r
C++	e04dg_a1w_hcppe.cpp	e04dg_a1w_hcppe.d	e04dg_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	e04dg_t1w_fe.f90	e04dg_t1w_fe.d	e04dg_t1w_fe.r
C++	e04dg_t1w_hcppe.cpp	e04dg_t1w_hcppe.d	e04dg_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	e04dg_p0w_fe.f90	e04dg_p0w_fe.d	e04dg_p0w_fe.r
C++	e04dg_p0w_hcppe.cpp	e04dg_p0w_hcppe.d	e04dg_p0w_hcppe.r

NAG Library Manual, Mark 29.3

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E04 (Opt) Chapter Contents

E04 (Opt) Chapter Introduction (FL)

e04dg: FL CL CPP AD

NAG AD Librarye04dg (uncon_conjgrd_comp)

▸▿ 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
e04dg (uncon_conjgrd_comp)