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.

## 1Purpose

e04dg_a1w_f is the adjoint version of the primal routine e04dgf.

## 2Specification

Fortran Interface
 Subroutine e04dg_a1w_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) Type (nagad_a1w_w_rtype), Intent (Inout) :: x(n), ruser(*), rwsav(475) Type (nagad_a1w_w_rtype), Intent (Out) :: objf, objgrd(n), work(13*n) Logical, Intent (Inout) :: lwsav(120) Type (c_ptr), Intent (In) :: ad_handle External :: objfun
The routine may be called by the names e04dg_a1w_f or nagf_opt_uncon_conjgrd_comp_a1w.

## 3Description

e04dg_a1w_f is the adjoint 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.

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e04dg_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: n – Integer Input
3: objfun – Subroutine External Procedure
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(*) Type (nagad_a1w_w_rtype), Intent (In) :: x(n) Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: objf, objgrd(n) Type (c_ptr), Intent (In) :: ad_handle
C++ Interface
1: ad_handle – Type (c_ptr) Input
On entry: a handle to the AD configuration data object.
2: mode – Integer Input/Output
3: n – Integer Input
4: Input
5: Output
6: Output
7: nstate – Integer Input
8: iuser – Integer array User Workspace
9: User Workspace
4: iter – Integer Output
5: Output
6: objgrd(n) – Type (nagad_a1w_w_rtype) array Output
7: x(n) – Type (nagad_a1w_w_rtype) array Input/Output
8: iwork($\mathbf{n}+1$) – Integer array Workspace
9: work($13×\mathbf{n}$) – Type (nagad_a1w_w_rtype) array Workspace
10: iuser($*$) – Integer array User Workspace
11: ruser($*$) – Type (nagad_a1w_w_rtype) array User Workspace
12: 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.
13: 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.
14: rwsav($475$) – Type (nagad_a1w_w_rtype) 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.
15: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e04dg_a1w_f preserves all error codes from e04dgf and in addition can return:
$\mathbf{ifail}=-89$
See Section 4.5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 4.5.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

e04dg_a1w_f is not threaded in any implementation.