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

e04ab_a1w_f is the adjoint version of the primal routine e04abf.

## 2Specification

Fortran Interface
 Subroutine e04ab_a1w_f ( ad_handle, funct, e1, e2, a, b, maxcal, x, f, iuser, ruser, ifail)
 Integer, Intent (Inout) :: maxcal, iuser(*), ifail Type (nagad_a1w_w_rtype), Intent (Inout) :: e1, e2, a, b, ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: x, f Type (c_ptr), Intent (In) :: ad_handle External :: funct
The routine may be called by the names e04ab_a1w_f or nagf_opt_one_var_func_a1w.

## 3Description

e04ab_a1w_f is the adjoint 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.

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e04ab_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: funct – Subroutine External Procedure
The specification of funct is:
Fortran Interface
 Subroutine funct ( ad_handle, xc, fc, iuser, ruser)
 Integer, Intent (Inout) :: iuser(*) Type (nagad_a1w_w_rtype), Intent (In) :: xc Type (nagad_a1w_w_rtype), Intent (Inout) :: ruser(*) Type (nagad_a1w_w_rtype), Intent (Out) :: fc 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: Input
3: Output
4: iuser($*$) – Integer array User Workspace
5: ruser($*$)Type (nagad_a1w_w_rtype) array User Workspace
3: Input/Output
4: Input/Output
5: Input/Output
6: Input/Output
7: maxcal – Integer Input/Output
8: Output
9: Output
10: iuser($*$) – Integer array User Workspace
User workspace.
11: ruser($*$) – Type (nagad_a1w_w_rtype) array User Workspace
User workspace.
12: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e04ab_a1w_f preserves all error codes from e04abf 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

e04ab_a1w_f is not threaded in any implementation.