Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

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## 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 (Inout) :: ad_handle External :: funct
The routine may be called by the names e04ab_a1w_f or nagf_opt_one_var_func_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 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.

## 4References

Gill P E and Murray W (1973) Safeguarded steplength algorithms for optimization using descent methods NPL Report NAC 37 National Physical Laboratory

## 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/Output
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 (Inout) :: ad_handle
1: ad_handle – Type (c_ptr) Input/Output
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 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

e04ab_a1w_f is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for e04abf, modified to demonstrate calling the NAG AD Library.