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## 1Purpose

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.

## 2Specification

Fortran Interface
 Subroutine e04ab_AD_f ( ad_handle, funct, e1, e2, a, b, maxcal, x, f, iuser, ruser, ifail)
 Integer, Intent (Inout) :: maxcal, iuser(*), ifail ADTYPE, Intent (Inout) :: e1, e2, a, b, ruser(*) ADTYPE, Intent (Out) :: x, f Type (c_ptr), Intent (Inout) :: ad_handle External :: funct
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:
#include <dco.hpp>
namespace nag {
}
}
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

## 3Description

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.

## 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 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.
On entry: a handle to the AD configuration data object, as created by x10aa.
2: funct – Subroutine External Procedure
The specification of funct is:
Fortran Interface
 Subroutine funct ( ad_handle, xc, fc, iuser, ruser)
 Integer, Intent (Inout) :: iuser(*) ADTYPE, Intent (In) :: xc ADTYPE, Intent (Inout) :: ruser(*) ADTYPE, Intent (Out) :: fc Type (c_ptr), Intent (Inout) :: ad_handle
On entry: a handle to the AD configuration data object.
2: Input
3: Output
4: iuser($*$) – Integer array User Workspace
5: ruser($*$)ADTYPE 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: liuser Input
User workspace dimension (C++ only), see x10af to specify the dimension from Fortran.
11: iuser($*$) – Integer array User Workspace
User workspace.
12: lruser Input
User workspace dimension (C++ only), see x10ae to specify the dimension from Fortran.
13: ruser($*$) – ADTYPE array User Workspace
User workspace.
14: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e04ab 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.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
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 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.
Description of the primal example.
A sketch of the function
 $F(x)=sin⁡xx$
shows that it has a minimum somewhere in the range $\left[3.5,5.0\right]$. The following program shows how e04ab can be used to obtain a good approximation to the position of a minimum.

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

### 10.2Tangent 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

### 10.3Passive 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