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## 1Purpose

e05jc is the AD Library version of the primal routine e05jcf. Based (in the C++ interface) on overload resolution, e05jc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine e05jc_AD_f ( iopts, comm, lcomm, ifail)
 Integer, Intent (In) :: iopts, lcomm Integer, Intent (Inout) :: ifail ADTYPE, Intent (Inout) :: comm(lcomm) Type (c_ptr), Intent (Inout) :: ad_handle
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:
C++ Interface
#include <dco.hpp>
namespace nag {
 void e05jc ( handle_t &ad_handle, const Integer &iopts, ADTYPE comm[], const Integer &lcomm, 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

## 3Description

e05jc is the AD Library version of the primal routine e05jcf.
e05jcf may be used to supply optional parameters to e05jbf from an external file. The initialization routine e05jaf must have been called before calling e05jcf. For further information see Section 3 in the documentation for e05jcf.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e05jc 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 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: iopts – Integer Input
3: comm(lcomm) – ADTYPE array Communication Array
4: lcomm – Integer Input
5: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e05jc preserves all error codes from e05jcf and in addition can return:
${\mathbf{ifail}}=-89$
See Error Handling in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
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.
${\mathbf{ifail}}=-444$
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 Error Handling in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

e05jc is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for e05jcf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example finds the global minimum of the ‘peaks’ function in two dimensions
 $F(x,y) = 3 (1-x) 2 exp(- x 2 - (y+1) 2 ) -10 ⁢ ( x 5 - x 3 - y 5 ) exp(- x 2 - y 2 ) - 1 3 exp(- (x+1) 2 - y 2 )$
on the box $\left[-3,3\right]×\left[-3,3\right]$.
The function $F$ has several local minima and one global minimum in the given box. The global minimum is approximately located at $\left(0.23,-1.63\right)$, where the function value is approximately $-6.55$.
By specifying an initialization list via list, numpts and initpt we can start e05jb looking close to one of the local minima and check that it really does move away from that point to one of the global minima.
More precisely, we choose $\left(-1,0\right)$ as our initial point (see Section 10.3), and let the initialization list be
 $( −3 −1 3 −3 0 3 ) .$
This example solves the optimization problem using some of the optional parameters described in Section 12 in e05jb.

Language Source File Data Results
Fortran e05jc_a1w_fe.f90 e05jc_a1w_fe.d e05jc_a1w_fe.r
C++ e05jc_a1w_hcppe.cpp e05jc_a1w_hcppe.d e05jc_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran e05jc_t1w_fe.f90 e05jc_t1w_fe.d e05jc_t1w_fe.r
C++ e05jc_t1w_hcppe.cpp e05jc_t1w_hcppe.d e05jc_t1w_hcppe.r

None.