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## 1Purpose

e04tj is the AD Library version of the primal routine e04tjf. Based (in the C++ interface) on overload resolution, e04tj can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine e04tj_AD_f ( handle, idlc, icolbj, bij, ifail)
 Integer, Intent (In) :: idlc, icolbj Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: bij Type (c_ptr), Intent (Inout) :: ad_handle Type (c_ptr), Intent (In) :: 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 e04tj ( handle_t &ad_handle, void *handle, const Integer &idlc, const Integer &icolbj, const ADTYPE &bij, 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

e04tj is the AD Library version of the primal routine e04tjf.
e04tjf is a part of the NAG optimization modelling suite and sets or modifies a single element in the linear constraint matrix of the problem. For further information see Section 3 in the documentation for e04tjf.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e04tj 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: handle – Type(c_ptr) Input
3: idlc – Integer Input
4: icolbj – Integer Input
5: Input
6: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e04tj preserves all error codes from e04tjf 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

e04tj is not threaded in any implementation.