Settings help

## 1Purpose

s01ba is the AD Library version of the primal routine s01baf. Based (in the C++ interface) on overload resolution, s01ba can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine s01ba_AD_f ( x, lnx1, ifail)
 Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: x ADTYPE, Intent (Out) :: lnx1 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 {
}
}
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

s01ba is the AD Library version of the primal routine s01baf.
s01baf returns a value of the shifted logarithmic function, $\mathrm{ln}\left(1+x\right)$, via the function name. For further information see Section 3 in the documentation for s01baf.

## 4References

Lyusternik L A, Chervonenkis O A and Yanpolskii A R (1965) Handbook for Computing Elementary Functions p. 57 Pergamon Press

## 5Arguments

In addition to the arguments present in the interface of the primal routine, s01ba 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.
Note that the primal routine is a function whereas s01ba_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, lnx1.
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: Input
On exit: the value of the shifted logarithmic function, $\mathrm{ln}\left(1+x\right)$.
4: ifail – Integer Input/Output

## 6Error Indicators and Warnings

s01ba preserves all error codes from s01baf 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

s01ba is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for s01baf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
The example program reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.

Language Source File Data Results
Fortran s01ba_a1w_fe.f90 s01ba_a1w_fe.d s01ba_a1w_fe.r
C++ s01ba_a1w_hcppe.cpp s01ba_a1w_hcppe.d s01ba_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran s01ba_t1w_fe.f90 s01ba_t1w_fe.d s01ba_t1w_fe.r
C++ s01ba_t1w_hcppe.cpp s01ba_t1w_hcppe.d s01ba_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran s01ba_p0w_fe.f90 s01ba_p0w_fe.d s01ba_p0w_fe.r
C++ s01ba_p0w_hcppe.cpp s01ba_p0w_hcppe.d s01ba_p0w_hcppe.r