Settings help

## 1Purpose

e01bg is the AD Library version of the primal routine e01bgf. Based (in the C++ interface) on overload resolution, e01bg can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

## 2Specification

Fortran Interface
 Subroutine e01bg_AD_f ( n, x, f, d, m, px, pf, pd, ifail)
 Integer, Intent (In) :: n, m Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: x(n), f(n), d(n), px(m) ADTYPE, Intent (Out) :: pf(m), pd(m) 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,
dco::gt1s<dco::gt1s<double>::type>::type,
dco::ga1s<dco::gt1s<double>::type>::type,

## 3Description

e01bg is the AD Library version of the primal routine e01bgf.
e01bgf evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. For further information see Section 3 in the documentation for e01bgf.

## 4References

Fritsch F N (1982) PCHIP final specifications Report UCID-30194 Lawrence Livermore National Laboratory

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e01bg 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: n – Integer Input
3: x(n) – ADTYPE array Input
4: f(n) – ADTYPE array Input
5: d(n) – ADTYPE array Input
6: m – Integer Input
7: px(m) – ADTYPE array Input
8: pf(m) – ADTYPE array Output
9: pd(m) – ADTYPE array Output
10: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e01bg preserves all error codes from e01bgf 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

e01bg is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for e01bgf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example reads in values of n, x, f and d, and calls e01bg to compute the values of the interpolant and its derivative at equally spaced points.

Language Source File Data Results
Fortran e01bg_a1t1w_fe.f90 e01bg_a1t1w_fe.d e01bg_a1t1w_fe.r
Fortran e01bg_a1w_fe.f90 e01bg_a1w_fe.d e01bg_a1w_fe.r
C++ e01bg_a1_algo_dcoe.cpp None e01bg_a1_algo_dcoe.r
C++ e01bg_a1t1_algo_dcoe.cpp None e01bg_a1t1_algo_dcoe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran e01bg_t1w_fe.f90 e01bg_t1w_fe.d e01bg_t1w_fe.r
Fortran e01bg_t2w_fe.f90 e01bg_t2w_fe.d e01bg_t2w_fe.r
C++ e01bg_t1_algo_dcoe.cpp None e01bg_t1_algo_dcoe.r
C++ e01bg_t2_algo_dcoe.cpp None e01bg_t2_algo_dcoe.r

### 10.3Passive mode

Language Source File Data Results
Fortran e01bg_p0w_fe.f90 e01bg_p0w_fe.d e01bg_p0w_fe.r
C++ e01bg_passive_dcoe.cpp None e01bg_passive_dcoe.r