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.

2 Specification

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:

when ADTYPE is	Real(kind=nag_wp)	then AD is p0w
when ADTYPE is	Type(nagad_a1w_w_rtype)	then AD is a1w
when ADTYPE is	Type(nagad_t1w_w_rtype)	then AD is t1w
when ADTYPE is	Type(nagad_a1t1w_w_rtype)	then AD is a1t1w
when ADTYPE is	Type(nagad_t2w_w_rtype)	then AD is t2w

C++ Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void e01bg (

handle_t &ad_handle, const Integer &n, const ADTYPE x[], const ADTYPE f[], const ADTYPE d[], const Integer &m, const ADTYPE px[], ADTYPE pf[], ADTYPE pd[], 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,
dco::gt1s<dco::gt1s<double>::type>::type,
dco::ga1s<dco::gt1s<double>::type>::type,

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

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.

4 References

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

5 Arguments

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.

1: ad_handle – nag::ad::handle_t Input/Output: 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

6 Error Indicators and Warnings

e01bg preserves all error codes from e01bgf and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Error Handling in the NAG AD Library Introduction for further information.

$ifail = - 199$: 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.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e01bg is not threaded in any implementation.

9 Further Comments

None.

10 Example

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.

10.1 Adjoint modes

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

10.2 Tangent 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