e01eb is the AD Library version of the primal routine e01ebf. Based (in the C++ interface) on overload resolution, e01eb can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e01eb_AD_f (

m, n, x, y, f, triang, px, py, pf, ifail)

Integer, Intent (In)	::	m, n, triang(7*n)
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x(n), y(n), f(n), px(m), py(m)
ADTYPE, Intent (Out)	::	pf(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

C++ Interface

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

void e01eb (

handle_t &ad_handle, const Integer &m, const Integer &n, const ADTYPE x[], const ADTYPE y[], const ADTYPE f[], const Integer triang[], const ADTYPE px[], const ADTYPE py[], ADTYPE pf[], 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

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

3 Description

e01eb is the AD Library version of the primal routine e01ebf.

e01ebf performs barycentric interpolation, at a given set of points, using a set of function values on a scattered grid and a triangulation of that grid computed by e01eaf. For further information see Section 3 in the documentation for e01ebf.

4 References

Cline A K and Renka R L (1984) A storage-efficient method for construction of a Thiessen triangulation Rocky Mountain J. Math. 14 119–139

Lawson C L (1977) Software for

C^{1}

surface interpolation Mathematical Software III (ed J R Rice) 161–194 Academic Press

Renka R L (1984) Algorithm 624: triangulation and interpolation of arbitrarily distributed points in the plane ACM Trans. Math. Software 10 440–442

Renka R L and Cline A K (1984) A triangle-based

C^{1}

interpolation method Rocky Mountain J. Math. 14 223–237

5 Arguments

In addition to the arguments present in the interface of the primal routine, e01eb 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: m – Integer Input
3: n – Integer Input
4: x(n) – ADTYPE array Input
5: y(n) – ADTYPE array Input
6: f(n) – ADTYPE array Input
7: triang( $7 \times n$ ) – Integer array Input
8: px(m) – ADTYPE array Input
9: py(m) – ADTYPE array Input
10: pf(m) – ADTYPE array Output
11: ifail – Integer Input/Output

6 Error Indicators and Warnings

e01eb preserves all error codes from e01ebf 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

e01eb is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e01ebf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	e01eb_a1w_fe.f90	e01eb_a1w_fe.d	e01eb_a1w_fe.r
C++	e01eb_a1w_hcppe.cpp	e01eb_a1w_hcppe.d	e01eb_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	e01eb_t1w_fe.f90	e01eb_t1w_fe.d	e01eb_t1w_fe.r
C++	e01eb_t1w_hcppe.cpp	e01eb_t1w_hcppe.d	e01eb_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	e01eb_p0w_fe.f90	e01eb_p0w_fe.d	e01eb_p0w_fe.r
C++	e01eb_p0w_hcppe.cpp	e01eb_p0w_hcppe.d	e01eb_p0w_hcppe.r

NAG Library Manual, Mark 28.6

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E01 (Interp) Chapter Contents

E01 (Interp) Chapter Introduction (FL)

e01eb: FL CL CPP AD

NAG AD Librarye01eb (dim2_triang_bary_eval)

▸▿ Contents

1 Purpose