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## 1Purpose

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.

## 2Specification

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:
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

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.

## 4References

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

## 5Arguments

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.
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($7×{\mathbf{n}}$) – 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

## 6Error Indicators and Warnings

e01eb preserves all error codes from e01ebf 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

e01eb is not threaded in any implementation.

None.

## 10Example

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

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

### 10.2Tangent 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

### 10.3Passive 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