e01ea is the AD Library version of the primal routine e01eaf. Based (in the C++ interface) on overload resolution, e01ea can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e01ea_AD_f (

n, x, y, triang, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	triang(7*n)
ADTYPE, Intent (In)	::	x(n), y(n)
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 e01ea (

handle_t &ad_handle, const Integer &n, const ADTYPE x[], const ADTYPE y[], Integer triang[], 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

e01ea is the AD Library version of the primal routine e01eaf.

e01eaf generates a triangulation for a given set of two-dimensional points using the method of Renka and Cline. For further information see Section 3 in the documentation for e01eaf.

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, e01ea 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: y(n) – ADTYPE array Input
5: triang( $7 \times n$ ) – Integer array Output
6: ifail – Integer Input/Output

6 Error Indicators and Warnings

e01ea preserves all error codes from e01eaf 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

e01ea is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e01eaf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

In this example, e01ea creates a triangulation from a set of data points. e01eb then evaluates the interpolant at a sample of points using this triangulation. Note that this example is not typical of a realistic problem: the number of data points would normally be larger, so that interpolants can be more accurately evaluated at the fine triangulated grid.

This example also demonstrates how to extract useful information from the data structure returned from e01ea. The provided routine convex_hull returns, for the nodes on the boundary of the triangulation, the number of such nodes and the list of indices (ordered in anti-clockwise direction) for these nodes. The provided routine triang2list returns: the number of triangles, the index of the vertices for each triangle, and whether the triangle has one or more edges on the boundary.