e01aa is the AD Library version of the primal routine e01aaf. Based (in the C++ interface) on overload resolution, e01aa can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e01aa_AD_f (

ad_handle, a, b, c, n1, n2, n, x, ifail)

Integer, Intent (In)	::	n1, n2, n
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x
ADTYPE, Intent (Inout)	::	a(n+1), b(n+1)
ADTYPE, Intent (Out)	::	c(n*(n+1)/2)
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++ Header Interface

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

void e01aa (

void *&ad_handle, ADTYPE a[], ADTYPE b[], ADTYPE c[], const Integer &n1, const Integer &n2, const Integer &n, const ADTYPE &x, 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

e01aa is the AD Library version of the primal routine e01aaf.

e01aaf interpolates a function of one variable at a given point

x

from a table of function values

y_{i}

evaluated at equidistant or non-equidistant points

x_{i}

, for

i = 1, 2, \dots, n + 1

, using Aitken's technique of successive linear interpolations. For further information see Section 3 in the documentation for e01aaf.

4 References

Fröberg C E (1970) Introduction to Numerical Analysis Addison–Wesley

5 Arguments

In addition to the arguments present in the interface of the primal routine, e01aa 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 – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: a( $n + 1$ ) – ADTYPE array Input/Output
3: b( $n + 1$ ) – ADTYPE array Input/Output
4: c( $n \times (n + 1) / 2$ ) – ADTYPE array Output
5: n1 – Integer Input
6: n2 – Integer Input
7: n – Integer Input
8: x – ADTYPE Input
9: ifail – Integer Input/Output: On entry: must be set to $0$ , $- 1 or 1$ . On exit: any errors are indicated as described in Section 6.

6 Error Indicators and Warnings

There are no specific error codes from e01aaf, however e01aa can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e01aa is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e01aaf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example interpolates at

x = 0.28

the function value of a curve defined by the points

(\begin{array}{r} x_{i} & - 1.00 & - 0.50 & 0.00 & 0.50 & 1.00 & 1.50 \\ y_{i} & 0.00 & - 0.53 & - 1.00 & - 0.46 & 2.00 & 11.09 \end{array}) .

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	e01aa_a1w_fe.f90	e01aa_a1w_fe.d	e01aa_a1w_fe.r
C++	e01aa_a1w_hcppe.cpp	e01aa_a1w_hcppe.d	e01aa_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	e01aa_t1w_fe.f90	e01aa_t1w_fe.d	e01aa_t1w_fe.r
C++	e01aa_t1w_hcppe.cpp	e01aa_t1w_hcppe.d	e01aa_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	e01aa_p0w_fe.f90	e01aa_p0w_fe.d	e01aa_p0w_fe.r
C++	e01aa_p0w_hcppe.cpp	e01aa_p0w_hcppe.d	e01aa_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

E01 (Interp) Chapter Contents

E01 (Interp) Chapter Introduction (FL)

e01aa: FL CL CPP AD

NAG AD Librarye01aa (dim1_aitken)

▸▿ Contents

1 Purpose