NAG AD Library
e01ba (dim1_spline)

e01ba is the AD Library version of the primal routine e01baf. Based (in the C++ interface) on overload resolution, e01ba can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine e01ba_AD_f (

ad_handle, m, x, y, lamda, c, lck, wrk, lwrk, ifail)

Integer, Intent (In)	::	m, lck, lwrk
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x(m), y(m)
ADTYPE, Intent (Out)	::	lamda(lck), c(lck), wrk(lwrk)
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 e01ba (

void *&ad_handle, const Integer &m, const ADTYPE x[], const ADTYPE y[], ADTYPE lamda[], ADTYPE c[], const Integer &lck, ADTYPE wrk[], const Integer &lwrk, 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

e01ba is the AD Library version of the primal routine e01baf.

e01baf determines a cubic spline interpolant to a given set of data. For further information see Section 3 in the documentation for e01baf.

4 References

Cox M G (1975) An algorithm for spline interpolation J. Inst. Math. Appl. 15 95–108

Cox M G (1977) A survey of numerical methods for data and function approximation The State of the Art in Numerical Analysis (ed D A H Jacobs) 627–668 Academic Press

5 Arguments

In addition to the arguments present in the interface of the primal routine, e01ba 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: m – Integer Input
3: x(m) – ADTYPE array Input
4: y(m) – ADTYPE array Input
5: lamda(lck) – ADTYPE array Output
6: c(lck) – ADTYPE array Output
7: lck – Integer Input
8: wrk(lwrk) – ADTYPE array Workspace
9: lwrk – Integer Input
10: ifail – Integer Input/Output

6 Error Indicators and Warnings

e01ba preserves all error codes from e01baf and in addition 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

e01ba is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for e01baf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example sets up data from

7

values of the exponential function in the interval

0

1

. e01ba is then called to compute a spline interpolant to these data.

The spline is evaluated by e02bb, at the data points and at points halfway between each adjacent pair of data points, and the spline values and the values of