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## 1Purpose

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.

## 2Specification

Fortran Interface
 Subroutine e01ba_AD_f ( 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:
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

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.

## 4References

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

## 5Arguments

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.
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: 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

## 6Error Indicators and Warnings

e01ba preserves all error codes from e01baf 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

e01ba is not threaded in any implementation.

None.

## 10Example

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 $0$ to $1$. 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 ${e}^{x}$ are printed out.

Language Source File Data Results
Fortran e01ba_a1w_fe.f90 None e01ba_a1w_fe.r
C++ e01ba_a1w_hcppe.cpp None e01ba_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran e01ba_t1w_fe.f90 None e01ba_t1w_fe.r
C++ e01ba_t1w_hcppe.cpp None e01ba_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran e01ba_p0w_fe.f90 None e01ba_p0w_fe.r
C++ e01ba_p0w_hcppe.cpp None e01ba_p0w_hcppe.r