Note: _a1w_ denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Further implementations, for example for higher order differentiation or using the tangent linear approach, may become available at later marks of the NAG AD Library. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

## 1Purpose

e01ba_a1w_f is the adjoint version of the primal routine e01baf.

## 2Specification

Fortran Interface
 Subroutine e01ba_a1w_f ( ad_handle, m, x, y, lamda, c, lck, wrk, lwrk, ifail)
 Integer, Intent (In) :: m, lck, lwrk Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x(m), y(m) Type (nagad_a1w_w_rtype), Intent (Out) :: lamda(lck), c(lck), wrk(lwrk) Type (c_ptr), Intent (In) :: ad_handle
The routine may be called by the names e01ba_a1w_f or nagf_interp_dim1_spline_a1w.

## 3Description

e01ba_a1w_f is the adjoint 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.

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e01ba_a1w_f 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 – Type (c_ptr) Input
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: m – Integer Input
3: x(m) – Type (nagad_a1w_w_rtype) array Input
4: y(m) – Type (nagad_a1w_w_rtype) array Input
5: lamda(lck) – Type (nagad_a1w_w_rtype) array Output
6: c(lck) – Type (nagad_a1w_w_rtype) array Output
7: lck – Integer Input
8: wrk(lwrk) – Type (nagad_a1w_w_rtype) array Workspace
9: lwrk – Integer Input
10: ifail – Integer Input/Output

## 6Error Indicators and Warnings

e01ba_a1w_f preserves all error codes from e01baf and in addition can return:
$\mathbf{ifail}=-89$
See Section 4.5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 4.5.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

e01ba_a1w_f is not threaded in any implementation.