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

e01aa_a1w_f is the adjoint version of the primal routine e01aaf.

## 2Specification

Fortran Interface
 Subroutine e01aa_a1w_f ( ad_handle, a, b, c, n1, n2, n, x, ifail)
 Integer, Intent (In) :: n1, n2, n Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x Type (nagad_a1w_w_rtype), Intent (Inout) :: a(n+1), b(n+1) Type (nagad_a1w_w_rtype), Intent (Out) :: c(n*(n+1)/2) Type (c_ptr), Intent (In) :: ad_handle
The routine may be called by the names e01aa_a1w_f or nagf_interp_dim1_aitken_a1w.

## 3Description

e01aa_a1w_f is the adjoint 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 $\mathit{i}=1,2,\dots ,n+1$, using Aitken's technique of successive linear interpolations. For further information see Section 3 in the documentation for e01aaf.

None.

## 5Arguments

In addition to the arguments present in the interface of the primal routine, e01aa_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: a($\mathbf{n}+1$) – Type (nagad_a1w_w_rtype) array Input/Output
3: b($\mathbf{n}+1$) – Type (nagad_a1w_w_rtype) array Input/Output
4: c($\mathbf{n}×\left(\mathbf{n}+1\right)/2$) – Type (nagad_a1w_w_rtype) array Output
5: n1 – Integer Input
6: n2 – Integer Input
7: n – Integer Input
8: Input
9: ifail – Integer Input/Output
On entry: must be set to $\mathrm{0}$, $-\mathrm{1}\text{ or }\mathrm{1}$. On exit: any errors are indicated as described in Section 6.

## 6Error Indicators and Warnings

There are no specific error codes from e01aaf, however e01aa_a1w_f 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

e01aa_a1w_f is not threaded in any implementation.