# NAG AD Library Routine Document

## e01be_a1w_f (dim1_monotonic_a1w)

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 routine name and corresponding argument types is described in the NAG AD Library Introduction.

## 1Purpose

e01be_a1w_f is the adjoint version of the primal routine e01bef .

## 2Specification

Fortran Interface
 Subroutine e01be_a1w_f ( ad_handle, n, x, f, d, ifail)
 Integer, Intent (In) :: n Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x(n), f(n) Type (nagad_a1w_w_rtype), Intent (Out) :: d(n) Type (c_ptr), Intent (In) :: ad_handle

## 3Description

e01bef computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. For further information see Section 3 in the documentation for e01bef .

None.

## 5Arguments

e01be_a1w_f provides access to all the arguments available in the primal routine. There are also additional arguments specific to AD. A tooltip popup for each argument can be found by hovering over the argument name in Section 2 and a summary of the arguments are provided below:
• ad_handle – a handle to the AD configuration data object, as created by x10aa_a1w_f.
• n$n$, the number of data points.
• x$\mathbf{x}\left(\mathit{r}\right)$ must be set to ${x}_{\mathit{r}}$, the $\mathit{r}$th value of the independent variable (abscissa), for $\mathit{r}=\mathrm{1},2, \dots ,n$.
• f$\mathbf{f}\left(\mathit{r}\right)$ must be set to ${f}_{\mathit{r}}$, the $\mathit{r}$th value of the dependent variable (ordinate), for $\mathit{r}=\mathrm{1},2, \dots ,n$.
• d – on exit: estimates of derivatives at the data points.
• ifail – on entry: ifail must be set to $\mathrm{0}$, $-\mathrm{1}\text{ or }\mathrm{1}$. on exit: ifail = 0 unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

e01be_a1w_f preserves all error codes from e01bef and in addition can return:
$\mathbf{ifail}=-89$
See Section 5.2 in the NAG AD Library Introduction for further information.
$\mathbf{ifail}=-899$
Dynamic memory allocation failed for AD.
See Section 5.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

e01be_a1w_f is not threaded in any implementation.