# NAG AD Library Routine Document

## e01bg_a1w_f (dim1_monotonic_deriv_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

e01bg_a1w_f is the adjoint version of the primal routine e01bgf .

## 2Specification

Fortran Interface
 Subroutine e01bg_a1w_f ( ad_handle, n, x, f, d, m, px, pf, pd, ifail)
 Integer, Intent (In) :: n, m Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x(n), f(n), d(n), px(m) Type (nagad_a1w_w_rtype), Intent (Out) :: pf(m), pd(m) Type (c_ptr), Intent (In) :: ad_handle
 void e01bg_a1w_f_ ( void *&ad_handle, const Integer &n, nagad_a1w_w_rtype x[], nagad_a1w_w_rtype f[], nagad_a1w_w_rtype d[], const Integer &m, nagad_a1w_w_rtype px[], nagad_a1w_w_rtype pf[], nagad_a1w_w_rtype pd[], Integer &ifail)

## 3Description

e01bgf evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. For further information see Section 3 in the documentation for e01bgf .

None.

## 5Arguments

e01bg_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.
• nn, x, f and d must be unchanged from the previous call of routine.
• xn, x, f and d must be unchanged from the previous call of routine.
• fn, x, f and d must be unchanged from the previous call of routine.
• dn, x, f and d must be unchanged from the previous call of routine.
• m$m$, the number of points at which the interpolant is to be evaluated.
• px – the $m$ values of $x$ at which the interpolant is to be evaluated.
• pf – on exit: $\mathbf{pf}\left(\mathit{i}\right)$ contains the value of the interpolant evaluated at the point $\mathbf{px}\left(\mathit{i}\right)$, for $\mathit{i}=\mathrm{1},2, \dots ,m$.
• pd – on exit: $\mathbf{pd}\left(\mathit{i}\right)$ contains the first derivative of the interpolant evaluated at the point $\mathbf{px}\left(\mathit{i}\right)$, for $\mathit{i}=\mathrm{1},2, \dots ,m$.
• 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

e01bg_a1w_f preserves all error codes from e01bgf 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

e01bg_a1w_f is not threaded in any implementation.