# NAG AD Library Routine Document

## e02bb_a1w_f (dim1_spline_eval_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

e02bb_a1w_f is the adjoint version of the primal routine e02bbf .

## 2Specification

Fortran Interface
 Subroutine e02bb_a1w_f ( ad_handle, ncap7, lamda, c, x, s, ifail)
 Integer, Intent (In) :: ncap7 Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: lamda(ncap7), c(ncap7), x Type (nagad_a1w_w_rtype), Intent (Out) :: s Type (c_ptr), Intent (In) :: ad_handle

## 3Description

e02bbf evaluates a cubic spline from its B-spline representation. For further information see Section 3 in the documentation for e02bbf .

None.

## 5Arguments

e02bb_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.
• ncap7$\stackrel{-}{n}+\mathrm{7}$, where $\stackrel{-}{n}$ is the number of intervals (one greater than the number of interior knots, i.e., the knots strictly within the range ${\lambda }_{\mathrm{4}}$ to ${\lambda }_{\stackrel{-}{n}+\mathrm{4}}$) over which the spline is defined.
• lamda$\mathbf{lamda}\left(\mathit{j}\right)$ must be set to the value of the $\mathit{j}$th member of the complete set of knots, ${\lambda }_{\mathit{j}}$, for $\mathit{j}=\mathrm{1},2, \dots ,\stackrel{-}{n}+\mathrm{7}$.
• c – the coefficient ${c}_{\mathit{i}}$ of the B-spline ${N}_{\mathit{i}}\left(x\right)$, for $\mathit{i}=\mathrm{1},2, \dots ,\stackrel{-}{n}+\mathrm{3}$.
• x – the argument $x$ at which the cubic spline is to be evaluated.
• s – on exit: the value of the spline, $s\left(x\right)$.
• 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

e02bb_a1w_f preserves all error codes from e02bbf 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

e02bb_a1w_f is not threaded in any implementation.