Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

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## 1Purpose

s18de_a1w_f is the adjoint version of the primal routine s18def.

## 2Specification

Fortran Interface
 Subroutine s18de_a1w_f ( ad_handle, fnu, z, n, scal, cy, nz, ifail)
 Integer, Intent (In) :: n Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: nz Type (nagad_a1w_w_rtype), Intent (In) :: fnu Type (nagad_a1w_w_ctype), Intent (In) :: z Type (nagad_a1w_w_ctype), Intent (Out) :: cy(n) Character (1), Intent (In) :: scal Type (c_ptr), Intent (Inout) :: ad_handle
 void s18de_a1w_f_ ( void *&ad_handle, const nagad_a1w_w_rtype &fnu, const nagad_w_rcype &z, const Integer &n, const char *scal, nagad_w_rcype cy[], Integer &nz, Integer &ifail, const Charlen length_scal)
The routine may be called by the names s18de_a1w_f or nagf_specfun_bessel_i_complex_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

s18de_a1w_f is the adjoint version of the primal routine s18def.
s18def returns a sequence of values for the modified Bessel functions ${I}_{\nu +n}\left(z\right)$ for complex $z$, non-negative $\nu$ and $n=0,1,\dots ,N-1$, with an option for exponential scaling. For further information see Section 3 in the documentation for s18def.

## 4References

NIST Digital Library of Mathematical Functions
Amos D E (1986) Algorithm 644: A portable package for Bessel functions of a complex argument and non-negative order ACM Trans. Math. Software 12 265–273

## 5Arguments

In addition to the arguments present in the interface of the primal routine, s18de_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/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: Input
3: z – Type (nagad_a1w_w_ctype) Input
4: n – Integer Input
5: scal – character Input
6: cy(n) – Type (nagad_a1w_w_ctype) array Output
7: nz – Integer Output
8: ifail – Integer Input/Output

## 6Error Indicators and Warnings

s18de_a1w_f preserves all error codes from s18def and in addition can return:
${\mathbf{ifail}}=-89$
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

s18de_a1w_f is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for s18def, modified to demonstrate calling the NAG AD Library.