NAG AD Library
s18de (bessel_i_complex)

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1 Purpose

s18de is the AD Library version of the primal routine s18def. Based (in the C++ interface) on overload resolution, s18de can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface
Subroutine s18de_AD_f ( fnu, z, n, scal, cy, nz, ifail)
Integer, Intent (In) :: n
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: nz
ADTYPE, Intent (In) :: fnu
ADCTYPE, Intent (In) :: z
ADCTYPE, Intent (Out) :: cy(n)
Character (1), Intent (In) :: scal
Type (c_ptr), Intent (Inout) :: ad_handle
Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:
when ADTYPE is Real(kind=nag_wp) then AD is p0w
when ADTYPE is Type(nagad_a1w_w_rtype) then AD is a1w
when ADTYPE is Type(nagad_t1w_w_rtype) then AD is t1w
C++ Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
void s18de ( handle_t &ad_handle, const ADTYPE &fnu, const ADCTYPE &z, const Integer &n, const char *scal, ADCTYPE cy[], Integer &nz, Integer &ifail)
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types:
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

s18de is the AD Library version of the primal routine s18def.
s18def returns a sequence of values for the modified Bessel functions Iν+n(z) for complex z, non-negative ν and n=0,1,,N-1, with an option for exponential scaling. For further information see Section 3 in the documentation for s18def.

4 References

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

5 Arguments

In addition to the arguments present in the interface of the primal routine, s18de 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_handlenag::ad::handle_t Input/Output
On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
2: fnuADTYPE Input
3: z – ADCTYPE Input
4: n – Integer Input
5: scal – character Input
6: cy(n) – ADCTYPE array Output
7: nz – Integer Output
8: ifail – Integer Input/Output

6 Error Indicators and Warnings

s18de preserves all error codes from s18def and in addition can return:
An unexpected AD error has been triggered by this routine. Please contact NAG.
See Error Handling in the NAG AD Library Introduction for further information.
The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

s18de is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for s18def, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example prints a caption and then proceeds to read sets of data from the input data stream. The first datum is a value for the order fnu, the second is a complex value for the argument, z, and the third is a character value to set the argument scal. The program calls the routine with n=2 to evaluate the function for orders fnu and fnu+1, and it prints the results. The process is repeated until the end of the input data stream is encountered.

10.1 Adjoint modes

Language Source File Data Results
Fortran s18de_a1w_fe.f90 None s18de_a1w_fe.r
C++ s18de_a1w_hcppe.cpp None s18de_a1w_hcppe.r

10.2 Tangent modes

Language Source File Data Results
Fortran s18de_t1w_fe.f90 None s18de_t1w_fe.r
C++ s18de_t1w_hcppe.cpp None s18de_t1w_hcppe.r

10.3 Passive mode

Language Source File Data Results
Fortran s18de_p0w_fe.f90 None s18de_p0w_fe.r
C++ s18de_p0w_hcppe.cpp None s18de_p0w_hcppe.r