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.
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:
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types: double, dco::ga1s<double>::type, dco::gt1s<double>::type
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.
3Description
s18de
is the AD Library 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.
Amos D E (1986) Algorithm 644: A portable package for Bessel functions of a complex argument and non-negative order ACM Trans. Math. Software12 265–273
5Arguments
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.
s18de preserves all error codes from s18def and in addition can return:
${\mathbf{ifail}}=-89$
An unexpected AD error has been triggered by this routine. Please
contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.
7Accuracy
Not applicable.
8Parallelism and Performance
s18de
is not threaded in any implementation.
9Further Comments
None.
10Example
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 ${\mathbf{n}}=2$ to evaluate the function for orders fnu and ${\mathbf{fnu}}+1$, and it prints the results. The process is repeated until the end of the input data stream is encountered.