NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
S (Specfun) Chapter Contents
S (Specfun) Chapter Introduction (FL)
s15ad:  FL   CL   CPP   AD 

NAG AD Library
s15ad_a1w_f (erfc_real_a1w)

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.
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
S (Specfun) Chapter Contents
S (Specfun) Chapter Introduction (FL)
s15ad:  FL   CL   CPP   AD 

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© The Numerical Algorithms Group Ltd. 2020
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1 Purpose

s15ad_a1w_f is the adjoint version of the primal routine s15adf.

2 Specification

Fortran Interface
Subroutine s15ad_a1w_f ( ad_handle, x, res, ifail)
Integer, Intent (Inout) :: ifail
Type (nagad_a1w_w_rtype), Intent (In) :: x
Type (nagad_a1w_w_rtype), Intent (Out) :: res
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void s15ad_a1w_f_ ( void *&ad_handle, const nagad_a1w_w_rtype &x, nagad_a1w_w_rtype &res, Integer &ifail)
The routine may be called by the names s15ad_a1w_f or nagf_specfun_erfc_real_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

s15ad_a1w_f is the adjoint version of the primal routine s15adf.
s15adf returns the value of the complementary error function, erfc(x), via the function name. For further information see Section 3 in the documentation for s15adf.

4 References

NIST Digital Library of Mathematical Functions
Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637

5 Arguments

In addition to the arguments present in the interface of the primal routine, s15ad_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.
Note that the primal routine is a function whereas s15ad_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, res.
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: x – Type (nagad_a1w_w_rtype) Input
3: res – Type (nagad_a1w_w_rtype) Output
On exit: the value of the complementary error function, erfc(x).
4: ifail – Integer Input/Output

6 Error Indicators and Warnings

There are no specific error codes from s15adf, however s15ad_a1w_f can return:
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.
ifail=-899
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

s15ad_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for s15adf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

LanguageSource FileDataResults
Fortrans15ad_a1w_fe.f90Nones15ad_a1w_fe.r
C++s15ad_a1w_hcppe.cppNones15ad_a1w_hcppe.r

10.2 Tangent mode (t1w)

LanguageSource FileDataResults
Fortrans15ad_t1w_fe.f90Nones15ad_t1w_fe.r
C++s15ad_t1w_hcppe.cppNones15ad_t1w_hcppe.r

10.3 Passive mode (p0w)

LanguageSource FileDataResults
Fortrans15ad_p0w_fe.f90Nones15ad_p0w_fe.r
C++s15ad_p0w_hcppe.cppNones15ad_p0w_hcppe.r
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
S (Specfun) Chapter Contents
S (Specfun) Chapter Introduction (FL)
s15ad:  FL   CL   CPP   AD 
© The Numerical Algorithms Group Ltd. 2020