s15ab is the AD Library version of the primal routine s15abf. Based (in the C++ interface) on overload resolution, s15ab can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine s15ab_AD_f (

ad_handle, x, p, ifail)

Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x
ADTYPE, Intent (Out)	::	p
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 s15ab (

handle_t &ad_handle, const ADTYPE &x, ADTYPE &p, Integer &ifail)

}
}

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.

3 Description

s15ab is the AD Library version of the primal routine s15abf.

s15abf returns the value of the cumulative Normal distribution function,

P (x)

, via the function name. For further information see Section 3 in the documentation for s15abf.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

In addition to the arguments present in the interface of the primal routine, s15ab 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 s15ab_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, p.

1: ad_handle – nag::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: x – ADTYPE Input
3: p – ADTYPE Output: On exit: the value of the cumulative Normal distribution function, $P (x)$ .
4: ifail – Integer Input/Output

6 Error Indicators and Warnings

There are no specific error codes from s15abf, however s15ab can return:

$ifail = - 89$: 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.

$ifail = - 199$: 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.

$ifail = - 444$: A C++ exception was thrown.
The error message will show the details of the C++ exception text.

$ifail = - 899$: 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

s15ab is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for s15abf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	s15ab_a1w_fe.f90	None	s15ab_a1w_fe.r
C++	s15ab_a1w_hcppe.cpp	None	s15ab_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	s15ab_t1w_fe.f90	None	s15ab_t1w_fe.r
C++	s15ab_t1w_hcppe.cpp	None	s15ab_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	s15ab_p0w_fe.f90	None	s15ab_p0w_fe.r
C++	s15ab_p0w_hcppe.cpp	None	s15ab_p0w_hcppe.r

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

S (Specfun) Chapter Contents

S (Specfun) Chapter Introduction (FL)

s15ab: FL CL CPP AD

NAG AD Librarys15ab (cdf_normal)

▸▿ Contents

1 Purpose