g01gc is the AD Library version of the primal routine g01gcf. Based (in the C++ interface) on overload resolution, g01gc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine g01gc_AD_f (

ad_handle, x, df, rlamda, tol, maxit, p, ifail)

Integer, Intent (In)	::	maxit
Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x, df, rlamda, tol
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 g01gc (

handle_t &ad_handle, const ADTYPE &x, const ADTYPE &df, const ADTYPE &rlamda, const ADTYPE &tol, const Integer &maxit, 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

g01gc is the AD Library version of the primal routine g01gcf.

g01gcf returns the probability associated with the lower tail of the noncentral

χ^{2}

-distribution. For further information see Section 3 in the documentation for g01gcf.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

In addition to the arguments present in the interface of the primal routine, g01gc 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 g01gc_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: df – ADTYPE Input
4: rlamda – ADTYPE Input
5: tol – ADTYPE Input
6: maxit – Integer Input
7: p – ADTYPE Output: On exit: the probability associated with the lower tail of the noncentral $χ^{2}$ -distribution.
8: ifail – Integer Input/Output

6 Error Indicators and Warnings

g01gc preserves all error codes from g01gcf and in addition 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

g01gc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for g01gcf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example reads values from various noncentral

χ^{2}

-distributions, calculates the lower tail probabilities and prints all these values until the end of data is reached.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	g01gc_a1w_fe.f90	g01gc_a1w_fe.d	g01gc_a1w_fe.r
C++	g01gc_a1w_hcppe.cpp	g01gc_a1w_hcppe.d	g01gc_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	g01gc_t1w_fe.f90	g01gc_t1w_fe.d	g01gc_t1w_fe.r
C++	g01gc_t1w_hcppe.cpp	g01gc_t1w_hcppe.d	g01gc_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	g01gc_p0w_fe.f90	g01gc_p0w_fe.d	g01gc_p0w_fe.r
C++	g01gc_p0w_hcppe.cpp	g01gc_p0w_hcppe.d	g01gc_p0w_hcppe.r

NAG Library Manual, Mark 30.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction (FL)

g01gc: FL CL CPP AD

NAG AD Libraryg01gc (prob_chisq_noncentral)

▸▿ Contents

1 Purpose