g01fc is the AD Library version of the primal routine g01fcf. Based (in the C++ interface) on overload resolution, g01fc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine g01fc_AD_f (

ad_handle, p, df, x, ifail)

Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	p, df
ADTYPE, Intent (Out)	::	x
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++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void g01fc (

void *&ad_handle, const ADTYPE &p, const ADTYPE &df, ADTYPE &x, 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

g01fc is the AD Library version of the primal routine g01fcf.

g01fcf returns the deviate associated with the given lower tail probability of the

χ^{2}

-distribution with real degrees of freedom. For further information see Section 3 in the documentation for g01fcf.

4 References

Best D J and Roberts D E (1975) Algorithm AS 91. The percentage points of the

χ^{2}

distribution Appl. Statist. 24 385–388

Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

5 Arguments

In addition to the arguments present in the interface of the primal routine, g01fc 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 g01fc_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, x.

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: p – ADTYPE Input
3: df – ADTYPE Input
4: x – ADTYPE Output: On exit: the deviate associated with the given lower tail probability of the $χ^{2}$ -distribution with real degrees of freedom.
5: ifail – Integer Input/Output

6 Error Indicators and Warnings

g01fc preserves all error codes from g01fcf and in addition 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.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g01fc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for g01fcf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example reads lower tail probabilities for several

χ^{2}

-distributions, and calculates and prints the corresponding deviates until the end of data is reached.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	g01fc_a1w_fe.f90	g01fc_a1w_fe.d	g01fc_a1w_fe.r
C++	g01fc_a1w_hcppe.cpp	g01fc_a1w_hcppe.d	g01fc_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	g01fc_t1w_fe.f90	g01fc_t1w_fe.d	g01fc_t1w_fe.r
C++	g01fc_t1w_hcppe.cpp	g01fc_t1w_hcppe.d	g01fc_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	g01fc_p0w_fe.f90	g01fc_p0w_fe.d	g01fc_p0w_fe.r
C++	g01fc_p0w_hcppe.cpp	g01fc_p0w_hcppe.d	g01fc_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction (FL)

g01fc: FL CL CPP AD

NAG AD Libraryg01fc (inv_cdf_chisq)

▸▿ Contents

1 Purpose