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## 1Purpose

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.

## 2Specification

Fortran Interface
 Subroutine g01fc_AD_f ( 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:
C++ Interface
#include <dco.hpp>
namespace nag {
}
}
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

## 3Description

g01fc is the AD Library version of the primal routine g01fcf.
g01fcf returns the deviate associated with the given lower tail probability of the ${\chi }^{2}$-distribution with real degrees of freedom. For further information see Section 3 in the documentation for g01fcf.

## 4References

Best D J and Roberts D E (1975) Algorithm AS 91. The percentage points of the ${\chi }^{2}$ 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

## 5Arguments

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.
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: Input
3: Input
On exit: the deviate associated with the given lower tail probability of the ${\chi }^{2}$-distribution with real degrees of freedom.
5: ifail – Integer Input/Output

## 6Error Indicators and Warnings

g01fc preserves all error codes from g01fcf and in addition can return:
${\mathbf{ifail}}=-89$
See Error Handling in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
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.
${\mathbf{ifail}}=-444$
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 Error Handling in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

g01fc is not threaded in any implementation.

None.

## 10Example

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 ${\chi }^{2}$-distributions, and calculates and prints the corresponding deviates until the end of data is reached.

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

### 10.2Tangent 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

### 10.3Passive 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