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## 1Purpose

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.

## 2Specification

Fortran Interface
 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:
#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

g01gc is the AD Library version of the primal routine g01gcf.
g01gcf returns the probability associated with the lower tail of the noncentral ${\chi }^{2}$-distribution. For further information see Section 3 in the documentation for g01gcf.

## 4References

NIST Digital Library of Mathematical Functions

## 5Arguments

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.
On entry: a handle to the AD configuration data object, as created by x10aa.
2: Input
3: Input
4: Input
5: Input
6: maxit – Integer Input
On exit: the probability associated with the lower tail of the noncentral ${\chi }^{2}$-distribution.
8: ifail – Integer Input/Output

## 6Error Indicators and Warnings

g01gc preserves all error codes from g01gcf and in addition can return:
${\mathbf{ifail}}=-89$
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
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 Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

g01gc is not threaded in any implementation.

None.

## 10Example

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 ${\chi }^{2}$-distributions, calculates the lower tail probabilities and prints all these values until the end of data is reached.

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

### 10.2Tangent 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

### 10.3Passive 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