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## 1Purpose

g01ec is the AD Library version of the primal routine g01ecf. Based (in the C++ interface) on overload resolution, g01ec can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: x, df ADTYPE, Intent (Out) :: p Character (1), Intent (In) :: tail 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

g01ec is the AD Library version of the primal routine g01ecf.
g01ecf returns the lower or upper tail probability for the ${\chi }^{2}$-distribution with real degrees of freedom. For further information see Section 3 in the documentation for g01ecf.

## 4References

NIST Digital Library of Mathematical Functions
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

## 5Arguments

In addition to the arguments present in the interface of the primal routine, g01ec 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 g01ec_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: tail – character Input
3: Input
4: Input
On exit: the lower or upper tail probability for the ${\chi }^{2}$-distribution, depending on the value of tail supplied.
6: ifail – Integer Input/Output

## 6Error Indicators and Warnings

g01ec preserves all error codes from g01ecf 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

g01ec is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for g01ecf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
Values from various ${\chi }^{2}$-distributions are read, the lower tail probabilities calculated, and all these values printed out, until the end of data is reached.

Language Source File Data Results
Fortran g01ec_a1w_fe.f90 g01ec_a1w_fe.d g01ec_a1w_fe.r
C++ g01ec_a1w_hcppe.cpp g01ec_a1w_hcppe.d g01ec_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran g01ec_t1w_fe.f90 g01ec_t1w_fe.d g01ec_t1w_fe.r
C++ g01ec_t1w_hcppe.cpp g01ec_t1w_hcppe.d g01ec_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran g01ec_p0w_fe.f90 g01ec_p0w_fe.d g01ec_p0w_fe.r
C++ g01ec_p0w_hcppe.cpp g01ec_p0w_hcppe.d g01ec_p0w_hcppe.r