# NAG AD Libraryg01ec_a1w_f (prob_chisq_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.

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## 1Purpose

g01ec_a1w_f is the adjoint version of the primal routine g01ecf.

## 2Specification

Fortran Interface
 Subroutine g01ec_a1w_f ( ad_handle, tail, x, df, p, ifail)
 Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: x, df Type (nagad_a1w_w_rtype), Intent (Out) :: p Character (1), Intent (In) :: tail Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
 void g01ec_a1w_f_ ( void *&ad_handle, const char *tail, const nagad_a1w_w_rtype &x, const nagad_a1w_w_rtype &df, nagad_a1w_w_rtype &p, Integer &ifail, const Charlen length_tail)
The routine may be called by the names g01ec_a1w_f or nagf_stat_prob_chisq_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

g01ec_a1w_f is the adjoint 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_a1w_f 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.
1: ad_handle – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: tail – character Input
3: Input
4: Input
5: Output
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_a1w_f preserves all error codes from g01ecf and in addition can return:
${\mathbf{ifail}}=-89$
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.
${\mathbf{ifail}}=-899$
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_a1w_f 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.

### 10.1Adjoint mode (a1w)

 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 mode (t1w)

 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 (p0w)

 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