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

g01fc_a1w_f is the adjoint version of the primal routine g01fcf.

## 2Specification

Fortran Interface
 Subroutine g01fc_a1w_f ( ad_handle, p, df, x, ifail)
 Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: p, df Type (nagad_a1w_w_rtype), Intent (Out) :: x Type (c_ptr), Intent (Inout) :: ad_handle
The routine may be called by the names g01fc_a1w_f or nagf_stat_inv_cdf_chisq_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

g01fc_a1w_f is the adjoint 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.
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_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 g01fc_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, x.
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: Input
3: Input
4: Output
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_a1w_f preserves all error codes from g01fcf and in addition can return:
${\mathbf{ifail}}=-89$
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

g01fc_a1w_f 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.