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

g01fe_a1w_f is the adjoint version of the primal routine g01fef.

## 2Specification

Fortran Interface
 Subroutine g01fe_a1w_f ( ad_handle, p, a, b, tol, x, ifail)
 Integer, Intent (Inout) :: ifail Type (nagad_a1w_w_rtype), Intent (In) :: p, a, b, tol Type (nagad_a1w_w_rtype), Intent (Out) :: x Type (c_ptr), Intent (Inout) :: ad_handle
The routine may be called by the names g01fe_a1w_f or nagf_stat_inv_cdf_beta_a1w. The corresponding t1w and p0w variants of this routine are also available.

## 3Description

g01fe_a1w_f is the adjoint version of the primal routine g01fef.
g01fef returns the deviate associated with the given lower tail probability of the beta distribution. For further information see Section 3 in the documentation for g01fef.

## 4References

Cran G W, Martin K J and Thomas G E (1977) Algorithm AS 109. Inverse of the incomplete beta function ratio Appl. Statist. 26 111–114
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, g01fe_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 g01fe_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: Input
5: Input
6: Output
On exit: the deviate associated with the given lower tail probability of the beta distribution.
7: ifail – Integer Input/Output

## 6Error Indicators and Warnings

g01fe_a1w_f preserves all error codes from g01fef 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

g01fe_a1w_f is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for g01fef, modified to demonstrate calling the NAG AD Library.