# NAG AD Libraryg01fb (inv_cdf_students_t)

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## 1Purpose

g01fb is the AD Library version of the primal routine g01fbf. Based (in the C++ interface) on overload resolution, g01fb can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

## 2Specification

Fortran Interface
 Subroutine g01fb_AD_f ( tail, p, df, x, ifail)
 Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: p, df ADTYPE, Intent (Out) :: x 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:
C++ Interface
#include <dco.hpp>
namespace nag {
 void g01fb ( handle_t &ad_handle, const char *tail, const ADTYPE &p, const ADTYPE &df, ADTYPE &x, Integer &ifail)
}
}
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
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

## 3Description

g01fb is the AD Library version of the primal routine g01fbf.
g01fbf returns the deviate associated with the given tail probability of Student's $t$-distribution with real degrees of freedom. For further information see Section 3 in the documentation for g01fbf.

## 4References

Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
Hill G W (1970) Student's $t$-distribution Comm. ACM 13(10) 617–619

## 5Arguments

In addition to the arguments present in the interface of the primal routine, g01fb 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 g01fb_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, x.
On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.
2: tail – character Input
3: Input
4: Input
On exit: the deviate associated with the given tail probability of Student’s $t$-distribution with real degrees of freedom.
6: ifail – Integer Input/Output

## 6Error Indicators and Warnings

g01fb preserves all error codes from g01fbf and in addition can return:
${\mathbf{ifail}}=-89$
See Error Handling in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-444$
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 Error Handling in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

g01fb is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for g01fbf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example reads the probability, the tail that probability represents and the degrees of freedom for a number of Student's $t$-distributions and computes the corresponding deviates.

Language Source File Data Results
Fortran g01fb_a1w_fe.f90 g01fb_a1w_fe.d g01fb_a1w_fe.r
C++ g01fb_a1w_hcppe.cpp g01fb_a1w_hcppe.d g01fb_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran g01fb_t1w_fe.f90 g01fb_t1w_fe.d g01fb_t1w_fe.r
C++ g01fb_t1w_hcppe.cpp g01fb_t1w_hcppe.d g01fb_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran g01fb_p0w_fe.f90 g01fb_p0w_fe.d g01fb_p0w_fe.r
C++ g01fb_p0w_hcppe.cpp g01fb_p0w_hcppe.d g01fb_p0w_hcppe.r