g01fb: FL CL CPP AD

NAG AD Library
g01fb_a1w_f (inv_cdf_students_t_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.

Keyword Search:

NAG Library Manual, Mark 27.1

Interfaces: FL CL CPP AD

NAG AD Library Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction (FL)

g01fb: FL CL CPP AD

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Adjoint mode (a1w)

10.2 Tangent mode (t1w)

10.3 Passive mode (p0w)

1 Purpose

g01fb_a1w_f is the adjoint version of the primal routine g01fbf.

2 Specification

Fortran Interface

Subroutine g01fb_a1w_f (

ad_handle, tail, 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
Character (1), Intent (In)	::	tail
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

#include <nagad.h>

void g01fb_a1w_f_ (

void *&ad_handle, const char *tail, const nagad_a1w_w_rtype &p, const nagad_a1w_w_rtype &df, nagad_a1w_w_rtype &x, Integer &ifail, const Charlen length_tail)

The routine may be called by the names g01fb_a1w_f or nagf_stat_inv_cdf_students_t_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

g01fb_a1w_f is the adjoint 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.

4 References

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

5 Arguments

In addition to the arguments present in the interface of the primal routine, g01fb_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 g01fb_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: tail – character Input
3: p – Type (nagad_a1w_w_rtype) Input
4: df – Type (nagad_a1w_w_rtype) Input
5: x – Type (nagad_a1w_w_rtype) Output: 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

6 Error Indicators and Warnings

g01fb_a1w_f preserves all error codes from g01fbf and in addition can return:

$ifail = - 89$: 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.

$ifail = - 899$: Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g01fb_a1w_f is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for g01fbf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint mode (a1w)

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

10.2 Tangent mode (t1w)

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

10.3 Passive mode (p0w)

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