NAG AD Libraryg01ec (prob_chisq)

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1Purpose

g01ec is the AD Library version of the primal routine g01ecf. Based (in the C++ interface) on overload resolution, g01ec can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2Specification

Fortran Interface
 Subroutine g01ec_AD_f ( tail, x, df, p, ifail)
 Integer, Intent (Inout) :: ifail ADTYPE, Intent (In) :: x, df ADTYPE, Intent (Out) :: p 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:
 when ADTYPE is Real(kind=nag_wp) then AD is p0w when ADTYPE is Type(nagad_a1w_w_rtype) then AD is a1w when ADTYPE is Type(nagad_t1w_w_rtype) then AD is t1w
C++ Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
 void g01ec ( handle_t &ad_handle, const char *tail, const ADTYPE &x, const ADTYPE &df, ADTYPE &p, 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

g01ec is the AD Library 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 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_handlenag::ad::handle_t Input/Output
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
5: pADTYPE 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 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 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

g01ec 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.
Description of the primal example.
Values from various ${\chi }^{2}$-distributions are read, the lower tail probabilities calculated, and all these values printed out, until the end of data is reached.

10.1Adjoint modes

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 modes

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

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