NAG AD Library
g01gc (prob_chisq_noncentral)

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1 Purpose

g01gc is the AD Library version of the primal routine g01gcf. Based (in the C++ interface) on overload resolution, g01gc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface
Subroutine g01gc_AD_f ( ad_handle, x, df, rlamda, tol, maxit, p, ifail)
Integer, Intent (In) :: maxit
Integer, Intent (Inout) :: ifail
ADTYPE, Intent (In) :: x, df, rlamda, tol
ADTYPE, Intent (Out) :: p
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 g01gc ( handle_t &ad_handle, const ADTYPE &x, const ADTYPE &df, const ADTYPE &rlamda, const ADTYPE &tol, const Integer &maxit, 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.

3 Description

g01gc is the AD Library version of the primal routine g01gcf.
g01gcf returns the probability associated with the lower tail of the noncentral χ2-distribution. For further information see Section 3 in the documentation for g01gcf.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

In addition to the arguments present in the interface of the primal routine, g01gc 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 g01gc_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: xADTYPE Input
3: dfADTYPE Input
4: rlamdaADTYPE Input
5: tolADTYPE Input
6: maxit – Integer Input
7: pADTYPE Output
On exit: the probability associated with the lower tail of the noncentral χ2-distribution.
8: ifail – Integer Input/Output

6 Error Indicators and Warnings

g01gc preserves all error codes from g01gcf and in addition can return:
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.
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.
ifail=-444
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
ifail=-899
Dynamic memory allocation failed for AD.
See Error Handling in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g01gc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for g01gcf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example reads values from various noncentral χ2-distributions, calculates the lower tail probabilities and prints all these values until the end of data is reached.

10.1 Adjoint modes

Language Source File Data Results
Fortran g01gc_a1w_fe.f90 g01gc_a1w_fe.d g01gc_a1w_fe.r
C++ g01gc_a1w_hcppe.cpp g01gc_a1w_hcppe.d g01gc_a1w_hcppe.r

10.2 Tangent modes

Language Source File Data Results
Fortran g01gc_t1w_fe.f90 g01gc_t1w_fe.d g01gc_t1w_fe.r
C++ g01gc_t1w_hcppe.cpp g01gc_t1w_hcppe.d g01gc_t1w_hcppe.r

10.3 Passive mode

Language Source File Data Results
Fortran g01gc_p0w_fe.f90 g01gc_p0w_fe.d g01gc_p0w_fe.r
C++ g01gc_p0w_hcppe.cpp g01gc_p0w_hcppe.d g01gc_p0w_hcppe.r