g01ha is the AD Library version of the primal routine g01haf. Based (in the C++ interface) on overload resolution, g01ha can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine g01ha_AD_f (

ad_handle, x, y, rho, p, ifail)

Integer, Intent (Inout)	::	ifail
ADTYPE, Intent (In)	::	x, y, rho
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++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void g01ha (

void *&ad_handle, const ADTYPE &x, const ADTYPE &y, const ADTYPE &rho, 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

g01ha is the AD Library version of the primal routine g01haf.

g01haf returns the lower tail probability for the bivariate Normal distribution. For further information see Section 3 in the documentation for g01haf.

4 References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

Genz A (2004) Numerical computation of rectangular bivariate and trivariate Normal and

t

probabilities Statistics and Computing 14 151–160

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

5 Arguments

In addition to the arguments present in the interface of the primal routine, g01ha 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 g01ha_a1w_f, is a subroutine, where the function value is returned in the additional output parameter, p.

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: x – ADTYPE Input
3: y – ADTYPE Input
4: rho – ADTYPE Input
5: p – ADTYPE Output: On exit: the lower tail probability for the bivariate Normal distribution.
6: ifail – Integer Input/Output

6 Error Indicators and Warnings

g01ha preserves all error codes from g01haf 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.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g01ha is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for g01haf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example reads values of

x

and

y

for a bivariate Normal distribution along with the value of

ρ

and computes the lower tail probabilities.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	g01ha_a1w_fe.f90	g01ha_a1w_fe.d	g01ha_a1w_fe.r
C++	g01ha_a1w_hcppe.cpp	g01ha_a1w_hcppe.d	g01ha_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	g01ha_t1w_fe.f90	g01ha_t1w_fe.d	g01ha_t1w_fe.r
C++	g01ha_t1w_hcppe.cpp	g01ha_t1w_hcppe.d	g01ha_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	g01ha_p0w_fe.f90	g01ha_p0w_fe.d	g01ha_p0w_fe.r
C++	g01ha_p0w_hcppe.cpp	g01ha_p0w_hcppe.d	g01ha_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction (FL)

g01ha: FL CL CPP AD

NAG AD Libraryg01ha (prob_bivariate_normal)

▸▿ Contents

1 Purpose