NAG AD Library
g01ha (prob_bivariate_normal)

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1 Purpose

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++ Interface
#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {
void g01ha ( handle_t &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:
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_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: yADTYPE Input
4: rhoADTYPE Input
5: pADTYPE 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:
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.
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.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
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

g01ha is not threaded in any implementation.

9 Further Comments


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