d02pq is the AD Library version of the primal routine d02pqf. Based (in the C++ interface) on overload resolution, d02pq can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

2 Specification

Fortran Interface

Subroutine d02pq_AD_f (

ad_handle, n, tstart, tend, yinit, tol, thresh, method, hstart, iwsav, rwsav, ifail)

Integer, Intent (In)	::	n, method
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	iwsav(130)
ADTYPE, Intent (In)	::	tstart, tend, yinit(n), tol, thresh(n), hstart
ADTYPE, Intent (Out)	::	rwsav(32*n+350)
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
when ADTYPE is	Type(nagad_a1t1w_w_rtype)	then AD is a1t1w
when ADTYPE is	Type(nagad_t2w_w_rtype)	then AD is t2w

C++ Interface

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

void d02pq (

handle_t &ad_handle, const Integer &n, const ADTYPE &tstart, const ADTYPE &tend, const ADTYPE yinit[], const ADTYPE &tol, const ADTYPE thresh[], const Integer &method, const ADTYPE &hstart, Integer iwsav[], ADTYPE rwsav[], 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,
dco::gt1s<dco::gt1s<double>::type>::type,
dco::ga1s<dco::gt1s<double>::type>::type

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

d02pq is the AD Library version of the primal routine d02pqf.

d02pqf is a setup routine which must be called prior to the first call of either of the integration routines d02pef, d02pff or d02pgf. For further information see Section 3 in the documentation for d02pqf.

4 References

Brankin R W, Gladwell I and Shampine L F (1991) RKSUITE: A suite of Runge–Kutta codes for the initial value problems for ODEs SoftReport 91-S1 Southern Methodist University

5 Arguments

In addition to the arguments present in the interface of the primal routine, d02pq 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.

1: ad_handle – nag::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: n – Integer Input
3: tstart – ADTYPE Input
4: tend – ADTYPE Input
5: yinit(n) – ADTYPE array Input
6: tol – ADTYPE Input
7: thresh(n) – ADTYPE array Input
8: method – Integer Input
9: hstart – ADTYPE Input
10: iwsav( $130$ ) – Integer array Communication Array
11: rwsav( $32 \times n + 350$ ) – ADTYPE array Communication Array
12: ifail – Integer Input/Output

6 Error Indicators and Warnings

d02pq preserves all error codes from d02pqf 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

d02pq is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d02pqf, modified to demonstrate calling the NAG AD Library.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	d02pq_a1w_fe.f90	d02pq_a1w_fe.d	d02pq_a1w_fe.r
C++	d02pq_a1_algo_dcoe.cpp	None	d02pq_a1_algo_dcoe.r
C++	d02pq_a1t1_algo_dcoe.cpp	None	d02pq_a1t1_algo_dcoe.r