d02pu is the AD Library version of the primal routine d02puf. Based (in the C++ interface) on overload resolution, d02pu can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

2 Specification

Fortran Interface

Subroutine d02pu_AD_f (

ad_handle, n, rmserr, errmax, terrmx, iwsav, rwsav, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	iwsav(130), ifail
ADTYPE, Intent (Inout)	::	rwsav(32*n+350)
ADTYPE, Intent (Out)	::	rmserr(n), errmax, terrmx
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 d02pu (

handle_t &ad_handle, const Integer &n, ADTYPE rmserr[], ADTYPE &errmax, ADTYPE &terrmx, 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

d02pu is the AD Library version of the primal routine d02puf.

d02puf provides details about global error assessment computed during an integration with either d02pef, d02pff or d02pgf. For further information see Section 3 in the documentation for d02puf.

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, d02pu 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: rmserr(n) – ADTYPE array Output
4: errmax – ADTYPE Output
5: terrmx – ADTYPE Output
6: iwsav( $130$ ) – Integer array Communication Array
7: rwsav( $32 \times n + 350$ ) – ADTYPE array Communication Array: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
8: ifail – Integer Input/Output

6 Error Indicators and Warnings

d02pu preserves all error codes from d02puf 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

d02pu is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for d02puf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example integrates a two body problem. The equations for the coordinates

(x (t), y (t))

of one body as functions of time

t

in a suitable frame of reference are

x^{''} = - \frac{x}{r^{3}}

y^{''} = - \frac{y}{r^{3}}, r = \sqrt{x^{2} + y^{2}} .

The initial conditions

\begin{array}{l} x (0) = 1 - ε, & x^{'} (0) = 0 \\ y (0) = 0, & y^{'} (0) = \sqrt{\frac{1 + ε}{1 - ε}} \end{array}

lead to elliptic motion with

0 < ε < 1

ε = 0.7

is selected and the system of ODEs is reposed as

\begin{array}{l} y_{1}^{'} = y_{3} \\ y_{2}^{'} = y_{4} \\ y_{3}^{'} = - \frac{y_{1}}{r^{3}} \\ y_{4}^{'} = - \frac{y_{2}}{r^{3}} \end{array}

over the range

[0, 3 π]

. Relative error control is used with threshold values of

1.0E−10

for each solution component and a high-order Runge–Kutta method (

method = 3

) with tolerance

tol = 1.0E−6

Note that for illustration purposes since it is not necessary for this problem, this example integrates to the end of the range regardless of efficiency concerns (i.e., returns from d02pe with

ifail = 2

3

4

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	d02pu_a1t1w_fe.f90	d02pu_a1t1w_fe.d	d02pu_a1t1w_fe.r
Fortran	d02pu_a1w_fe.f90	d02pu_a1w_fe.d	d02pu_a1w_fe.r
C++	d02pu_a1_algo_dcoe.cpp	None	d02pu_a1_algo_dcoe.r
C++	d02pu_a1t1_algo_dcoe.cpp	None	d02pu_a1t1_algo_dcoe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	d02pu_t1w_fe.f90	d02pu_t1w_fe.d	d02pu_t1w_fe.r
Fortran	d02pu_t2w_fe.f90	d02pu_t2w_fe.d	d02pu_t2w_fe.r
C++	d02pu_t1_algo_dcoe.cpp	None	d02pu_t1_algo_dcoe.r
C++	d02pu_t2_algo_dcoe.cpp	None	d02pu_t2_algo_dcoe.r