d02pr
is the AD Library version of the primal routine
d02prf.
Based (in the C++ interface) on overload resolution,
d02pr can be used for primal, tangent and adjoint
evaluation. It supports tangents and adjoints of first and second order.
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:
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.
3Description
d02pr
is the AD Library version of the primal routine
d02prf.
d02prf resets the end point in an integration performed by d02pff or d02pgf.
For further information see Section 3 in the documentation for d02prf.
4References
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
5Arguments
In addition to the arguments present in the interface of the primal routine,
d02pr 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.
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.
d02pr preserves all error codes from d02prf 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.
7Accuracy
Not applicable.
8Parallelism and Performance
d02pr
is not threaded in any implementation.
9Further Comments
None.
10Example
The following examples are variants of the example for
d02prf,
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 of one body as functions of time in a suitable frame of reference are
The initial conditions
lead to elliptic motion with . is selected and the system of ODEs is reposed as
over the range . Relative error control is used with threshold values of for each solution component and compute the solution at intervals of length across the range using d02pr to reset the end of the integration range. A high-order Runge–Kutta method () is also used with tolerances and in turn so that the solutions may be compared.