NAG AD Library
d02ps (ivp_rkts_interp)

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1 Purpose

d02ps is the AD Library version of the primal routine d02psf. Based (in the C++ interface) on overload resolution, d02ps can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

2 Specification

Fortran Interface
Subroutine d02ps_AD_f ( n, twant, ideriv, nwant, ywant, ypwant, f, wcomm, lwcomm, iuser, ruser, iwsav, rwsav, ifail)
Integer, Intent (In) :: n, ideriv, nwant, lwcomm
Integer, Intent (Inout) :: iuser(*), iwsav(130), ifail
ADTYPE, Intent (In) :: twant
ADTYPE, Intent (Inout) :: wcomm(lwcomm), ruser(*), rwsav(32*n+350)
ADTYPE, Intent (Out) :: ywant(nwant), ypwant(nwant)
Type (c_ptr), Intent (Inout) :: ad_handle
External :: f
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 {
template <typename F_T>
void d02ps ( handle_t &ad_handle, const Integer &n, const ADTYPE &twant, const Integer &ideriv, const Integer &nwant, ADTYPE ywant[], ADTYPE ypwant[], F_T &&f, ADTYPE wcomm[], const Integer &lwcomm, 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:
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

d02ps is the AD Library version of the primal routine d02psf.
d02psf computes the solution of a system of ordinary differential equations using interpolation anywhere on an integration step taken by d02pff. For further information see Section 3 in the documentation for d02psf.

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, d02ps 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_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: n – Integer Input
3: twantADTYPE Input
4: ideriv – Integer Input
5: nwant – Integer Input
6: ywant(nwant) – ADTYPE array Output
7: ypwant(nwant) – ADTYPE array Output
8: f – Callable Input
f needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.
The specification of f is:
Fortran Interface
Subroutine f ( t, n, y, yp, iuser, ruser)
Integer, Intent (In) :: n
Integer, Intent (Inout) :: iuser(*)
ADTYPE, Intent (In) :: t, y(n)
ADTYPE, Intent (Inout) :: ruser(*)
ADTYPE, Intent (Out) :: yp(n)
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Interface
auto f = [&]( const handle_t &ad_handle, const ADTYPE &t, const Integer &n, const ADTYPE y[], ADTYPE yp[])
1: ad_handlenag::ad::handle_t Input/Output
On entry: a handle to the AD handle object.
2: tADTYPE Input
3: n – Integer Input
4: yADTYPE array Input
5: ypADTYPE array Output
*: iuser – Integer array User Workspace
*: ruserADTYPE array User Workspace
9: wcomm(lwcomm) – ADTYPE array Communication Array
Please consult Overwriting of Inputs in the NAG AD Library Introduction.
10: lwcomm – Integer Input
*: iuser(*) – Integer array User Workspace
*: ruser(*) – ADTYPE array User Workspace
Please consult Overwriting of Inputs in the NAG AD Library Introduction.
11: iwsav(130) – Integer array Communication Array
12: rwsav(32×n+350) – ADTYPE array Communication Array
Please consult Overwriting of Inputs in the NAG AD Library Introduction.
13: ifail – Integer Input/Output

6 Error Indicators and Warnings

d02ps preserves all error codes from d02psf 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

d02ps is not threaded in any implementation.

9 Further Comments


10 Example

The following examples are variants of the example for d02psf, modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example solves the equation
y = -y ,   y(0)=0,   y(0)=1  
reposed as
y1 = y2  
y2 = -y1  
over the range [0,2π] with initial conditions y1=0.0 and y2=1.0. Relative error control is used with threshold values of 1.0E−8 for each solution component. d02pf is used to integrate the problem one step at a time and d02ps is used to compute the first component of the solution and its derivative at intervals of length π/8 across the range whenever these points lie in one of those integration steps. A low order Runge–Kutta method (method=−1) is also used with tolerances tol=1.0E−4 and tol=1.0E−5 in turn so that solutions may be compared.

10.1 Adjoint modes

Language Source File Data Results
Fortran d02ps_a1t1w_fe.f90 d02ps_a1t1w_fe.d d02ps_a1t1w_fe.r
Fortran d02ps_a1w_fe.f90 d02ps_a1w_fe.d d02ps_a1w_fe.r
C++ d02ps_a1_algo_dcoe.cpp None d02ps_a1_algo_dcoe.r
C++ d02ps_a1t1_algo_dcoe.cpp None d02ps_a1t1_algo_dcoe.r

10.2 Tangent modes

Language Source File Data Results
Fortran d02ps_t1w_fe.f90 d02ps_t1w_fe.d d02ps_t1w_fe.r
Fortran d02ps_t2w_fe.f90 d02ps_t2w_fe.d d02ps_t2w_fe.r
C++ d02ps_t1_algo_dcoe.cpp None d02ps_t1_algo_dcoe.r
C++ d02ps_t2_algo_dcoe.cpp None d02ps_t2_algo_dcoe.r

10.3 Passive mode

Language Source File Data Results
Fortran d02ps_p0w_fe.f90 d02ps_p0w_fe.d d02ps_p0w_fe.r
C++ d02ps_passive_dcoe.cpp None d02ps_passive_dcoe.r