d02ps (ivp_rkts_interp) : NAG AD Library Routine Document, Mark 30

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 (

ad_handle, 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(32n+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:
double,
dco::ga1s<double>::type,
dco::gt1s<double>::type,
dco::gt1s<dco::gt1s<double>::type>::type,
dco::ga1s<dco::gt1s<double>::type>::type

3 Description

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

5 Arguments

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.

6 Error Indicators and Warnings

d02ps preserves all error codes from d02psf 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

8 Parallelism and Performance

9 Further Comments

10 Example

This example solves the equation

y^{''} = - y, y (0) = 0, y^{'} (0) = 1

reposed as

y_{1}^{'} = y_{2}

y_{2}^{'} = - y_{1}

over the range

[0, 2 π]

with initial conditions

y_{1} = 0.0

and

y_{2} = 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.

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

Language

Source File

Data

Results

Fortran

Fortran

C++

d02ps_a1_algo_dcoe.cpp

None

d02ps_a1_algo_dcoe.r

C++

d02ps_a1t1_algo_dcoe.cpp

None

d02ps_a1t1_algo_dcoe.r

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

Language

Source File

Data

Results

Fortran

Fortran