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## 1Purpose

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.

## 2Specification

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(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:
#include <dco.hpp>
namespace nag {
}
}
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,

## 3Description

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.

## 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, 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.
On entry: a handle to the AD configuration data object, as created by x10aa.
2: n – Integer Input
3: Input
4: ideriv – Integer Input
5: nwant – Integer Input
6: ywant(nwant) – ADTYPE array Output
7: ypwant(nwant) – ADTYPE array Output
8: f – Subroutine External Procedure
The specification of f is:
Fortran Interface
 Subroutine f ( ad_handle, 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
On entry: a handle to the AD configuration data object.
2: Input
3: n – Integer Input
6: iuser – Integer array User Workspace
9: wcomm(lwcomm) – ADTYPE array Communication Array
10: lwcomm – Integer Input
11: liuser Input
User workspace dimension (C++ only), see x10af to specify the dimension from Fortran.
12: iuser($*$) – Integer array User Workspace
13: lruser Input
User workspace dimension (C++ only), see x10ae to specify the dimension from Fortran.
14: ruser($*$) – ADTYPE array User Workspace
15: iwsav($130$) – Integer array Communication Array
16: rwsav($32×{\mathbf{n}}+350$) – ADTYPE array Communication Array
17: ifail – Integer Input/Output

## 6Error Indicators and Warnings

d02ps preserves all error codes from d02psf and in addition can return:
${\mathbf{ifail}}=-89$
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

Not applicable.

## 8Parallelism and Performance

d02ps is not threaded in any implementation.

None.

## 10Example

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 $\left[0,2\pi \right]$ with initial conditions ${y}_{1}=0.0$ and ${y}_{2}=1.0$. Relative error control is used with threshold values of $\text{1.0E−8}$ 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 $\pi /8$ across the range whenever these points lie in one of those integration steps. A low order Runge–Kutta method (${\mathbf{method}}=-1$) is also used with tolerances ${\mathbf{tol}}=\text{1.0E−4}$ and ${\mathbf{tol}}=\text{1.0E−5}$ in turn so that solutions may be compared.

Language Source File Data Results
Fortran d02ps_a1w_fe.f90 d02ps_a1w_fe.d d02ps_a1w_fe.r
C++ d02ps_a1w_hcppe.cpp None d02ps_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran d02ps_t1w_fe.f90 d02ps_t1w_fe.d d02ps_t1w_fe.r
C++ d02ps_t1w_hcppe.cpp None d02ps_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran d02ps_p0w_fe.f90 d02ps_p0w_fe.d d02ps_p0w_fe.r
C++ d02ps_p0w_hcppe.cpp None d02ps_p0w_hcppe.r