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## 1Purpose

d02pf is the AD Library version of the primal routine d02pff. Based (in the C++ interface) on overload resolution, d02pf can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

## 2Specification

Fortran Interface
 Subroutine d02pf_AD_f ( ad_handle, f, n, tnow, ynow, ypnow, iuser, ruser, iwsav, rwsav, ifail)
 Integer, Intent (In) :: n Integer, Intent (Inout) :: iuser(*), iwsav(130), ifail ADTYPE, Intent (Inout) :: ruser(*), rwsav(32*n+350) ADTYPE, Intent (Out) :: tnow, ynow(n), ypnow(n) 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

d02pf is the AD Library version of the primal routine d02pff.
d02pff is a one-step routine for solving an initial value problem for a first-order system of ordinary differential equations using Runge–Kutta methods. For further information see Section 3 in the documentation for d02pff.

## 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, d02pf 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: 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
3: n – Integer Input
4: Output
5: ynow(n) – ADTYPE array Output
6: ypnow(n) – ADTYPE array Output
7: liuser Input
User workspace dimension (C++ only), see x10af to specify the dimension from Fortran.
8: iuser($*$) – Integer array User Workspace
9: lruser Input
User workspace dimension (C++ only), see x10ae to specify the dimension from Fortran.
10: ruser($*$) – ADTYPE array User Workspace
11: iwsav($130$) – Integer array Communication Array
12: rwsav($32×{\mathbf{n}}+350$) – ADTYPE array Communication Array
13: ifail – Integer Input/Output

## 6Error Indicators and Warnings

d02pf preserves all error codes from d02pff 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

d02pf is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for d02pff, 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 ${y}_{2}=1.0$. We use relative error control with threshold values of $\text{1.0E−8}$ for each solution component and print the solution at each integration step across the range. We use a medium order Runge–Kutta method (${\mathbf{method}}=2$) with tolerances ${\mathbf{tol}}=\text{1.0E−4}$ and ${\mathbf{tol}}=\text{1.0E−5}$ in turn so that we may compare the solutions.

Language Source File Data Results
Fortran d02pf_a1w_fe.f90 d02pf_a1w_fe.d d02pf_a1w_fe.r
C++ d02pf_a1w_hcppe.cpp None d02pf_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran d02pf_t1w_fe.f90 d02pf_t1w_fe.d d02pf_t1w_fe.r
C++ d02pf_t1w_hcppe.cpp None d02pf_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran d02pf_p0w_fe.f90 d02pf_p0w_fe.d d02pf_p0w_fe.r
C++ d02pf_p0w_hcppe.cpp None d02pf_p0w_hcppe.r