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## 1Purpose

d02pu is the AD Library version of the primal routine d02puf. Based (in the C++ interface) on overload resolution, d02pu can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first and second order.

## 2Specification

Fortran Interface
 Integer, Intent (In) :: n Integer, Intent (Inout) :: iwsav(130), ifail ADTYPE, Intent (Inout) :: rwsav(32*n+350) ADTYPE, Intent (Out) :: rmserr(n), errmax, terrmx Type (c_ptr), Intent (Inout) :: ad_handle
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

d02pu is the AD Library version of the primal routine d02puf.
d02puf provides details about global error assessment computed during an integration with either d02pef, d02pff or d02pgf. For further information see Section 3 in the documentation for d02puf.

## 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, d02pu 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: rmserr(n) – ADTYPE array Output
4: Output
5: Output
6: iwsav($130$) – Integer array Communication Array
7: rwsav($32×{\mathbf{n}}+350$) – ADTYPE array Communication Array
8: ifail – Integer Input/Output

## 6Error Indicators and Warnings

d02pu preserves all error codes from d02puf 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

d02pu is not threaded in any implementation.

None.

## 10Example

The following examples are variants of the example for d02puf, 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 $\left(x\left(t\right),y\left(t\right)\right)$ of one body as functions of time $t$ in a suitable frame of reference are
 $x′′=-xr3$
 $y′′=-yr3, r=x2+y2.$
The initial conditions
 $x(0)=1-ε, x′(0)=0 y(0)=0, y′(0)= 1+ε 1-ε$
lead to elliptic motion with $0<\epsilon <1$. $\epsilon =0.7$ is selected and the system of ODEs is reposed as
 $y1′=y3 y2′=y4 y3′=- y1r3 y4′=- y2r3$
over the range $\left[0,3\pi \right]$. Relative error control is used with threshold values of $\text{1.0E−10}$ for each solution component and a high-order Runge–Kutta method (${\mathbf{method}}=3$) with tolerance ${\mathbf{tol}}=\text{1.0E−6}$.
Note that for illustration purposes since it is not necessary for this problem, this example integrates to the end of the range regardless of efficiency concerns (i.e., returns from d02pe with ${\mathbf{ifail}}={\mathbf{2}}$, ${\mathbf{3}}$ or ${\mathbf{4}}$).

Language Source File Data Results
Fortran d02pu_a1w_fe.f90 d02pu_a1w_fe.d d02pu_a1w_fe.r
C++ d02pu_a1w_hcppe.cpp None d02pu_a1w_hcppe.r

### 10.2Tangent modes

Language Source File Data Results
Fortran d02pu_t1w_fe.f90 d02pu_t1w_fe.d d02pu_t1w_fe.r
C++ d02pu_t1w_hcppe.cpp None d02pu_t1w_hcppe.r

### 10.3Passive mode

Language Source File Data Results
Fortran d02pu_p0w_fe.f90 d02pu_p0w_fe.d d02pu_p0w_fe.r
C++ d02pu_p0w_hcppe.cpp None d02pu_p0w_hcppe.r