c05rd is the AD Library version of the primal routine c05rdf. Based (in the C++ interface) on overload resolution, c05rd can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine c05rd_AD_f (

ad_handle, irevcm, n, x, fvec, fjac, xtol, mode, diag, factor, r, qtf, iwsav, rwsav, ifail)

Integer, Intent (In)	::	n, mode
Integer, Intent (Inout)	::	irevcm, iwsav(17), ifail
ADTYPE, Intent (In)	::	xtol, factor
ADTYPE, Intent (Inout)	::	x(n), fvec(n), fjac(n,n), diag(n), r(n(n+1)/2), qtf(n), rwsav(4n+10)
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:

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

C++ Header Interface

#include <dco.hpp>
#include <nagad.h>
namespace nag {
namespace ad {

void c05rd (

void *&ad_handle, Integer &irevcm, const Integer &n, ADTYPE x[], ADTYPE fvec[], ADTYPE fjac[], const ADTYPE &xtol, const Integer &mode, ADTYPE diag[], const ADTYPE &factor, ADTYPE r[], ADTYPE qtf[], 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

Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

c05rd is the AD Library version of the primal routine c05rdf.

c05rdf is a comprehensive reverse communication routine that finds a solution of a system of nonlinear equations by a modification of the Powell hybrid method. You must provide the Jacobian. For further information see Section 3 in the documentation for c05rdf.

4 References

Moré J J, Garbow B S and Hillstrom K E (1980) User guide for MINPACK-1 Technical Report ANL-80-74 Argonne National Laboratory

Powell M J D (1970) A hybrid method for nonlinear algebraic equations Numerical Methods for Nonlinear Algebraic Equations (ed P Rabinowitz) Gordon and Breach

5 Arguments

In addition to the arguments present in the interface of the primal routine, c05rd 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_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object, as created by x10aa.
2: irevcm – Integer Input/Output
3: n – Integer Input
4: x(n) – ADTYPE array Input/Output
5: fvec(n) – ADTYPE array Input/Output
6: fjac(n, n) – ADTYPE array Input/Output
7: xtol – ADTYPE Input
8: mode – Integer Input
9: diag(n) – ADTYPE array Input/Output
10: factor – ADTYPE Input
11: r( $n \times (n + 1) / 2$ ) – ADTYPE array Input/Output
12: qtf(n) – ADTYPE array Input/Output
13: iwsav( $17$ ) – Integer array Communication Array
14: rwsav( $4 \times n + 10$ ) – ADTYPE array Communication Array
15: ifail – Integer Input/Output

6 Error Indicators and Warnings

c05rd preserves all error codes from c05rdf and in addition can return:

$ifail = - 89$: An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.

$ifail = - 199$: The routine was called using a mode that has not yet been implemented.

$ifail = - 443$: On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.

$ifail = - 444$: 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 Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

c05rd is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for c05rdf, modified to demonstrate calling the NAG AD Library.

Description of the primal example.

This example determines the values

x_{1}, \dots, x_{9}

which satisfy the tridiagonal equations:

\begin{array}{rcl} (3 - 2 x_{1}) x_{1} - 2 x_{2} & = & −1, \\ - x_{i - 1} + (3 - 2 x_{i}) x_{i} - 2 x_{i + 1} & = & −1, i = 2, 3, \dots, 8 \\ - x_{8} + (3 - 2 x_{9}) x_{9} & = & −1 . \end{array}

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	c05rd_a1w_fe.f90	None	c05rd_a1w_fe.r
C++	c05rd_a1w_hcppe.cpp	None	c05rd_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	c05rd_t1w_fe.f90	None	c05rd_t1w_fe.r
C++	c05rd_t1w_hcppe.cpp	None	c05rd_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	c05rd_p0w_fe.f90	None	c05rd_p0w_fe.r
C++	c05rd_p0w_hcppe.cpp	None	c05rd_p0w_hcppe.r

NAG Library Manual, Mark 27.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

C05 (Roots) Chapter Contents

C05 (Roots) Chapter Introduction (FL)

c05rd: FL CL CPP AD

NAG AD Libraryc05rd (sys_deriv_rcomm)

▸▿ Contents

1 Purpose