c05rb is the AD Library version of the primal routine c05rbf. Based (in the C++ interface) on overload resolution, c05rb can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine c05rb_AD_f (

ad_handle, fcn, n, x, fvec, fjac, xtol, iuser, ruser, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	iuser(*), ifail
ADTYPE, Intent (In)	::	xtol
ADTYPE, Intent (Inout)	::	x(n), ruser(*)
ADTYPE, Intent (Out)	::	fvec(n), fjac(n,n)
Type (c_ptr), Intent (Inout)	::	ad_handle
External	::	fcn

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 c05rb (

void *&ad_handle,
void (NAG_CALL fcn)(void *&ad_handle, const Integer &n, const ADTYPE x[], ADTYPE fvec[], ADTYPE fjac[], Integer iuser[], ADTYPE ruser[], Integer &iflag),
const Integer &n, ADTYPE x[], ADTYPE fvec[], ADTYPE fjac[], const ADTYPE &xtol, const Integer &liuser, Integer iuser[], const Integer &lruser, ADTYPE ruser[], 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

c05rb is the AD Library version of the primal routine c05rbf.

c05rbf is an easy-to-use 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 c05rbf.

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, c05rb 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: fcn – Subroutine External Procedure

The specification of fcn is:

Fortran Interface

Subroutine fcn (

ad_handle, n, x, fvec, fjac, iuser, ruser, iflag)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	iuser(*), iflag
ADTYPE, Intent (In)	::	x(n)
ADTYPE, Intent (Inout)	::	fvec(n), fjac(n,n), ruser(*)
Type (c_ptr), Intent (Inout)	::	ad_handle

C++ Header Interface

void fcn (

void *&ad_handle, const Integer &n, const ADTYPE x[], ADTYPE fvec[], ADTYPE fjac[], Integer iuser[], ADTYPE ruser[], Integer &iflag)

1: ad_handle – Pointer to AD Data Input/Output: On entry: a handle to the AD configuration data object.
2: n – Integer Input
3: x – ADTYPE array Input
4: fvec – ADTYPE array Input/Output
5: fjac – ADTYPE array Input/Output
6: iuser – Integer array User Workspace
7: ruser – ADTYPE array User Workspace
8: iflag – Integer Input/Output

3: n – Integer Input

4: x(n) – ADTYPE array Input/Output

5: fvec(n) – ADTYPE array Output

6: fjac(n, n) – ADTYPE array Output

7: xtol – ADTYPE Input

8: liuser Input

User workspace dimension (C++ only), see x10af to specify the dimension from Fortran.

9: iuser( $*$ ) – Integer array User Workspace

10: lruser Input

User workspace dimension (C++ only), see x10ae to specify the dimension from Fortran.

11: ruser( $*$ ) – ADTYPE array User Workspace

12: ifail – Integer Input/Output

6 Error Indicators and Warnings

c05rb preserves all error codes from c05rbf 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

c05rb is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for c05rbf, 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	c05rb_a1w_fe.f90	None	c05rb_a1w_fe.r
C++	c05rb_a1w_hcppe.cpp	None	c05rb_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	c05rb_t1w_fe.f90	None	c05rb_t1w_fe.r
C++	c05rb_t1w_hcppe.cpp	None	c05rb_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	c05rb_p0w_fe.f90	None	c05rb_p0w_fe.r
C++	c05rb_p0w_hcppe.cpp	None	c05rb_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)

c05rb: FL CL CPP AD

NAG AD Libraryc05rb (sys_deriv_easy)

▸▿ Contents

1 Purpose