c05rc is the AD Library version of the primal routine c05rcf. Based (in the C++ interface) on overload resolution, c05rc can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine c05rc_AD_f (

fcn, n, x, fvec, fjac, xtol, maxfev, mode, diag, factor, nprint, nfev, njev, r, qtf, iuser, ruser, ifail)

Integer, Intent (In)	::	n, maxfev, mode, nprint
Integer, Intent (Inout)	::	iuser(*), ifail
Integer, Intent (Out)	::	nfev, njev
ADTYPE, Intent (In)	::	xtol, factor
ADTYPE, Intent (Inout)	::	x(n), diag(n), ruser(*)
ADTYPE, Intent (Out)	::	fvec(n), fjac(n,n), r(n*(n+1)/2), qtf(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++ Interface

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

void c05rc (

handle_t &ad_handle, FCN_T &&fcn, const Integer &n, ADTYPE x[], ADTYPE fvec[], ADTYPE fjac[], const ADTYPE &xtol, const Integer &maxfev, const Integer &mode, ADTYPE diag[], const ADTYPE &factor, const Integer &nprint, Integer &nfev, Integer &njev, ADTYPE r[], ADTYPE qtf[], 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

c05rc is the AD Library version of the primal routine c05rcf.

c05rcf is a comprehensive 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 c05rcf.

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, c05rc 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 – nag::ad::handle_t Input/Output

On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.

2: fcn – Callable Input

fcn needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of fcn is:

Fortran Interface

Subroutine fcn (

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++ Interface

auto fcn = [&](

const handle_t &ad_handle, const Integer &n, const ADTYPE x[], ADTYPE fvec[], ADTYPE fjac[], Integer &iflag)

1: ad_handle – nag::ad::handle_t Input/Output: On entry: a handle to the AD handle object.
2: n – Integer Input
3: x – ADTYPE array Input
4: fvec – ADTYPE array Input/Output
5: fjac – ADTYPE array Input/Output
*: iuser – Integer array User Workspace
*: ruser – ADTYPE array User Workspace
6: iflag – Integer Input/Output

3: n – Integer Input

4: x(n) – ADTYPE array Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

5: fvec(n) – ADTYPE array Output

6: fjac(n, n) – ADTYPE array Output

7: xtol – ADTYPE Input

8: maxfev – Integer Input

9: mode – Integer Input

10: diag(n) – ADTYPE array Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

11: factor – ADTYPE Input

12: nprint – Integer Input

13: nfev – Integer Output

14: njev – Integer Output

15: r( $n \times (n + 1) / 2$ ) – ADTYPE array Output

16: qtf(n) – ADTYPE array Output

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

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

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

17: ifail – Integer Input/Output

6 Error Indicators and Warnings

c05rc preserves all error codes from c05rcf and in addition can return:

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

$ifail = - 199$: The routine was called using a strategy that has not yet been implemented.
See AD Strategies in the NAG AD Library Introduction for further information.

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

7 Accuracy

Not applicable.

8 Parallelism and Performance

c05rc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for c05rcf, 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	c05rc_a1w_fe.f90	None	c05rc_a1w_fe.r
C++	c05rc_a1w_hcppe.cpp	None	c05rc_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	c05rc_t1w_fe.f90	None	c05rc_t1w_fe.r
C++	c05rc_t1w_hcppe.cpp	None	c05rc_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	c05rc_p0w_fe.f90	None	c05rc_p0w_fe.r
C++	c05rc_p0w_hcppe.cpp	None	c05rc_p0w_hcppe.r

NAG Library Manual, Mark 29

Interfaces: FL CL CPP AD

NAG AD Library Introduction

C05 (Roots) Chapter Contents

C05 (Roots) Chapter Introduction (FL)

c05rc: FL CL CPP AD

NAG AD Libraryc05rc (sys_deriv_expert)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Adjoint modes

10.2 Tangent modes

10.3 Passive mode

NAG AD Library
c05rc (sys_deriv_expert)