c05qs is the AD Library version of the primal routine c05qsf. Based (in the C++ interface) on overload resolution, c05qs can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine c05qs_AD_f (

fcn, n, x, fvec, xtol, init, rcomm, lrcomm, icomm, licomm, iuser, ruser, ifail)

Integer, Intent (In)	::	n, lrcomm, licomm
Integer, Intent (Inout)	::	icomm(licomm), iuser(*), ifail
ADTYPE, Intent (In)	::	xtol
ADTYPE, Intent (Inout)	::	x(n), rcomm(lrcomm), ruser(*)
ADTYPE, Intent (Out)	::	fvec(n)
Logical, Intent (In)	::	init
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 c05qs (

handle_t &ad_handle, FCN_T &&fcn, const Integer &n, ADTYPE x[], ADTYPE fvec[], const ADTYPE &xtol, const logical &init, ADTYPE rcomm[], const Integer &lrcomm, Integer icomm[], const Integer &licomm, 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

c05qs is the AD Library version of the primal routine c05qsf.

c05qsf is an easy-to-use routine that finds a solution of a sparse system of nonlinear equations by a modification of the Powell hybrid method. For further information see Section 3 in the documentation for c05qsf.

4 References

Broyden C G (1965) A class of methods for solving nonlinear simultaneous equations Mathematics of Computation 19(92) 577–593

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

Schubert L K (1970) Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian Mathematics of Computation 24(109) 27–30

5 Arguments

In addition to the arguments present in the interface of the primal routine, c05qs 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, lindf, indf, x, fvec, iuser, ruser, iflag)

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

C++ Interface

auto fcn = [&](

const handle_t &ad_handle, const Integer &n, const Integer &lindf, const Integer indf[], const ADTYPE x[], ADTYPE fvec[], 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: lindf – Integer Input
4: indf – Integer array Input
5: x – ADTYPE array Input
6: fvec – ADTYPE array Output
*: iuser – Integer array User Workspace
*: ruser – ADTYPE array User Workspace
7: 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: xtol – ADTYPE Input

7: init – logical Input

8: rcomm(lrcomm) – ADTYPE array Communication Array

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

9: lrcomm – Integer Input

10: icomm(licomm) – Integer array Communication Array

11: licomm – Integer Input

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

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

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

12: ifail – Integer Input/Output

6 Error Indicators and Warnings

c05qs preserves all error codes from c05qsf 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

c05qs is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following examples are variants of the example for c05qsf, 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}

It then perturbs the equations by a small amount and solves the new system.

10.1 Adjoint modes

Language	Source File	Data	Results
Fortran	c05qs_a1w_fe.f90	None	c05qs_a1w_fe.r
C++	c05qs_a1w_hcppe.cpp	None	c05qs_a1w_hcppe.r

10.2 Tangent modes

Language	Source File	Data	Results
Fortran	c05qs_t1w_fe.f90	None	c05qs_t1w_fe.r
C++	c05qs_t1w_hcppe.cpp	None	c05qs_t1w_hcppe.r

10.3 Passive mode

Language	Source File	Data	Results
Fortran	c05qs_p0w_fe.f90	None	c05qs_p0w_fe.r
C++	c05qs_p0w_hcppe.cpp	None	c05qs_p0w_hcppe.r

NAG Library Manual, Mark 29.2

Interfaces: FL CL CPP AD

NAG AD Library Introduction

C05 (Roots) Chapter Contents

C05 (Roots) Chapter Introduction (FL)

c05qs: FL CL CPP AD

NAG AD Libraryc05qs (sparsys_func_easy)

▸▿ 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
c05qs (sparsys_func_easy)