NAG Library Manual, Mark 29.2
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 Library
c05rc (sys_deriv_expert)

NAG Library Manual, Mark 29.2
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
C05 (Roots) Chapter Contents
C05 (Roots) Chapter Introduction (FL)
c05rc:  FL   CL   CPP   AD 

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© The Numerical Algorithms Group Ltd. 2023
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1 Purpose

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 and second 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
when ADTYPE is Type(nagad_a1t1w_w_rtype) then AD is a1t1w
when ADTYPE is Type(nagad_t2w_w_rtype) then AD is t2w
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,
dco::gt1s<dco::gt1s<double>::type>::type,
dco::ga1s<dco::gt1s<double>::type>::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×(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 x1 , … , x9 which satisfy the tridiagonal equations:
(3-2x1)x1-2x2 = −1, -xi-1+(3-2xi)xi-2xi+1 = −1,  i=2,3,…,8 -x8+(3-2x9)x9 = −1.  

10.1 Adjoint modes

Language Source File Data Results
Fortran c05rc_a1t1w_fe.f90 None c05rc_a1t1w_fe.r
Fortran c05rc_a1w_fe.f90 None c05rc_a1w_fe.r
C++ c05rc_a1_algo_dcoe.cpp None c05rc_a1_algo_dcoe.r
C++ c05rc_a1t1_algo_dcoe.cpp None c05rc_a1t1_algo_dcoe.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
Fortran c05rc_t2w_fe.f90 None c05rc_t2w_fe.r
C++ c05rc_t1_algo_dcoe.cpp None c05rc_t1_algo_dcoe.r
C++ c05rc_t1w_hcppe.cpp None c05rc_t1w_hcppe.r
C++ c05rc_t2_algo_dcoe.cpp None c05rc_t2_algo_dcoe.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
C++ c05rc_passive_dcoe.cpp None c05rc_passive_dcoe.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)
c05rc:  FL   CL   CPP   AD 
© The Numerical Algorithms Group Ltd. 2023