f11da is the AD Library version of the primal routine f11daf. Based (in the C++ interface) on overload resolution, f11da can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface

Subroutine f11da_AD_f (

ad_handle, n, nnz, a, la, irow, icol, lfill, dtol, pstrat, milu, ipivp, ipivq, istr, idiag, nnzc, npivm, iwork, liwork, ifail)

Integer, Intent (In)	::	n, nnz, la, lfill, liwork
Integer, Intent (Inout)	::	irow(la), icol(la), ipivp(n), ipivq(n), ifail
Integer, Intent (Out)	::	istr(n+1), idiag(n), nnzc, npivm, iwork(liwork)
ADTYPE, Intent (In)	::	dtol
ADTYPE, Intent (Inout)	::	a(la)
Character (1), Intent (In)	::	pstrat, milu
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++ Interface

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

void f11da (

handle_t &ad_handle, const Integer &n, const Integer &nnz, ADTYPE a[], const Integer &la, Integer irow[], Integer icol[], const Integer &lfill, const ADTYPE &dtol, const char *pstrat, const char *milu, Integer ipivp[], Integer ipivq[], Integer istr[], Integer idiag[], Integer &nnzc, Integer &npivm, Integer iwork[], const Integer &liwork, 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

f11da is the AD Library version of the primal routine f11daf.

f11daf computes an incomplete

L U

factorization of a real sparse nonsymmetric matrix, represented in coordinate storage format. This factorization may be used as a preconditioner in combination with f11dcf or f11bef. For further information see Section 3 in the documentation for f11daf.

4 References

Meijerink J and Van der Vorst H (1977) An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix Math. Comput. 31 148–162

Meijerink J and Van der Vorst H (1981) Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems J. Comput. Phys. 44 134–155

Salvini S A and Shaw G J (1996) An evaluation of new NAG Library solvers for large sparse unsymmetric linear systems NAG Technical Report TR2/96

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11da 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: n – Integer Input
3: nnz – Integer Input
4: a(la) – ADTYPE array Input/Output: Please consult Overwriting of Inputs in the NAG AD Library Introduction.
5: la – Integer Input
6: irow(la) – Integer array Input/Output
7: icol(la) – Integer array Input/Output
8: lfill – Integer Input
9: dtol – ADTYPE Input
10: pstrat – character Input
11: milu – character Input
12: ipivp(n) – Integer array Input/Output
13: ipivq(n) – Integer array Input/Output
14: istr( $n + 1$ ) – Integer array Output
15: idiag(n) – Integer array Output
16: nnzc – Integer Output
17: npivm – Integer Output
18: iwork(liwork) – Integer array Workspace
19: liwork – Integer Input
20: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11da preserves all error codes from f11daf 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

f11da is not threaded in any implementation.

9 Further Comments

None.

10 Example

A NAG AD Library example is not yet available, please refer to the NAG AD Library Introduction for information on calling routines from the AD Library.

NAG Library Manual, Mark 30

Interfaces: FL CL CPP AD

NAG AD Library Introduction

F11 (Sparse) Chapter Contents

F11 (Sparse) Chapter Introduction (FL)

f11da: FL CL CPP AD

NAG AD Libraryf11da (real_gen_precon_ilu)

▸▿ Contents

1 Purpose