NAG AD Library
f11ja (real_symm_precon_ichol)

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1 Purpose

f11ja is the AD Library version of the primal routine f11jaf. Based (in the C++ interface) on overload resolution, f11ja can be used for primal, tangent and adjoint evaluation. It supports tangents and adjoints of first order.

2 Specification

Fortran Interface
Subroutine f11ja_AD_f ( n, nnz, a, la, irow, icol, lfill, dtol, mic, dscale, pstrat, ipiv, istr, nnzc, npivm, iwork, liwork, ifail)
Integer, Intent (In) :: n, nnz, la, lfill, liwork
Integer, Intent (Inout) :: irow(la), icol(la), ipiv(n), ifail
Integer, Intent (Out) :: istr(n+1), nnzc, npivm, iwork(liwork)
ADTYPE, Intent (In) :: dtol, dscale
ADTYPE, Intent (Inout) :: a(la)
Character (1), Intent (In) :: mic, pstrat
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 f11ja ( 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 *mic, const ADTYPE &dscale, const char *pstrat, Integer ipiv[], Integer istr[], 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:
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.

3 Description

f11ja is the AD Library version of the primal routine f11jaf.
f11jaf computes an incomplete Cholesky factorization of a real sparse symmetric matrix, represented in symmetric coordinate storage format. This factorization may be used as a preconditioner in combination with f11jcf. For further information see Section 3 in the documentation for f11jaf.

4 References

Chan T F (1991) Fourier analysis of relaxed incomplete factorization preconditioners SIAM J. Sci. Statist. Comput. 12(2) 668–680
Markowitz H M (1957) The elimination form of the inverse and its application to linear programming Management Sci. 3 255–269
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
Salvini S A and Shaw G J (1995) An evaluation of new NAG Library solvers for large sparse symmetric linear systems NAG Technical Report TR1/95
Van der Vorst H A (1990) The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors Lecture Notes in Mathematics (eds O Axelsson and L Y Kolotilina) 1457 Springer–Verlag

5 Arguments

In addition to the arguments present in the interface of the primal routine, f11ja 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_handlenag::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: dtolADTYPE Input
10: mic – character Input
11: dscaleADTYPE Input
12: pstrat – character Input
13: ipiv(n) – Integer array Input/Output
14: istr(n+1) – Integer array Output
15: nnzc – Integer Output
16: npivm – Integer Output
17: iwork(liwork) – Integer array Workspace
18: liwork – Integer Input
19: ifail – Integer Input/Output

6 Error Indicators and Warnings

f11ja preserves all error codes from f11jaf and in addition can return:
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.
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.
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
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

f11ja is not threaded in any implementation.

9 Further Comments


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.