NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
F11 (Sparse) Chapter Contents
F11 (Sparse) Chapter Introduction (FL)
f11ja:  FL   CL   CPP   AD 

NAG AD Library
f11ja_a1w_f (real_symm_precon_ichol_a1w)

Note: a1w denotes that first order adjoints are computed in working precision; this has the corresponding argument type nagad_a1w_w_rtype. Also available is the t1w (first order tangent linear) mode, the interface of which is implied by replacing a1w by t1w throughout this document. Additionally, the p0w (passive interface, as alternative to the FL interface) mode is available and can be inferred by replacing of active types by the corresponding passive types. The method of codifying AD implementations in the routine name and corresponding argument types is described in the NAG AD Library Introduction.
NAG Library Manual, Mark 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
F11 (Sparse) Chapter Contents
F11 (Sparse) Chapter Introduction (FL)
f11ja:  FL   CL   CPP   AD 

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© The Numerical Algorithms Group Ltd. 2020
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1 Purpose

f11ja_a1w_f is the adjoint version of the primal routine f11jaf.

2 Specification

Fortran Interface
Subroutine f11ja_a1w_f ( ad_handle, 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)
Type (nagad_a1w_w_rtype), Intent (In) :: dtol, dscale
Type (nagad_a1w_w_rtype), Intent (Inout) :: a(la)
Character (1), Intent (In) :: mic, pstrat
Type (c_ptr), Intent (Inout) :: ad_handle
C++ Header Interface
#include <nagad.h>
void f11ja_a1w_f_ ( void *&ad_handle, const Integer &n, const Integer &nnz, nagad_a1w_w_rtype a[], const Integer &la, Integer irow[], Integer icol[], const Integer &lfill, const nagad_a1w_w_rtype &dtol, const char *mic, const nagad_a1w_w_rtype &dscale, const char *pstrat, Integer ipiv[], Integer istr[], Integer &nnzc, Integer &npivm, Integer iwork[], const Integer &liwork, Integer &ifail, const Charlen length_mic, const Charlen length_pstrat)
The routine may be called by the names f11ja_a1w_f or nagf_sparse_real_symm_precon_ichol_a1w. The corresponding t1w and p0w variants of this routine are also available.

3 Description

f11ja_a1w_f is the adjoint 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_a1w_f 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 – Type (c_ptr) Input/Output
On entry: a handle to the AD configuration data object, as created by x10aa_a1w_f.
2: n – Integer Input
3: nnz – Integer Input
4: a(la) – Type (nagad_a1w_w_rtype) array Input/Output
5: la – Integer Input
6: irow(la) – Integer array Input/Output
7: icol(la) – Integer array Input/Output
8: lfill – Integer Input
9: dtol – Type (nagad_a1w_w_rtype) Input
10: mic – character Input
11: dscale – Type (nagad_a1w_w_rtype) 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_a1w_f preserves all error codes from f11jaf and in addition can return:
ifail=-89
An unexpected AD error has been triggered by this routine. Please contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.
ifail=-899
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f11ja_a1w_f 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 27.1
Interfaces:  FL   CL   CPP   AD 
NAG AD Library Introduction
F11 (Sparse) Chapter Contents
F11 (Sparse) Chapter Introduction (FL)
f11ja:  FL   CL   CPP   AD 
© The Numerical Algorithms Group Ltd. 2020