NAG Library Routine Document

f11drf (complex_gen_precon_ssor_solve)


f11drf solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a complex sparse non-Hermitian matrix, represented in coordinate storage format.


Fortran Interface
Subroutine f11drf ( trans, n, nnz, a, irow, icol, rdiag, omega, check, y, x, iwork, ifail)
Integer, Intent (In):: n, nnz, irow(nnz), icol(nnz)
Integer, Intent (Inout):: ifail
Integer, Intent (Out):: iwork(2*n+1)
Real (Kind=nag_wp), Intent (In):: omega
Complex (Kind=nag_wp), Intent (In):: a(nnz), rdiag(n), y(n)
Complex (Kind=nag_wp), Intent (Out):: x(n)
Character (1), Intent (In):: trans, check
C Header Interface
#include <nagmk26.h>
void  f11drf_ (const char *trans, const Integer *n, const Integer *nnz, const Complex a[], const Integer irow[], const Integer icol[], const Complex rdiag[], const double *omega, const char *check, const Complex y[], Complex x[], Integer iwork[], Integer *ifail, const Charlen length_trans, const Charlen length_check)


f11drf solves a system of linear equations
Mx=y,   or  MHx=y,  
according to the value of the argument trans, where the matrix
M=1ω2-ω D+ω L D-1 D+ω U  
corresponds to symmetric successive-over-relaxation (SSOR) Young (1971) applied to a linear system Ax=b, where A is a complex sparse non-Hermitian matrix stored in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction).
In the definition of M given above D is the diagonal part of A, L is the strictly lower triangular part of A, U is the strictly upper triangular part of A, and ω is a user-defined relaxation parameter.
It is envisaged that a common use of f11drf will be to carry out the preconditioning step required in the application of f11bsf to sparse linear systems. For an illustration of this use of f11drf see the example program given in Section 10. f11drf is also used for this purpose by the Black Box routine f11dsf.


Young D (1971) Iterative Solution of Large Linear Systems Academic Press, New York


1:     trans – Character(1)Input
On entry: specifies whether or not the matrix M is transposed.
Mx=y is solved.
MHx=y is solved.
Constraint: trans='N' or 'T'.
2:     n – IntegerInput
On entry: n, the order of the matrix A.
Constraint: n1.
3:     nnz – IntegerInput
On entry: the number of nonzero elements in the matrix A.
Constraint: 1nnzn2.
4:     annz – Complex (Kind=nag_wp) arrayInput
On entry: the nonzero elements in the matrix A, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The routine f11znf may be used to order the elements in this way.
5:     irownnz – Integer arrayInput
6:     icolnnz – Integer arrayInput
On entry: the row and column indices of the nonzero elements supplied in a.
irow and icol must satisfy the following constraints (which may be imposed by a call to f11znf):
  • 1irowin and 1icolin, for i=1,2,,nnz;
  • either irowi-1<irowi or both irowi-1=irowi and icoli-1<icoli, for i=2,3,,nnz.
7:     rdiagn – Complex (Kind=nag_wp) arrayInput
On entry: the elements of the diagonal matrix D-1, where D is the diagonal part of A.
8:     omega – Real (Kind=nag_wp)Input
On entry: the relaxation parameter ω.
Constraint: 0.0<omega<2.0.
9:     check – Character(1)Input
On entry: specifies whether or not the CS representation of the matrix M should be checked.
Checks are carried on the values of n, nnz, irow, icol and omega.
None of these checks are carried out.
See also Section 9.2.
Constraint: check='C' or 'N'.
10:   yn – Complex (Kind=nag_wp) arrayInput
On entry: the right-hand side vector y.
11:   xn – Complex (Kind=nag_wp) arrayOutput
On exit: the solution vector x.
12:   iwork2×n+1 – Integer arrayWorkspace
13:   ifail – IntegerInput/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this argument, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

Error Indicators and Warnings

If on entry ifail=0 or -1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, check'C' or 'N': check=value.
On entry, trans'N' or 'T': trans=value.
On entry, n=value.
Constraint: n1.
On entry, nnz=value.
Constraint: nnz1.
On entry, nnz=value and n=value.
Constraint: nnzn2.
On entry, omega=value.
Constraint: 0.0<omega<2.0 
On entry, ai is out of order: i=value.
On entry, i=value, icoli=value and n=value.
Constraint: icoli1 and icolin.
On entry, i=value, irowi=value and n=value.
Constraint: irowi1 and irowin.
On entry, the location (irowI,icolI) is a duplicate: I=value.
A nonzero element has been supplied which does not lie in the matrix A, is out of order, or has duplicate row and column indices. Consider calling f11znf to reorder and sum or remove duplicates.
The matrix A has no diagonal entry in row value.
The SSOR preconditioner is not appropriate for this problem.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.


If trans='N' the computed solution x is the exact solution of a perturbed system of equations M+δMx=y, where
cn is a modest linear function of n, and ε is the machine precision. An equivalent result holds when trans='T'.

Parallelism and Performance

f11drf is not threaded in any implementation.

Further Comments


The time taken for a call to f11drf is proportional to nnz.

Use of check

It is expected that a common use of f11drf will be to carry out the preconditioning step required in the application of f11bsf to sparse linear systems. In this situation f11drf is likely to be called many times with the same matrix M. In the interests of both reliability and efficiency, you are recommended to set check='C' for the first of such calls, and check='N' for all subsequent calls.


This example solves a complex sparse linear system of equations
using RGMRES with SSOR preconditioning.
The RGMRES algorithm itself is implemented by the reverse communication routine f11bsf, which returns repeatedly to the calling program with various values of the argument irevcm. This argument indicates the action to be taken by the calling program.
For further details see the routine document for f11bsf.

Program Text

Program Text (f11drfe.f90)

Program Data

Program Data (f11drfe.d)

Program Results

Program Results (f11drfe.r)