NAG Library Routine Document
F11JRF solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a complex sparse Hermitian matrix, represented in symmetric coordinate storage format.
|SUBROUTINE F11JRF (
||N, NNZ, A, IROW, ICOL, RDIAG, OMEGA, CHECK, Y, X, IWORK, IFAIL)
||N, NNZ, IROW(NNZ), ICOL(NNZ), IWORK(N+1), IFAIL
||A(NNZ), Y(N), X(N)
F11JRF solves a system of equations
involving the preconditioning matrix
corresponding to symmetric successive-over-relaxation (SSOR) (see Young (1971)
) on a linear system
is a sparse complex Hermitian matrix stored in symmetric coordinate storage (SCS) format (see Section 2.1.2
in the F11 Chapter Introduction).
In the definition of given above is the diagonal part of , is the strictly lower triangular part of and is a user-defined relaxation parameter. Note that since is Hermitian the matrix is necessarily real.
Young D (1971) Iterative Solution of Large Linear Systems Academic Press, New York
- 1: N – INTEGERInput
On entry: , the order of the matrix .
- 2: NNZ – INTEGERInput
On entry: the number of nonzero elements in the lower triangular part of the matrix .
- 3: A(NNZ) – COMPLEX (KIND=nag_wp) arrayInput
: the nonzero elements in the lower triangular part of the matrix
, 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 F11ZPF
may be used to order the elements in this way.
- 4: IROW(NNZ) – INTEGER arrayInput
- 5: ICOL(NNZ) – INTEGER arrayInput
: the row and column indices of the nonzero elements supplied in array A
must satisfy the following constraints (which may be imposed by a call to F11ZPF
- and , for ;
- or and , for .
- 6: RDIAG(N) – REAL (KIND=nag_wp) arrayInput
On entry: the elements of the diagonal matrix , where is the diagonal part of . Note that since is Hermitian the elements of are necessarily real.
- 7: OMEGA – REAL (KIND=nag_wp)Input
On entry: the relaxation parameter .
- 8: CHECK – CHARACTER(1)Input
: specifies whether or not the input data should be checked.
- Checks are carried out on the values of N, NNZ, IROW, ICOL and OMEGA.
- None of these checks are carried out.
- 9: Y(N) – COMPLEX (KIND=nag_wp) arrayInput
On entry: the right-hand side vector .
- 10: X(N) – COMPLEX (KIND=nag_wp) arrayOutput
On exit: the solution vector .
- 11: IWORK() – INTEGER arrayWorkspace
- 12: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
|On entry,|| or .|
|or||OMEGA lies outside the interval .|
On entry, the arrays IROW
fail to satisfy the following constraints:
- and , for ;
- or and , for .
Therefore a nonzero element has been supplied which does not lie in the lower triangular part of
, is out of order, or has duplicate row and column indices. Call F11ZPF
to reorder and sum or remove duplicates.
|On entry,||a row of has no diagonal entry.|
The computed solution
is the exact solution of a perturbed system of equations
is a modest linear function of
is the machine precision
The time taken for a call to F11JRF is proportional to NNZ
This example program solves the preconditioning equation for a by sparse complex Hermitian matrix , given in symmetric coordinate storage (SCS) format.
9.1 Program Text
Program Text (f11jrfe.f90)
9.2 Program Data
Program Data (f11jrfe.d)
9.3 Program Results
Program Results (f11jrfe.r)