NAG Library Routine Document
F11JDF
1 Purpose
F11JDF solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a real sparse symmetric matrix, represented in symmetric coordinate storage format.
2 Specification
SUBROUTINE F11JDF ( |
N, NNZ, A, IROW, ICOL, RDIAG, OMEGA, CHECK, Y, X, IWORK, IFAIL) |
INTEGER |
N, NNZ, IROW(NNZ), ICOL(NNZ), IWORK(N+1), IFAIL |
REAL (KIND=nag_wp) |
A(NNZ), RDIAG(N), OMEGA, Y(N), X(N) |
CHARACTER(1) |
CHECK |
|
3 Description
F11JDF solves a system of equations
involving the preconditioning matrix
corresponding to symmetric successive-over-relaxation (SSOR) (see
Young (1971)) on a linear system
, where
is a sparse symmetric 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.
It is envisaged that a common use of F11JDF will be to carry out the preconditioning step required in the application of
F11GEF to sparse linear systems. For an illustration of this use of F11JDF see the example program given in
Section 10.1. F11JDF is also used for this purpose by the Black Box routine
F11JEF.
4 References
Young D (1971) Iterative Solution of Large Linear Systems Academic Press, New York
5 Parameters
- 1: – INTEGERInput
-
On entry: , the order of the matrix .
Constraint:
.
- 2: – INTEGERInput
-
On entry: the number of nonzero elements in the lower triangular part of .
Constraint:
.
- 3: – REAL (KIND=nag_wp) arrayInput
-
On entry: 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
F11ZBF may be used to order the elements in this way.
- 4: – INTEGER arrayInput
- 5: – INTEGER arrayInput
-
On entry: the row and column indices of the nonzero elements supplied in array
A.
Constraints:
IROW and
ICOL must satisfy these constraints (which may be imposed by a call to
F11ZBF):
- and , for ;
- or and , for .
- 6: – REAL (KIND=nag_wp) arrayInput
-
On entry: the elements of the diagonal matrix , where is the diagonal part of .
- 7: – REAL (KIND=nag_wp)Input
-
On entry: the relaxation parameter .
Constraint:
.
- 8: – CHARACTER(1)Input
-
On entry: 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.
Constraint:
or .
- 9: – REAL (KIND=nag_wp) arrayInput
-
On entry: the right-hand side vector .
- 10: – REAL (KIND=nag_wp) arrayOutput
-
On exit: the solution vector .
- 11: – INTEGER arrayWorkspace
-
- 12: – INTEGERInput/Output
-
On entry:
IFAIL 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.
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
or
, 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 . |
-
On entry, | , |
or | , |
or | , |
or | OMEGA lies outside the interval , |
-
On entry, the arrays
IROW and
ICOL 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
F11ZBF to reorder and sum or remove duplicates.
An unexpected error has been triggered by this routine. Please
contact
NAG.
See
Section 3.8 in the Essential Introduction for further information.
Your licence key may have expired or may not have been installed correctly.
See
Section 3.7 in the Essential Introduction for further information.
Dynamic memory allocation failed.
See
Section 3.6 in the Essential Introduction for further information.
7 Accuracy
The computed solution
is the exact solution of a perturbed system of equations
, where
is a modest linear function of
, and
is the
machine precision.
8 Parallelism and Performance
Not applicable.
The time taken for a call to F11JDF is proportional to
NNZ.
It is expected that a common use of F11JDF will be to carry out the preconditioning step required in the application of
F11GEF to sparse symmetric linear systems. In this situation F11JDF is likely to be called many times with the same matrix
. In the interests of both reliability and efficiency, you are recommended to set
for the first of such calls, and to set
for all subsequent calls.
10 Example
This example solves a sparse symmetric linear system of equations
using the conjugate-gradient (CG) method with SSOR preconditioning.
The CG algorithm itself is implemented by the reverse communication routine
F11GEF, which returns repeatedly to the calling program with various values of the parameter
IREVCM. This parameter indicates the action to be taken by the calling program.
- If , a matrix-vector product is required. This is implemented by a call to F11XEF.
- If , a solution of the preconditioning equation is required. This is achieved by a call to F11JDF.
- If , F11GEF has completed its tasks. Either the iteration has terminated, or an error condition has arisen.
For further details see the routine document for
F11GEF.
10.1 Program Text
Program Text (f11jdfe.f90)
10.2 Program Data
Program Data (f11jdfe.d)
10.3 Program Results
Program Results (f11jdfe.r)