NAG FL Interface
f11ddf (real_​gen_​precon_​ssor_​solve)

Settings help

FL Name Style:

FL Specification Language:

1 Purpose

f11ddf solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a real sparse nonsymmetric matrix, represented in coordinate storage format.

2 Specification

Fortran Interface
Subroutine f11ddf ( 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) :: a(nnz), rdiag(n), omega, y(n)
Real (Kind=nag_wp), Intent (Out) :: x(n)
Character (1), Intent (In) :: trans, check
C Header Interface
#include <nag.h>
void  f11ddf_ (const char *trans, const Integer *n, const Integer *nnz, const double a[], const Integer irow[], const Integer icol[], const double rdiag[], const double *omega, const char *check, const double y[], double x[], Integer iwork[], Integer *ifail, const Charlen length_trans, const Charlen length_check)
The routine may be called by the names f11ddf or nagf_sparse_real_gen_precon_ssor_solve.

3 Description

f11ddf solves a system of linear equations
Mx=y, or MTx=y,  
according to the value of the argument trans, where the matrix
M=1ω(2-ω) (D+ωL) D-1 (D+ωU)  
corresponds to symmetric successive-over-relaxation (SSOR) (see Young (1971)) applied to a linear system Ax=b, where A is a real sparse nonsymmetric 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 f11ddf will be to carry out the preconditioning step required in the application of f11bef to sparse linear systems. f11ddf is also used for this purpose by the Black Box routine f11def.

4 References

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

5 Arguments

1: trans Character(1) Input
On entry: specifies whether or not the matrix M is transposed.
Mx=y is solved.
MTx=y is solved.
Constraint: trans='N' or 'T'.
2: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n1.
3: nnz Integer Input
On entry: the number of nonzero elements in the matrix A.
Constraint: 1nnzn2.
4: a(nnz) Real (Kind=nag_wp) array Input
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 f11zaf may be used to order the elements in this way.
5: irow(nnz) Integer array Input
6: icol(nnz) Integer array Input
On entry: the row and column indices of the nonzero elements supplied in array a.
irow and icol must satisfy the following constraints (which may be imposed by a call to f11zaf):
  • 1irow(i)n and 1icol(i)n, for i=1,2,,nnz;
  • either irow(i-1)<irow(i) or both irow(i-1)=irow(i) and icol(i-1)<icol(i), for i=2,3,,nnz.
7: rdiag(n) Real (Kind=nag_wp) array Input
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: y(n) Real (Kind=nag_wp) array Input
On entry: the right-hand side vector y.
11: x(n) Real (Kind=nag_wp) array Output
On exit: the solution vector x.
12: iwork(2×n+1) Integer array Workspace
13: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value 0 is recommended. 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).

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=value.
Constraint: check='C' or 'N'.
On entry, trans=value.
Constraint: trans='N' or 'T'.
On entry, n=value.
Constraint: n1.
On entry, nnz=value.
Constraint: 1nnzn2.
On entry, nnz=value and n=value.
Constraint: 1nnzn2.
On entry, omega=value.
Constraint: 0.0<omega<2.0.
On entry, a(i) is out of order: i=value.
On entry, i=value, icol(i)=value and n=value.
Constraint: icol(i)1 and icol(i)n.
On entry, i=value, irow(i)=value and n=value.
Constraint: irow(i)1 and irow(i)n.
On entry, the location (irow(I),icol(I)) is a duplicate: I=value.
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 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

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

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f11ddf is not threaded in any implementation.

9 Further Comments

9.1 Timing

The time taken for a call to f11ddf is proportional to nnz.

9.2 Use of check

It is expected that a common use of f11ddf will be to carry out the preconditioning step required in the application of f11bef to sparse linear systems. In this situation f11ddf 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 for all subsequent calls set check='N'.

10 Example

This example solves a sparse linear system of equations:
using RGMRES with SSOR preconditioning.
The RGMRES algorithm itself is implemented by the reverse communication routine f11bef, 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 f11bef.

10.1 Program Text

Program Text (f11ddfe.f90)

10.2 Program Data

Program Data (f11ddfe.d)

10.3 Program Results

Program Results (f11ddfe.r)