The routine may be called by the names f11jrf or nagf_sparse_complex_herm_precon_ssor_solve.
f11jrf 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 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: – IntegerInput
On entry: , the order of the matrix .
2: – IntegerInput
On entry: the number of nonzero elements in the lower triangular part of the matrix .
3: – Complex (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 f11zpf 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.
irow and icol must satisfy the following constraints (which may be imposed by a call to f11zpf):
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 . Note that since is Hermitian the elements of are necessarily real.
7: – Real (Kind=nag_wp)Input
On entry: the relaxation parameter .
8: – Character(1)Input
On entry: specifies whether or not the input data should be checked.
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or 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).
6Error 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, .
Constraint: or .
On entry, .
On entry, .
On entry, and .
On entry, .
On entry, is out of order: .
On entry, , , .
On entry, , and .
On entry, the location () is a duplicate: .
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. Consider calling f11zpf to reorder and sum or remove duplicates.
The matrix has no diagonal entry in row .
An unexpected error has been triggered by this routine. Please
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.
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.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
f11jrf is not threaded in any implementation.
The time taken for a call to f11jrf is proportional to nnz.
This example program solves the preconditioning equation for a sparse complex Hermitian matrix , given in symmetric coordinate storage (SCS) format.