The function may be called by the names: f11jrc, nag_sparse_complex_herm_precon_ssor_solve or nag_sparse_herm_precon_ssor_solve.
f11jrc 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: – const ComplexInput
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 function f11zpc may be used to order the elements in this way.
4: – const IntegerInput
5: – const IntegerInput
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 f11zpc):
and , for ;
or and , for .
6: – const doubleInput
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: – doubleInput
On entry: the relaxation parameter .
8: – Nag_SparseSym_CheckDataInput
On entry: specifies whether or not the input data should be checked.
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
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 f11zpc to reorder and sum or remove duplicates.
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
On entry, .
On entry, and .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
On entry, , , .
On entry, , and .
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, is out of order: .
On entry, the location () is a duplicate: .
On entry, .
The matrix has no diagonal entry in row .
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.
f11jrc is not threaded in any implementation.
The time taken for a call to f11jrc is proportional to nnz.
This example program solves the preconditioning equation for a sparse complex Hermitian matrix , given in symmetric coordinate storage (SCS) format.