naginterfaces.library.sparse.complex_​herm_​precon_​ssor_​solve

naginterfaces.library.sparse.complex_herm_precon_ssor_solve(a, irow, icol, rdiag, omega, y, check='N')[source]

complex_herm_precon_ssor_solve 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.

For full information please refer to the NAG Library document for f11jr

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f11/f11jrf.html

Parameters
acomplex, array-like, shape

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 complex_herm_sort() may be used to order the elements in this way.

irowint, array-like, shape

The row indices of the nonzero elements supplied in array .

icolint, array-like, shape

The column indices of the nonzero elements supplied in array .

rdiagfloat, array-like, shape

The elements of the diagonal matrix , where is the diagonal part of . Note that since is Hermitian the elements of are necessarily real.

omegafloat

The relaxation parameter .

ycomplex, array-like, shape

The right-hand side vector .

checkstr, length 1, optional

Specifies whether or not the input data should be checked.

Checks are carried out on the values of , , , and .

None of these checks are carried out.

Returns
xcomplex, ndarray, shape

The solution vector .

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, the location () is a duplicate: .

(errno )

On entry, is out of order: .

(errno )

On entry, , , .

Constraint: .

(errno )

On entry, , and .

Constraint: .

(errno )

The matrix has no diagonal entry in row .

Notes

complex_herm_precon_ssor_solve 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 the F11 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.

References

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