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

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

complex_gen_precon_ssor_solve solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a complex sparse non-Hermitian matrix, represented in coordinate storage format.

For full information please refer to the NAG Library document for f11dr

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f11/f11drf.html

Parameters
transstr, length 1

Specifies whether or not the matrix is transposed.

is solved.

is solved.

acomplex, array-like, shape

The nonzero elements in 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_gen_sort() may be used to order the elements in this way.

irowint, array-like, shape

The row indices of the nonzero elements supplied in .

icolint, array-like, shape

The column indices of the nonzero elements supplied in .

rdiagcomplex, array-like, shape

The elements of the diagonal matrix , where is the diagonal part of .

omegafloat

The relaxation parameter .

ycomplex, array-like, shape

The right-hand side vector .

checkstr, length 1, optional

Specifies whether or not the CS representation of the matrix should be checked.

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

None of these checks are carried out.

See also Further Comments.

Returns
xcomplex, ndarray, shape

The solution vector .

Raises
NagValueError
(errno )

On entry, or : .

(errno )

On entry, 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, , and .

Constraint: and .

(errno )

On entry, , and .

Constraint: and .

(errno )

The matrix has no diagonal entry in row .

Notes

complex_gen_precon_ssor_solve solves a system of linear equations

according to the value of the argument , where the matrix

corresponds to symmetric successive-over-relaxation (SSOR) Young (1971) applied to a linear system , where is a complex sparse non-Hermitian matrix stored in coordinate storage (CS) format (see the F11 Introduction).

In the definition of given above is the diagonal part of , is the strictly lower triangular part of , is the strictly upper triangular part of , and is a user-defined relaxation parameter.

It is envisaged that a common use of complex_gen_precon_ssor_solve will be to carry out the preconditioning step required in the application of complex_gen_basic_solver() to sparse linear systems. complex_gen_precon_ssor_solve is also used for this purpose by the Black Box function complex_gen_solve_jacssor().

References

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