naginterfaces.library.sparse.complex_​gen_​solve_​bdilu

naginterfaces.library.sparse.complex_gen_solve_bdilu(method, nnz, a, irow, icol, istb, indb, ipivp, ipivq, istr, idiag, b, m, tol, maxitn, x)[source]

complex_gen_solve_bdilu solves a complex sparse non-Hermitian system of linear equations, represented in coordinate storage format, using a restarted generalized minimal residual (RGMRES), conjugate gradient squared (CGS), stabilized bi-conjugate gradient (BI-CGSTAB), or transpose-free quasi-minimal residual (TFQMR) method, with block Jacobi or additive Schwarz preconditioning.

For full information please refer to the NAG Library document for f11du

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f11/f11duf.html

Parameters
methodstr

Specifies the iterative method to be used.

Restarted generalized minimum residual method.

Conjugate gradient squared method.

Bi-conjugate gradient stabilized () method.

Transpose-free quasi-minimal residual method.

nnzint

The value of as supplied to a previous call to complex_gen_precon_bdilu()

acomplex, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

irowint, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

icolint, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

istbint, array-like, shape

The value of as supplied to a previous call to complex_gen_precon_bdilu()

indbint, array-like, shape

The value of as supplied to a previous call to complex_gen_precon_bdilu()

ipivpint, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

ipivqint, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

istrint, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

idiagint, array-like, shape

The value of returned by a previous call to complex_gen_precon_bdilu()

bcomplex, array-like, shape

The right-hand side vector .

mint

If , is the dimension of the restart subspace.

If , is the order of the polynomial BI-CGSTAB method.

Otherwise, is not referenced.

tolfloat

The required tolerance. Let denote the approximate solution at iteration , and the corresponding residual. The algorithm is considered to have converged at iteration if

If , is used, where is the machine precision. Otherwise is used.

maxitnint

The maximum number of iterations allowed.

xcomplex, array-like, shape

An initial approximation to the solution vector .

Returns
xcomplex, ndarray, shape

An improved approximation to the solution vector .

rnormfloat

The final value of the residual norm , where is the output value of .

itnint

The number of iterations carried out.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, for , and .

Constraint: , for .

(errno )

On entry, and .

Constraint: , for

(errno )

On entry, , and .

Constraint: .

(errno )

On entry, .

Constraint: , or .

(errno )

On entry, and .

Constraint: if , .

If , .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: , for .

Check that , , , , , and have not been corrupted between calls to complex_gen_precon_bdilu() and complex_gen_solve_bdilu.

(errno )

On entry, and .

Constraint: , for .

Check that , , , , , and have not been corrupted between calls to complex_gen_precon_bdilu() and complex_gen_solve_bdilu.

(errno )

On entry, element of was out of order.

Check that , , , , , and have not been corrupted between calls to complex_gen_precon_bdilu() and complex_gen_solve_bdilu.

(errno )

On entry, location of was a duplicate.

Check that , , , , , and have not been corrupted between calls to complex_gen_precon_bdilu() and complex_gen_solve_bdilu.

(errno )

The CS representation of the preconditioner is invalid.

Check that , , , , , and have not been corrupted between calls to complex_gen_precon_bdilu() and complex_gen_solve_bdilu.

(errno )

The required accuracy could not be obtained. However, a reasonable accuracy may have been achieved.

(errno )

The solution has not converged after iterations.

(errno )

Algorithmic breakdown. A solution is returned, although it is possible that it is completely inaccurate.

Notes

complex_gen_solve_bdilu solves a complex sparse non-Hermitian linear system of equations

using a preconditioned RGMRES (see Saad and Schultz (1986)), CGS (see Sonneveld (1989)), BI-CGSTAB() (see Van der Vorst (1989) and Sleijpen and Fokkema (1993)), or TFQMR (see Freund and Nachtigal (1991) and Freund (1993)) method.

complex_gen_solve_bdilu uses the incomplete (possibly overlapping) block factorization determined by complex_gen_precon_bdilu() as the preconditioning matrix. A call to complex_gen_solve_bdilu must always be preceded by a call to complex_gen_precon_bdilu(). Alternative preconditioners for the same storage scheme are available by calling complex_gen_solve_ilu() or complex_gen_solve_jacssor().

The matrix , and the preconditioning matrix , are represented in coordinate storage (CS) format (see the F11 Introduction) in the arrays , and , as returned from complex_gen_precon_bdilu(). The array holds the nonzero entries in these matrices, while and hold the corresponding row and column indices.

complex_gen_solve_bdilu is a Black Box function which calls complex_gen_basic_setup(), complex_gen_basic_solver() and complex_gen_basic_diag(). If you wish to use an alternative storage scheme, preconditioner, or termination criterion, or require additional diagnostic information, you should call these underlying functions directly.

References

Freund, R W, 1993, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comput. (14), 470–482

Freund, R W and Nachtigal, N, 1991, QMR: a Quasi-Minimal Residual Method for Non-Hermitian Linear Systems, Numer. Math. (60), 315–339

Saad, Y and Schultz, M, 1986, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. (7), 856–869

Sleijpen, G L G and Fokkema, D R, 1993, BiCGSTAB for linear equations involving matrices with complex spectrum, ETNA (1), 11–32

Sonneveld, P, 1989, CGS, a fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. (10), 36–52

Van der Vorst, H, 1989, Bi-CGSTAB, a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. (13), 631–644