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

naginterfaces.library.sparse.complex_herm_precon_ilu_solve(a, irow, icol, ipiv, istr, y, check='N')[source]

complex_herm_precon_ilu_solve solves a system of complex linear equations involving the incomplete Cholesky preconditioning matrix generated by complex_herm_precon_ichol().

For full information please refer to the NAG Library document for f11jp

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f11/f11jpf.html

Parameters
acomplex, array-like, shape

The values returned in the array by a previous call to complex_herm_precon_ichol().

irowint, array-like, shape

The values returned in arrays , , and by a previous call to complex_herm_precon_ichol().

icolint, array-like, shape

The values returned in arrays , , and by a previous call to complex_herm_precon_ichol().

ipivint, array-like, shape

The values returned in arrays , , and by a previous call to complex_herm_precon_ichol().

istrint, array-like, shape

The values returned in arrays , , and by a previous call to complex_herm_precon_ichol().

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, is a repeated value: .

(errno )

On entry, , , .

Constraint: and .

(errno )

On entry, is inconsistent with : .

(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 )

On entry, appears to be invalid.

Notes

complex_herm_precon_ilu_solve solves a system of linear equations

involving the preconditioning matrix , corresponding to an incomplete Cholesky decomposition of a complex sparse Hermitian matrix stored in symmetric coordinate storage (SCS) format (see the F11 Introduction), as generated by complex_herm_precon_ichol().

In the above decomposition is a complex lower triangular sparse matrix with unit diagonal, is a real diagonal matrix and is a permutation matrix. and are supplied to complex_herm_precon_ilu_solve through the matrix

which is a lower triangular complex sparse matrix, stored in SCS format, as returned by complex_herm_precon_ichol(). The permutation matrix is returned from complex_herm_precon_ichol() via the array .

complex_herm_precon_ilu_solve may also be used in combination with complex_herm_precon_ichol() to solve a sparse complex Hermitian positive definite system of linear equations directly (see complex_herm_precon_ichol()).