naginterfaces.library.sparse.real_gen_precon_ilu_solve¶
- naginterfaces.library.sparse.real_gen_precon_ilu_solve(trans, a, irow, icol, ipivp, ipivq, istr, idiag, y, check='N')[source]¶
real_gen_precon_ilu_solve
solves a system of linear equations involving the incomplete preconditioning matrix generated byreal_gen_precon_ilu()
.For full information please refer to the NAG Library document for f11db
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/f11/f11dbf.html
- Parameters
- transstr, length 1
Specifies whether or not the matrix is transposed.
is solved.
is solved.
- afloat, array-like, shape
The values returned in the array by a previous call to
real_gen_precon_ilu()
.- irowint, array-like, shape
The values returned in arrays , , , , and by a previous call to
real_gen_precon_ilu()
.- icolint, array-like, shape
The values returned in arrays , , , , and by a previous call to
real_gen_precon_ilu()
.- ipivpint, array-like, shape
The values returned in arrays , , , , and by a previous call to
real_gen_precon_ilu()
.- ipivqint, array-like, shape
The values returned in arrays , , , , and by a previous call to
real_gen_precon_ilu()
.- istrint, array-like, shape
The values returned in arrays , , , , and by a previous call to
real_gen_precon_ilu()
.- idiagint, array-like, shape
The values returned in arrays , , , , and by a previous call to
real_gen_precon_ilu()
.- yfloat, 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
- xfloat, ndarray, shape
The solution vector .
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: or .
- (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 a repeated value: .
- (errno )
On entry, , , .
Constraint: and .
- (errno )
On entry, is inconsistent with : .
- (errno )
On entry, appears to be incorrect: .
- (errno )
On entry, the location () is a duplicate: .
- (errno )
On entry, is out of order: .
- (errno )
On entry, , , and .
Constraint: and .
- (errno )
On entry, , , .
Constraint: and .
- (errno )
On entry, appears to be invalid.
- Notes
real_gen_precon_ilu_solve
solves a system of linear equationsaccording to the value of the argument , where the matrix , corresponds to an incomplete decomposition of a sparse matrix stored in coordinate storage (CS) format (see the F11 Introduction), as generated by
real_gen_precon_ilu()
.In the above decomposition is a lower triangular sparse matrix with unit diagonal elements, is a diagonal matrix, is an upper triangular sparse matrix with unit diagonal elements and, and are permutation matrices. , and are supplied to
real_gen_precon_ilu_solve
through the matrixwhich is an by sparse matrix, stored in CS format, as returned by
real_gen_precon_ilu()
. The permutation matrices and are returned fromreal_gen_precon_ilu()
via the arrays and .It is envisaged that a common use of
real_gen_precon_ilu_solve
will be to carry out the preconditioning step required in the application ofreal_gen_basic_solver()
to sparse linear systems.real_gen_precon_ilu_solve
is used for this purpose by the Black Box functionreal_gen_solve_ilu()
.real_gen_precon_ilu_solve
may also be used in combination withreal_gen_precon_ilu()
to solve a sparse system of linear equations directly (see Further Comments).