# naginterfaces.library.sparse.real_​symm_​precon_​ichol_​solve¶

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

real_symm_precon_ichol_solve solves a system of linear equations involving the incomplete Cholesky preconditioning matrix generated by real_symm_precon_ichol().

For full information please refer to the NAG Library document for f11jb

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/f11/f11jbf.html

Parameters
afloat, array-like, shape

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

irowint, array-like, shape

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

icolint, array-like, shape

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

ipivint, array-like, shape

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

istrint, array-like, shape

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

yfloat, 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 .

No checks are carried out.

Returns
xfloat, 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

real_symm_precon_ichol_solve solves a system of linear equations

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

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

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

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

real_symm_precon_ichol_solve may also be used in combination with real_symm_precon_ichol() to solve a sparse symmetric positive definite system of linear equations directly (see Further Comments).