Package jline.api.mc

Class Ctmc_gmres

java.lang.Object

jline.api.mc.Ctmc_gmres

public final class Ctmc_gmres
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Ctmc_gmres.GmresResult	Outcome of a GMRES solve.

Field Summary

Fields

Modifier and Type	Field	Description
static final int	GMRES_DEFAULT_RESTART	Default Krylov subspace dimension between restarts.
static final double	GMRES_DEFAULT_TOL	Default linear-solve residual.
static final double	ILUT_DROP_TOL	Relative threshold below which ILUT discards a fill-in entry.
static final double	ILUT_FILL_FACTOR	Factor bounding the ILUT factors, as a multiple of the nonzeros per row of A.

Method Summary

Modifier and Type	Method	Description
static Ctmc_gmres.GmresResult	ctmc_gmres(Matrix A, Matrix b)	Solve A*x = b by restarted GMRES with the default tolerance, restart and iteration cap, starting from a uniform initial guess.
static Matrix	ctmc_gmres(Matrix A, Matrix B, double tol, int restart, int maxit)	Solve A*X = B for every column of B, reusing one incomplete factorization across all of them and starting each column from the previous solution.
static Ctmc_gmres.GmresResult	ctmc_gmres(Matrix A, Matrix b, double tol, int restart, int maxit, Matrix x0)	Solve A*x = b by restarted GMRES.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

GMRES_DEFAULT_TOL

public static final double GMRES_DEFAULT_TOL

Default linear-solve residual. Much tighter than the fixed-point tolerance options.iter_tol (1e-4): switching from the direct solve to GMRES must not move a reported performance metric.

See Also:

• Constant Field Values

GMRES_DEFAULT_RESTART

public static final int GMRES_DEFAULT_RESTART

Default Krylov subspace dimension between restarts.

See Also:

• Constant Field Values

ILUT_DROP_TOL

public static final double ILUT_DROP_TOL

Relative threshold below which ILUT discards a fill-in entry.

See Also:

• Constant Field Values

ILUT_FILL_FACTOR

public static final double ILUT_FILL_FACTOR

Factor bounding the ILUT factors, as a multiple of the nonzeros per row of A.

See Also:

• Constant Field Values

Method Details

ctmc_gmres

public static Ctmc_gmres.GmresResult ctmc_gmres(Matrix A,
 Matrix b)

Solve A*x = b by restarted GMRES with the default tolerance, restart and iteration cap, starting from a uniform initial guess.

Parameters:

A - Coefficient matrix

b - Right-hand side, as a column vector

Returns:

Solution, convergence flag, relative residual and iteration count

ctmc_gmres

public static Ctmc_gmres.GmresResult ctmc_gmres(Matrix A,
 Matrix b,
 double tol,
 int restart,
 int maxit,
 Matrix x0)

Solve A*x = b by restarted GMRES.

Parameters:

A - Coefficient matrix

b - Right-hand side, as a column vector

tol - Relative residual tolerance, nonpositive for the default 1e-12

restart - Krylov subspace dimension, nonpositive for the default min(n,50)

maxit - Maximum number of restart cycles, nonpositive for ceil(n/restart)

x0 - Initial guess, null for the uniform vector 1/n

Returns:

Solution, convergence flag, relative residual and iteration count

ctmc_gmres

public static Matrix ctmc_gmres(Matrix A,
 Matrix B,
 double tol,
 int restart,
 int maxit)

Solve A*X = B for every column of B, reusing one incomplete factorization across all of them and starting each column from the previous solution. This is the shape of the stochastic complement, whose right-hand side is a whole block of the generator: refactorizing per column would cost more than the direct solve it replaces.

Parameters:

A - Coefficient matrix

B - Right-hand sides, one per column

tol - Relative residual tolerance, nonpositive for the default 1e-12

restart - Krylov subspace dimension, nonpositive for the default min(n,50)

maxit - Maximum number of restart cycles, nonpositive for ceil(n/restart)

Returns:

The solution block, or null if any column failed to converge. Returning null rather than a partial block keeps the caller's fallback all-or-nothing.