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3.2.5
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A GMRES solver for sparse square problems. More...
Inherits IterativeSolverBase< GMRES< _MatrixType, _Preconditioner > >.
Public Member Functions | |
int | get_restart () |
GMRES (const MatrixType &A) | |
GMRES () | |
void | set_restart (const int restart) |
template<typename Rhs , typename Guess > | |
const internal::solve_retval_with_guess < GMRES, Rhs, Guess > | solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const |
A GMRES solver for sparse square problems.
This class allows to solve for A.x = b sparse linear problems using a generalized minimal residual method. The vectors x and b can be either dense or sparse.
_MatrixType | the type of the sparse matrix A, can be a dense or a sparse matrix. | |
_Preconditioner | the type of the preconditioner. Default is DiagonalPreconditioner |
The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.
This class can be used as the direct solver classes. Here is a typical usage example:
int n = 10000; VectorXd x(n), b(n); SparseMatrix<double> A(n,n); // fill A and b GMRES<SparseMatrix<double> > solver(A); x = solver.solve(b); std::cout << "#iterations: " << solver.iterations() << std::endl; std::cout << "estimated error: " << solver.error() << std::endl; // update b, and solve again x = solver.solve(b);
By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method.
GMRES | ( | ) | [inline] |
Default constructor.
GMRES | ( | const MatrixType & | A | ) | [inline] |
Initialize the solver with matrix A for further Ax=b
solving.
This constructor is a shortcut for the default constructor followed by a call to compute().
int get_restart | ( | ) | [inline] |
Get the number of iterations after that a restart is performed.
void set_restart | ( | const int | restart | ) | [inline] |
Set the number of iterations after that a restart is performed.
restart | number of iterations for a restarti, default is 30. |
const internal::solve_retval_with_guess<GMRES, Rhs, Guess> solveWithGuess | ( | const MatrixBase< Rhs > & | b, | |
const Guess & | x0 | |||
) | const [inline] |