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BiCGSTAB< _MatrixType, _Preconditioner > Class Template Reference
IterativeLinearSolvers module

Detailed Description

template<typename _MatrixType, typename _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar>>
class Eigen::BiCGSTAB< _MatrixType, _Preconditioner >

A bi conjugate gradient stabilized solver for sparse square problems.

This class allows to solve for A.x = b sparse linear problems using a bi conjugate gradient stabilized algorithm. The vectors x and b can be either dense or sparse.

Template Parameters
_MatrixTypethe type of the sparse matrix A, can be a dense or a sparse matrix.
_Preconditionerthe 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
* BiCGSTAB<SparseMatrix<double> > solver;
* solver.compute(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.

See Also
class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
+ Inheritance diagram for BiCGSTAB< _MatrixType, _Preconditioner >:

Public Member Functions

BiCGSTAB< _MatrixType,
_Preconditioner > & 		analyzePattern (const EigenBase< InputDerived > &A)
 
 BiCGSTAB ()
 
template<typename MatrixDerived >
 BiCGSTAB (const EigenBase< MatrixDerived > &A)
 
BiCGSTAB< _MatrixType,
_Preconditioner > & 		compute (const EigenBase< InputDerived > &A)
 
RealScalar error () const
 
BiCGSTAB< _MatrixType,
_Preconditioner > & 		factorize (const EigenBase< InputDerived > &A)
 
ComputationInfo info () const
 
int iterations () const
 
int maxIterations () const
 
Preconditioner & preconditioner ()
 
const Preconditioner & preconditioner () const
 
BiCGSTAB< _MatrixType,
_Preconditioner > & 		setMaxIterations (int maxIters)
 
BiCGSTAB< _MatrixType,
_Preconditioner > & 		setTolerance (const RealScalar &tolerance)
 
const internal::solve_retval
< BiCGSTAB< _MatrixType,
_Preconditioner >, Rhs > 		solve (const MatrixBase< Rhs > &b) const
 
const
internal::sparse_solve_retval
< IterativeSolverBase, Rhs > 		solve (const SparseMatrixBase< Rhs > &b) const
 
template<typename Rhs , typename Guess >
const
internal::solve_retval_with_guess
< BiCGSTAB, Rhs, Guess > 		solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
 
RealScalar tolerance () const
 

Constructor & Destructor Documentation

BiCGSTAB ( )
inline

Default constructor.

Referenced by BiCGSTAB< _MatrixType, _Preconditioner >::solveWithGuess().

BiCGSTAB ( const EigenBase< MatrixDerived > &  A)
inlineexplicit

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().

Warning
this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.

Member Function Documentation

BiCGSTAB< _MatrixType, _Preconditioner > & analyzePattern ( const EigenBase< InputDerived > &  A)
inlineinherited

Initializes the iterative solver for the sparcity pattern of the matrix A for further solving Ax=b problems.

Currently, this function mostly call analyzePattern on the preconditioner. In the future we might, for instance, implement column reodering for faster matrix vector products.

BiCGSTAB< _MatrixType, _Preconditioner > & compute ( const EigenBase< InputDerived > &  A)
inlineinherited

Initializes the iterative solver with the matrix A for further solving Ax=b problems.

Currently, this function mostly initialized/compute the preconditioner. In the future we might, for instance, implement column reodering for faster matrix vector products.

Warning
this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.
RealScalar error ( ) const
inlineinherited
Returns
the tolerance error reached during the last solve
BiCGSTAB< _MatrixType, _Preconditioner > & factorize ( const EigenBase< InputDerived > &  A)
inlineinherited

Initializes the iterative solver with the numerical values of the matrix A for further solving Ax=b problems.

Currently, this function mostly call factorize on the preconditioner.

Warning
this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.
ComputationInfo info ( ) const
inlineinherited
Returns
Success if the iterations converged, and NoConvergence otherwise.
int iterations ( ) const
inlineinherited
Returns
the number of iterations performed during the last solve
int maxIterations ( ) const
inlineinherited
Returns
the max number of iterations
Preconditioner& preconditioner ( )
inlineinherited
Returns
a read-write reference to the preconditioner for custom configuration.
const Preconditioner& preconditioner ( ) const
inlineinherited
Returns
a read-only reference to the preconditioner.
BiCGSTAB< _MatrixType, _Preconditioner > & setMaxIterations ( int  maxIters)
inlineinherited

Sets the max number of iterations

BiCGSTAB< _MatrixType, _Preconditioner > & setTolerance ( const RealScalar &  tolerance)
inlineinherited

Sets the tolerance threshold used by the stopping criteria

const internal::solve_retval<BiCGSTAB< _MatrixType, _Preconditioner > , Rhs> solve ( const MatrixBase< Rhs > &  b) const
inlineinherited
Returns
the solution x of $ A x = b $ using the current decomposition of A.
See Also
compute()
const internal::sparse_solve_retval<IterativeSolverBase, Rhs> solve ( const SparseMatrixBase< Rhs > &  b) const
inlineinherited
Returns
the solution x of $ A x = b $ using the current decomposition of A.
See Also
compute()
const internal::solve_retval_with_guess<BiCGSTAB, Rhs, Guess> solveWithGuess ( const MatrixBase< Rhs > &  b,
const Guess &  x0 
) const
inline
Returns
the solution x of $ A x = b $ using the current decomposition of A x0 as an initial solution.
See Also
compute()

References BiCGSTAB< _MatrixType, _Preconditioner >::BiCGSTAB().

RealScalar tolerance ( ) const
inlineinherited
Returns
the tolerance threshold used by the stopping criteria
The documentation for this class was generated from the following file: