Eigen  3.2.8
Public Member Functions
BiCGSTAB< _MatrixType, _Preconditioner > Class Template Reference
IterativeLinearSolvers module

Detailed Description

template<typename _MatrixType, typename _Preconditioner>
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 >:

List of all members.

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) [inline, explicit]

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) [inline, inherited]

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) [inline, inherited]

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 [inline, inherited]
Returns:
the tolerance error reached during the last solve
BiCGSTAB< _MatrixType, _Preconditioner > & factorize ( const EigenBase< InputDerived > &  A) [inline, inherited]

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 [inline, inherited]
Returns:
Success if the iterations converged, and NoConvergence otherwise.
int iterations ( ) const [inline, inherited]
Returns:
the number of iterations performed during the last solve
int maxIterations ( ) const [inline, inherited]
Returns:
the max number of iterations
Preconditioner& preconditioner ( ) [inline, inherited]
Returns:
a read-write reference to the preconditioner for custom configuration.
const Preconditioner& preconditioner ( ) const [inline, inherited]
Returns:
a read-only reference to the preconditioner.
BiCGSTAB< _MatrixType, _Preconditioner > & setMaxIterations ( int  maxIters) [inline, inherited]

Sets the max number of iterations

BiCGSTAB< _MatrixType, _Preconditioner > & setTolerance ( const RealScalar &  tolerance) [inline, inherited]

Sets the tolerance threshold used by the stopping criteria

const internal::solve_retval<BiCGSTAB< _MatrixType, _Preconditioner > , Rhs> solve ( const MatrixBase< Rhs > &  b) const [inline, inherited]
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 [inline, inherited]
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 [inline, inherited]
Returns:
the tolerance threshold used by the stopping criteria
The documentation for this class was generated from the following file:
 All Classes Functions Variables Typedefs Enumerations Enumerator Friends