Public Member Functions | List of all members
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > Class Template Reference

A conjugate gradient solver for sparse self-adjoint problems. More...

#include <ConjugateGradient.h>

+ Inheritance diagram for ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >:

Public Member Functions

ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
analyzePattern (const MatrixType &A)
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
compute (const MatrixType &A)
 ConjugateGradient ()
 ConjugateGradient (const MatrixType &A)
RealScalar error () const
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
factorize (const MatrixType &A)
ComputationInfo info () const
int iterations () const
int maxIterations () const
Preconditioner & preconditioner ()
const Preconditioner & preconditioner () const
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
setMaxIterations (int maxIters)
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
setTolerance (RealScalar tolerance)
const internal::solve_retval
< ConjugateGradient
< _MatrixType, _UpLo,
_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
< ConjugateGradient, Rhs,
Guess > 
solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
RealScalar tolerance () const

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
class Eigen::ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >

A conjugate gradient solver for sparse self-adjoint problems.

This class allows to solve for A.x = b sparse linear problems using a conjugate gradient algorithm. The sparse matrix A must be selfadjoint. 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.
_UpLothe triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
_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
ConjugateGradient<SparseMatrix<double> > cg;
cg.compute(A);
x = cg.solve(b);
std::cout << "#iterations: " << cg.iterations() << std::endl;
std::cout << "estimated error: " << cg.error() << std::endl;
// update b, and solve again
x = cg.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. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error:

See Also
class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Constructor & Destructor Documentation

ConjugateGradient ( )
inline
ConjugateGradient ( 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().

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

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & analyzePattern ( const MatrixType &  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.

References Eigen::Success.

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & compute ( const MatrixType &  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.

References Eigen::Success.

RealScalar error ( ) const
inlineinherited
Returns
the tolerance error reached during the last solve
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & factorize ( const MatrixType &  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.

References Eigen::Success.

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.
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & setMaxIterations ( int  maxIters)
inlineinherited

Sets the max number of iterations

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & setTolerance ( RealScalar  tolerance)
inlineinherited

Sets the tolerance threshold used by the stopping criteria

References IterativeSolverBase< Derived >::tolerance().

const internal::solve_retval<ConjugateGradient< _MatrixType, _UpLo, _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()

References EigenBase< Derived >::derived(), and SparseMatrixBase< Derived >::rows().

const internal::solve_retval_with_guess<ConjugateGradient, 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 ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >::ConjugateGradient().

RealScalar tolerance ( ) const
inlineinherited
Returns
the tolerance threshold used by the stopping criteria

The documentation for this class was generated from the following file: