Public Types | Public Member Functions | Protected Member Functions | Protected Attributes
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 >:

List of all members.

Public Types

enum  { UpLo }
typedef MatrixType::Index Index
typedef _MatrixType MatrixType
typedef _Preconditioner Preconditioner
typedef MatrixType::RealScalar RealScalar
typedef MatrixType::Scalar Scalar

Public Member Functions

template<typename Rhs , typename Dest >
void _solve (const Rhs &b, Dest &x) const
void _solve_sparse (const Rhs &b, SparseMatrix< DestScalar, DestOptions, DestIndex > &dest) const
template<typename Rhs , typename Dest >
void _solveWithGuess (const Rhs &b, Dest &x) const
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
analyzePattern (const MatrixType &A)
Index cols () const
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
compute (const MatrixType &A)
 ConjugateGradient ()
 ConjugateGradient (const MatrixType &A)
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
derived ()
const ConjugateGradient
< _MatrixType, _UpLo,
_Preconditioner > & 
derived () const
RealScalar error () const
ConjugateGradient< _MatrixType,
_UpLo, _Preconditioner > & 
factorize (const MatrixType &A)
ComputationInfo info () const
int iterations () const
int maxIterations () const
Preconditionerpreconditioner ()
const Preconditionerpreconditioner () const
Index rows () 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
 ~ConjugateGradient ()

Protected Member Functions

void init ()

Protected Attributes

bool m_analysisIsOk
RealScalar m_error
bool m_factorizationIsOk
ComputationInfo m_info
bool m_isInitialized
int m_iterations
int m_maxIterations
Preconditioner m_preconditioner
RealScalar m_tolerance
const MatrixTypemp_matrix

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: *

 x = VectorXd::Random(n);
 cg.setMaxIterations(1);
 int i = 0;
 do {
   x = cg.solveWithGuess(b,x);
   std::cout << i << " : " << cg.error() << std::endl;
   ++i;
 } while (cg.info()!=Success && i<100);

Note that such a step by step excution is slightly slower.

See also:
class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Member Typedef Documentation

typedef MatrixType::Index Index
typedef _MatrixType MatrixType
typedef _Preconditioner Preconditioner
typedef MatrixType::RealScalar RealScalar
typedef MatrixType::Scalar Scalar

Member Enumeration Documentation

anonymous enum
Enumerator:
UpLo 

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.
~ConjugateGradient ( ) [inline]

Member Function Documentation

void _solve ( const Rhs &  b,
Dest &  x 
) const [inline]
void _solve_sparse ( const Rhs &  b,
SparseMatrix< DestScalar, DestOptions, DestIndex > &  dest 
) const [inline, inherited]
void _solveWithGuess ( const Rhs &  b,
Dest &  x 
) const [inline]
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & analyzePattern ( const MatrixType 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.

References IterativeSolverBase< Derived >::derived(), IterativeSolverBase< Derived >::m_analysisIsOk, IterativeSolverBase< Derived >::m_info, IterativeSolverBase< Derived >::m_isInitialized, IterativeSolverBase< Derived >::m_preconditioner, and Eigen::Success.

Index cols ( void  ) const [inline, inherited]
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & compute ( const MatrixType 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.

References IterativeSolverBase< Derived >::derived(), IterativeSolverBase< Derived >::m_analysisIsOk, IterativeSolverBase< Derived >::m_factorizationIsOk, IterativeSolverBase< Derived >::m_info, IterativeSolverBase< Derived >::m_isInitialized, IterativeSolverBase< Derived >::m_preconditioner, IterativeSolverBase< Derived >::mp_matrix, and Eigen::Success.

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & derived ( ) [inline, inherited]
const ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & derived ( ) const [inline, inherited]
RealScalar error ( ) const [inline, inherited]
Returns:
the tolerance error reached during the last solve

References IterativeSolverBase< Derived >::m_error, and IterativeSolverBase< Derived >::m_isInitialized.

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

References IterativeSolverBase< Derived >::derived(), IterativeSolverBase< Derived >::m_analysisIsOk, IterativeSolverBase< Derived >::m_factorizationIsOk, IterativeSolverBase< Derived >::m_info, IterativeSolverBase< Derived >::m_preconditioner, IterativeSolverBase< Derived >::mp_matrix, and Eigen::Success.

ComputationInfo info ( ) const [inline, inherited]
Returns:
Success if the iterations converged, and NoConvergence otherwise.

References IterativeSolverBase< Derived >::m_info, and IterativeSolverBase< Derived >::m_isInitialized.

void init ( ) [inline, protected, inherited]
int iterations ( ) const [inline, inherited]
Returns:
the number of iterations performed during the last solve

References IterativeSolverBase< Derived >::m_isInitialized, and IterativeSolverBase< Derived >::m_iterations.

int maxIterations ( ) const [inline, inherited]
Preconditioner& preconditioner ( ) [inline, inherited]
Returns:
a read-write reference to the preconditioner for custom configuration.

References IterativeSolverBase< Derived >::m_preconditioner.

const Preconditioner& preconditioner ( ) const [inline, inherited]
Returns:
a read-only reference to the preconditioner.

References IterativeSolverBase< Derived >::m_preconditioner.

Index rows ( void  ) const [inline, inherited]
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & setMaxIterations ( int  maxIters) [inline, inherited]
ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & setTolerance ( RealScalar  tolerance) [inline, inherited]
const internal::solve_retval<ConjugateGradient< _MatrixType, _UpLo, _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()

References IterativeSolverBase< Derived >::derived(), IterativeSolverBase< Derived >::m_isInitialized, and IterativeSolverBase< Derived >::rows().

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()

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

const internal::solve_retval_with_guess<ConjugateGradient, Rhs, Guess> solveWithGuess ( const MatrixBase< Rhs > &  b,
const Guess &  x0 
) const [inline]
RealScalar tolerance ( ) const [inline, inherited]
Returns:
the tolerance threshold used by the stopping criteria

References IterativeSolverBase< Derived >::m_tolerance.


Member Data Documentation

bool m_analysisIsOk [mutable, protected, inherited]
RealScalar m_error [mutable, protected, inherited]
bool m_factorizationIsOk [mutable, protected, inherited]
ComputationInfo m_info [mutable, protected, inherited]
bool m_isInitialized [mutable, protected, inherited]
int m_iterations [mutable, protected, inherited]
int m_maxIterations [protected, inherited]
Preconditioner m_preconditioner [protected, inherited]
RealScalar m_tolerance [protected, inherited]
const MatrixType* mp_matrix [protected, inherited]

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