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

_MatrixType	the type of the sparse matrix A, can be a dense or a sparse matrix.
_UpLo	the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
_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
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

Constructor & Destructor Documentation

ConjugateGradient() [1/2]

template<typename _MatrixType, int _UpLo, typename _Preconditioner>

ConjugateGradient ( )

inline

Default constructor.

Referenced by solveWithGuess().

ConjugateGradient() [2/2]

template<typename _MatrixType, int _UpLo, typename _Preconditioner>

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

analyzePattern()

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.

compute()

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.

error()

RealScalar error ( ) const

inlineinherited

Returns

the tolerance error reached during the last solve

factorize()

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.

info()

ComputationInfo info ( ) const

inlineinherited

Returns

Success if the iterations converged, and NoConvergence otherwise.

iterations()

int iterations ( ) const

inlineinherited

Returns

the number of iterations performed during the last solve

maxIterations()

int maxIterations ( ) const

inlineinherited

Returns

the max number of iterations

preconditioner() [1/2]

Preconditioner & preconditioner ( )

inlineinherited

Returns

a read-write reference to the preconditioner for custom configuration.

preconditioner() [2/2]

const Preconditioner & preconditioner ( ) const

inlineinherited

Returns

a read-only reference to the preconditioner.

setMaxIterations()

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

inlineinherited

Sets the max number of iterations

setTolerance()

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

inlineinherited

Sets the tolerance threshold used by the stopping criteria

solve() [1/2]

const internal::solve_retval< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >, Rhs > solve ( const MatrixBase< Rhs > & b ) const

inlineinherited

Returns

the solution x of using the current decomposition of A.

See also

compute()

solve() [2/2]

const internal::sparse_solve_retval< IterativeSolverBase, Rhs > solve ( const SparseMatrixBase< Rhs > & b ) const

inlineinherited

Returns

the solution x of using the current decomposition of A.

See also

compute()

solveWithGuess()

template<typename _MatrixType, int _UpLo, typename _Preconditioner>

template<typename Rhs, typename Guess>

const internal::solve_retval_with_guess< ConjugateGradient, Rhs, Guess > solveWithGuess ( const MatrixBase< Rhs > & b, const Guess & x0 ) const

inline

Returns

the solution x of using the current decomposition of A x0 as an initial solution.

See also

compute()

References ConjugateGradient().

tolerance()

RealScalar tolerance ( ) const

inlineinherited

Returns

the tolerance threshold used by the stopping criteria

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

• ConjugateGradient.h