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Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > Class Template Reference
Sparse linear algebra » Reference » IterativeLinearSolvers module

A conjugate gradient solver for sparse (or dense) least-square problems. More...

+ Inheritance diagram for Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >:

Public Types

typedef MatrixType_ MatrixType
 
typedef Preconditioner_ Preconditioner
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 
- Public Types inherited from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >
enum  
 
typedef internal::traits< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >::MatrixType MatrixType
 
typedef internal::traits< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >::Preconditioner Preconditioner
 
typedef MatrixType::RealScalar RealScalar
 
typedef MatrixType::Scalar Scalar
 
typedef MatrixType::StorageIndex StorageIndex
 

Public Member Functions

template<typename Rhs , typename Dest >
void _solve_vector_with_guess_impl (const Rhs &b, Dest &x) const
 
 LeastSquaresConjugateGradient ()
 
template<typename MatrixDerived >
 LeastSquaresConjugateGradient (const EigenBase< MatrixDerived > &A)
 
 ~LeastSquaresConjugateGradient ()
 
- Public Member Functions inherited from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >
void _solve_impl (const Rhs &b, Dest &x) const
 
std::enable_if_t< Rhs::ColsAtCompileTime!=1 &&DestDerived::ColsAtCompileTime!=1 > _solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &aDest) const
 
std::enable_if_t< Rhs::ColsAtCompileTime==1||DestDerived::ColsAtCompileTime==1 > _solve_with_guess_impl (const Rhs &b, MatrixBase< DestDerived > &dest) const
 
void _solve_with_guess_impl (const Rhs &b, SparseMatrixBase< DestDerived > &aDest) const
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & analyzePattern (const EigenBase< MatrixDerived > &A)
 
EIGEN_CONSTEXPR Index cols () const EIGEN_NOEXCEPT
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & compute (const EigenBase< MatrixDerived > &A)
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & derived ()
 
const LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & derived () const
 
RealScalar error () const
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & factorize (const EigenBase< MatrixDerived > &A)
 
ComputationInfo info () const
 
Index iterations () const
 
 IterativeSolverBase ()
 
 IterativeSolverBase (const EigenBase< MatrixDerived > &A)
 
 IterativeSolverBase (IterativeSolverBase &&)=default
 
Index maxIterations () const
 
Preconditioner & preconditioner ()
 
const Preconditioner & preconditioner () const
 
EIGEN_CONSTEXPR Index rows () const EIGEN_NOEXCEPT
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & setMaxIterations (Index maxIters)
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & setTolerance (const RealScalar &tolerance)
 
const SolveWithGuess< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >, Rhs, Guess > solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
 
RealScalar tolerance () const
 
 ~IterativeSolverBase ()
 
- Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
Derived & derived ()
 
const Derived & derived () const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const MatrixBase< Rhs > &b) const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const SparseMatrixBase< Rhs > &b) const
 
 SparseSolverBase ()
 
 SparseSolverBase (SparseSolverBase &&other)
 
 ~SparseSolverBase ()
 

Private Types

typedef IterativeSolverBase< LeastSquaresConjugateGradient > Base
 

Private Member Functions

const ActualMatrixType & matrix () const
 

Private Attributes

RealScalar m_error
 
ComputationInfo m_info
 
bool m_isInitialized
 
Index m_iterations
 

Additional Inherited Members

- Protected Types inherited from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >
typedef MatrixWrapper::ActualMatrixType ActualMatrixType
 
typedef SparseSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > > Base
 
typedef internal::generic_matrix_wrapper< MatrixType > MatrixWrapper
 
- Protected Member Functions inherited from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >
void grab (const InputType &A)
 
void init ()
 
const ActualMatrixType & matrix () const
 
- Protected Attributes inherited from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >
bool m_analysisIsOk
 
RealScalar m_error
 
bool m_factorizationIsOk
 
ComputationInfo m_info
 
bool m_isInitialized
 
Index m_iterations
 
MatrixWrapper m_matrixWrapper
 
Index m_maxIterations
 
Preconditioner m_preconditioner
 
RealScalar m_tolerance
 
- Protected Attributes inherited from Eigen::SparseSolverBase< Derived >
bool m_isInitialized
 

Detailed Description

template<typename MatrixType_, typename Preconditioner_>
class Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >

A conjugate gradient solver for sparse (or dense) least-square problems.

This class solves for the least-squares solution to A x = b using an iterative conjugate gradient algorithm. The matrix A can be non symmetric and rectangular, but the matrix A' A should be positive-definite to guaranty stability. Otherwise, the SparseLU or SparseQR classes might be preferable. The matrix A and the vectors x and b can be either dense or sparse.

Template Parameters
MatrixType_the type of the matrix A, can be a dense or a sparse matrix.
Preconditioner_the type of the preconditioner. Default is LeastSquareDiagonalPreconditioner

This class follows the sparse solver concept .

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 m=1000000, n = 10000;
VectorXd x(n), b(m);
SparseMatrix<double> A(m,n);
// fill A and b
LeastSquaresConjugateGradient<SparseMatrix<double> > lscg;
lscg.compute(A);
x = lscg.solve(b);
std::cout << "#iterations: " << lscg.iterations() << std::endl;
std::cout << "estimated error: " << lscg.error() << std::endl;
// update b, and solve again
x = lscg.solve(b);
m
Matrix3f m
Definition: AngleAxis_mimic_euler.cpp:1
b
Array< int, 3, 1 > b
Definition: Array_variadic_ctor_cxx11.cpp:2
n
int n
Definition: BiCGSTAB_simple.cpp:1
x
x
Definition: BiCGSTAB_simple.cpp:7
A
MatrixXcf A
Definition: ComplexEigenSolver_compute.cpp:1
Eigen::VectorXd
Matrix< double, Dynamic, 1 > VectorXd
Dynamic×1 vector of type double.
Definition: Matrix.h:502
Code

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 ConjugateGradient, SparseLU, SparseQR

Definition at line 151 of file LeastSquareConjugateGradient.h.

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , typename Preconditioner_ >
typedef IterativeSolverBase<LeastSquaresConjugateGradient> Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::Base
private

Definition at line 153 of file LeastSquareConjugateGradient.h.

◆ MatrixType

template<typename MatrixType_ , typename Preconditioner_ >
typedef MatrixType_ Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::MatrixType

Definition at line 160 of file LeastSquareConjugateGradient.h.

◆ Preconditioner

template<typename MatrixType_ , typename Preconditioner_ >
typedef Preconditioner_ Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::Preconditioner

Definition at line 163 of file LeastSquareConjugateGradient.h.

◆ RealScalar

template<typename MatrixType_ , typename Preconditioner_ >
typedef MatrixType::RealScalar Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::RealScalar

Definition at line 162 of file LeastSquareConjugateGradient.h.

◆ Scalar

template<typename MatrixType_ , typename Preconditioner_ >
typedef MatrixType::Scalar Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::Scalar

Definition at line 161 of file LeastSquareConjugateGradient.h.

Constructor & Destructor Documentation

◆ LeastSquaresConjugateGradient() [1/2]

template<typename MatrixType_ , typename Preconditioner_ >
Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::LeastSquaresConjugateGradient ( )
inline

Default constructor.

Definition at line 168 of file LeastSquareConjugateGradient.h.

168 : Base() {}
Eigen::LeastSquaresConjugateGradient::Base
IterativeSolverBase< LeastSquaresConjugateGradient > Base
Definition: LeastSquareConjugateGradient.h:153
Code

◆ LeastSquaresConjugateGradient() [2/2]

template<typename MatrixType_ , typename Preconditioner_ >
template<typename MatrixDerived >
Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::LeastSquaresConjugateGradient ( 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.

Definition at line 181 of file LeastSquareConjugateGradient.h.

181 : Base(A.derived()) {}
Code

◆ ~LeastSquaresConjugateGradient()

template<typename MatrixType_ , typename Preconditioner_ >
Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::~LeastSquaresConjugateGradient ( )
inline

Definition at line 183 of file LeastSquareConjugateGradient.h.

183 {}
Code

Member Function Documentation

◆ _solve_vector_with_guess_impl()

template<typename MatrixType_ , typename Preconditioner_ >
template<typename Rhs , typename Dest >
void Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ >::_solve_vector_with_guess_impl ( const Rhs &  b,
Dest &  x 
) const
inline

Definition at line 187 of file LeastSquareConjugateGradient.h.

188  {
189  m_iterations = Base::maxIterations();
190  m_error = Base::m_tolerance;
191 
192  internal::least_square_conjugate_gradient(matrix(), b, x, Base::m_preconditioner, m_iterations, m_error);
193  m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
194  }
Eigen::LeastSquaresConjugateGradient::matrix
const ActualMatrixType & matrix() const
Definition: IterativeSolverBase.h:424
Eigen::Success
@ Success
Definition: Constants.h:446
Eigen::NoConvergence
@ NoConvergence
Definition: Constants.h:450
Eigen::internal::least_square_conjugate_gradient
EIGEN_DONT_INLINE void least_square_conjugate_gradient(const MatrixType &mat, const Rhs &rhs, Dest &x, const Preconditioner &precond, Index &iters, typename Dest::RealScalar &tol_error)
Definition: LeastSquareConjugateGradient.h:30
Code

◆ matrix()

template<typename MatrixType_ , typename Preconditioner_ >
const ActualMatrixType& Eigen::IterativeSolverBase< Derived >::matrix
inlineprivate

Definition at line 424 of file IterativeSolverBase.h.

425  {
426  return m_matrixWrapper.matrix();
427  }
Code

Member Data Documentation

◆ m_error

template<typename MatrixType_ , typename Preconditioner_ >
RealScalar Eigen::IterativeSolverBase< Derived >::m_error
mutableprivate

Definition at line 441 of file IterativeSolverBase.h.

◆ m_info

template<typename MatrixType_ , typename Preconditioner_ >
ComputationInfo Eigen::IterativeSolverBase< Derived >::m_info
mutableprivate

Definition at line 443 of file IterativeSolverBase.h.

◆ m_isInitialized

template<typename MatrixType_ , typename Preconditioner_ >
bool Eigen::SparseSolverBase< Derived >::m_isInitialized
mutableprivate

Definition at line 149 of file SparseSolverBase.h.

◆ m_iterations

template<typename MatrixType_ , typename Preconditioner_ >
Index Eigen::IterativeSolverBase< Derived >::m_iterations
mutableprivate

Definition at line 442 of file IterativeSolverBase.h.

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