Eigen  3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)
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Eigen::LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > Class Template Reference
Sparse linear algebra » Reference » IterativeLinearSolvers module

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);
Eigen::VectorXd
Matrix< double, Dynamic, 1 > VectorXd
Dynamic×1 vector of type double.
Definition: Matrix.h:501

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

Public Member Functions

 LeastSquaresConjugateGradient ()
 
template<typename MatrixDerived >
 LeastSquaresConjugateGradient (const EigenBase< MatrixDerived > &A)
 
- Public Member Functions inherited from Eigen::IterativeSolverBase< LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > >
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & analyzePattern (const EigenBase< MatrixDerived > &A)
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & compute (const EigenBase< MatrixDerived > &A)
 
RealScalar error () const
 
LeastSquaresConjugateGradient< MatrixType_, Preconditioner_ > & factorize (const EigenBase< MatrixDerived > &A)
 
ComputationInfo info () const
 
Index iterations () const
 
 IterativeSolverBase ()
 
 IterativeSolverBase (const EigenBase< MatrixDerived > &A)
 
Index maxIterations () const
 
Preconditioner & preconditioner ()
 
const Preconditioner & preconditioner () const
 
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
 
- Public Member Functions inherited from Eigen::SparseSolverBase< Derived >
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 ()
 

Constructor & Destructor Documentation

◆ LeastSquaresConjugateGradient() [1/2]

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

Default constructor.

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