Eigen8b7c:f320:99b9:690f:4595:cd17:293a:c069onjugateGradient  
template<typename _MatrixType, int _UpLo, typename _Preconditioner> class Eigen8b7c:f320:99b9:690f:4595:cd17:293a:c069onjugateGradient< _MatrixType, _UpLo, _Preconditioner > A conjugate gradient solver for sparse (or dense) self-adjoint problems.  This class allows to solve for A.x = b linear problems using an iterative conjugate gradient algorithm. The matrix A must be selfadjoint. 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. 
 
_UpLo
the triangular part that will be used for the computations. It can be Lower, Upper, or Lower|Upper in which the full matrix entries will be considered. Default is Lower, best performance is Lower|Upper. 
 
_Preconditioner
the type of the preconditioner. Default is DiagonalPreconditioner

    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>8b7c:f320:99b9:690f:4595:cd17:293a:c069psilon() for the tolerance. The tolerance corresponds to the relative residual error: |Ax-b|/|b| Performance: Even though the default value of _UpLo is Lower, significantly higher performance is achieved when using a complete matrix and Lower|Upper as the _UpLo template parameter. Moreover, in this case multi-threading can be exploited if the user code is compiled with OpenMP enabled. See Eigen and multi-threading for details. 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>, Lower|Upper> cg;
cg.compute(A);
x = cg.solve(b);
st8b7c:f320:99b9:690f:4595:cd17:293a:c069cout << "#iterations:     " << cg.iterations() << st8b7c:f320:99b9:690f:4595:cd17:293a:c069endl;
st8b7c:f320:99b9:690f:4595:cd17:293a:c069cout << "estimated error: " << cg.error()      << st8b7c:f320:99b9:690f:4595:cd17:293a:c069endl;
// 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. ConjugateGradient can also be used in a matrix-free context, see the following example . 
See also
class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner 
              
 

ConjugateGradient ()
   template<typename MatrixDerived >  
 

ConjugateGradient (const EigenBase< MatrixDerived > &A)
   
 Public Member Functions inherited from Eigen8b7c:f320:99b9:690f:4595:cd17:293a:c069IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >
 

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & 

analyzePattern (const EigenBase< MatrixDerived > &A)
   

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & 

compute (const EigenBase< MatrixDerived > &A)
   
RealScalar 

error () const
   

ConjugateGradient< _MatrixType, _UpLo, _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
   

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & 

setMaxIterations (Index maxIters)
   

ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > & 

setTolerance (const RealScalar &tolerance)
   
const SolveWithGuess< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner >, Rhs, Guess > 

solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const
   
RealScalar 

tolerance () const
   
 Public Member Functions inherited from Eigen8b7c:f320:99b9:690f:4595:cd17:293a:c069SparseSolverBase< 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 ()
     ConjugateGradient() [1/2]
    template<typename _MatrixType , int _UpLo, typename _Preconditioner >       
Eigen8b7c:f320:99b9:690f:4595:cd17:293a:c069onjugateGradient< _MatrixType, _UpLo, _Preconditioner >8b7c:f320:99b9:690f:4595:cd17:293a:c069onjugateGradient  ( 
)      inline    
 Default constructor.     ConjugateGradient() [2/2]
    template<typename _MatrixType , int _UpLo, typename _Preconditioner >   template<typename MatrixDerived >       
Eigen8b7c:f320:99b9:690f:4595:cd17:293a:c069onjugateGradient< _MatrixType, _UpLo, _Preconditioner >8b7c:f320:99b9:690f:4595:cd17:293a:c069onjugateGradient  ( 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: ConjugateGradient.h   

    
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