Eigen
3.3.9

A conjugate gradient solver for sparse (or dense) selfadjoint 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.
_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 LowerUpper in which the full matrix entries will be considered. Default is Lower , best performance is LowerUpper . 
_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>::epsilon() for the tolerance.
The tolerance corresponds to the relative residual error: Axb/b
Performance: Even though the default value of _UpLo
is Lower
, significantly higher performance is achieved when using a complete matrix and LowerUpper as the _UpLo template parameter. Moreover, in this case multithreading can be exploited if the user code is compiled with OpenMP enabled. See Eigen and multithreading for details.
This class can be used as the direct solver classes. Here is a typical usage example:
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 matrixfree context, see the following example .
Public Member Functions  
ConjugateGradient ()  
template<typename MatrixDerived >  
ConjugateGradient (const EigenBase< MatrixDerived > &A)  

inline 
Default constructor.

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().