matrixfree_cg.cpp File Reference

#include <iostream>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/IterativeLinearSolvers>
#include <unsupported/Eigen/IterativeSolvers>

Classes
struct	Eigen::internal::traits< MatrixReplacement >
class	MatrixReplacement
struct	Eigen::internal::generic_product_impl< MatrixReplacement, Rhs, SparseShape, DenseShape, GemvProduct >

Namespaces
	Eigen
	Namespace containing all symbols from the Eigen library.
	Eigen::internal
	Namespace containing low-level routines from the Eigen library.

Functions
int	main ()

Function Documentation

main()

int main

(

)

           {
  int n = 10;
  Eigen::SparseMatrix<double> S = Eigen::MatrixXd::Random(n, n).sparseView(0.5, 1);
  S = S.transpose() * S;
 
  MatrixReplacement A;
  A.attachMyMatrix(S);
 
  Eigen::VectorXd b(n), x;
  b.setRandom();
 
  // Solve Ax = b using various iterative solver with matrix-free version:
  {
    Eigen::ConjugateGradient<MatrixReplacement, Eigen::Lower | Eigen::Upper, Eigen::IdentityPreconditioner> cg;
    cg.compute(A);
    x = cg.solve(b);
    std::cout << "CG:       #iterations: " << cg.iterations() << ", estimated error: " << cg.error() << std::endl;
  }
 
  {
    Eigen::BiCGSTAB<MatrixReplacement, Eigen::IdentityPreconditioner> bicg;
    bicg.compute(A);
    x = bicg.solve(b);
    std::cout << "BiCGSTAB: #iterations: " << bicg.iterations() << ", estimated error: " << bicg.error() << std::endl;
  }
 
  {
    Eigen::GMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;
    gmres.compute(A);
    x = gmres.solve(b);
    std::cout << "GMRES:    #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl;
  }
 
  {
    Eigen::DGMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;
    gmres.compute(A);
    x = gmres.solve(b);
    std::cout << "DGMRES:   #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl;
  }
 
  {
    Eigen::MINRES<MatrixReplacement, Eigen::Lower | Eigen::Upper, Eigen::IdentityPreconditioner> minres;
    minres.compute(A);
    x = minres.solve(b);
    std::cout << "MINRES:   #iterations: " << minres.iterations() << ", estimated error: " << minres.error()
              << std::endl;
  }
}

References b, Eigen::IterativeSolverBase< Derived >::compute(), Eigen::IterativeSolverBase< Derived >::error(), Eigen::internal::gmres(), Eigen::IterativeSolverBase< Derived >::iterations(), Eigen::internal::minres(), n, oomph::QuadTreeNames::S, Eigen::SparseSolverBase< Derived >::solve(), and plotDoE::x.