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      1 #include <iostream>
      2 #include <Eigen/Core>
      3 #include <Eigen/Dense>
      4 #include <Eigen/IterativeLinearSolvers>
      5 #include <unsupported/Eigen/IterativeSolvers>
      6 
      7 class MatrixReplacement;
      8 using Eigen::SparseMatrix;
      9 
     10 namespace Eigen {
     11 namespace internal {
     12   // MatrixReplacement looks-like a SparseMatrix, so let's inherits its traits:
     13   template<>
     14   struct traits<MatrixReplacement> :  public Eigen::internal::traits<Eigen::SparseMatrix<double> >
     15   {};
     16 }
     17 }
     18 
     19 // Example of a matrix-free wrapper from a user type to Eigen's compatible type
     20 // For the sake of simplicity, this example simply wrap a Eigen::SparseMatrix.
     21 class MatrixReplacement : public Eigen::EigenBase<MatrixReplacement> {
     22 public:
     23   // Required typedefs, constants, and method:
     24   typedef double Scalar;
     25   typedef double RealScalar;
     26   typedef int StorageIndex;
     27   enum {
     28     ColsAtCompileTime = Eigen::Dynamic,
     29     MaxColsAtCompileTime = Eigen::Dynamic,
     30     IsRowMajor = false
     31   };
     32 
     33   Index rows() const { return mp_mat->rows(); }
     34   Index cols() const { return mp_mat->cols(); }
     35 
     36   template<typename Rhs>
     37   Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct> operator*(const Eigen::MatrixBase<Rhs>& x) const {
     38     return Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct>(*this, x.derived());
     39   }
     40 
     41   // Custom API:
     42   MatrixReplacement() : mp_mat(0) {}
     43 
     44   void attachMyMatrix(const SparseMatrix<double> &mat) {
     45     mp_mat = &mat;
     46   }
     47   const SparseMatrix<double> my_matrix() const { return *mp_mat; }
     48 
     49 private:
     50   const SparseMatrix<double> *mp_mat;
     51 };
     52 
     53 
     54 // Implementation of MatrixReplacement * Eigen::DenseVector though a specialization of internal::generic_product_impl:
     55 namespace Eigen {
     56 namespace internal {
     57 
     58   template<typename Rhs>
     59   struct generic_product_impl<MatrixReplacement, Rhs, SparseShape, DenseShape, GemvProduct> // GEMV stands for matrix-vector
     60   : generic_product_impl_base<MatrixReplacement,Rhs,generic_product_impl<MatrixReplacement,Rhs> >
     61   {
     62     typedef typename Product<MatrixReplacement,Rhs>::Scalar Scalar;
     63 
     64     template<typename Dest>
     65     static void scaleAndAddTo(Dest& dst, const MatrixReplacement& lhs, const Rhs& rhs, const Scalar& alpha)
     66     {
     67       // This method should implement "dst += alpha * lhs * rhs" inplace,
     68       // however, for iterative solvers, alpha is always equal to 1, so let's not bother about it.
     69       assert(alpha==Scalar(1) && "scaling is not implemented");
     70 
     71       // Here we could simply call dst.noalias() += lhs.my_matrix() * rhs,
     72       // but let's do something fancier (and less efficient):
     73       for(Index i=0; i<lhs.cols(); ++i)
     74         dst += rhs(i) * lhs.my_matrix().col(i);
     75     }
     76   };
     77 
     78 }
     79 }
     80 
     81 int main()
     82 {
     83   int n = 10;
     84   Eigen::SparseMatrix<double> S = Eigen::MatrixXd::Random(n,n).sparseView(0.5,1);
     85   S = S.transpose()*S;
     86 
     87   MatrixReplacement A;
     88   A.attachMyMatrix(S);
     89 
     90   Eigen::VectorXd b(n), x;
     91   b.setRandom();
     92 
     93   // Solve Ax = b using various iterative solver with matrix-free version:
     94   {
     95     Eigen::ConjugateGradient<MatrixReplacement, Eigen::Lower|Eigen::Upper, Eigen::IdentityPreconditioner> cg;
     96     cg.compute(A);
     97     x = cg.solve(b);
     98     std::cout << "CG:       #iterations: " << cg.iterations() << ", estimated error: " << cg.error() << std::endl;
     99   }
    100 
    101   {
    102     Eigen::BiCGSTAB<MatrixReplacement, Eigen::IdentityPreconditioner> bicg;
    103     bicg.compute(A);
    104     x = bicg.solve(b);
    105     std::cout << "BiCGSTAB: #iterations: " << bicg.iterations() << ", estimated error: " << bicg.error() << std::endl;
    106   }
    107 
    108   {
    109     Eigen::GMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;
    110     gmres.compute(A);
    111     x = gmres.solve(b);
    112     std::cout << "GMRES:    #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl;
    113   }
    114 
    115   {
    116     Eigen::DGMRES<MatrixReplacement, Eigen::IdentityPreconditioner> gmres;
    117     gmres.compute(A);
    118     x = gmres.solve(b);
    119     std::cout << "DGMRES:   #iterations: " << gmres.iterations() << ", estimated error: " << gmres.error() << std::endl;
    120   }
    121 
    122   {
    123     Eigen::MINRES<MatrixReplacement, Eigen::Lower|Eigen::Upper, Eigen::IdentityPreconditioner> minres;
    124     minres.compute(A);
    125     x = minres.solve(b);
    126     std::cout << "MINRES:   #iterations: " << minres.iterations() << ", estimated error: " << minres.error() << std::endl;
    127   }
    128 }
    129