Add matrix-free solver example

1 files changed, 128 insertions, 0 deletions

diff --git a/doc/examples/matrixfree_cg.cpp b/doc/examples/matrixfree_cg.cpp
new file mode 100644
index 000000000..6a205aea3
--- /dev/null
+++ b/doc/examples/matrixfree_cg.cpp
@@ -0,0 +1,128 @@
+#include <iostream>
+#include <Eigen/Core>
+#include <Eigen/Dense>
+#include <Eigen/IterativeLinearSolvers>
+#include <unsupported/Eigen/IterativeSolvers>
+
+class MatrixReplacement;
+using Eigen::SparseMatrix;
+
+namespace Eigen {
+namespace internal {
+  // MatrixReplacement looks-like a SparseMatrix, so let's inherits its traits:
+  template<>
+  struct traits<MatrixReplacement> :  public Eigen::internal::traits<Eigen::SparseMatrix<double> >
+  {};
+}
+}
+
+// Example of a matrix-free wrapper from a user type to Eigen's compatible type
+// For the sake of simplicity, this example simply wrap a Eigen::SparseMatrix.
+class MatrixReplacement : public Eigen::EigenBase<MatrixReplacement> {
+public:
+  // Required typedefs, constants, and method:
+  typedef double Scalar;
+  typedef double RealScalar;
+  typedef int StorageIndex;
+  enum {
+    ColsAtCompileTime = Eigen::Dynamic,
+    MaxColsAtCompileTime = Eigen::Dynamic,
+    IsRowMajor = false
+  };
+
+  Index rows() const { return mp_mat->rows(); }
+  Index cols() const { return mp_mat->cols(); }
+
+  template<typename Rhs>
+  Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct> operator*(const Eigen::MatrixBase<Rhs>& x) const {
+    return Eigen::Product<MatrixReplacement,Rhs,Eigen::AliasFreeProduct>(*this, x.derived());
+  }
+
+  // Custom API:
+  MatrixReplacement() : mp_mat(0) {}
+
+  void attachMyMatrix(const SparseMatrix<double> &mat) {
+    mp_mat = &mat;
+  }
+  const SparseMatrix<double> my_matrix() const { return *mp_mat; }
+
+private:
+  const SparseMatrix<double> *mp_mat;
+};
+
+
+// Implementation of MatrixReplacement * Eigen::DenseVector though a specialization of internal::generic_product_impl:
+namespace Eigen {
+namespace internal {
+
+  template<typename Rhs>
+  struct generic_product_impl<MatrixReplacement, Rhs, SparseShape, DenseShape, GemvProduct> // GEMV stands for matrix-vector
+  : generic_product_impl_base<MatrixReplacement,Rhs,generic_product_impl<MatrixReplacement,Rhs> >
+  {
+    typedef typename Product<MatrixReplacement,Rhs>::Scalar Scalar;
+
+    template<typename Dest>
+    static void scaleAndAddTo(Dest& dst, const MatrixReplacement& lhs, const Rhs& rhs, const Scalar& alpha)
+    {
+      // This method should implement "dst += alpha * lhs * rhs" inplace,
+      // however, for iterative solvers, alpha is always equal to 1, so let's not bother about it.
+      assert(alpha==Scalar(1) && "scaling is not implemented");
+
+      // Here we could simply call dst.noalias() += lhs.my_matrix() * rhs,
+      // but let's do something fancier (and less efficient):
+      for(Index i=0; i<lhs.cols(); ++i)
+        dst += rhs(i) * lhs.my_matrix().col(i);
+    }
+  };
+
+}
+}
+
+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;
+  }
+}