iterative-eigen.cpp

The following tutorial shows how to use the iterative solvers in ViennaCL with objects from the Eigen Library directly.

Note

Eigen provides its own iterative solvers in the meanwhile. Check these first.

We begin with including the necessary headers:

// System headers
#include <iostream>

#ifndef NDEBUG
 #define NDEBUG
#endif


// Eigen headers
#include <Eigen/Core>
#include <Eigen/Sparse>

// Must be set prior to any ViennaCL includes if you want to use ViennaCL algorithms on Eigen objects
#define VIENNACL_WITH_EIGEN 1

// ViennaCL headers
#include "viennacl/linalg/ilu.hpp"
#include "viennacl/linalg/cg.hpp"
#include "viennacl/linalg/bicgstab.hpp"
#include "viennacl/linalg/gmres.hpp"
#include "viennacl/io/matrix_market.hpp"


// Some helper functions for this tutorial:
#include "vector-io.hpp"

In the following we run the CG method, the BiCGStab method, and the GMRES method with Eigen types directly. First, the matrices are set up, then the respective solvers are called.

int main(int, char *[])
{
  typedef float ScalarType;

  Eigen::SparseMatrix<ScalarType, Eigen::RowMajor> eigen_matrix(65025, 65025);
  Eigen::VectorXf eigen_rhs;
  Eigen::VectorXf eigen_result;
  Eigen::VectorXf ref_result;
  Eigen::VectorXf residual;

Read system from file

std::cout << "Reading matrix (this might take some time)..." << std::endl;
eigen_matrix.reserve(65025 * 7);
if (!viennacl::io::read_matrix_market_file(eigen_matrix, "../examples/testdata/mat65k.mtx"))
{
  std::cout << "Error reading Matrix file. Make sure you run from the build/-folder." << std::endl;
  return EXIT_FAILURE;
}
//eigen_matrix.endFill();
std::cout << "Done: reading matrix" << std::endl;

if (!readVectorFromFile("../examples/testdata/rhs65025.txt", eigen_rhs))
{
  std::cout << "Error reading RHS file" << std::endl;
  return EXIT_FAILURE;
}

if (!readVectorFromFile("../examples/testdata/result65025.txt", ref_result))
{
  std::cout << "Error reading Result file" << std::endl;
  return EXIT_FAILURE;
}

Conjugate Gradient (CG) solver:

std::cout << "----- Running CG -----" << std::endl;
eigen_result = viennacl::linalg::solve(eigen_matrix, eigen_rhs, viennacl::linalg::cg_tag());

residual = eigen_matrix * eigen_result - eigen_rhs;
std::cout << "Relative residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(eigen_rhs) << std::endl;

Stabilized Bi-Conjugate Gradient (BiCGStab) solver:

std::cout << "----- Running BiCGStab -----" << std::endl;
eigen_result = viennacl::linalg::solve(eigen_matrix, eigen_rhs, viennacl::linalg::bicgstab_tag());

residual = eigen_matrix * eigen_result - eigen_rhs;
std::cout << "Relative residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(eigen_rhs) << std::endl;

Generalized Minimum Residual (GMRES) solver:

std::cout << "----- Running GMRES -----" << std::endl;
eigen_result = viennacl::linalg::solve(eigen_matrix, eigen_rhs, viennacl::linalg::gmres_tag());

residual = eigen_matrix * eigen_result - eigen_rhs;
std::cout << "Relative residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(eigen_rhs) << std::endl;

That's it. Print a success message and exit.

  std::cout << std::endl;
  std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;
  std::cout << std::endl;
}

Full Example Code

/* =========================================================================
   Copyright (c) 2010-2016, Institute for Microelectronics,
                            Institute for Analysis and Scientific Computing,
                            TU Wien.
   Portions of this software are copyright by UChicago Argonne, LLC.

                            -----------------
                  ViennaCL - The Vienna Computing Library
                            -----------------

   Project Head:    Karl Rupp                   rupp@iue.tuwien.ac.at

   (A list of authors and contributors can be found in the PDF manual)

   License:         MIT (X11), see file LICENSE in the base directory
============================================================================= */

// System headers
#include <iostream>

#ifndef NDEBUG
 #define NDEBUG
#endif


// Eigen headers
#include <Eigen/Core>
#include <Eigen/Sparse>

// Must be set prior to any ViennaCL includes if you want to use ViennaCL algorithms on Eigen objects
#define VIENNACL_WITH_EIGEN 1

// ViennaCL headers
#include "viennacl/linalg/ilu.hpp"
#include "viennacl/linalg/cg.hpp"
#include "viennacl/linalg/bicgstab.hpp"
#include "viennacl/linalg/gmres.hpp"
#include "viennacl/io/matrix_market.hpp"


// Some helper functions for this tutorial:
#include "vector-io.hpp"

int main(int, char *[])
{
  typedef float ScalarType;

  Eigen::SparseMatrix<ScalarType, Eigen::RowMajor> eigen_matrix(65025, 65025);
  Eigen::VectorXf eigen_rhs;
  Eigen::VectorXf eigen_result;
  Eigen::VectorXf ref_result;
  Eigen::VectorXf residual;

  std::cout << "Reading matrix (this might take some time)..." << std::endl;
  eigen_matrix.reserve(65025 * 7);
  if (!viennacl::io::read_matrix_market_file(eigen_matrix, "../examples/testdata/mat65k.mtx"))
  {
    std::cout << "Error reading Matrix file. Make sure you run from the build/-folder." << std::endl;
    return EXIT_FAILURE;
  }
  //eigen_matrix.endFill();
  std::cout << "Done: reading matrix" << std::endl;

  if (!readVectorFromFile("../examples/testdata/rhs65025.txt", eigen_rhs))
  {
    std::cout << "Error reading RHS file" << std::endl;
    return EXIT_FAILURE;
  }

  if (!readVectorFromFile("../examples/testdata/result65025.txt", ref_result))
  {
    std::cout << "Error reading Result file" << std::endl;
    return EXIT_FAILURE;
  }

  std::cout << "----- Running CG -----" << std::endl;
  eigen_result = viennacl::linalg::solve(eigen_matrix, eigen_rhs, viennacl::linalg::cg_tag());

  residual = eigen_matrix * eigen_result - eigen_rhs;
  std::cout << "Relative residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(eigen_rhs) << std::endl;

  std::cout << "----- Running BiCGStab -----" << std::endl;
  eigen_result = viennacl::linalg::solve(eigen_matrix, eigen_rhs, viennacl::linalg::bicgstab_tag());

  residual = eigen_matrix * eigen_result - eigen_rhs;
  std::cout << "Relative residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(eigen_rhs) << std::endl;

  std::cout << "----- Running GMRES -----" << std::endl;
  eigen_result = viennacl::linalg::solve(eigen_matrix, eigen_rhs, viennacl::linalg::gmres_tag());

  residual = eigen_matrix * eigen_result - eigen_rhs;
  std::cout << "Relative residual: " << viennacl::linalg::norm_2(residual) / viennacl::linalg::norm_2(eigen_rhs) << std::endl;

  std::cout << std::endl;
  std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;
  std::cout << std::endl;
}