iterative-mtl4.cpp

The following tutorial shows how to use the iterative solvers in ViennaCL with objects from the MTL4 Library directly.

Note

MTL4 provides iterative solvers through the ITK library. You might also want to check these.

We begin with including the necessary headers:

// include necessary system headers
#include <iostream>

// MTL4 headers
#include <boost/numeric/mtl/mtl.hpp>
#include <boost/numeric/itl/itl.hpp>

// Must be set prior to any ViennaCL includes if you want to use ViennaCL algorithms on Eigen objects
#define VIENNACL_WITH_MTL4 1

// ViennaCL includes
#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 MTL4 types directly. First, the matrices are set up, then the respective solvers are called.

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

  mtl::compressed2D<ScalarType> mtl4_matrix;
  mtl4_matrix.change_dim(65025, 65025);
  set_to_zero(mtl4_matrix);

  mtl::dense_vector<ScalarType> mtl4_rhs(65025, 1.0);
  mtl::dense_vector<ScalarType> mtl4_result(65025, 0.0);
  mtl::dense_vector<ScalarType> mtl4_residual(65025, 0.0);

Read system from file

mtl::io::matrix_market_istream("../examples/testdata/mat65k.mtx") >> mtl4_matrix;

Conjugate Gradient (CG) solver:

std::cout << "----- Running CG -----" << std::endl;
mtl4_result = viennacl::linalg::solve(mtl4_matrix, mtl4_rhs, viennacl::linalg::cg_tag());

mtl4_residual = mtl4_matrix * mtl4_result - mtl4_rhs;
std::cout << "Relative residual: " << viennacl::linalg::norm_2(mtl4_residual) / viennacl::linalg::norm_2(mtl4_rhs) << std::endl;

Stabilized Bi-Conjugate Gradient (BiCGStab) solver:

std::cout << "----- Running BiCGStab -----" << std::endl;
mtl4_result = viennacl::linalg::solve(mtl4_matrix, mtl4_rhs, viennacl::linalg::bicgstab_tag());

mtl4_residual = mtl4_matrix * mtl4_result - mtl4_rhs;
std::cout << "Relative residual: " << viennacl::linalg::norm_2(mtl4_residual) / viennacl::linalg::norm_2(mtl4_rhs) << std::endl;

Generalized Minimum Residual (GMRES) solver:

std::cout << "----- Running GMRES -----" << std::endl;
mtl4_result = viennacl::linalg::solve(mtl4_matrix, mtl4_rhs, viennacl::linalg::gmres_tag());

mtl4_residual = mtl4_matrix * mtl4_result - mtl4_rhs;
std::cout << "Relative residual: " << viennacl::linalg::norm_2(mtl4_residual) / viennacl::linalg::norm_2(mtl4_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) 2010-2015, 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
============================================================================= */

// include necessary system headers
#include <iostream>

// MTL4 headers
#include <boost/numeric/mtl/mtl.hpp>
#include <boost/numeric/itl/itl.hpp>

// Must be set prior to any ViennaCL includes if you want to use ViennaCL algorithms on Eigen objects
#define VIENNACL_WITH_MTL4 1

// ViennaCL includes
#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 double    ScalarType;

  mtl::compressed2D<ScalarType> mtl4_matrix;
  mtl4_matrix.change_dim(65025, 65025);
  set_to_zero(mtl4_matrix);

  mtl::dense_vector<ScalarType> mtl4_rhs(65025, 1.0);
  mtl::dense_vector<ScalarType> mtl4_result(65025, 0.0);
  mtl::dense_vector<ScalarType> mtl4_residual(65025, 0.0);

  mtl::io::matrix_market_istream("../examples/testdata/mat65k.mtx") >> mtl4_matrix;

  std::cout << "----- Running CG -----" << std::endl;
  mtl4_result = viennacl::linalg::solve(mtl4_matrix, mtl4_rhs, viennacl::linalg::cg_tag());

  mtl4_residual = mtl4_matrix * mtl4_result - mtl4_rhs;
  std::cout << "Relative residual: " << viennacl::linalg::norm_2(mtl4_residual) / viennacl::linalg::norm_2(mtl4_rhs) << std::endl;

  std::cout << "----- Running BiCGStab -----" << std::endl;
  mtl4_result = viennacl::linalg::solve(mtl4_matrix, mtl4_rhs, viennacl::linalg::bicgstab_tag());

  mtl4_residual = mtl4_matrix * mtl4_result - mtl4_rhs;
  std::cout << "Relative residual: " << viennacl::linalg::norm_2(mtl4_residual) / viennacl::linalg::norm_2(mtl4_rhs) << std::endl;

  std::cout << "----- Running GMRES -----" << std::endl;
  mtl4_result = viennacl::linalg::solve(mtl4_matrix, mtl4_rhs, viennacl::linalg::gmres_tag());

  mtl4_residual = mtl4_matrix * mtl4_result - mtl4_rhs;
  std::cout << "Relative residual: " << viennacl::linalg::norm_2(mtl4_residual) / viennacl::linalg::norm_2(mtl4_rhs) << std::endl;

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