ViennaCL - The Vienna Computing Library: iterative-ublas.cpp

ViennaCL - The Vienna Computing Library 1.7.1 Free open-source GPU-accelerated linear algebra and solver library. |

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iterative-ublas.cpp

In this example we show how one can use the iterative solvers in ViennaCL with objects from Boost.uBLAS.

The first step is to include the necessary headers:

//
// include necessary system headers
//
#include <iostream>
//
// Necessary to obtain a suitable performance in ublas
#ifndef NDEBUG
#define BOOST_UBLAS_NDEBUG
#endif
//
// ublas includes
//
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/operation_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/lu.hpp>
// Must be set if you want to use ViennaCL algorithms on ublas objects
#define VIENNACL_WITH_UBLAS 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"

A shortcut for convience (use `ublas::` instead of `boost::numeric::ublas::`)

using namespace boost::numeric;

In the main() routine we create matrices and vectors using Boost.uBLAS types, fill them with data and launch the iterative solvers.

int main()
{
typedef float ScalarType;
//
// Set up some ublas objects
//
ublas::vector<ScalarType> rhs;
ublas::vector<ScalarType> ref_result;
ublas::vector<ScalarType> result;
ublas::compressed_matrix<ScalarType> ublas_matrix;

Read system from matrix-market file

if (!viennacl::io::read_matrix_market_file(ublas_matrix, "../examples/testdata/mat65k.mtx"))
{
std::cout << "Error reading Matrix file" << std::endl;
return EXIT_FAILURE;
}

Read associated vectors from files

if (!readVectorFromFile("../examples/testdata/rhs65025.txt", rhs))
{
std::cout << "Error reading RHS file" << std::endl;
return EXIT_FAILURE;
}
//std::cout << "done reading rhs" << std::endl;
if (!readVectorFromFile("../examples/testdata/result65025.txt", ref_result))
{
std::cout << "Error reading Result file" << std::endl;
return EXIT_FAILURE;
}
//std::cout << "done reading result" << std::endl;

Set up ILUT preconditioners for ViennaCL and ublas objects. Other preconditioners can also be used, see Preconditioners

viennacl::linalg::ilut_precond< ublas::compressed_matrix<ScalarType> > ublas_ilut(ublas_matrix, viennacl::linalg::ilut_tag());
viennacl::linalg::ilu0_precond< ublas::compressed_matrix<ScalarType> > ublas_ilu0(ublas_matrix, viennacl::linalg::ilu0_tag());
viennacl::linalg::block_ilu_precond< ublas::compressed_matrix<ScalarType>,
viennacl::linalg::ilu0_tag> ublas_block_ilu0(ublas_matrix, viennacl::linalg::ilu0_tag());

First we run an conjugate gradient solver with different preconditioners:

std::cout << "----- CG Test -----" << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag());
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag(1e-6, 20), ublas_ilut);
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag(1e-6, 20), ublas_ilu0);
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag(1e-6, 20), ublas_block_ilu0);
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;

Run the stabilized BiConjugate gradient solver without and with preconditioners (ILUT, ILU0)

std::cout << "----- BiCGStab Test -----" << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::bicgstab_tag()); //without preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::bicgstab_tag(1e-6, 20), ublas_ilut); //with preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::bicgstab_tag(1e-6, 20), ublas_ilu0); //with preconditioner

Run the generalized minimum residual method witout and with preconditioners (ILUT, ILU0):

std::cout << "----- GMRES Test -----" << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::gmres_tag()); //without preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::gmres_tag(1e-6, 20), ublas_ilut);//with preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::gmres_tag(1e-6, 20), ublas_ilu0);//with preconditioner

That's it.

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

## 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
============================================================================= */
//
// include necessary system headers
//
#include <iostream>
//
// Necessary to obtain a suitable performance in ublas
#ifndef NDEBUG
#define BOOST_UBLAS_NDEBUG
#endif
//
// ublas includes
//
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/operation_sparse.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/lu.hpp>
// Must be set if you want to use ViennaCL algorithms on ublas objects
#define VIENNACL_WITH_UBLAS 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"
using namespace boost::numeric;
int main()
{
typedef float ScalarType;
//
// Set up some ublas objects
//
ublas::vector<ScalarType> rhs;
ublas::vector<ScalarType> ref_result;
ublas::vector<ScalarType> result;
ublas::compressed_matrix<ScalarType> ublas_matrix;
if (!viennacl::io::read_matrix_market_file(ublas_matrix, "../examples/testdata/mat65k.mtx"))
{
std::cout << "Error reading Matrix file" << std::endl;
return EXIT_FAILURE;
}
if (!readVectorFromFile("../examples/testdata/rhs65025.txt", rhs))
{
std::cout << "Error reading RHS file" << std::endl;
return EXIT_FAILURE;
}
//std::cout << "done reading rhs" << std::endl;
if (!readVectorFromFile("../examples/testdata/result65025.txt", ref_result))
{
std::cout << "Error reading Result file" << std::endl;
return EXIT_FAILURE;
}
//std::cout << "done reading result" << std::endl;
viennacl::linalg::ilut_precond< ublas::compressed_matrix<ScalarType> > ublas_ilut(ublas_matrix, viennacl::linalg::ilut_tag());
viennacl::linalg::ilu0_precond< ublas::compressed_matrix<ScalarType> > ublas_ilu0(ublas_matrix, viennacl::linalg::ilu0_tag());
viennacl::linalg::block_ilu_precond< ublas::compressed_matrix<ScalarType>,
viennacl::linalg::ilu0_tag> ublas_block_ilu0(ublas_matrix, viennacl::linalg::ilu0_tag());
std::cout << "----- CG Test -----" << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag());
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag(1e-6, 20), ublas_ilut);
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag(1e-6, 20), ublas_ilu0);
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::cg_tag(1e-6, 20), ublas_block_ilu0);
std::cout << "Residual norm: " << norm_2(prod(ublas_matrix, result) - rhs) << std::endl;
std::cout << "----- BiCGStab Test -----" << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::bicgstab_tag()); //without preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::bicgstab_tag(1e-6, 20), ublas_ilut); //with preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::bicgstab_tag(1e-6, 20), ublas_ilu0); //with preconditioner
std::cout << "----- GMRES Test -----" << std::endl;
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::gmres_tag()); //without preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::gmres_tag(1e-6, 20), ublas_ilut);//with preconditioner
result = viennacl::linalg::solve(ublas_matrix, rhs, viennacl::linalg::gmres_tag(1e-6, 20), ublas_ilu0);//with preconditioner
std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;
return EXIT_SUCCESS;
}