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power-iter.cpp

This tutorial demonstrates the calculation of the eigenvalue with largest modulus using the power iteration method.

We start with including the necessary headers:

// Sparse matrices in uBLAS are *very* slow if debug mode is enabled. Disable it:
#ifndef NDEBUG
#define BOOST_UBLAS_NDEBUG
#endif
// Include necessary system headers
#include <iostream>
#include <fstream>
#include <limits>
#include <string>
#define VIENNACL_WITH_UBLAS
// Include basic scalar and vector types of ViennaCL
#include "viennacl/scalar.hpp"
#include "viennacl/vector.hpp"
#include "viennacl/compressed_matrix.hpp"
#include "viennacl/linalg/power_iter.hpp"
#include "viennacl/io/matrix_market.hpp"
// Some helper functions for this tutorial:
#include <iostream>
// Boost includes:
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/matrix_expression.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/vector_expression.hpp>

To run the power iteration, we set up a sparse matrix using Boost.uBLAS, transfer it over to a ViennaCL matrix, and then run the algorithm.

int main()
{
// This example relies on double precision to be available and will provide only poor results with single precision
typedef double ScalarType;

Create the sparse uBLAS matrix and read the matrix from the matrix-market file:

boost::numeric::ublas::compressed_matrix<ScalarType> ublas_A;
if (!viennacl::io::read_matrix_market_file(ublas_A, "../examples/testdata/mat65k.mtx"))
{
std::cout << "Error reading Matrix file" << std::endl;
return EXIT_FAILURE;
}

Transfer the data from the uBLAS matrix over to the ViennaCL sparse matrix:

viennacl::compressed_matrix<ScalarType> vcl_A(ublas_A.size1(), ublas_A.size2());
viennacl::copy(ublas_A, vcl_A);

Run the power iteration up until the largest eigenvalue changes by less than the specified tolerance. Print the results of running with uBLAS as well as ViennaCL and exit.

viennacl::linalg::power_iter_tag ptag(1e-6);
std::cout << "Starting computation of eigenvalue with largest modulus (might take about a minute)..." << std::endl;
std::cout << "Result of power iteration with ublas matrix (single-threaded): " << viennacl::linalg::eig(ublas_A, ptag) << std::endl;
std::cout << "Result of power iteration with ViennaCL (OpenCL accelerated): " << viennacl::linalg::eig(vcl_A, ptag) << std::endl;

You can also obtain the associated approximated eigenvector by passing it as a third argument to eig() Tighten the tolerance passed to ptag above in order to obtain more accurate results.

viennacl::vector<ScalarType> eigenvector(vcl_A.size1());
viennacl::linalg::eig(vcl_A, ptag, eigenvector);
std::cout << "First three entries in eigenvector: " << eigenvector[0] << " " << eigenvector[1] << " " << eigenvector[2] << std::endl;
viennacl::vector<ScalarType> Ax = viennacl::linalg::prod(vcl_A, eigenvector);
std::cout << "First three entries in A*eigenvector: " << Ax[0] << " " << Ax[1] << " " << Ax[2] << 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
============================================================================= */
// Sparse matrices in uBLAS are *very* slow if debug mode is enabled. Disable it:
#ifndef NDEBUG
#define BOOST_UBLAS_NDEBUG
#endif
// Include necessary system headers
#include <iostream>
#include <fstream>
#include <limits>
#include <string>
#define VIENNACL_WITH_UBLAS
// Include basic scalar and vector types of ViennaCL
#include "viennacl/scalar.hpp"
#include "viennacl/vector.hpp"
#include "viennacl/compressed_matrix.hpp"
#include "viennacl/linalg/power_iter.hpp"
#include "viennacl/io/matrix_market.hpp"
// Some helper functions for this tutorial:
#include <iostream>
// Boost includes:
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/matrix_expression.hpp>
#include <boost/numeric/ublas/matrix_sparse.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/operation.hpp>
#include <boost/numeric/ublas/vector_expression.hpp>
int main()
{
// This example relies on double precision to be available and will provide only poor results with single precision
typedef double ScalarType;
boost::numeric::ublas::compressed_matrix<ScalarType> ublas_A;
if (!viennacl::io::read_matrix_market_file(ublas_A, "../examples/testdata/mat65k.mtx"))
{
std::cout << "Error reading Matrix file" << std::endl;
return EXIT_FAILURE;
}
viennacl::compressed_matrix<ScalarType> vcl_A(ublas_A.size1(), ublas_A.size2());
viennacl::copy(ublas_A, vcl_A);
viennacl::linalg::power_iter_tag ptag(1e-6);
std::cout << "Starting computation of eigenvalue with largest modulus (might take about a minute)..." << std::endl;
std::cout << "Result of power iteration with ublas matrix (single-threaded): " << viennacl::linalg::eig(ublas_A, ptag) << std::endl;
std::cout << "Result of power iteration with ViennaCL (OpenCL accelerated): " << viennacl::linalg::eig(vcl_A, ptag) << std::endl;
viennacl::vector<ScalarType> eigenvector(vcl_A.size1());
viennacl::linalg::eig(vcl_A, ptag, eigenvector);
std::cout << "First three entries in eigenvector: " << eigenvector[0] << " " << eigenvector[1] << " " << eigenvector[2] << std::endl;
viennacl::vector<ScalarType> Ax = viennacl::linalg::prod(vcl_A, eigenvector);
std::cout << "First three entries in A*eigenvector: " << Ax[0] << " " << Ax[1] << " " << Ax[2] << std::endl;
return EXIT_SUCCESS;
}