power_iter.hpp

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#ifndef VIENNACL_LINALG_POWER_ITER_HPP_
#define VIENNACL_LINALG_POWER_ITER_HPP_

/* =========================================================================
   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 manual)

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

#include <cmath>
#include <vector>
#include "viennacl/linalg/bisect.hpp"
#include "viennacl/linalg/prod.hpp"
#include "viennacl/linalg/norm_2.hpp"

namespace viennacl
{
  namespace linalg
  {
    class power_iter_tag
    {
      public:

        power_iter_tag(double tfac = 1e-8, vcl_size_t max_iters = 50000) : termination_factor_(tfac), max_iterations_(max_iters) {}

        void factor(double fct){ termination_factor_ = fct; }

        double factor() const { return termination_factor_; }

        vcl_size_t max_iterations() const { return max_iterations_; }
        void max_iterations(vcl_size_t new_max) { max_iterations_ = new_max; }

      private:
        double termination_factor_;
        vcl_size_t max_iterations_;

    };

    template<typename MatrixT, typename VectorT >
    typename viennacl::result_of::cpu_value_type<typename MatrixT::value_type>::type
    eig(MatrixT const& A, power_iter_tag const & tag, VectorT & eigenvec)
    {

      typedef typename viennacl::result_of::value_type<MatrixT>::type           ScalarType;
      typedef typename viennacl::result_of::cpu_value_type<ScalarType>::type    CPU_ScalarType;

      vcl_size_t matrix_size = A.size1();
      VectorT r(eigenvec);
      std::vector<CPU_ScalarType> s(matrix_size);

      for (vcl_size_t i=0; i<s.size(); ++i)
        s[i] = CPU_ScalarType(i % 3) * CPU_ScalarType(0.1234) - CPU_ScalarType(0.5);   //'random' starting vector

      detail::copy_vec_to_vec(s, eigenvec);

      double epsilon = tag.factor();
      CPU_ScalarType norm = norm_2(eigenvec);
      CPU_ScalarType norm_prev = 0;
      long numiter = 0;

      for (vcl_size_t i=0; i<tag.max_iterations(); ++i)
      {
        if (std::fabs(norm - norm_prev) / std::fabs(norm) < epsilon)
          break;

        eigenvec /= norm;
        r = viennacl::linalg::prod(A, eigenvec);  //using helper vector r for the computation of x <- A * x in order to avoid the repeated creation of temporaries
        eigenvec = r;
        norm_prev = norm;
        norm = norm_2(eigenvec);
        numiter++;
      }

      return norm;
    }

    template< typename MatrixT >
    typename viennacl::result_of::cpu_value_type<typename MatrixT::value_type>::type
    eig(MatrixT const& A, power_iter_tag const & tag)
    {
      typedef typename viennacl::result_of::vector_for_matrix<MatrixT>::type    VectorT;

      VectorT eigenvec(A.size1());
      return eig(A, tag, eigenvec);
    }

  } // end namespace linalg
} // end namespace viennacl
#endif