/usr/include/viennacl/linalg/bisect.hpp is in libviennacl-dev 1.7.1+dfsg1-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 | #ifndef VIENNACL_LINALG_BISECT_HPP_
#define VIENNACL_LINALG_BISECT_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
============================================================================= */
/** @file viennacl/linalg/bisect.hpp
* @brief Implementation of the algorithm for finding eigenvalues of a tridiagonal matrix.
*
* Contributed by Guenther Mader and Astrid Rupp.
*/
#include <vector>
#include <cmath>
#include <limits>
#include <cstddef>
#include "viennacl/meta/result_of.hpp"
namespace viennacl
{
namespace linalg
{
namespace detail
{
/**
* @brief overloaded function for copying vectors
*/
template<typename NumericT, typename OtherVectorT>
void copy_vec_to_vec(viennacl::vector<NumericT> const & src, OtherVectorT & dest)
{
viennacl::copy(src, dest);
}
template<typename OtherVectorT, typename NumericT>
void copy_vec_to_vec(OtherVectorT const & src, viennacl::vector<NumericT> & dest)
{
viennacl::copy(src, dest);
}
template<typename VectorT1, typename VectorT2>
void copy_vec_to_vec(VectorT1 const & src, VectorT2 & dest)
{
for (vcl_size_t i=0; i<src.size(); ++i)
dest[i] = src[i];
}
} //namespace detail
/**
* @brief Implementation of the bisect-algorithm for the calculation of the eigenvalues of a tridiagonal matrix. Experimental - interface might change.
*
* Refer to "Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection" in the Handbook Series Linear Algebra, contributed by Barth, Martin, and Wilkinson.
* http://www.maths.ed.ac.uk/~aar/papers/bamawi.pdf
*
* @param alphas Elements of the main diagonal
* @param betas Elements of the secondary diagonal
* @return Returns the eigenvalues of the tridiagonal matrix defined by alpha and beta
*/
template<typename VectorT>
std::vector<
typename viennacl::result_of::cpu_value_type<typename VectorT::value_type>::type
>
bisect(VectorT const & alphas, VectorT const & betas)
{
typedef typename viennacl::result_of::value_type<VectorT>::type NumericType;
typedef typename viennacl::result_of::cpu_value_type<NumericType>::type CPU_NumericType;
vcl_size_t size = betas.size();
std::vector<CPU_NumericType> x_temp(size);
std::vector<CPU_NumericType> beta_bisect;
std::vector<CPU_NumericType> wu;
double rel_error = std::numeric_limits<CPU_NumericType>::epsilon();
beta_bisect.push_back(0);
for (vcl_size_t i = 1; i < size; i++)
beta_bisect.push_back(betas[i] * betas[i]);
double xmin = alphas[size - 1] - std::fabs(betas[size - 1]);
double xmax = alphas[size - 1] + std::fabs(betas[size - 1]);
for (vcl_size_t i = 0; i < size - 1; i++)
{
double h = std::fabs(betas[i]) + std::fabs(betas[i + 1]);
if (alphas[i] + h > xmax)
xmax = alphas[i] + h;
if (alphas[i] - h < xmin)
xmin = alphas[i] - h;
}
double eps1 = 1e-6;
/*double eps2 = (xmin + xmax > 0) ? (rel_error * xmax) : (-rel_error * xmin);
if (eps1 <= 0)
eps1 = eps2;
else
eps2 = 0.5 * eps1 + 7.0 * eps2; */
double x0 = xmax;
for (vcl_size_t i = 0; i < size; i++)
{
x_temp[i] = xmax;
wu.push_back(xmin);
}
for (long k = static_cast<long>(size) - 1; k >= 0; --k)
{
double xu = xmin;
for (long i = k; i >= 0; --i)
{
if (xu < wu[vcl_size_t(k-i)])
{
xu = wu[vcl_size_t(i)];
break;
}
}
if (x0 > x_temp[vcl_size_t(k)])
x0 = x_temp[vcl_size_t(k)];
double x1 = (xu + x0) / 2.0;
while (x0 - xu > 2.0 * rel_error * (std::fabs(xu) + std::fabs(x0)) + eps1)
{
vcl_size_t a = 0;
double q = 1;
for (vcl_size_t i = 0; i < size; i++)
{
if (q > 0 || q < 0)
q = alphas[i] - x1 - beta_bisect[i] / q;
else
q = alphas[i] - x1 - std::fabs(betas[i] / rel_error);
if (q < 0)
a++;
}
if (a <= static_cast<vcl_size_t>(k))
{
xu = x1;
if (a < 1)
wu[0] = x1;
else
{
wu[a] = x1;
if (x_temp[a - 1] > x1)
x_temp[a - 1] = x1;
}
}
else
x0 = x1;
x1 = (xu + x0) / 2.0;
}
x_temp[vcl_size_t(k)] = x1;
}
return x_temp;
}
} // end namespace linalg
} // end namespace viennacl
#endif
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