/usr/include/viennacl/linalg/tql2.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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 | #ifndef VIENNACL_LINALG_TQL2_HPP
#define VIENNACL_LINALG_TQL2_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/tql2.hpp
@brief Implementation of the tql2-algorithm for eigenvalue computations.
*/
#include "viennacl/vector.hpp"
#include "viennacl/matrix.hpp"
#include <iomanip>
#include "viennacl/linalg/qr-method-common.hpp"
#include "viennacl/linalg/prod.hpp"
namespace viennacl
{
namespace linalg
{
// Symmetric tridiagonal QL algorithm.
// This is derived from the Algol procedures tql1, by Bowdler, Martin, Reinsch, and Wilkinson,
// Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.
template <typename SCALARTYPE, typename VectorType>
void tql1(vcl_size_t n,
VectorType & d,
VectorType & e)
{
for (vcl_size_t i = 1; i < n; i++)
e[i - 1] = e[i];
e[n - 1] = 0;
SCALARTYPE f = 0.;
SCALARTYPE tst1 = 0.;
SCALARTYPE eps = static_cast<SCALARTYPE>(1e-6);
for (vcl_size_t l = 0; l < n; l++)
{
// Find small subdiagonal element.
tst1 = std::max<SCALARTYPE>(tst1, std::fabs(d[l]) + std::fabs(e[l]));
vcl_size_t m = l;
while (m < n)
{
if (std::fabs(e[m]) <= eps * tst1)
break;
m++;
}
// If m == l, d[l) is an eigenvalue, otherwise, iterate.
if (m > l)
{
vcl_size_t iter = 0;
do
{
iter = iter + 1; // (Could check iteration count here.)
// Compute implicit shift
SCALARTYPE g = d[l];
SCALARTYPE p = (d[l + 1] - g) / (2 * e[l]);
SCALARTYPE r = viennacl::linalg::detail::pythag<SCALARTYPE>(p, 1);
if (p < 0)
{
r = -r;
}
d[l] = e[l] / (p + r);
d[l + 1] = e[l] * (p + r);
SCALARTYPE h = g - d[l];
for (vcl_size_t i = l + 2; i < n; i++)
{
d[i] -= h;
}
f = f + h;
// Implicit QL transformation.
p = d[m];
SCALARTYPE c = 1;
SCALARTYPE s = 0;
for (int i = int(m - 1); i >= int(l); i--)
{
g = c * e[vcl_size_t(i)];
h = c * p;
r = viennacl::linalg::detail::pythag<SCALARTYPE>(p, e[vcl_size_t(i)]);
e[vcl_size_t(i) + 1] = s * r;
s = e[vcl_size_t(i)] / r;
c = p / r;
p = c * d[vcl_size_t(i)] - s * g;
d[vcl_size_t(i) + 1] = h + s * (c * g + s * d[vcl_size_t(i)]);
}
e[l] = s * p;
d[l] = c * p;
// Check for convergence.
}
while (std::fabs(e[l]) > eps * tst1);
}
d[l] = d[l] + f;
e[l] = 0;
}
}
// Symmetric tridiagonal QL algorithm.
// This is derived from the Algol procedures tql2, by Bowdler, Martin, Reinsch, and Wilkinson,
// Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.
template <typename SCALARTYPE, typename VectorType, typename F>
void tql2(matrix_base<SCALARTYPE, F> & Q,
VectorType & d,
VectorType & e)
{
vcl_size_t n = static_cast<vcl_size_t>(viennacl::traits::size1(Q));
//boost::numeric::ublas::vector<SCALARTYPE> cs(n), ss(n);
std::vector<SCALARTYPE> cs(n), ss(n);
viennacl::vector<SCALARTYPE> tmp1(n), tmp2(n);
for (vcl_size_t i = 1; i < n; i++)
e[i - 1] = e[i];
e[n - 1] = 0;
SCALARTYPE f = 0;
SCALARTYPE tst1 = 0;
SCALARTYPE eps = static_cast<SCALARTYPE>(viennacl::linalg::detail::EPS);
for (vcl_size_t l = 0; l < n; l++)
{
// Find small subdiagonal element.
tst1 = std::max<SCALARTYPE>(tst1, std::fabs(d[l]) + std::fabs(e[l]));
vcl_size_t m = l;
while (m < n)
{
if (std::fabs(e[m]) <= eps * tst1)
break;
m++;
}
// If m == l, d[l) is an eigenvalue, otherwise, iterate.
if (m > l)
{
vcl_size_t iter = 0;
do
{
iter = iter + 1; // (Could check iteration count here.)
// Compute implicit shift
SCALARTYPE g = d[l];
SCALARTYPE p = (d[l + 1] - g) / (2 * e[l]);
SCALARTYPE r = viennacl::linalg::detail::pythag<SCALARTYPE>(p, 1);
if (p < 0)
{
r = -r;
}
d[l] = e[l] / (p + r);
d[l + 1] = e[l] * (p + r);
SCALARTYPE dl1 = d[l + 1];
SCALARTYPE h = g - d[l];
for (vcl_size_t i = l + 2; i < n; i++)
{
d[i] -= h;
}
f = f + h;
// Implicit QL transformation.
p = d[m];
SCALARTYPE c = 1;
SCALARTYPE c2 = c;
SCALARTYPE c3 = c;
SCALARTYPE el1 = e[l + 1];
SCALARTYPE s = 0;
SCALARTYPE s2 = 0;
for (int i = int(m - 1); i >= int(l); i--)
{
c3 = c2;
c2 = c;
s2 = s;
g = c * e[vcl_size_t(i)];
h = c * p;
r = viennacl::linalg::detail::pythag(p, e[vcl_size_t(i)]);
e[vcl_size_t(i) + 1] = s * r;
s = e[vcl_size_t(i)] / r;
c = p / r;
p = c * d[vcl_size_t(i)] - s * g;
d[vcl_size_t(i) + 1] = h + s * (c * g + s * d[vcl_size_t(i)]);
cs[vcl_size_t(i)] = c;
ss[vcl_size_t(i)] = s;
}
p = -s * s2 * c3 * el1 * e[l] / dl1;
e[l] = s * p;
d[l] = c * p;
viennacl::copy(cs, tmp1);
viennacl::copy(ss, tmp2);
viennacl::linalg::givens_next(Q, tmp1, tmp2, int(l), int(m));
// Check for convergence.
}
while (std::fabs(e[l]) > eps * tst1);
}
d[l] = d[l] + f;
e[l] = 0;
}
// Sort eigenvalues and corresponding vectors.
/*
for (int i = 0; i < n-1; i++) {
int k = i;
SCALARTYPE p = d[i];
for (int j = i+1; j < n; j++) {
if (d[j] > p) {
k = j;
p = d[j);
}
}
if (k != i) {
d[k] = d[i];
d[i] = p;
for (int j = 0; j < n; j++) {
p = Q(j, i);
Q(j, i) = Q(j, k);
Q(j, k) = p;
}
}
}
*/
}
} // namespace linalg
} // namespace viennacl
#endif
|