ergo
bisection.h
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1 /* Ergo, version 3.2, a program for linear scaling electronic structure
2  * calculations.
3  * Copyright (C) 2012 Elias Rudberg, Emanuel H. Rubensson, and Pawel Salek.
4  *
5  * This program is free software: you can redistribute it and/or modify
6  * it under the terms of the GNU General Public License as published by
7  * the Free Software Foundation, either version 3 of the License, or
8  * (at your option) any later version.
9  *
10  * This program is distributed in the hope that it will be useful,
11  * but WITHOUT ANY WARRANTY; without even the implied warranty of
12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13  * GNU General Public License for more details.
14  *
15  * You should have received a copy of the GNU General Public License
16  * along with this program. If not, see <http://www.gnu.org/licenses/>.
17  *
18  * Primary academic reference:
19  * Kohn−Sham Density Functional Theory Electronic Structure Calculations
20  * with Linearly Scaling Computational Time and Memory Usage,
21  * Elias Rudberg, Emanuel H. Rubensson, and Pawel Salek,
22  * J. Chem. Theory Comput. 7, 340 (2011),
23  * <http://dx.doi.org/10.1021/ct100611z>
24  *
25  * For further information about Ergo, see <http://www.ergoscf.org>.
26  */
27 
34 #ifndef MAT_BISECTION
35 #define MAT_BISECTION
36 #include <cmath>
37 namespace mat {
45  template<typename Treal>
46  inline int sign(Treal value) {
47  if (value > 0)
48  return 1;
49  else if (value < 0)
50  return -1;
51  else
52  return 0;
53  }
54 
55 
67  template<typename Treal, typename Tfun>
68  Treal bisection(Tfun const & fun, Treal min, Treal max, Treal const tol) {
69  int sign_min = sign(fun.eval(min));
70  int sign_max = sign(fun.eval(max));
71  if (sign_min == sign_max)
72  throw Failure("bisection(Tfun&, Treal, Treal, Treal): interval "
73  "incorrect");
74  Treal middle = (max + min) / 2;
75  int sign_middle = sign(fun.eval(middle));
76  while (template_blas_fabs(max - min) > tol * 2 && sign_middle != 0) {
77  if (sign_middle == sign_min) {
78  min = middle;
79  sign_min = sign_middle;
80  }
81  else { /* (sign_middle == sign_max) */
82  max = middle;
83  sign_max = sign_middle;
84  }
85  middle = (max + min) / 2;
86  sign_middle = sign(fun.eval(middle));
87  }
88  return middle;
89  }
90 
91 } /* end namespace mat */
92 #endif