ergo
bisection.h
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1/* Ergo, version 3.8.2, a program for linear scaling electronic structure
2 * calculations.
3 * Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
4 * and Anastasia Kruchinina.
5 *
6 * This program is free software: you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation, either version 3 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU General Public License for more details.
15 *
16 * You should have received a copy of the GNU General Public License
17 * along with this program. If not, see <http://www.gnu.org/licenses/>.
18 *
19 * Primary academic reference:
20 * Ergo: An open-source program for linear-scaling electronic structure
21 * calculations,
22 * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
23 * Kruchinina,
24 * SoftwareX 7, 107 (2018),
25 * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
26 *
27 * For further information about Ergo, see <http://www.ergoscf.org>.
28 */
29
36#ifndef MAT_BISECTION
37#define MAT_BISECTION
38#include <cmath>
39namespace mat {
47 template<typename Treal>
48 inline int sign(Treal value) {
49 if (value > 0)
50 return 1;
51 else if (value < 0)
52 return -1;
53 else
54 return 0;
55 }
56
57
69 template<typename Treal, typename Tfun>
70 Treal bisection(Tfun const & fun, Treal min, Treal max, Treal const tol) {
71 int sign_min = sign(fun.eval(min));
72 int sign_max = sign(fun.eval(max));
73 if (sign_min == sign_max)
74 throw Failure("bisection(Tfun&, Treal, Treal, Treal): interval "
75 "incorrect");
76 Treal middle = (max + min) / 2;
77 int sign_middle = sign(fun.eval(middle));
78 while (template_blas_fabs(max - min) > tol * 2 && sign_middle != 0) {
79 if (sign_middle == sign_min) {
80 min = middle;
81 sign_min = sign_middle;
82 }
83 else { /* (sign_middle == sign_max) */
84 max = middle;
85 sign_max = sign_middle;
86 }
87 middle = (max + min) / 2;
88 sign_middle = sign(fun.eval(middle));
89 }
90 return middle;
91 }
92
93} /* end namespace mat */
94#endif
Definition Failure.h:57
#define max(a, b)
Definition integrator.cc:87
int min(int a, int b)
Definition lin_trans.cc:66
Definition allocate.cc:39
Treal bisection(Tfun const &fun, Treal min, Treal max, Treal const tol)
Bisection algorithm for root finding.
Definition bisection.h:70
int sign(Treal value)
Sign function returns the sign of the input.
Definition bisection.h:48
Treal template_blas_fabs(Treal x)