1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16 package org.apache.commons.math.analysis;
17
18
19 import org.apache.commons.math.ConvergenceException;
20 import org.apache.commons.math.FunctionEvaluationException;
21
22 /***
23 * Implements the <a href="http://mathworld.wolfram.com/BrentsMethod.html">
24 * Brent algorithm</a> for finding zeros of real univariate functions.
25 * <p>
26 * The function should be continuous but not necessarily smooth.
27 *
28 * @version $Revision: 1.18 $ $Date: 2004/11/07 02:17:56 $
29 */
30 public class BrentSolver extends UnivariateRealSolverImpl {
31
32 /*** Serializable version identifier */
33 static final long serialVersionUID = 3350616277306882875L;
34
35 /***
36 * Construct a solver for the given function.
37 *
38 * @param f function to solve.
39 */
40 public BrentSolver(UnivariateRealFunction f) {
41 super(f, 100, 1E-6);
42 }
43
44 /***
45 * Find a zero in the given interval.
46 * <p>
47 * Throws <code>ConvergenceException</code> if the values of the function
48 * at the endpoints of the interval have the same sign.
49 *
50 * @param min the lower bound for the interval.
51 * @param max the upper bound for the interval.
52 * @param initial the start value to use (ignored).
53 * @return the value where the function is zero
54 * @throws ConvergenceException the maximum iteration count is exceeded
55 * @throws FunctionEvaluationException if an error occurs evaluating
56 * the function
57 * @throws IllegalArgumentException if initial is not between min and max
58 */
59 public double solve(double min, double max, double initial)
60 throws ConvergenceException, FunctionEvaluationException {
61
62 return solve(min, max);
63 }
64
65 /***
66 * Find a zero in the given interval.
67 * <p>
68 * Requires that the values of the function at the endpoints have opposite
69 * signs. An <code>IllegalArgumentException</code> is thrown if this is not
70 * the case.
71 *
72 * @param min the lower bound for the interval.
73 * @param max the upper bound for the interval.
74 * @return the value where the function is zero
75 * @throws ConvergenceException if the maximum iteration count is exceeded
76 * @throws FunctionEvaluationException if an error occurs evaluating the
77 * function
78 * @throws IllegalArgumentException if min is not less than max or the
79 * signs of the values of the function at the endpoints are not opposites
80 */
81 public double solve(double min, double max) throws ConvergenceException,
82 FunctionEvaluationException {
83
84 clearResult();
85 verifyBracketing(min, max, f);
86
87
88
89
90 double x0 = min;
91 double x1 = max;
92 double y0;
93 double y1;
94 y0 = f.value(x0);
95 y1 = f.value(x1);
96
97 double x2 = x0;
98 double y2 = y0;
99 double delta = x1 - x0;
100 double oldDelta = delta;
101
102 int i = 0;
103 while (i < maximalIterationCount) {
104 if (Math.abs(y2) < Math.abs(y1)) {
105 x0 = x1;
106 x1 = x2;
107 x2 = x0;
108 y0 = y1;
109 y1 = y2;
110 y2 = y0;
111 }
112 if (Math.abs(y1) <= functionValueAccuracy) {
113
114
115
116 setResult(x1, i);
117 return result;
118 }
119 double dx = (x2 - x1);
120 double tolerance =
121 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy);
122 if (Math.abs(dx) <= tolerance) {
123 setResult(x1, i);
124 return result;
125 }
126 if ((Math.abs(oldDelta) < tolerance) ||
127 (Math.abs(y0) <= Math.abs(y1))) {
128
129 delta = 0.5 * dx;
130 oldDelta = delta;
131 } else {
132 double r3 = y1 / y0;
133 double p;
134 double p1;
135 if (x0 == x2) {
136
137 p = dx * r3;
138 p1 = 1.0 - r3;
139 } else {
140
141 double r1 = y0 / y2;
142 double r2 = y1 / y2;
143 p = r3 * (dx * r1 * (r1 - r2) - (x1 - x0) * (r2 - 1.0));
144 p1 = (r1 - 1.0) * (r2 - 1.0) * (r3 - 1.0);
145 }
146 if (p > 0.0) {
147 p1 = -p1;
148 } else {
149 p = -p;
150 }
151 if (2.0 * p >= 1.5 * dx * p1 - Math.abs(tolerance * p1) ||
152 p >= Math.abs(0.5 * oldDelta * p1)) {
153
154
155
156 delta = 0.5 * dx;
157 oldDelta = delta;
158 } else {
159 oldDelta = delta;
160 delta = p / p1;
161 }
162 }
163
164 x0 = x1;
165 y0 = y1;
166
167 if (Math.abs(delta) > tolerance) {
168 x1 = x1 + delta;
169 } else if (dx > 0.0) {
170 x1 = x1 + 0.5 * tolerance;
171 } else if (dx <= 0.0) {
172 x1 = x1 - 0.5 * tolerance;
173 }
174 y1 = f.value(x1);
175 if ((y1 > 0) == (y2 > 0)) {
176 x2 = x0;
177 y2 = y0;
178 delta = x1 - x0;
179 oldDelta = delta;
180 }
181 i++;
182 }
183 throw new ConvergenceException("Maximum number of iterations exceeded.");
184 }
185 }