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16 package org.apache.commons.math.analysis;
17
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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: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $
29 */
30 public class BrentSolver extends UnivariateRealSolverImpl {
31
32 /** Serializable version identifier */
33 private 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 verifyInterval(min, max);
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
98 if (y0 * y1 >= 0) {
99 throw new IllegalArgumentException
100 ("Function values at endpoints do not have different signs." +
101 " Endpoints: [" + min + "," + max + "]" +
102 " Values: [" + y0 + "," + y1 + "]");
103 }
104
105 double x2 = x0;
106 double y2 = y0;
107 double delta = x1 - x0;
108 double oldDelta = delta;
109
110 int i = 0;
111 while (i < maximalIterationCount) {
112 if (Math.abs(y2) < Math.abs(y1)) {
113 x0 = x1;
114 x1 = x2;
115 x2 = x0;
116 y0 = y1;
117 y1 = y2;
118 y2 = y0;
119 }
120 if (Math.abs(y1) <= functionValueAccuracy) {
121
122
123
124 setResult(x1, i);
125 return result;
126 }
127 double dx = (x2 - x1);
128 double tolerance =
129 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy);
130 if (Math.abs(dx) <= tolerance) {
131 setResult(x1, i);
132 return result;
133 }
134 if ((Math.abs(oldDelta) < tolerance) ||
135 (Math.abs(y0) <= Math.abs(y1))) {
136
137 delta = 0.5 * dx;
138 oldDelta = delta;
139 } else {
140 double r3 = y1 / y0;
141 double p;
142 double p1;
143 if (x0 == x2) {
144
145 p = dx * r3;
146 p1 = 1.0 - r3;
147 } else {
148
149 double r1 = y0 / y2;
150 double r2 = y1 / y2;
151 p = r3 * (dx * r1 * (r1 - r2) - (x1 - x0) * (r2 - 1.0));
152 p1 = (r1 - 1.0) * (r2 - 1.0) * (r3 - 1.0);
153 }
154 if (p > 0.0) {
155 p1 = -p1;
156 } else {
157 p = -p;
158 }
159 if (2.0 * p >= 1.5 * dx * p1 - Math.abs(tolerance * p1) ||
160 p >= Math.abs(0.5 * oldDelta * p1)) {
161
162
163
164 delta = 0.5 * dx;
165 oldDelta = delta;
166 } else {
167 oldDelta = delta;
168 delta = p / p1;
169 }
170 }
171
172 x0 = x1;
173 y0 = y1;
174
175 if (Math.abs(delta) > tolerance) {
176 x1 = x1 + delta;
177 } else if (dx > 0.0) {
178 x1 = x1 + 0.5 * tolerance;
179 } else if (dx <= 0.0) {
180 x1 = x1 - 0.5 * tolerance;
181 }
182 y1 = f.value(x1);
183 if ((y1 > 0) == (y2 > 0)) {
184 x2 = x0;
185 y2 = y0;
186 delta = x1 - x0;
187 oldDelta = delta;
188 }
189 i++;
190 }
191 throw new ConvergenceException("Maximum number of iterations exceeded.");
192 }
193 }