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Java > Open Source Codes > org > apache > commons > math > analysis > BrentSolver


1 /*
2  * Copyright 2003-2005 The Apache Software Foundation.
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  * http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
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 $Revision$ $Date: 2005-06-03 22:36:42 -0700 (Fri, 03 Jun 2005) $
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         verifyInterval(min, max);
86         
87         // Index 0 is the old approximation for the root.
88 // Index 1 is the last calculated approximation for the root.
89 // Index 2 is a bracket for the root with respect to x1.
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         // Verify bracketing
98 if (y0 * y1 >= 0) {
99             throw new IllegalArgumentException JavaDoc
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                 // Avoid division by very small values. Assume
122 // the iteration has converged (the problem may
123 // still be ill conditioned)
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                 // Force bisection.
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                     // Linear interpolation.
145 p = dx * r3;
146                     p1 = 1.0 - r3;
147                 } else {
148                     // Inverse quadratic interpolation.
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                     // Inverse quadratic interpolation gives a value
162 // in the wrong direction, or progress is slow.
163 // Fall back to bisection.
164 delta = 0.5 * dx;
165                     oldDelta = delta;
166                 } else {
167                     oldDelta = delta;
168                     delta = p / p1;
169                 }
170             }
171             // Save old X1, Y1
172 x0 = x1;
173             y0 = y1;
174             // Compute new X1, Y1
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 }
194
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