View Javadoc

1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.math.analysis;
18  
19  import java.io.Serializable;
20  
21  import org.apache.commons.math.FunctionEvaluationException;
22  import org.apache.commons.math.MaxIterationsExceededException;
23  
24  
25  /**
26   * Implements a modified version of the 
27   * <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a>
28   * for approximating a zero of a real univariate function.  
29   * <p>
30   * The algorithm is modified to maintain bracketing of a root by successive
31   * approximations. Because of forced bracketing, convergence may be slower than
32   * the unrestricted secant algorithm. However, this implementation should in
33   * general outperform the 
34   * <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html">
35   * regula falsi method.</a></p>
36   * <p>
37   * The function is assumed to be continuous but not necessarily smooth.</p>
38   *  
39   * @version $Revision: 615734 $ $Date: 2008-01-27 23:10:03 -0700 (Sun, 27 Jan 2008) $
40   */
41  public class SecantSolver extends UnivariateRealSolverImpl implements Serializable {
42      
43      /** Serializable version identifier */
44      private static final long serialVersionUID = 1984971194738974867L;
45  
46      /**
47       * Construct a solver for the given function.
48       * @param f function to solve.
49       */
50      public SecantSolver(UnivariateRealFunction f) {
51          super(f, 100, 1E-6);
52      }
53  
54      /**
55       * Find a zero in the given interval.
56       * 
57       * @param min the lower bound for the interval
58       * @param max the upper bound for the interval
59       * @param initial the start value to use (ignored)
60       * @return the value where the function is zero
61       * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
62       * @throws FunctionEvaluationException if an error occurs evaluating the
63       * function 
64       * @throws IllegalArgumentException if min is not less than max or the
65       * signs of the values of the function at the endpoints are not opposites
66       */
67      public double solve(double min, double max, double initial)
68          throws MaxIterationsExceededException, FunctionEvaluationException {
69              
70          return solve(min, max);
71      }
72      
73      /**
74       * Find a zero in the given interval.
75       * @param min the lower bound for the interval.
76       * @param max the upper bound for the interval.
77       * @return the value where the function is zero
78       * @throws MaxIterationsExceededException  if the maximum iteration count is exceeded
79       * @throws FunctionEvaluationException if an error occurs evaluating the
80       * function 
81       * @throws IllegalArgumentException if min is not less than max or the
82       * signs of the values of the function at the endpoints are not opposites
83       */
84      public double solve(double min, double max) throws MaxIterationsExceededException, 
85          FunctionEvaluationException {
86          
87          clearResult();
88          verifyInterval(min, max);
89          
90          // Index 0 is the old approximation for the root.
91          // Index 1 is the last calculated approximation  for the root.
92          // Index 2 is a bracket for the root with respect to x0.
93          // OldDelta is the length of the bracketing interval of the last
94          // iteration.
95          double x0 = min;
96          double x1 = max;
97          double y0 = f.value(x0);
98          double y1 = f.value(x1);
99          
100         // Verify bracketing
101         if (y0 * y1 >= 0) {
102             throw new IllegalArgumentException
103             ("Function values at endpoints do not have different signs." +
104                     "  Endpoints: [" + min + "," + max + "]" + 
105                     "  Values: [" + y0 + "," + y1 + "]");       
106         }
107         
108         double x2 = x0;
109         double y2 = y0;
110         double oldDelta = x2 - x1;
111         int i = 0;
112         while (i < maximalIterationCount) {
113             if (Math.abs(y2) < Math.abs(y1)) {
114                 x0 = x1;
115                 x1 = x2;
116                 x2 = x0;
117                 y0 = y1;
118                 y1 = y2;
119                 y2 = y0;
120             }
121             if (Math.abs(y1) <= functionValueAccuracy) {
122                 setResult(x1, i);
123                 return result;
124             }
125             if (Math.abs(oldDelta) <
126                 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy)) {
127                 setResult(x1, i);
128                 return result;
129             }
130             double delta;
131             if (Math.abs(y1) > Math.abs(y0)) {
132                 // Function value increased in last iteration. Force bisection.
133                 delta = 0.5 * oldDelta;
134             } else {
135                 delta = (x0 - x1) / (1 - y0 / y1);
136                 if (delta / oldDelta > 1) {
137                     // New approximation falls outside bracket.
138                     // Fall back to bisection.
139                     delta = 0.5 * oldDelta;
140                 }
141             }
142             x0 = x1;
143             y0 = y1;
144             x1 = x1 + delta;
145             y1 = f.value(x1);
146             if ((y1 > 0) == (y2 > 0)) {
147                 // New bracket is (x0,x1).                    
148                 x2 = x0;
149                 y2 = y0;
150             }
151             oldDelta = x2 - x1;
152             i++;
153         }
154         throw new MaxIterationsExceededException(maximalIterationCount);
155     }
156 
157 }