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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 org.apache.commons.math.FunctionEvaluationException;
20  import org.apache.commons.math.MaxIterationsExceededException;
21  import org.apache.commons.math.util.MathUtils;
22  
23  /**
24   * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
25   * Ridders' Method</a> for root finding of real univariate functions. For
26   * reference, see C. Ridders, <i>A new algorithm for computing a single root
27   * of a real continuous function </i>, IEEE Transactions on Circuits and
28   * Systems, 26 (1979), 979 - 980.
29   * <p>
30   * The function should be continuous but not necessarily smooth.</p>
31   *  
32   * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
33   * @since 1.2
34   */
35  public class RiddersSolver extends UnivariateRealSolverImpl {
36  
37      /** serializable version identifier */
38      private static final long serialVersionUID = -4703139035737911735L;
39  
40      /**
41       * Construct a solver for the given function.
42       * 
43       * @param f function to solve
44       */
45      public RiddersSolver(UnivariateRealFunction f) {
46          super(f, 100, 1E-6);
47      }
48  
49      /**
50       * Find a root in the given interval with initial value.
51       * <p>
52       * Requires bracketing condition.</p>
53       * 
54       * @param min the lower bound for the interval
55       * @param max the upper bound for the interval
56       * @param initial the start value to use
57       * @return the point at which the function value is zero
58       * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
59       * @throws FunctionEvaluationException if an error occurs evaluating the
60       * function
61       * @throws IllegalArgumentException if any parameters are invalid
62       */
63      public double solve(double min, double max, double initial) throws
64          MaxIterationsExceededException, FunctionEvaluationException {
65  
66          // check for zeros before verifying bracketing
67          if (f.value(min) == 0.0) { return min; }
68          if (f.value(max) == 0.0) { return max; }
69          if (f.value(initial) == 0.0) { return initial; }
70  
71          verifyBracketing(min, max, f);
72          verifySequence(min, initial, max);
73          if (isBracketing(min, initial, f)) {
74              return solve(min, initial);
75          } else {
76              return solve(initial, max);
77          }
78      }
79  
80      /**
81       * Find a root in the given interval.
82       * <p>
83       * Requires bracketing condition.</p>
84       * 
85       * @param min the lower bound for the interval
86       * @param max the upper bound for the interval
87       * @return the point at which the function value is zero
88       * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
89       * @throws FunctionEvaluationException if an error occurs evaluating the
90       * function 
91       * @throws IllegalArgumentException if any parameters are invalid
92       */
93      public double solve(double min, double max) throws MaxIterationsExceededException, 
94          FunctionEvaluationException {
95  
96          // [x1, x2] is the bracketing interval in each iteration
97          // x3 is the midpoint of [x1, x2]
98          // x is the new root approximation and an endpoint of the new interval
99          double x1, x2, x3, x, oldx, y1, y2, y3, y, delta, correction, tolerance;
100 
101         x1 = min; y1 = f.value(x1);
102         x2 = max; y2 = f.value(x2);
103 
104         // check for zeros before verifying bracketing
105         if (y1 == 0.0) { return min; }
106         if (y2 == 0.0) { return max; }
107         verifyBracketing(min, max, f);
108 
109         int i = 1;
110         oldx = Double.POSITIVE_INFINITY;
111         while (i <= maximalIterationCount) {
112             // calculate the new root approximation
113             x3 = 0.5 * (x1 + x2);
114             y3 = f.value(x3);
115             if (Math.abs(y3) <= functionValueAccuracy) {
116                 setResult(x3, i);
117                 return result;
118             }
119             delta = 1 - (y1 * y2) / (y3 * y3);  // delta > 1 due to bracketing
120             correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *
121                          (x3 - x1) / Math.sqrt(delta);
122             x = x3 - correction;                // correction != 0
123             y = f.value(x);
124 
125             // check for convergence
126             tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy);
127             if (Math.abs(x - oldx) <= tolerance) {
128                 setResult(x, i);
129                 return result;
130             }
131             if (Math.abs(y) <= functionValueAccuracy) {
132                 setResult(x, i);
133                 return result;
134             }
135 
136             // prepare the new interval for next iteration
137             // Ridders' method guarantees x1 < x < x2
138             if (correction > 0.0) {             // x1 < x < x3
139                 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {
140                     x2 = x; y2 = y;
141                 } else {
142                     x1 = x; x2 = x3;
143                     y1 = y; y2 = y3;
144                 }
145             } else {                            // x3 < x < x2
146                 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {
147                     x1 = x; y1 = y;
148                 } else {
149                     x1 = x3; x2 = x;
150                     y1 = y3; y2 = y;
151                 }
152             }
153             oldx = x;
154             i++;
155         }
156         throw new MaxIterationsExceededException(maximalIterationCount);
157     }
158 }