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.solvers;
18  
19  import org.apache.commons.math.ConvergenceException;
20  import org.apache.commons.math.FunctionEvaluationException;
21  import org.apache.commons.math.MathRuntimeException;
22  import org.apache.commons.math.MaxIterationsExceededException;
23  import org.apache.commons.math.analysis.UnivariateRealFunction;
24  
25  
26  /**
27   * Implements a modified version of the 
28   * <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a>
29   * for approximating a zero of a real univariate function.  
30   * <p>
31   * The algorithm is modified to maintain bracketing of a root by successive
32   * approximations. Because of forced bracketing, convergence may be slower than
33   * the unrestricted secant algorithm. However, this implementation should in
34   * general outperform the 
35   * <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html">
36   * regula falsi method.</a></p>
37   * <p>
38   * The function is assumed to be continuous but not necessarily smooth.</p>
39   *  
40   * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $
41   */
42  public class SecantSolver extends UnivariateRealSolverImpl {
43      
44      /**
45       * Construct a solver for the given function.
46       * @param f function to solve.
47       * @deprecated as of 2.0 the function to solve is passed as an argument
48       * to the {@link #solve(UnivariateRealFunction, double, double)} or
49       * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}
50       * method.
51       */
52      @Deprecated
53      public SecantSolver(UnivariateRealFunction f) {
54          super(f, 100, 1E-6);
55      }
56  
57      /**
58       * Construct a solver.
59       */
60      public SecantSolver() {
61          super(100, 1E-6);
62      }
63  
64      /** {@inheritDoc} */
65      @Deprecated
66      public double solve(final double min, final double max)
67          throws ConvergenceException, FunctionEvaluationException {
68          return solve(f, min, max);
69      }
70  
71      /** {@inheritDoc} */
72      @Deprecated
73      public double solve(final double min, final double max, final double initial)
74          throws ConvergenceException, FunctionEvaluationException {
75          return solve(f, min, max, initial);
76      }
77  
78      /**
79       * Find a zero in the given interval.
80       * 
81       * @param f the function to solve
82       * @param min the lower bound for the interval
83       * @param max the upper bound for the interval
84       * @param initial the start value to use (ignored)
85       * @return the value where the function is zero
86       * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
87       * @throws FunctionEvaluationException if an error occurs evaluating the
88       * function 
89       * @throws IllegalArgumentException if min is not less than max or the
90       * signs of the values of the function at the endpoints are not opposites
91       */
92      public double solve(final UnivariateRealFunction f,
93                          final double min, final double max, final double initial)
94          throws MaxIterationsExceededException, FunctionEvaluationException {
95          return solve(f, min, max);
96      }
97      
98      /**
99       * Find a zero in the given interval.
100      * @param f the function to solve
101      * @param min the lower bound for the interval.
102      * @param max the upper bound for the interval.
103      * @return the value where the function is zero
104      * @throws MaxIterationsExceededException  if the maximum iteration count is exceeded
105      * @throws FunctionEvaluationException if an error occurs evaluating the
106      * function 
107      * @throws IllegalArgumentException if min is not less than max or the
108      * signs of the values of the function at the endpoints are not opposites
109      */
110     public double solve(final UnivariateRealFunction f,
111                         final double min, final double max)
112         throws MaxIterationsExceededException, FunctionEvaluationException {
113         
114         clearResult();
115         verifyInterval(min, max);
116         
117         // Index 0 is the old approximation for the root.
118         // Index 1 is the last calculated approximation  for the root.
119         // Index 2 is a bracket for the root with respect to x0.
120         // OldDelta is the length of the bracketing interval of the last
121         // iteration.
122         double x0 = min;
123         double x1 = max;
124         double y0 = f.value(x0);
125         double y1 = f.value(x1);
126         
127         // Verify bracketing
128         if (y0 * y1 >= 0) {
129             throw MathRuntimeException.createIllegalArgumentException(
130                   "function values at endpoints do not have different signs, " +
131                   "endpoints: [{0}, {1}], values: [{2}, {3}]",
132                   min, max, y0, y1);       
133         }
134         
135         double x2 = x0;
136         double y2 = y0;
137         double oldDelta = x2 - x1;
138         int i = 0;
139         while (i < maximalIterationCount) {
140             if (Math.abs(y2) < Math.abs(y1)) {
141                 x0 = x1;
142                 x1 = x2;
143                 x2 = x0;
144                 y0 = y1;
145                 y1 = y2;
146                 y2 = y0;
147             }
148             if (Math.abs(y1) <= functionValueAccuracy) {
149                 setResult(x1, i);
150                 return result;
151             }
152             if (Math.abs(oldDelta) <
153                 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy)) {
154                 setResult(x1, i);
155                 return result;
156             }
157             double delta;
158             if (Math.abs(y1) > Math.abs(y0)) {
159                 // Function value increased in last iteration. Force bisection.
160                 delta = 0.5 * oldDelta;
161             } else {
162                 delta = (x0 - x1) / (1 - y0 / y1);
163                 if (delta / oldDelta > 1) {
164                     // New approximation falls outside bracket.
165                     // Fall back to bisection.
166                     delta = 0.5 * oldDelta;
167                 }
168             }
169             x0 = x1;
170             y0 = y1;
171             x1 = x1 + delta;
172             y1 = f.value(x1);
173             if ((y1 > 0) == (y2 > 0)) {
174                 // New bracket is (x0,x1).                    
175                 x2 = x0;
176                 y2 = y0;
177             }
178             oldDelta = x2 - x1;
179             i++;
180         }
181         throw new MaxIterationsExceededException(maximalIterationCount);
182     }
183 
184 }