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


1 /*
2  * Copyright 2004 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
17 package org.apache.commons.math.analysis;
18
19 import org.apache.commons.math.ConvergenceException;
20 import org.apache.commons.math.FunctionEvaluationException;
21
22 /**
23  * Implements <a HREF="http://mathworld.wolfram.com/NewtonsMethod.html">
24  * Newton's Method</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: 2005-02-26 05:11:52 -0800 (Sat, 26 Feb 2005) $
29  */
30 public class NewtonSolver extends UnivariateRealSolverImpl {
31     
32     /** Serializable version identifier */
33     static final long serialVersionUID = 2606474895443431607L;
34     
35     /** The first derivative of the target function. */
36     private UnivariateRealFunction derivative;
37     
38     /**
39      * Construct a solver for the given function.
40      * @param f function to solve.
41      */
42     public NewtonSolver(DifferentiableUnivariateRealFunction f) {
43         super(f, 100, 1E-6);
44         derivative = f.derivative();
45     }
46
47     /**
48      * Find a zero near the midpoint of <code>min</code> and <code>max</code>.
49      *
50      * @param min the lower bound for the interval
51      * @param max the upper bound for the interval
52      * @return the value where the function is zero
53      * @throws ConvergenceException if the maximum iteration count is exceeded
54      * @throws FunctionEvaluationException if an error occurs evaluating the
55      * function or derivative
56      * @throws IllegalArgumentException if min is not less than max
57      */
58     public double solve(double min, double max) throws ConvergenceException,
59         FunctionEvaluationException {
60         return solve(min, max, UnivariateRealSolverUtils.midpoint(min, max));
61     }
62
63     /**
64      * Find a zero near the value <code>startValue</code>.
65      *
66      * @param min the lower bound for the interval (ignored).
67      * @param max the upper bound for the interval (ignored).
68      * @param startValue the start value to use.
69      * @return the value where the function is zero
70     * @throws ConvergenceException if the maximum iteration count is exceeded
71      * @throws FunctionEvaluationException if an error occurs evaluating the
72      * function or derivative
73      * @throws IllegalArgumentException if startValue is not between min and max
74      */
75     public double solve(double min, double max, double startValue)
76         throws ConvergenceException, FunctionEvaluationException {
77         
78         clearResult();
79         verifySequence(min, startValue, max);
80
81         double x0 = startValue;
82         double x1;
83         
84         int i = 0;
85         while (i < maximalIterationCount) {
86             x1 = x0 - (f.value(x0) / derivative.value(x0));
87             if (Math.abs(x1 - x0) <= absoluteAccuracy) {
88                 
89                 setResult(x1, i);
90                 return x1;
91             }
92             
93             x0 = x1;
94             ++i;
95         }
96         
97         throw new ConvergenceException
98             ("Maximum number of iterations exceeded " + i);
99     }
100
101 }
102
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