Classes in this File | Line Coverage | Branch Coverage | Complexity | ||||||||
SimpsonIntegrator |
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| 4.0;4 |
1 | /* |
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2 | * Copyright 2005 The Apache Software Foundation. |
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3 | * |
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4 | * Licensed under the Apache License, Version 2.0 (the "License"); |
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5 | * you may not use this file except in compliance with the License. |
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6 | * You may obtain a copy of the License at |
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7 | * |
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8 | * http://www.apache.org/licenses/LICENSE-2.0 |
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9 | * |
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10 | * Unless required by applicable law or agreed to in writing, software |
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11 | * distributed under the License is distributed on an "AS IS" BASIS, |
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12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
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13 | * See the License for the specific language governing permissions and |
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14 | * limitations under the License. |
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15 | */ |
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16 | package org.apache.commons.math.analysis; |
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17 | ||
18 | import org.apache.commons.math.ConvergenceException; |
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19 | import org.apache.commons.math.FunctionEvaluationException; |
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20 | ||
21 | /** |
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22 | * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html"> |
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23 | * Simpson's Rule</a> for integration of real univariate functions. For |
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24 | * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, |
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25 | * chapter 3. |
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26 | * <p> |
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27 | * This implementation employs basic trapezoid rule as building blocks to |
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28 | * calculate the Simpson's rule of alternating 2/3 and 4/3. |
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29 | * |
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30 | * @version $Revision$ $Date: 2005-08-24 15:27:44 -0700 (Wed, 24 Aug 2005) $ |
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31 | */ |
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32 | public class SimpsonIntegrator extends UnivariateRealIntegratorImpl { |
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33 | ||
34 | /** serializable version identifier */ |
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35 | static final long serialVersionUID = 3405465123320678216L; |
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36 | ||
37 | /** |
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38 | * Construct an integrator for the given function. |
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39 | * |
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40 | * @param f function to integrate |
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41 | */ |
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42 | public SimpsonIntegrator(UnivariateRealFunction f) { |
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43 | 6 | super(f, 64); |
44 | 6 | } |
45 | ||
46 | /** |
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47 | * Integrate the function in the given interval. |
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48 | * |
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49 | * @param min the lower bound for the interval |
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50 | * @param max the upper bound for the interval |
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51 | * @return the value of integral |
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52 | * @throws ConvergenceException if the maximum iteration count is exceeded |
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53 | * or the integrator detects convergence problems otherwise |
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54 | * @throws FunctionEvaluationException if an error occurs evaluating the |
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55 | * function |
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56 | * @throws IllegalArgumentException if any parameters are invalid |
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57 | */ |
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58 | public double integrate(double min, double max) throws ConvergenceException, |
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59 | FunctionEvaluationException, IllegalArgumentException { |
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60 | ||
61 | 16 | int i = 1; |
62 | double s, olds, t, oldt; |
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63 | ||
64 | 16 | clearResult(); |
65 | 16 | verifyInterval(min, max); |
66 | 14 | verifyIterationCount(); |
67 | ||
68 | 10 | TrapezoidIntegrator qtrap = new TrapezoidIntegrator(this.f); |
69 | 10 | if (minimalIterationCount == 1) { |
70 | 0 | s = (4 * qtrap.stage(min, max, 1) - qtrap.stage(min, max, 0)) / 3.0; |
71 | 0 | setResult(s, 1); |
72 | 0 | return result; |
73 | } |
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74 | // Simpson's rule requires at least two trapezoid stages. |
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75 | 10 | olds = 0; |
76 | 10 | oldt = qtrap.stage(min, max, 0); |
77 | 62 | while (i <= maximalIterationCount) { |
78 | 62 | t = qtrap.stage(min, max, i); |
79 | 62 | s = (4 * t - oldt) / 3.0; |
80 | 62 | if (i >= minimalIterationCount) { |
81 | 42 | if (Math.abs(s - olds) <= Math.abs(relativeAccuracy * olds)) { |
82 | 10 | setResult(s, i); |
83 | 10 | return result; |
84 | } |
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85 | } |
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86 | 52 | olds = s; |
87 | 52 | oldt = t; |
88 | 52 | i++; |
89 | } |
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90 | 0 | throw new ConvergenceException("Maximum number of iterations exceeded."); |
91 | } |
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92 | ||
93 | /** |
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94 | * Verifies that the iteration limits are valid and within the range. |
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95 | * |
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96 | * @throws IllegalArgumentException if not |
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97 | */ |
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98 | protected void verifyIterationCount() throws IllegalArgumentException { |
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99 | 20 | super.verifyIterationCount(); |
100 | // at most 64 bisection refinements |
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101 | 18 | if (maximalIterationCount > 64) { |
102 | 2 | throw new IllegalArgumentException |
103 | ("Iteration upper limit out of [0, 64] range: " + |
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104 | maximalIterationCount); |
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105 | } |
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106 | 16 | } |
107 | } |