Classes in this File | Line Coverage | Branch Coverage | Complexity | ||||||||
RombergIntegrator |
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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/RombergIntegration.html"> |
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23 | * Romberg Algorithm</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 | * Romberg integration employs k successvie refinements of the trapezoid |
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28 | * rule to remove error terms less than order O(N^(-2k)). Simpson's rule |
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29 | * is a special case of k = 2. |
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30 | * |
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31 | * @version $Revision$ $Date: 2005-08-24 15:27:44 -0700 (Wed, 24 Aug 2005) $ |
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32 | */ |
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33 | public class RombergIntegrator extends UnivariateRealIntegratorImpl { |
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34 | ||
35 | /** serializable version identifier */ |
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36 | static final long serialVersionUID = -1058849527738180243L; |
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37 | ||
38 | /** |
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39 | * Construct an integrator for the given function. |
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40 | * |
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41 | * @param f function to integrate |
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42 | */ |
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43 | public RombergIntegrator(UnivariateRealFunction f) { |
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44 | 6 | super(f, 32); |
45 | 6 | } |
46 | ||
47 | /** |
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48 | * Integrate the function in the given interval. |
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49 | * |
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50 | * @param min the lower bound for the interval |
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51 | * @param max the upper bound for the interval |
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52 | * @return the value of integral |
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53 | * @throws ConvergenceException if the maximum iteration count is exceeded |
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54 | * or the integrator detects convergence problems otherwise |
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55 | * @throws FunctionEvaluationException if an error occurs evaluating the |
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56 | * function |
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57 | * @throws IllegalArgumentException if any parameters are invalid |
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58 | */ |
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59 | public double integrate(double min, double max) throws ConvergenceException, |
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60 | FunctionEvaluationException, IllegalArgumentException { |
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61 | ||
62 | 16 | int i = 1, j, m = maximalIterationCount + 1; |
63 | // Array strcture here can be improved for better space |
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64 | // efficiency because only the lower triangle is used. |
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65 | 16 | double r, t[][] = new double[m][m], s, olds; |
66 | ||
67 | 16 | clearResult(); |
68 | 16 | verifyInterval(min, max); |
69 | 14 | verifyIterationCount(); |
70 | ||
71 | 10 | TrapezoidIntegrator qtrap = new TrapezoidIntegrator(this.f); |
72 | 10 | t[0][0] = qtrap.stage(min, max, 0); |
73 | 10 | olds = t[0][0]; |
74 | 34 | while (i <= maximalIterationCount) { |
75 | 34 | t[i][0] = qtrap.stage(min, max, i); |
76 | 112 | for (j = 1; j <= i; j++) { |
77 | // Richardson extrapolation coefficient |
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78 | 78 | r = (1L << (2 * j)) -1; |
79 | 78 | t[i][j] = t[i][j-1] + (t[i][j-1] - t[i-1][j-1]) / r; |
80 | } |
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81 | 34 | s = t[i][i]; |
82 | 34 | if (i >= minimalIterationCount) { |
83 | 14 | if (Math.abs(s - olds) <= Math.abs(relativeAccuracy * olds)) { |
84 | 10 | setResult(s, i); |
85 | 10 | return result; |
86 | } |
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87 | } |
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88 | 24 | olds = s; |
89 | 24 | i++; |
90 | } |
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91 | 0 | throw new ConvergenceException("Maximum number of iterations exceeded."); |
92 | } |
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93 | ||
94 | /** |
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95 | * Verifies that the iteration limits are valid and within the range. |
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96 | * |
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97 | * @throws IllegalArgumentException if not |
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98 | */ |
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99 | protected void verifyIterationCount() throws IllegalArgumentException { |
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100 | 20 | super.verifyIterationCount(); |
101 | // at most 32 bisection refinements due to higher order divider |
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102 | 18 | if (maximalIterationCount > 32) { |
103 | 2 | throw new IllegalArgumentException |
104 | ("Iteration upper limit out of [0, 32] range: " + |
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105 | maximalIterationCount); |
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106 | } |
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107 | 16 | } |
108 | } |