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
22 /**
23 * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
24 * Romberg Algorithm</a> for integration of real univariate functions. For
25 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
26 * chapter 3.
27 * <p>
28 * Romberg integration employs k successvie refinements of the trapezoid
29 * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
30 * is a special case of k = 2.</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 RombergIntegrator extends UnivariateRealIntegratorImpl {
36
37 /** serializable version identifier */
38 private static final long serialVersionUID = -1058849527738180243L;
39
40 /**
41 * Construct an integrator for the given function.
42 *
43 * @param f function to integrate
44 */
45 public RombergIntegrator(UnivariateRealFunction f) {
46 super(f, 32);
47 }
48
49 /**
50 * Integrate the function in the given interval.
51 *
52 * @param min the lower bound for the interval
53 * @param max the upper bound for the interval
54 * @return the value of integral
55 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
56 * or the integrator detects convergence problems otherwise
57 * @throws FunctionEvaluationException if an error occurs evaluating the
58 * function
59 * @throws IllegalArgumentException if any parameters are invalid
60 */
61 public double integrate(double min, double max) throws MaxIterationsExceededException,
62 FunctionEvaluationException, IllegalArgumentException {
63
64 int i = 1, j, m = maximalIterationCount + 1;
65 // Array strcture here can be improved for better space
66 // efficiency because only the lower triangle is used.
67 double r, t[][] = new double[m][m], s, olds;
68
69 clearResult();
70 verifyInterval(min, max);
71 verifyIterationCount();
72
73 TrapezoidIntegrator qtrap = new TrapezoidIntegrator(this.f);
74 t[0][0] = qtrap.stage(min, max, 0);
75 olds = t[0][0];
76 while (i <= maximalIterationCount) {
77 t[i][0] = qtrap.stage(min, max, i);
78 for (j = 1; j <= i; j++) {
79 // Richardson extrapolation coefficient
80 r = (1L << (2 * j)) -1;
81 t[i][j] = t[i][j-1] + (t[i][j-1] - t[i-1][j-1]) / r;
82 }
83 s = t[i][i];
84 if (i >= minimalIterationCount) {
85 if (Math.abs(s - olds) <= Math.abs(relativeAccuracy * olds)) {
86 setResult(s, i);
87 return result;
88 }
89 }
90 olds = s;
91 i++;
92 }
93 throw new MaxIterationsExceededException(maximalIterationCount);
94 }
95
96 /**
97 * Verifies that the iteration limits are valid and within the range.
98 *
99 * @throws IllegalArgumentException if not
100 */
101 protected void verifyIterationCount() throws IllegalArgumentException {
102 super.verifyIterationCount();
103 // at most 32 bisection refinements due to higher order divider
104 if (maximalIterationCount > 32) {
105 throw new IllegalArgumentException
106 ("Iteration upper limit out of [0, 32] range: " +
107 maximalIterationCount);
108 }
109 }
110 }