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.integration;
18
19 import org.apache.commons.math.FunctionEvaluationException;
20 import org.apache.commons.math.MathRuntimeException;
21 import org.apache.commons.math.MaxIterationsExceededException;
22 import org.apache.commons.math.analysis.UnivariateRealFunction;
23
24 /**
25 * Implements the <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
26 * Simpson's Rule</a> for integration of real univariate functions. For
27 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
28 * chapter 3.
29 * <p>
30 * This implementation employs basic trapezoid rule as building blocks to
31 * calculate the Simpson's rule of alternating 2/3 and 4/3.</p>
32 *
33 * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $
34 * @since 1.2
35 */
36 public class SimpsonIntegrator extends UnivariateRealIntegratorImpl {
37
38 /**
39 * Construct an integrator for the given function.
40 *
41 * @param f function to integrate
42 * @deprecated as of 2.0 the integrand function is passed as an argument
43 * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
44 */
45 @Deprecated
46 public SimpsonIntegrator(UnivariateRealFunction f) {
47 super(f, 64);
48 }
49
50 /**
51 * Construct an integrator.
52 */
53 public SimpsonIntegrator() {
54 super(64);
55 }
56
57 /** {@inheritDoc} */
58 @Deprecated
59 public double integrate(final double min, final double max)
60 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
61 return integrate(f, min, max);
62 }
63
64 /** {@inheritDoc} */
65 public double integrate(final UnivariateRealFunction f,
66 final double min, final double max)
67 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
68
69 int i = 1;
70 double s, olds, t, oldt;
71
72 clearResult();
73 verifyInterval(min, max);
74 verifyIterationCount();
75
76 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
77 if (minimalIterationCount == 1) {
78 s = (4 * qtrap.stage(f, min, max, 1) - qtrap.stage(f, min, max, 0)) / 3.0;
79 setResult(s, 1);
80 return result;
81 }
82 // Simpson's rule requires at least two trapezoid stages.
83 olds = 0;
84 oldt = qtrap.stage(f, min, max, 0);
85 while (i <= maximalIterationCount) {
86 t = qtrap.stage(f, min, max, i);
87 s = (4 * t - oldt) / 3.0;
88 if (i >= minimalIterationCount) {
89 final double delta = Math.abs(s - olds);
90 final double rLimit =
91 relativeAccuracy * (Math.abs(olds) + Math.abs(s)) * 0.5;
92 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
93 setResult(s, i);
94 return result;
95 }
96 }
97 olds = s;
98 oldt = t;
99 i++;
100 }
101 throw new MaxIterationsExceededException(maximalIterationCount);
102 }
103
104 /** {@inheritDoc} */
105 @Override
106 protected void verifyIterationCount() throws IllegalArgumentException {
107 super.verifyIterationCount();
108 // at most 64 bisection refinements
109 if (maximalIterationCount > 64) {
110 throw MathRuntimeException.createIllegalArgumentException(
111 "invalid iteration limits: min={0}, max={1}",
112 0, 64);
113 }
114 }
115 }