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.math4.legacy.analysis.integration;
18
19 import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
20 import org.apache.commons.math4.core.jdkmath.JdkMath;
21
22 /**
23 * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
24 * Simpson's Rule</a> for integration of real univariate functions.
25 *
26 * See <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, chapter 3.
27 *
28 * <p>
29 * This implementation employs the basic trapezoid rule to calculate Simpson's
30 * rule.
31 *
32 * <p>
33 * <em>Caveat:</em> At each iteration, the algorithm refines the estimation by
34 * evaluating the function twice as many times as in the previous iteration;
35 * When specifying a {@link #integrate(int,UnivariateFunction,double,double)
36 * maximum number of function evaluations}, the caller must ensure that it
37 * is compatible with the {@link #SimpsonIntegrator(int,int) requested minimal
38 * number of iterations}.
39 *
40 * @since 1.2
41 */
42 public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
43 /** Maximal number of iterations for Simpson. */
44 private static final int SIMPSON_MAX_ITERATIONS_COUNT = 30;
45
46 /**
47 * Build a Simpson integrator with given accuracies and iterations counts.
48 * @param relativeAccuracy relative accuracy of the result
49 * @param absoluteAccuracy absolute accuracy of the result
50 * @param minimalIterationCount Minimum number of iterations.
51 * @param maximalIterationCount Maximum number of iterations.
52 * It must be less than or equal to 30.
53 * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException
54 * if {@code minimalIterationCount <= 0}.
55 * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException
56 * if {@code maximalIterationCount < minimalIterationCount}.
57 * is lesser than or equal to the minimal number of iterations
58 * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}.
59 */
60 public SimpsonIntegrator(final double relativeAccuracy,
61 final double absoluteAccuracy,
62 final int minimalIterationCount,
63 final int maximalIterationCount) {
64 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
65 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
66 throw new NumberIsTooLargeException(maximalIterationCount,
67 SIMPSON_MAX_ITERATIONS_COUNT, false);
68 }
69 }
70
71 /**
72 * Build a Simpson integrator with given iteration counts.
73 * @param minimalIterationCount Minimum number of iterations.
74 * @param maximalIterationCount Maximum number of iterations.
75 * It must be less than or equal to 30.
76 * @throws org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException
77 * if {@code minimalIterationCount <= 0}.
78 * @throws org.apache.commons.math4.legacy.exception.NumberIsTooSmallException
79 * if {@code maximalIterationCount < minimalIterationCount}.
80 * is lesser than or equal to the minimal number of iterations
81 * @throws NumberIsTooLargeException if {@code maximalIterationCount > 30}.
82 */
83 public SimpsonIntegrator(final int minimalIterationCount,
84 final int maximalIterationCount) {
85 super(minimalIterationCount, maximalIterationCount);
86 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
87 throw new NumberIsTooLargeException(maximalIterationCount,
88 SIMPSON_MAX_ITERATIONS_COUNT, false);
89 }
90 }
91
92 /**
93 * Construct an integrator with default settings.
94 */
95 public SimpsonIntegrator() {
96 super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
97 }
98
99 /** {@inheritDoc} */
100 @Override
101 protected double doIntegrate() {
102 // Simpson's rule requires at least two trapezoid stages.
103 // So we set the first sum using two trapezoid stages.
104 final TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
105
106 final double s0 = qtrap.stage(this, 0);
107 double oldt = qtrap.stage(this, 1);
108 double olds = (4 * oldt - s0) / 3.0;
109 while (true) {
110 // The first iteration is the first refinement of the sum.
111 iterations.increment();
112 final int i = getIterations();
113 final double t = qtrap.stage(this, i + 1); // 1-stage ahead of the iteration
114 final double s = (4 * t - oldt) / 3.0;
115 if (i >= getMinimalIterationCount()) {
116 final double delta = JdkMath.abs(s - olds);
117 final double rLimit = getRelativeAccuracy() * (JdkMath.abs(olds) + JdkMath.abs(s)) * 0.5;
118 if (delta <= rLimit ||
119 delta <= getAbsoluteAccuracy()) {
120 return s;
121 }
122 }
123 olds = s;
124 oldt = t;
125 }
126 }
127 }