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 * https://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
18 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.analysis.integration;
23
24 import org.hipparchus.exception.LocalizedCoreFormats;
25 import org.hipparchus.exception.MathIllegalArgumentException;
26 import org.hipparchus.exception.MathIllegalStateException;
27 import org.hipparchus.util.FastMath;
28
29 /**
30 * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
31 * Simpson's Rule</a> for integration of real univariate functions. For
32 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
33 * chapter 3.
34 * <p>
35 * This implementation employs the basic trapezoid rule to calculate Simpson's
36 * rule.</p>
37 *
38 */
39 public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
40
41 /** Maximal number of iterations for Simpson. */
42 public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
43
44 /**
45 * Build a Simpson integrator with given accuracies and iterations counts.
46 * @param relativeAccuracy relative accuracy of the result
47 * @param absoluteAccuracy absolute accuracy of the result
48 * @param minimalIterationCount minimum number of iterations
49 * @param maximalIterationCount maximum number of iterations
50 * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
51 * @exception MathIllegalArgumentException if minimal number of iterations
52 * is not strictly positive
53 * @exception MathIllegalArgumentException if maximal number of iterations
54 * is lesser than or equal to the minimal number of iterations
55 * @exception MathIllegalArgumentException if maximal number of iterations
56 * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
57 */
58 public SimpsonIntegrator(final double relativeAccuracy,
59 final double absoluteAccuracy,
60 final int minimalIterationCount,
61 final int maximalIterationCount)
62 throws MathIllegalArgumentException {
63 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
64 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
65 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
66 maximalIterationCount, SIMPSON_MAX_ITERATIONS_COUNT);
67 }
68 }
69
70 /**
71 * Build a Simpson integrator with given iteration counts.
72 * @param minimalIterationCount minimum number of iterations
73 * @param maximalIterationCount maximum number of iterations
74 * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
75 * @exception MathIllegalArgumentException if minimal number of iterations
76 * is not strictly positive
77 * @exception MathIllegalArgumentException if maximal number of iterations
78 * is lesser than or equal to the minimal number of iterations
79 * @exception MathIllegalArgumentException if maximal number of iterations
80 * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
81 */
82 public SimpsonIntegrator(final int minimalIterationCount,
83 final int maximalIterationCount)
84 throws MathIllegalArgumentException {
85 super(minimalIterationCount, maximalIterationCount);
86 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
87 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
88 maximalIterationCount, SIMPSON_MAX_ITERATIONS_COUNT);
89 }
90 }
91
92 /**
93 * Construct an integrator with default settings.
94 * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
95 */
96 public SimpsonIntegrator() {
97 super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
98 }
99
100 /** {@inheritDoc} */
101 @Override
102 protected double doIntegrate()
103 throws MathIllegalStateException {
104
105 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
106 if (getMinimalIterationCount() == 1) {
107 return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
108 }
109
110 // Simpson's rule requires at least two trapezoid stages.
111 double olds = 0;
112 double oldt = qtrap.stage(this, 0);
113 while (true) {
114 final double t = qtrap.stage(this, iterations.getCount());
115 iterations.increment();
116 final double s = (4 * t - oldt) / 3.0;
117 if (iterations.getCount() >= getMinimalIterationCount()) {
118 final double delta = FastMath.abs(s - olds);
119 final double rLimit =
120 getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
121 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
122 return s;
123 }
124 }
125 olds = s;
126 oldt = t;
127 }
128
129 }
130
131 }