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 the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
31 * Romberg Algorithm</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 * Romberg integration employs k successive refinements of the trapezoid
36 * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
37 * is a special case of k = 2.</p>
38 *
39 */
40 public class RombergIntegrator extends BaseAbstractUnivariateIntegrator {
41
42 /** Maximal number of iterations for Romberg. */
43 public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;
44
45 /**
46 * Build a Romberg integrator with given accuracies and iterations counts.
47 * @param relativeAccuracy relative accuracy of the result
48 * @param absoluteAccuracy absolute accuracy of the result
49 * @param minimalIterationCount minimum number of iterations
50 * @param maximalIterationCount maximum number of iterations
51 * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
52 * @exception MathIllegalArgumentException if minimal number of iterations
53 * is not strictly positive
54 * @exception MathIllegalArgumentException if maximal number of iterations
55 * is lesser than or equal to the minimal number of iterations
56 * @exception MathIllegalArgumentException if maximal number of iterations
57 * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}
58 */
59 public RombergIntegrator(final double relativeAccuracy,
60 final double absoluteAccuracy,
61 final int minimalIterationCount,
62 final int maximalIterationCount)
63 throws MathIllegalArgumentException {
64 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
65 if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
66 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
67 maximalIterationCount, ROMBERG_MAX_ITERATIONS_COUNT);
68 }
69 }
70
71 /**
72 * Build a Romberg integrator with given iteration counts.
73 * @param minimalIterationCount minimum number of iterations
74 * @param maximalIterationCount maximum number of iterations
75 * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
76 * @exception MathIllegalArgumentException if minimal number of iterations
77 * is not strictly positive
78 * @exception MathIllegalArgumentException if maximal number of iterations
79 * is lesser than or equal to the minimal number of iterations
80 * @exception MathIllegalArgumentException if maximal number of iterations
81 * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}
82 */
83 public RombergIntegrator(final int minimalIterationCount,
84 final int maximalIterationCount)
85 throws MathIllegalArgumentException {
86 super(minimalIterationCount, maximalIterationCount);
87 if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
88 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
89 maximalIterationCount, ROMBERG_MAX_ITERATIONS_COUNT);
90 }
91 }
92
93 /**
94 * Construct a Romberg integrator with default settings
95 * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
96 */
97 public RombergIntegrator() {
98 super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);
99 }
100
101 /** {@inheritDoc} */
102 @Override
103 protected double doIntegrate()
104 throws MathIllegalStateException {
105
106 final int m = iterations.getMaximalCount() + 1;
107 double[] previousRow = new double[m];
108 double[] currentRow = new double[m];
109
110 TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
111 currentRow[0] = qtrap.stage(this, 0);
112 iterations.increment();
113 double olds = currentRow[0];
114 while (true) {
115
116 final int i = iterations.getCount();
117
118 // switch rows
119 final double[] tmpRow = previousRow;
120 previousRow = currentRow;
121 currentRow = tmpRow;
122
123 currentRow[0] = qtrap.stage(this, i);
124 iterations.increment();
125 for (int j = 1; j <= i; j++) {
126 // Richardson extrapolation coefficient
127 final double r = (1L << (2 * j)) - 1;
128 final double tIJm1 = currentRow[j - 1];
129 currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
130 }
131 final double s = currentRow[i];
132 if (i >= getMinimalIterationCount()) {
133 final double delta = FastMath.abs(s - olds);
134 final double rLimit = getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
135 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
136 return s;
137 }
138 }
139 olds = s;
140 }
141
142 }
143
144 }