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/TrapezoidalRule.html">
31 * Trapezoid 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 * The function should be integrable.</p>
36 *
37 */
38 public class TrapezoidIntegrator extends BaseAbstractUnivariateIntegrator {
39
40 /** Maximum number of iterations for trapezoid. */
41 public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
42
43 /** Intermediate result. */
44 private double s;
45
46 /**
47 * Build a trapezoid 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 * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
53 * @exception MathIllegalArgumentException if minimal number of iterations
54 * is not strictly positive
55 * @exception MathIllegalArgumentException if maximal number of iterations
56 * is lesser than or equal to the minimal number of iterations
57 * @exception MathIllegalArgumentException if maximal number of iterations
58 * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
59 */
60 public TrapezoidIntegrator(final double relativeAccuracy,
61 final double absoluteAccuracy,
62 final int minimalIterationCount,
63 final int maximalIterationCount)
64 throws MathIllegalArgumentException {
65 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
66 if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
67 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
68 maximalIterationCount, TRAPEZOID_MAX_ITERATIONS_COUNT);
69 }
70 }
71
72 /**
73 * Build a trapezoid integrator with given iteration counts.
74 * @param minimalIterationCount minimum number of iterations
75 * @param maximalIterationCount maximum number of iterations
76 * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
77 * @exception MathIllegalArgumentException if minimal number of iterations
78 * is not strictly positive
79 * @exception MathIllegalArgumentException if maximal number of iterations
80 * is lesser than or equal to the minimal number of iterations
81 * @exception MathIllegalArgumentException if maximal number of iterations
82 * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
83 */
84 public TrapezoidIntegrator(final int minimalIterationCount,
85 final int maximalIterationCount)
86 throws MathIllegalArgumentException {
87 super(minimalIterationCount, maximalIterationCount);
88 if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
89 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
90 maximalIterationCount, TRAPEZOID_MAX_ITERATIONS_COUNT);
91 }
92 }
93
94 /**
95 * Construct a trapezoid integrator with default settings.
96 * (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
97 */
98 public TrapezoidIntegrator() {
99 super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
100 }
101
102 /**
103 * Compute the n-th stage integral of trapezoid rule. This function
104 * should only be called by API <code>integrate()</code> in the package.
105 * To save time it does not verify arguments - caller does.
106 * <p>
107 * The interval is divided equally into 2^n sections rather than an
108 * arbitrary m sections because this configuration can best utilize the
109 * already computed values.</p>
110 *
111 * @param baseIntegrator integrator holding integration parameters
112 * @param n the stage of 1/2 refinement, n = 0 is no refinement
113 * @return the value of n-th stage integral
114 * @throws MathIllegalStateException if the maximal number of evaluations
115 * is exceeded.
116 */
117 double stage(final BaseAbstractUnivariateIntegrator baseIntegrator, final int n)
118 throws MathIllegalStateException {
119
120 if (n == 0) {
121 final double max = baseIntegrator.getMax();
122 final double min = baseIntegrator.getMin();
123 s = 0.5 * (max - min) *
124 (baseIntegrator.computeObjectiveValue(min) +
125 baseIntegrator.computeObjectiveValue(max));
126 return s;
127 } else {
128 final long np = 1L << (n-1); // number of new points in this stage
129 double sum = 0;
130 final double max = baseIntegrator.getMax();
131 final double min = baseIntegrator.getMin();
132 // spacing between adjacent new points
133 final double spacing = (max - min) / np;
134 double x = min + 0.5 * spacing; // the first new point
135 for (long i = 0; i < np; i++) {
136 sum += baseIntegrator.computeObjectiveValue(x);
137 x += spacing;
138 }
139 // add the new sum to previously calculated result
140 s = 0.5 * (s + sum * spacing);
141 return s;
142 }
143 }
144
145 /** {@inheritDoc} */
146 @Override
147 protected double doIntegrate()
148 throws MathIllegalArgumentException, MathIllegalStateException {
149
150 double oldt = stage(this, 0);
151 iterations.increment();
152 while (true) {
153 final int i = iterations.getCount();
154 final double t = stage(this, i);
155 if (i >= getMinimalIterationCount()) {
156 final double delta = FastMath.abs(t - oldt);
157 final double rLimit =
158 getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
159 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
160 return t;
161 }
162 }
163 oldt = t;
164 iterations.increment();
165 }
166
167 }
168
169 }