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://en.wikipedia.org/wiki/Midpoint_method">
31 * Midpoint Rule</a> for integration of real univariate functions. For
32 * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595,
33 * chapter 9.2.
34 * <p>
35 * The function should be integrable.</p>
36 *
37 */
38 public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {
39
40 /** Maximum number of iterations for midpoint. */
41 public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;
42
43 /**
44 * Build a midpoint integrator with given accuracies and iterations counts.
45 * @param relativeAccuracy relative accuracy of the result
46 * @param absoluteAccuracy absolute accuracy of the result
47 * @param minimalIterationCount minimum number of iterations
48 * @param maximalIterationCount maximum number of iterations
49 * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
50 * @exception MathIllegalArgumentException if minimal number of iterations
51 * is not strictly positive
52 * @exception MathIllegalArgumentException if maximal number of iterations
53 * is lesser than or equal to the minimal number of iterations
54 * @exception MathIllegalArgumentException if maximal number of iterations
55 * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
56 */
57 public MidPointIntegrator(final double relativeAccuracy,
58 final double absoluteAccuracy,
59 final int minimalIterationCount,
60 final int maximalIterationCount)
61 throws MathIllegalArgumentException {
62 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
63 if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
64 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
65 maximalIterationCount, MIDPOINT_MAX_ITERATIONS_COUNT);
66 }
67 }
68
69 /**
70 * Build a midpoint integrator with given iteration counts.
71 * @param minimalIterationCount minimum number of iterations
72 * @param maximalIterationCount maximum number of iterations
73 * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
74 * @exception MathIllegalArgumentException if minimal number of iterations
75 * is not strictly positive
76 * @exception MathIllegalArgumentException if maximal number of iterations
77 * is lesser than or equal to the minimal number of iterations
78 * @exception MathIllegalArgumentException if maximal number of iterations
79 * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
80 */
81 public MidPointIntegrator(final int minimalIterationCount,
82 final int maximalIterationCount)
83 throws MathIllegalArgumentException {
84 super(minimalIterationCount, maximalIterationCount);
85 if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
86 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
87 maximalIterationCount, MIDPOINT_MAX_ITERATIONS_COUNT);
88 }
89 }
90
91 /**
92 * Construct a midpoint integrator with default settings.
93 * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
94 */
95 public MidPointIntegrator() {
96 super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
97 }
98
99 /**
100 * Compute the n-th stage integral of midpoint rule.
101 * This function should only be called by API <code>integrate()</code> in the package.
102 * To save time it does not verify arguments - caller does.
103 * <p>
104 * The interval is divided equally into 2^n sections rather than an
105 * arbitrary m sections because this configuration can best utilize the
106 * already computed values.</p>
107 *
108 * @param n the stage of 1/2 refinement. Must be larger than 0.
109 * @param previousStageResult Result from the previous call to the
110 * {@code stage} method.
111 * @param min Lower bound of the integration interval.
112 * @param diffMaxMin Difference between the lower bound and upper bound
113 * of the integration interval.
114 * @return the value of n-th stage integral
115 * @throws MathIllegalStateException if the maximal number of evaluations
116 * is exceeded.
117 */
118 private double stage(final int n,
119 double previousStageResult,
120 double min,
121 double diffMaxMin)
122 throws MathIllegalStateException {
123
124 // number of new points in this stage
125 final long np = 1L << (n - 1);
126 double sum = 0;
127
128 // spacing between adjacent new points
129 final double spacing = diffMaxMin / np;
130
131 // the first new point
132 double x = min + 0.5 * spacing;
133 for (long i = 0; i < np; i++) {
134 sum += computeObjectiveValue(x);
135 x += spacing;
136 }
137 // add the new sum to previously calculated result
138 return 0.5 * (previousStageResult + sum * spacing);
139 }
140
141
142 /** {@inheritDoc} */
143 @Override
144 protected double doIntegrate()
145 throws MathIllegalArgumentException, MathIllegalStateException {
146
147 final double min = getMin();
148 final double diff = getMax() - min;
149 final double midPoint = min + 0.5 * diff;
150
151 double oldt = diff * computeObjectiveValue(midPoint);
152
153 while (true) {
154 iterations.increment();
155 final int i = iterations.getCount();
156 final double t = stage(i, oldt, min, diff);
157 if (i >= getMinimalIterationCount()) {
158 final double delta = FastMath.abs(t - oldt);
159 final double rLimit =
160 getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
161 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
162 return t;
163 }
164 }
165 oldt = t;
166 }
167
168 }
169
170 }