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.CalculusFieldElement;
25 import org.hipparchus.Field;
26 import org.hipparchus.exception.LocalizedCoreFormats;
27 import org.hipparchus.exception.MathIllegalArgumentException;
28 import org.hipparchus.exception.MathIllegalStateException;
29 import org.hipparchus.util.FastMath;
30
31 /**
32 * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
33 * Simpson's Rule</a> for integration of real univariate functions. For
34 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
35 * chapter 3.
36 * <p>
37 * This implementation employs the basic trapezoid rule to calculate Simpson's
38 * rule.</p>
39 * @param <T> Type of the field elements.
40 * @since 2.0
41 */
42 public class FieldSimpsonIntegrator<T extends CalculusFieldElement<T>> extends BaseAbstractFieldUnivariateIntegrator<T> {
43
44 /** Maximal number of iterations for Simpson. */
45 public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
46
47 /**
48 * Build a Simpson integrator with given accuracies and iterations counts.
49 * @param field field to which function argument and value belong
50 * @param relativeAccuracy relative accuracy of the result
51 * @param absoluteAccuracy absolute accuracy of the result
52 * @param minimalIterationCount minimum number of iterations
53 * @param maximalIterationCount maximum number of iterations
54 * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
55 * @exception MathIllegalArgumentException if minimal number of iterations
56 * is not strictly positive
57 * @exception MathIllegalArgumentException if maximal number of iterations
58 * is lesser than or equal to the minimal number of iterations
59 * @exception MathIllegalArgumentException if maximal number of iterations
60 * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
61 */
62 public FieldSimpsonIntegrator(final Field<T> field,
63 final double relativeAccuracy,
64 final double absoluteAccuracy,
65 final int minimalIterationCount,
66 final int maximalIterationCount)
67 throws MathIllegalArgumentException {
68 super(field, relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
69 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
70 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
71 maximalIterationCount, SIMPSON_MAX_ITERATIONS_COUNT);
72 }
73 }
74
75 /**
76 * Build a Simpson integrator with given iteration counts.
77 * @param field field to which function argument and value belong
78 * @param minimalIterationCount minimum number of iterations
79 * @param maximalIterationCount maximum number of iterations
80 * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
81 * @exception MathIllegalArgumentException if minimal number of iterations
82 * is not strictly positive
83 * @exception MathIllegalArgumentException if maximal number of iterations
84 * is lesser than or equal to the minimal number of iterations
85 * @exception MathIllegalArgumentException if maximal number of iterations
86 * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
87 */
88 public FieldSimpsonIntegrator(final Field<T> field,
89 final int minimalIterationCount,
90 final int maximalIterationCount)
91 throws MathIllegalArgumentException {
92 super(field, minimalIterationCount, maximalIterationCount);
93 if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
94 throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
95 maximalIterationCount, SIMPSON_MAX_ITERATIONS_COUNT);
96 }
97 }
98
99 /**
100 * Construct an integrator with default settings.
101 * @param field field to which function argument and value belong
102 * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
103 */
104 public FieldSimpsonIntegrator(final Field<T> field) {
105 super(field, DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
106 }
107
108 /** {@inheritDoc} */
109 @Override
110 protected T doIntegrate()
111 throws MathIllegalStateException {
112
113 FieldTrapezoidIntegrator<T> qtrap = new FieldTrapezoidIntegrator<>(getField());
114 if (getMinimalIterationCount() == 1) {
115 return qtrap.stage(this, 1).multiply(4).subtract(qtrap.stage(this, 0)).divide(3.0);
116 }
117
118 // Simpson's rule requires at least two trapezoid stages.
119 T olds = getField().getZero();
120 T oldt = qtrap.stage(this, 0);
121 while (true) {
122 final T t = qtrap.stage(this, iterations.getCount());
123 iterations.increment();
124 final T s = t.multiply(4).subtract(oldt).divide(3.0);
125 if (iterations.getCount() >= getMinimalIterationCount()) {
126 final double delta = FastMath.abs(s.subtract(olds)).getReal();
127 final double rLimit = FastMath.abs(olds).add(FastMath.abs(s)).multiply(0.5 * getRelativeAccuracy()).getReal();
128 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
129 return s;
130 }
131 }
132 olds = s;
133 oldt = t;
134 }
135
136 }
137
138 }