001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017 package org.apache.commons.math.analysis.integration;
018
019 import org.apache.commons.math.exception.MaxCountExceededException;
020 import org.apache.commons.math.exception.NotStrictlyPositiveException;
021 import org.apache.commons.math.exception.NumberIsTooLargeException;
022 import org.apache.commons.math.exception.NumberIsTooSmallException;
023 import org.apache.commons.math.exception.TooManyEvaluationsException;
024 import org.apache.commons.math.util.FastMath;
025
026 /**
027 * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html">
028 * Trapezoid Rule</a> for integration of real univariate functions. For
029 * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
030 * chapter 3.
031 * <p>
032 * The function should be integrable.</p>
033 *
034 * @version $Id: TrapezoidIntegrator.java 1179926 2011-10-07 03:18:05Z psteitz $
035 * @since 1.2
036 */
037 public class TrapezoidIntegrator extends UnivariateRealIntegratorImpl {
038
039 /** Maximum number of iterations for trapezoid. */
040 public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
041
042 /** Intermediate result. */
043 private double s;
044
045 /**
046 * Build a trapezoid integrator with given accuracies and iterations counts.
047 * @param relativeAccuracy relative accuracy of the result
048 * @param absoluteAccuracy absolute accuracy of the result
049 * @param minimalIterationCount minimum number of iterations
050 * @param maximalIterationCount maximum number of iterations
051 * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
052 * @exception NotStrictlyPositiveException if minimal number of iterations
053 * is not strictly positive
054 * @exception NumberIsTooSmallException if maximal number of iterations
055 * is lesser than or equal to the minimal number of iterations
056 * @exception NumberIsTooLargeException if maximal number of iterations
057 * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
058 */
059 public TrapezoidIntegrator(final double relativeAccuracy,
060 final double absoluteAccuracy,
061 final int minimalIterationCount,
062 final int maximalIterationCount)
063 throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
064 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
065 if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
066 throw new NumberIsTooLargeException(maximalIterationCount,
067 TRAPEZOID_MAX_ITERATIONS_COUNT, false);
068 }
069 }
070
071 /**
072 * Build a trapezoid integrator with given iteration counts.
073 * @param minimalIterationCount minimum number of iterations
074 * @param maximalIterationCount maximum number of iterations
075 * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
076 * @exception NotStrictlyPositiveException if minimal number of iterations
077 * is not strictly positive
078 * @exception NumberIsTooSmallException if maximal number of iterations
079 * is lesser than or equal to the minimal number of iterations
080 * @exception NumberIsTooLargeException if maximal number of iterations
081 * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
082 */
083 public TrapezoidIntegrator(final int minimalIterationCount,
084 final int maximalIterationCount)
085 throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
086 super(minimalIterationCount, maximalIterationCount);
087 if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
088 throw new NumberIsTooLargeException(maximalIterationCount,
089 TRAPEZOID_MAX_ITERATIONS_COUNT, false);
090 }
091 }
092
093 /**
094 * Construct a trapezoid integrator with default settings.
095 * (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
096 */
097 public TrapezoidIntegrator() {
098 super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
099 }
100
101 /**
102 * Compute the n-th stage integral of trapezoid rule. This function
103 * should only be called by API <code>integrate()</code> in the package.
104 * To save time it does not verify arguments - caller does.
105 * <p>
106 * The interval is divided equally into 2^n sections rather than an
107 * arbitrary m sections because this configuration can best utilize the
108 * already computed values.</p>
109 *
110 * @param baseIntegrator integrator holding integration parameters
111 * @param n the stage of 1/2 refinement, n = 0 is no refinement
112 * @return the value of n-th stage integral
113 * @throws TooManyEvaluationsException if the maximal number of evaluations
114 * is exceeded.
115 */
116 double stage(final UnivariateRealIntegratorImpl baseIntegrator, final int n)
117 throws TooManyEvaluationsException {
118
119 if (n == 0) {
120 s = 0.5 * (baseIntegrator.max - baseIntegrator.min) *
121 (baseIntegrator.computeObjectiveValue(baseIntegrator.min) +
122 baseIntegrator.computeObjectiveValue(baseIntegrator.max));
123 return s;
124 } else {
125 final long np = 1L << (n-1); // number of new points in this stage
126 double sum = 0;
127 // spacing between adjacent new points
128 final double spacing = (baseIntegrator.max - baseIntegrator.min) / np;
129 double x = baseIntegrator.min + 0.5 * spacing; // the first new point
130 for (long i = 0; i < np; i++) {
131 sum += baseIntegrator.computeObjectiveValue(x);
132 x += spacing;
133 }
134 // add the new sum to previously calculated result
135 s = 0.5 * (s + sum * spacing);
136 return s;
137 }
138 }
139
140 /** {@inheritDoc} */
141 protected double doIntegrate()
142 throws TooManyEvaluationsException, MaxCountExceededException {
143
144 double oldt = stage(this, 0);
145 iterations.incrementCount();
146 while (true) {
147 final int i = iterations.getCount();
148 final double t = stage(this, i);
149 if (i >= minimalIterationCount) {
150 final double delta = FastMath.abs(t - oldt);
151 final double rLimit =
152 relativeAccuracy * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
153 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
154 return t;
155 }
156 }
157 oldt = t;
158 iterations.incrementCount();
159 }
160
161 }
162
163 }