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 * http://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 package org.apache.commons.math4.legacy.analysis.integration; 18 19 import org.apache.commons.numbers.core.ArithmeticUtils; 20 import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException; 21 import org.apache.commons.math4.core.jdkmath.JdkMath; 22 23 /** 24 * Implements the <a href="https://en.wikipedia.org/wiki/Riemann_sum#Midpoint_rule"> 25 * Midpoint Rule</a> for integration of real univariate functions. For 26 * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595, 27 * chapter 9.2. 28 * <p> 29 * The function should be integrable.</p> 30 * 31 * @since 3.3 32 */ 33 public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator { 34 35 /** Maximum number of iterations for midpoint. 39 = floor(log_3(2^63)), the 36 * maximum number of triplings allowed before exceeding 64-bit bounds. 37 */ 38 private static final int MIDPOINT_MAX_ITERATIONS_COUNT = 39; 39 40 /** 41 * Build a midpoint integrator with given accuracies and iterations counts. 42 * @param relativeAccuracy relative accuracy of the result 43 * @param absoluteAccuracy absolute accuracy of the result 44 * @param minimalIterationCount minimum number of iterations 45 * @param maximalIterationCount maximum number of iterations 46 * @exception org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException if minimal number of iterations 47 * is not strictly positive 48 * @exception org.apache.commons.math4.legacy.exception.NumberIsTooSmallException if maximal number of iterations 49 * is lesser than or equal to the minimal number of iterations 50 * @exception NumberIsTooLargeException if maximal number of iterations 51 * is greater than 39. 52 */ 53 public MidPointIntegrator(final double relativeAccuracy, 54 final double absoluteAccuracy, 55 final int minimalIterationCount, 56 final int maximalIterationCount) { 57 super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount); 58 if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) { 59 throw new NumberIsTooLargeException(maximalIterationCount, 60 MIDPOINT_MAX_ITERATIONS_COUNT, false); 61 } 62 } 63 64 /** 65 * Build a midpoint integrator with given iteration counts. 66 * @param minimalIterationCount minimum number of iterations 67 * @param maximalIterationCount maximum number of iterations 68 * @exception org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException if minimal number of iterations 69 * is not strictly positive 70 * @exception org.apache.commons.math4.legacy.exception.NumberIsTooSmallException if maximal number of iterations 71 * is lesser than or equal to the minimal number of iterations 72 * @exception NumberIsTooLargeException if maximal number of iterations 73 * is greater than 39. 74 */ 75 public MidPointIntegrator(final int minimalIterationCount, 76 final int maximalIterationCount) { 77 super(minimalIterationCount, maximalIterationCount); 78 if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) { 79 throw new NumberIsTooLargeException(maximalIterationCount, 80 MIDPOINT_MAX_ITERATIONS_COUNT, false); 81 } 82 } 83 84 /** 85 * Construct a midpoint integrator with default settings. 86 * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}) 87 */ 88 public MidPointIntegrator() { 89 super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT); 90 } 91 92 /** 93 * Compute the n-th stage integral of midpoint rule. 94 * This function should only be called by API <code>integrate()</code> in the package. 95 * To save time it does not verify arguments - caller does. 96 * <p> 97 * The interval is divided equally into 3^n sections rather than an 98 * arbitrary m sections because this configuration can best utilize the 99 * already computed values.</p> 100 * 101 * @param n the stage of 1/3 refinement. Must be larger than 0. 102 * @param previousStageResult Result from the previous call to the 103 * {@code stage} method. 104 * @param min Lower bound of the integration interval. 105 * @param diffMaxMin Difference between the lower bound and upper bound 106 * of the integration interval. 107 * @return the value of n-th stage integral 108 * @throws org.apache.commons.math4.legacy.exception.TooManyEvaluationsException if the maximal number of evaluations 109 * is exceeded. 110 */ 111 private double stage(final int n, 112 double previousStageResult, 113 double min, 114 double diffMaxMin) { 115 // number of points in the previous stage. This stage will contribute 116 // 2*3^{n-1} more points. 117 final long np = ArithmeticUtils.pow(3L, n - 1); 118 double sum = 0; 119 120 // spacing between adjacent new points 121 final double spacing = diffMaxMin / np; 122 final double leftOffset = spacing / 6; 123 final double rightOffset = 5 * leftOffset; 124 125 double x = min; 126 for (long i = 0; i < np; i++) { 127 // The first and second new points are located at the new midpoints 128 // generated when each previous integration slice is split into 3. 129 // 130 // |--------x--------| 131 // |--x--|--x--|--x--| 132 sum += computeObjectiveValue(x + leftOffset); 133 sum += computeObjectiveValue(x + rightOffset); 134 x += spacing; 135 } 136 // add the new sum to previously calculated result 137 return (previousStageResult + sum * spacing) / 3.0; 138 } 139 140 141 /** {@inheritDoc} */ 142 @Override 143 protected double doIntegrate() { 144 final double min = getMin(); 145 final double diff = getMax() - min; 146 final double midPoint = min + 0.5 * diff; 147 148 double oldt = diff * computeObjectiveValue(midPoint); 149 150 while (true) { 151 iterations.increment(); 152 final int i = iterations.getCount(); 153 final double t = stage(i, oldt, min, diff); 154 if (i >= getMinimalIterationCount()) { 155 final double delta = JdkMath.abs(t - oldt); 156 final double rLimit = 157 getRelativeAccuracy() * (JdkMath.abs(oldt) + JdkMath.abs(t)) * 0.5; 158 if (delta <= rLimit || delta <= getAbsoluteAccuracy()) { 159 return t; 160 } 161 } 162 oldt = t; 163 } 164 } 165 }