| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math4.legacy.analysis.integration; |
| |
| import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException; |
| import org.apache.commons.math4.core.jdkmath.JdkMath; |
| |
| /** |
| * Implements the <a href="https://en.wikipedia.org/wiki/Riemann_sum#Midpoint_rule"> |
| * Midpoint Rule</a> for integration of real univariate functions. For |
| * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595, |
| * chapter 9.2. |
| * <p> |
| * The function should be integrable.</p> |
| * |
| * @since 3.3 |
| */ |
| public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator { |
| |
| /** Maximum number of iterations for midpoint. 39 = floor(log_3(2^63)), the |
| * maximum number of triplings allowed before exceeding 64-bit bounds. |
| */ |
| private static final int MIDPOINT_MAX_ITERATIONS_COUNT = 39; |
| |
| /** |
| * Build a midpoint integrator with given accuracies and iterations counts. |
| * @param relativeAccuracy relative accuracy of the result |
| * @param absoluteAccuracy absolute accuracy of the result |
| * @param minimalIterationCount minimum number of iterations |
| * @param maximalIterationCount maximum number of iterations |
| * @exception org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException if minimal number of iterations |
| * is not strictly positive |
| * @exception org.apache.commons.math4.legacy.exception.NumberIsTooSmallException if maximal number of iterations |
| * is lesser than or equal to the minimal number of iterations |
| * @exception NumberIsTooLargeException if maximal number of iterations |
| * is greater than 39. |
| */ |
| public MidPointIntegrator(final double relativeAccuracy, |
| final double absoluteAccuracy, |
| final int minimalIterationCount, |
| final int maximalIterationCount) { |
| super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount); |
| if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) { |
| throw new NumberIsTooLargeException(maximalIterationCount, |
| MIDPOINT_MAX_ITERATIONS_COUNT, false); |
| } |
| } |
| |
| /** |
| * Build a midpoint integrator with given iteration counts. |
| * @param minimalIterationCount minimum number of iterations |
| * @param maximalIterationCount maximum number of iterations |
| * @exception org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException if minimal number of iterations |
| * is not strictly positive |
| * @exception org.apache.commons.math4.legacy.exception.NumberIsTooSmallException if maximal number of iterations |
| * is lesser than or equal to the minimal number of iterations |
| * @exception NumberIsTooLargeException if maximal number of iterations |
| * is greater than 39. |
| */ |
| public MidPointIntegrator(final int minimalIterationCount, |
| final int maximalIterationCount) { |
| super(minimalIterationCount, maximalIterationCount); |
| if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) { |
| throw new NumberIsTooLargeException(maximalIterationCount, |
| MIDPOINT_MAX_ITERATIONS_COUNT, false); |
| } |
| } |
| |
| /** |
| * Construct a midpoint integrator with default settings. |
| * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}) |
| */ |
| public MidPointIntegrator() { |
| super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT); |
| } |
| |
| /** |
| * Compute the n-th stage integral of midpoint rule. |
| * This function should only be called by API <code>integrate()</code> in the package. |
| * To save time it does not verify arguments - caller does. |
| * <p> |
| * The interval is divided equally into 3^n sections rather than an |
| * arbitrary m sections because this configuration can best utilize the |
| * already computed values.</p> |
| * |
| * @param n the stage of 1/3 refinement. Must be larger than 0. |
| * @param previousStageResult Result from the previous call to the |
| * {@code stage} method. |
| * @param min Lower bound of the integration interval. |
| * @param diffMaxMin Difference between the lower bound and upper bound |
| * of the integration interval. |
| * @return the value of n-th stage integral |
| * @throws org.apache.commons.math4.legacy.exception.TooManyEvaluationsException if the maximal number of evaluations |
| * is exceeded. |
| */ |
| private double stage(final int n, |
| double previousStageResult, |
| double min, |
| double diffMaxMin) { |
| // number of points in the previous stage. This stage will contribute |
| // 2*3^{n-1} more points. |
| final long np = (long) JdkMath.pow(3, n - 1); |
| double sum = 0; |
| |
| // spacing between adjacent new points |
| final double spacing = diffMaxMin / np; |
| final double leftOffset = spacing / 6; |
| final double rightOffset = 5 * leftOffset; |
| |
| double x = min; |
| for (long i = 0; i < np; i++) { |
| // The first and second new points are located at the new midpoints |
| // generated when each previous integration slice is split into 3. |
| // |
| // |--------x--------| |
| // |--x--|--x--|--x--| |
| sum += computeObjectiveValue(x + leftOffset); |
| sum += computeObjectiveValue(x + rightOffset); |
| x += spacing; |
| } |
| // add the new sum to previously calculated result |
| return (previousStageResult + sum * spacing) / 3.0; |
| } |
| |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected double doIntegrate() { |
| final double min = getMin(); |
| final double diff = getMax() - min; |
| final double midPoint = min + 0.5 * diff; |
| |
| double oldt = diff * computeObjectiveValue(midPoint); |
| |
| while (true) { |
| iterations.increment(); |
| final int i = iterations.getCount(); |
| final double t = stage(i, oldt, min, diff); |
| if (i >= getMinimalIterationCount()) { |
| final double delta = JdkMath.abs(t - oldt); |
| final double rLimit = |
| getRelativeAccuracy() * (JdkMath.abs(oldt) + JdkMath.abs(t)) * 0.5; |
| if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) { |
| return t; |
| } |
| } |
| oldt = t; |
| } |
| |
| } |
| |
| } |