1dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/* 2dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Licensed to the Apache Software Foundation (ASF) under one or more 3dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * contributor license agreements. See the NOTICE file distributed with 4dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * this work for additional information regarding copyright ownership. 5dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The ASF licenses this file to You under the Apache License, Version 2.0 6dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * (the "License"); you may not use this file except in compliance with 7dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * the License. You may obtain a copy of the License at 8dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 9dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * http://www.apache.org/licenses/LICENSE-2.0 10dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 11dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Unless required by applicable law or agreed to in writing, software 12dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * distributed under the License is distributed on an "AS IS" BASIS, 13dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * See the License for the specific language governing permissions and 15dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * limitations under the License. 16dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 17dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpackage org.apache.commons.math.analysis.integration; 18dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 19dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.FunctionEvaluationException; 20dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.MathRuntimeException; 21dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.MaxIterationsExceededException; 22dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.analysis.UnivariateRealFunction; 23dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.exception.util.LocalizedFormats; 24dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondimport org.apache.commons.math.util.FastMath; 25dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 26dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond/** 27dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html"> 28dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Trapezoidal Rule</a> for integration of real univariate functions. For 29dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X, 30dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * chapter 3. 31dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 32dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The function should be integrable.</p> 33dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 34dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ 35dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @since 1.2 36dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 37dee0849a9704d532af0b550146cbafbaa6ee1d19Raymondpublic class TrapezoidIntegrator extends UnivariateRealIntegratorImpl { 38dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 39dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** Intermediate result. */ 40dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond private double s; 41dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 42dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 43dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Construct an integrator for the given function. 44dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 45dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param f function to integrate 46dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @deprecated as of 2.0 the integrand function is passed as an argument 47dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * to the {@link #integrate(UnivariateRealFunction, double, double)}method. 48dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 49dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Deprecated 50dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public TrapezoidIntegrator(UnivariateRealFunction f) { 51dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(f, 64); 52dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 53dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 54dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 55dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Construct an integrator. 56dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 57dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public TrapezoidIntegrator() { 58dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super(64); 59dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 60dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 61dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** 62dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * Compute the n-th stage integral of trapezoid rule. This function 63dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * should only be called by API <code>integrate()</code> in the package. 64dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * To save time it does not verify arguments - caller does. 65dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * <p> 66dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * The interval is divided equally into 2^n sections rather than an 67dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * arbitrary m sections because this configuration can best utilize the 68dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * alrealy computed values.</p> 69dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * 70dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param f the integrand function 71dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param min the lower bound for the interval 72dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param max the upper bound for the interval 73dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @param n the stage of 1/2 refinement, n = 0 is no refinement 74dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @return the value of n-th stage integral 75dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond * @throws FunctionEvaluationException if an error occurs evaluating the function 76dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond */ 77dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double stage(final UnivariateRealFunction f, 78dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double min, final double max, final int n) 79dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws FunctionEvaluationException { 80dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 81dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (n == 0) { 82dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond s = 0.5 * (max - min) * (f.value(min) + f.value(max)); 83dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return s; 84dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } else { 85dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final long np = 1L << (n-1); // number of new points in this stage 86dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double sum = 0; 87dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double spacing = (max - min) / np; // spacing between adjacent new points 88dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double x = min + 0.5 * spacing; // the first new point 89dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (long i = 0; i < np; i++) { 90dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond sum += f.value(x); 91dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond x += spacing; 92dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 93dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // add the new sum to previously calculated result 94dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond s = 0.5 * (s + sum * spacing); 95dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return s; 96dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 97dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 98dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 99dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 100dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Deprecated 101dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public double integrate(final double min, final double max) 102dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 103dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return integrate(f, min, max); 104dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 105dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 106dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 107dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond public double integrate(final UnivariateRealFunction f, final double min, final double max) 108dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 109dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 110dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond clearResult(); 111dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond verifyInterval(min, max); 112dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond verifyIterationCount(); 113dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 114dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond double oldt = stage(f, min, max, 0); 115dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond for (int i = 1; i <= maximalIterationCount; ++i) { 116dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double t = stage(f, min, max, i); 117dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (i >= minimalIterationCount) { 118dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double delta = FastMath.abs(t - oldt); 119dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond final double rLimit = 120dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond relativeAccuracy * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5; 121dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { 122dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond setResult(t, i); 123dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond return result; 124dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 125dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 126dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond oldt = t; 127dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 128dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw new MaxIterationsExceededException(maximalIterationCount); 129dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 130dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 131dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond /** {@inheritDoc} */ 132dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond @Override 133dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond protected void verifyIterationCount() throws IllegalArgumentException { 134dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond super.verifyIterationCount(); 135dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond // at most 64 bisection refinements 136dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond if (maximalIterationCount > 64) { 137dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond throw MathRuntimeException.createIllegalArgumentException( 138dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond LocalizedFormats.INVALID_ITERATIONS_LIMITS, 139dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond 0, 64); 140dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 141dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond } 142dee0849a9704d532af0b550146cbafbaa6ee1d19Raymond} 143