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.FunctionEvaluationException; 020 import org.apache.commons.math.MathRuntimeException; 021 import org.apache.commons.math.MaxIterationsExceededException; 022 import org.apache.commons.math.analysis.UnivariateRealFunction; 023 import org.apache.commons.math.exception.util.LocalizedFormats; 024 import org.apache.commons.math.util.FastMath; 025 026 /** 027 * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html"> 028 * Trapezoidal 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 $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $ 035 * @since 1.2 036 */ 037 public class TrapezoidIntegrator extends UnivariateRealIntegratorImpl { 038 039 /** Intermediate result. */ 040 private double s; 041 042 /** 043 * Construct an integrator for the given function. 044 * 045 * @param f function to integrate 046 * @deprecated as of 2.0 the integrand function is passed as an argument 047 * to the {@link #integrate(UnivariateRealFunction, double, double)}method. 048 */ 049 @Deprecated 050 public TrapezoidIntegrator(UnivariateRealFunction f) { 051 super(f, 64); 052 } 053 054 /** 055 * Construct an integrator. 056 */ 057 public TrapezoidIntegrator() { 058 super(64); 059 } 060 061 /** 062 * Compute the n-th stage integral of trapezoid rule. This function 063 * should only be called by API <code>integrate()</code> in the package. 064 * To save time it does not verify arguments - caller does. 065 * <p> 066 * The interval is divided equally into 2^n sections rather than an 067 * arbitrary m sections because this configuration can best utilize the 068 * alrealy computed values.</p> 069 * 070 * @param f the integrand function 071 * @param min the lower bound for the interval 072 * @param max the upper bound for the interval 073 * @param n the stage of 1/2 refinement, n = 0 is no refinement 074 * @return the value of n-th stage integral 075 * @throws FunctionEvaluationException if an error occurs evaluating the function 076 */ 077 double stage(final UnivariateRealFunction f, 078 final double min, final double max, final int n) 079 throws FunctionEvaluationException { 080 081 if (n == 0) { 082 s = 0.5 * (max - min) * (f.value(min) + f.value(max)); 083 return s; 084 } else { 085 final long np = 1L << (n-1); // number of new points in this stage 086 double sum = 0; 087 final double spacing = (max - min) / np; // spacing between adjacent new points 088 double x = min + 0.5 * spacing; // the first new point 089 for (long i = 0; i < np; i++) { 090 sum += f.value(x); 091 x += spacing; 092 } 093 // add the new sum to previously calculated result 094 s = 0.5 * (s + sum * spacing); 095 return s; 096 } 097 } 098 099 /** {@inheritDoc} */ 100 @Deprecated 101 public double integrate(final double min, final double max) 102 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 103 return integrate(f, min, max); 104 } 105 106 /** {@inheritDoc} */ 107 public double integrate(final UnivariateRealFunction f, final double min, final double max) 108 throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException { 109 110 clearResult(); 111 verifyInterval(min, max); 112 verifyIterationCount(); 113 114 double oldt = stage(f, min, max, 0); 115 for (int i = 1; i <= maximalIterationCount; ++i) { 116 final double t = stage(f, min, max, i); 117 if (i >= minimalIterationCount) { 118 final double delta = FastMath.abs(t - oldt); 119 final double rLimit = 120 relativeAccuracy * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5; 121 if ((delta <= rLimit) || (delta <= absoluteAccuracy)) { 122 setResult(t, i); 123 return result; 124 } 125 } 126 oldt = t; 127 } 128 throw new MaxIterationsExceededException(maximalIterationCount); 129 } 130 131 /** {@inheritDoc} */ 132 @Override 133 protected void verifyIterationCount() throws IllegalArgumentException { 134 super.verifyIterationCount(); 135 // at most 64 bisection refinements 136 if (maximalIterationCount > 64) { 137 throw MathRuntimeException.createIllegalArgumentException( 138 LocalizedFormats.INVALID_ITERATIONS_LIMITS, 139 0, 64); 140 } 141 } 142 }