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.solvers; 018 019 import org.apache.commons.math.FunctionEvaluationException; 020 import org.apache.commons.math.ConvergenceException; 021 import org.apache.commons.math.MathRuntimeException; 022 import org.apache.commons.math.analysis.UnivariateRealFunction; 023 024 /** 025 * Utility routines for {@link UnivariateRealSolver} objects. 026 * 027 * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $ 028 */ 029 public class UnivariateRealSolverUtils { 030 /** 031 * Default constructor. 032 */ 033 private UnivariateRealSolverUtils() { 034 super(); 035 } 036 037 /** 038 * Convenience method to find a zero of a univariate real function. A default 039 * solver is used. 040 * 041 * @param f the function. 042 * @param x0 the lower bound for the interval. 043 * @param x1 the upper bound for the interval. 044 * @return a value where the function is zero. 045 * @throws ConvergenceException if the iteration count was exceeded 046 * @throws FunctionEvaluationException if an error occurs evaluating 047 * the function 048 * @throws IllegalArgumentException if f is null or the endpoints do not 049 * specify a valid interval 050 */ 051 public static double solve(UnivariateRealFunction f, double x0, double x1) 052 throws ConvergenceException, FunctionEvaluationException { 053 setup(f); 054 return LazyHolder.FACTORY.newDefaultSolver().solve(f, x0, x1); 055 } 056 057 /** 058 * Convenience method to find a zero of a univariate real function. A default 059 * solver is used. 060 * 061 * @param f the function 062 * @param x0 the lower bound for the interval 063 * @param x1 the upper bound for the interval 064 * @param absoluteAccuracy the accuracy to be used by the solver 065 * @return a value where the function is zero 066 * @throws ConvergenceException if the iteration count is exceeded 067 * @throws FunctionEvaluationException if an error occurs evaluating the 068 * function 069 * @throws IllegalArgumentException if f is null, the endpoints do not 070 * specify a valid interval, or the absoluteAccuracy is not valid for the 071 * default solver 072 */ 073 public static double solve(UnivariateRealFunction f, double x0, double x1, 074 double absoluteAccuracy) throws ConvergenceException, 075 FunctionEvaluationException { 076 077 setup(f); 078 UnivariateRealSolver solver = LazyHolder.FACTORY.newDefaultSolver(); 079 solver.setAbsoluteAccuracy(absoluteAccuracy); 080 return solver.solve(f, x0, x1); 081 } 082 083 /** 084 * This method attempts to find two values a and b satisfying <ul> 085 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li> 086 * <li> <code> f(a) * f(b) < 0 </code></li> 087 * </ul> 088 * If f is continuous on <code>[a,b],</code> this means that <code>a</code> 089 * and <code>b</code> bracket a root of f. 090 * <p> 091 * The algorithm starts by setting 092 * <code>a := initial -1; b := initial +1,</code> examines the value of the 093 * function at <code>a</code> and <code>b</code> and keeps moving 094 * the endpoints out by one unit each time through a loop that terminates 095 * when one of the following happens: <ul> 096 * <li> <code> f(a) * f(b) < 0 </code> -- success!</li> 097 * <li> <code> a = lower </code> and <code> b = upper</code> 098 * -- ConvergenceException </li> 099 * <li> <code> Integer.MAX_VALUE</code> iterations elapse 100 * -- ConvergenceException </li> 101 * </ul></p> 102 * <p> 103 * <strong>Note: </strong> this method can take 104 * <code>Integer.MAX_VALUE</code> iterations to throw a 105 * <code>ConvergenceException.</code> Unless you are confident that there 106 * is a root between <code>lowerBound</code> and <code>upperBound</code> 107 * near <code>initial,</code> it is better to use 108 * {@link #bracket(UnivariateRealFunction, double, double, double, int)}, 109 * explicitly specifying the maximum number of iterations.</p> 110 * 111 * @param function the function 112 * @param initial initial midpoint of interval being expanded to 113 * bracket a root 114 * @param lowerBound lower bound (a is never lower than this value) 115 * @param upperBound upper bound (b never is greater than this 116 * value) 117 * @return a two element array holding {a, b} 118 * @throws ConvergenceException if a root can not be bracketted 119 * @throws FunctionEvaluationException if an error occurs evaluating the 120 * function 121 * @throws IllegalArgumentException if function is null, maximumIterations 122 * is not positive, or initial is not between lowerBound and upperBound 123 */ 124 public static double[] bracket(UnivariateRealFunction function, 125 double initial, double lowerBound, double upperBound) 126 throws ConvergenceException, FunctionEvaluationException { 127 return bracket( function, initial, lowerBound, upperBound, 128 Integer.MAX_VALUE ) ; 129 } 130 131 /** 132 * This method attempts to find two values a and b satisfying <ul> 133 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li> 134 * <li> <code> f(a) * f(b) <= 0 </code> </li> 135 * </ul> 136 * If f is continuous on <code>[a,b],</code> this means that <code>a</code> 137 * and <code>b</code> bracket a root of f. 138 * <p> 139 * The algorithm starts by setting 140 * <code>a := initial -1; b := initial +1,</code> examines the value of the 141 * function at <code>a</code> and <code>b</code> and keeps moving 142 * the endpoints out by one unit each time through a loop that terminates 143 * when one of the following happens: <ul> 144 * <li> <code> f(a) * f(b) <= 0 </code> -- success!</li> 145 * <li> <code> a = lower </code> and <code> b = upper</code> 146 * -- ConvergenceException </li> 147 * <li> <code> maximumIterations</code> iterations elapse 148 * -- ConvergenceException </li></ul></p> 149 * 150 * @param function the function 151 * @param initial initial midpoint of interval being expanded to 152 * bracket a root 153 * @param lowerBound lower bound (a is never lower than this value) 154 * @param upperBound upper bound (b never is greater than this 155 * value) 156 * @param maximumIterations maximum number of iterations to perform 157 * @return a two element array holding {a, b}. 158 * @throws ConvergenceException if the algorithm fails to find a and b 159 * satisfying the desired conditions 160 * @throws FunctionEvaluationException if an error occurs evaluating the 161 * function 162 * @throws IllegalArgumentException if function is null, maximumIterations 163 * is not positive, or initial is not between lowerBound and upperBound 164 */ 165 public static double[] bracket(UnivariateRealFunction function, 166 double initial, double lowerBound, double upperBound, 167 int maximumIterations) throws ConvergenceException, 168 FunctionEvaluationException { 169 170 if (function == null) { 171 throw MathRuntimeException.createIllegalArgumentException("function is null"); 172 } 173 if (maximumIterations <= 0) { 174 throw MathRuntimeException.createIllegalArgumentException( 175 "bad value for maximum iterations number: {0}", maximumIterations); 176 } 177 if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) { 178 throw MathRuntimeException.createIllegalArgumentException( 179 "invalid bracketing parameters: lower bound={0}, initial={1}, upper bound={2}", 180 lowerBound, initial, upperBound); 181 } 182 double a = initial; 183 double b = initial; 184 double fa; 185 double fb; 186 int numIterations = 0 ; 187 188 do { 189 a = Math.max(a - 1.0, lowerBound); 190 b = Math.min(b + 1.0, upperBound); 191 fa = function.value(a); 192 193 fb = function.value(b); 194 numIterations++ ; 195 } while ((fa * fb > 0.0) && (numIterations < maximumIterations) && 196 ((a > lowerBound) || (b < upperBound))); 197 198 if (fa * fb > 0.0 ) { 199 throw new ConvergenceException( 200 "number of iterations={0}, maximum iterations={1}, " + 201 "initial={2}, lower bound={3}, upper bound={4}, final a value={5}, " + 202 "final b value={6}, f(a)={7}, f(b)={8}", 203 numIterations, maximumIterations, initial, 204 lowerBound, upperBound, a, b, fa, fb); 205 } 206 207 return new double[]{a, b}; 208 } 209 210 /** 211 * Compute the midpoint of two values. 212 * 213 * @param a first value. 214 * @param b second value. 215 * @return the midpoint. 216 */ 217 public static double midpoint(double a, double b) { 218 return (a + b) * .5; 219 } 220 221 /** 222 * Checks to see if f is null, throwing IllegalArgumentException if so. 223 * @param f input function 224 * @throws IllegalArgumentException if f is null 225 */ 226 private static void setup(UnivariateRealFunction f) { 227 if (f == null) { 228 throw MathRuntimeException.createIllegalArgumentException("function is null"); 229 } 230 } 231 232 /** Holder for the factory. 233 * <p>We use here the Initialization On Demand Holder Idiom.</p> 234 */ 235 private static class LazyHolder { 236 /** Cached solver factory */ 237 private static final UnivariateRealSolverFactory FACTORY = 238 UnivariateRealSolverFactory.newInstance(); 239 } 240 241 }