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.ConvergenceException; 020 import org.apache.commons.math.FunctionEvaluationException; 021 import org.apache.commons.math.MathRuntimeException; 022 import org.apache.commons.math.analysis.UnivariateRealFunction; 023 import org.apache.commons.math.exception.util.LocalizedFormats; 024 import org.apache.commons.math.exception.NullArgumentException; 025 import org.apache.commons.math.util.FastMath; 026 027 /** 028 * Utility routines for {@link UnivariateRealSolver} objects. 029 * 030 * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $ 031 */ 032 public class UnivariateRealSolverUtils { 033 034 /** 035 * Default constructor. 036 */ 037 private UnivariateRealSolverUtils() { 038 super(); 039 } 040 041 /** 042 * Convenience method to find a zero of a univariate real function. A default 043 * solver is used. 044 * 045 * @param f the function. 046 * @param x0 the lower bound for the interval. 047 * @param x1 the upper bound for the interval. 048 * @return a value where the function is zero. 049 * @throws ConvergenceException if the iteration count was exceeded 050 * @throws FunctionEvaluationException if an error occurs evaluating the function 051 * @throws IllegalArgumentException if f is null or the endpoints do not 052 * specify a valid interval 053 */ 054 public static double solve(UnivariateRealFunction f, double x0, double x1) 055 throws ConvergenceException, FunctionEvaluationException { 056 setup(f); 057 return LazyHolder.FACTORY.newDefaultSolver().solve(f, x0, x1); 058 } 059 060 /** 061 * Convenience method to find a zero of a univariate real function. A default 062 * solver is used. 063 * 064 * @param f the function 065 * @param x0 the lower bound for the interval 066 * @param x1 the upper bound for the interval 067 * @param absoluteAccuracy the accuracy to be used by the solver 068 * @return a value where the function is zero 069 * @throws ConvergenceException if the iteration count is exceeded 070 * @throws FunctionEvaluationException if an error occurs evaluating the function 071 * @throws IllegalArgumentException if f is null, the endpoints do not 072 * specify a valid interval, or the absoluteAccuracy is not valid for the 073 * default solver 074 */ 075 public static double solve(UnivariateRealFunction f, double x0, double x1, 076 double absoluteAccuracy) throws ConvergenceException, 077 FunctionEvaluationException { 078 079 setup(f); 080 UnivariateRealSolver solver = LazyHolder.FACTORY.newDefaultSolver(); 081 solver.setAbsoluteAccuracy(absoluteAccuracy); 082 return solver.solve(f, x0, x1); 083 } 084 085 /** 086 * This method attempts to find two values a and b satisfying <ul> 087 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li> 088 * <li> <code> f(a) * f(b) < 0 </code></li> 089 * </ul> 090 * If f is continuous on <code>[a,b],</code> this means that <code>a</code> 091 * and <code>b</code> bracket a root of f. 092 * <p> 093 * The algorithm starts by setting 094 * <code>a := initial -1; b := initial +1,</code> examines the value of the 095 * function at <code>a</code> and <code>b</code> and keeps moving 096 * the endpoints out by one unit each time through a loop that terminates 097 * when one of the following happens: <ul> 098 * <li> <code> f(a) * f(b) < 0 </code> -- success!</li> 099 * <li> <code> a = lower </code> and <code> b = upper</code> 100 * -- ConvergenceException </li> 101 * <li> <code> Integer.MAX_VALUE</code> iterations elapse 102 * -- ConvergenceException </li> 103 * </ul></p> 104 * <p> 105 * <strong>Note: </strong> this method can take 106 * <code>Integer.MAX_VALUE</code> iterations to throw a 107 * <code>ConvergenceException.</code> Unless you are confident that there 108 * is a root between <code>lowerBound</code> and <code>upperBound</code> 109 * near <code>initial,</code> it is better to use 110 * {@link #bracket(UnivariateRealFunction, double, double, double, int)}, 111 * explicitly specifying the maximum number of iterations.</p> 112 * 113 * @param function the function 114 * @param initial initial midpoint of interval being expanded to 115 * bracket a root 116 * @param lowerBound lower bound (a is never lower than this value) 117 * @param upperBound upper bound (b never is greater than this 118 * value) 119 * @return a two element array holding {a, b} 120 * @throws ConvergenceException if a root can not be bracketted 121 * @throws FunctionEvaluationException if an error occurs evaluating the function 122 * @throws IllegalArgumentException if function is null, maximumIterations 123 * is not positive, or initial is not between lowerBound and upperBound 124 */ 125 public static double[] bracket(UnivariateRealFunction function, 126 double initial, double lowerBound, double upperBound) 127 throws ConvergenceException, FunctionEvaluationException { 128 return bracket( function, initial, lowerBound, upperBound, 129 Integer.MAX_VALUE ) ; 130 } 131 132 /** 133 * This method attempts to find two values a and b satisfying <ul> 134 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li> 135 * <li> <code> f(a) * f(b) <= 0 </code> </li> 136 * </ul> 137 * If f is continuous on <code>[a,b],</code> this means that <code>a</code> 138 * and <code>b</code> bracket a root of f. 139 * <p> 140 * The algorithm starts by setting 141 * <code>a := initial -1; b := initial +1,</code> examines the value of the 142 * function at <code>a</code> and <code>b</code> and keeps moving 143 * the endpoints out by one unit each time through a loop that terminates 144 * when one of the following happens: <ul> 145 * <li> <code> f(a) * f(b) <= 0 </code> -- success!</li> 146 * <li> <code> a = lower </code> and <code> b = upper</code> 147 * -- ConvergenceException </li> 148 * <li> <code> maximumIterations</code> iterations elapse 149 * -- ConvergenceException </li></ul></p> 150 * 151 * @param function the function 152 * @param initial initial midpoint of interval being expanded to 153 * bracket a root 154 * @param lowerBound lower bound (a is never lower than this value) 155 * @param upperBound upper bound (b never is greater than this 156 * value) 157 * @param maximumIterations maximum number of iterations to perform 158 * @return a two element array holding {a, b}. 159 * @throws ConvergenceException if the algorithm fails to find a and b 160 * satisfying the desired conditions 161 * @throws FunctionEvaluationException if an error occurs evaluating the 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 new NullArgumentException(LocalizedFormats.FUNCTION); 172 } 173 if (maximumIterations <= 0) { 174 throw MathRuntimeException.createIllegalArgumentException( 175 LocalizedFormats.INVALID_MAX_ITERATIONS, maximumIterations); 176 } 177 if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) { 178 throw MathRuntimeException.createIllegalArgumentException( 179 LocalizedFormats.INVALID_BRACKETING_PARAMETERS, 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 = FastMath.max(a - 1.0, lowerBound); 190 b = FastMath.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 LocalizedFormats.FAILED_BRACKETING, 201 numIterations, maximumIterations, initial, 202 lowerBound, upperBound, a, b, fa, fb); 203 } 204 205 return new double[]{a, b}; 206 } 207 208 /** 209 * Compute the midpoint of two values. 210 * 211 * @param a first value. 212 * @param b second value. 213 * @return the midpoint. 214 */ 215 public static double midpoint(double a, double b) { 216 return (a + b) * .5; 217 } 218 219 /** 220 * Checks to see if f is null, throwing IllegalArgumentException if so. 221 * @param f input function 222 * @throws IllegalArgumentException if f is null 223 */ 224 private static void setup(UnivariateRealFunction f) { 225 if (f == null) { 226 throw new NullArgumentException(LocalizedFormats.FUNCTION); 227 } 228 } 229 230 // CHECKSTYLE: stop HideUtilityClassConstructor 231 /** Holder for the factory. 232 * <p>We use here the Initialization On Demand Holder Idiom.</p> 233 */ 234 private static class LazyHolder { 235 /** Cached solver factory */ 236 private static final UnivariateRealSolverFactory FACTORY = UnivariateRealSolverFactory.newInstance(); 237 } 238 // CHECKSTYLE: resume HideUtilityClassConstructor 239 240 }