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.MaxIterationsExceededException; 022 import org.apache.commons.math.analysis.UnivariateRealFunction; 023 import org.apache.commons.math.util.MathUtils; 024 025 /** 026 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html"> 027 * Ridders' Method</a> for root finding of real univariate functions. For 028 * reference, see C. Ridders, <i>A new algorithm for computing a single root 029 * of a real continuous function </i>, IEEE Transactions on Circuits and 030 * Systems, 26 (1979), 979 - 980. 031 * <p> 032 * The function should be continuous but not necessarily smooth.</p> 033 * 034 * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $ 035 * @since 1.2 036 */ 037 public class RiddersSolver extends UnivariateRealSolverImpl { 038 039 /** 040 * Construct a solver for the given function. 041 * 042 * @param f function to solve 043 * @deprecated as of 2.0 the function to solve is passed as an argument 044 * to the {@link #solve(UnivariateRealFunction, double, double)} or 045 * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)} 046 * method. 047 */ 048 @Deprecated 049 public RiddersSolver(UnivariateRealFunction f) { 050 super(f, 100, 1E-6); 051 } 052 053 /** 054 * Construct a solver. 055 */ 056 public RiddersSolver() { 057 super(100, 1E-6); 058 } 059 060 /** {@inheritDoc} */ 061 @Deprecated 062 public double solve(final double min, final double max) 063 throws ConvergenceException, FunctionEvaluationException { 064 return solve(f, min, max); 065 } 066 067 /** {@inheritDoc} */ 068 @Deprecated 069 public double solve(final double min, final double max, final double initial) 070 throws ConvergenceException, FunctionEvaluationException { 071 return solve(f, min, max, initial); 072 } 073 074 /** 075 * Find a root in the given interval with initial value. 076 * <p> 077 * Requires bracketing condition.</p> 078 * 079 * @param f the function to solve 080 * @param min the lower bound for the interval 081 * @param max the upper bound for the interval 082 * @param initial the start value to use 083 * @return the point at which the function value is zero 084 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 085 * @throws FunctionEvaluationException if an error occurs evaluating the 086 * function 087 * @throws IllegalArgumentException if any parameters are invalid 088 */ 089 public double solve(final UnivariateRealFunction f, 090 final double min, final double max, final double initial) 091 throws MaxIterationsExceededException, FunctionEvaluationException { 092 093 // check for zeros before verifying bracketing 094 if (f.value(min) == 0.0) { return min; } 095 if (f.value(max) == 0.0) { return max; } 096 if (f.value(initial) == 0.0) { return initial; } 097 098 verifyBracketing(min, max, f); 099 verifySequence(min, initial, max); 100 if (isBracketing(min, initial, f)) { 101 return solve(f, min, initial); 102 } else { 103 return solve(f, initial, max); 104 } 105 } 106 107 /** 108 * Find a root in the given interval. 109 * <p> 110 * Requires bracketing condition.</p> 111 * 112 * @param f the function to solve 113 * @param min the lower bound for the interval 114 * @param max the upper bound for the interval 115 * @return the point at which the function value is zero 116 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 117 * @throws FunctionEvaluationException if an error occurs evaluating the 118 * function 119 * @throws IllegalArgumentException if any parameters are invalid 120 */ 121 public double solve(final UnivariateRealFunction f, 122 final double min, final double max) 123 throws MaxIterationsExceededException, FunctionEvaluationException { 124 125 // [x1, x2] is the bracketing interval in each iteration 126 // x3 is the midpoint of [x1, x2] 127 // x is the new root approximation and an endpoint of the new interval 128 double x1 = min; 129 double y1 = f.value(x1); 130 double x2 = max; 131 double y2 = f.value(x2); 132 133 // check for zeros before verifying bracketing 134 if (y1 == 0.0) { 135 return min; 136 } 137 if (y2 == 0.0) { 138 return max; 139 } 140 verifyBracketing(min, max, f); 141 142 int i = 1; 143 double oldx = Double.POSITIVE_INFINITY; 144 while (i <= maximalIterationCount) { 145 // calculate the new root approximation 146 final double x3 = 0.5 * (x1 + x2); 147 final double y3 = f.value(x3); 148 if (Math.abs(y3) <= functionValueAccuracy) { 149 setResult(x3, i); 150 return result; 151 } 152 final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing 153 final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) * 154 (x3 - x1) / Math.sqrt(delta); 155 final double x = x3 - correction; // correction != 0 156 final double y = f.value(x); 157 158 // check for convergence 159 final double tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy); 160 if (Math.abs(x - oldx) <= tolerance) { 161 setResult(x, i); 162 return result; 163 } 164 if (Math.abs(y) <= functionValueAccuracy) { 165 setResult(x, i); 166 return result; 167 } 168 169 // prepare the new interval for next iteration 170 // Ridders' method guarantees x1 < x < x2 171 if (correction > 0.0) { // x1 < x < x3 172 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) { 173 x2 = x; 174 y2 = y; 175 } else { 176 x1 = x; 177 x2 = x3; 178 y1 = y; 179 y2 = y3; 180 } 181 } else { // x3 < x < x2 182 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) { 183 x1 = x; 184 y1 = y; 185 } else { 186 x1 = x3; 187 x2 = x; 188 y1 = y3; 189 y2 = y; 190 } 191 } 192 oldx = x; 193 i++; 194 } 195 throw new MaxIterationsExceededException(maximalIterationCount); 196 } 197 }