1 /* 2 * Licensed to the Apache Software Foundation (ASF) under one or more 3 * contributor license agreements. See the NOTICE file distributed with 4 * this work for additional information regarding copyright ownership. 5 * The ASF licenses this file to You under the Apache License, Version 2.0 6 * (the "License"); you may not use this file except in compliance with 7 * the License. You may obtain a copy of the License at 8 * 9 * http://www.apache.org/licenses/LICENSE-2.0 10 * 11 * Unless required by applicable law or agreed to in writing, software 12 * distributed under the License is distributed on an "AS IS" BASIS, 13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 14 * See the License for the specific language governing permissions and 15 * limitations under the License. 16 */ 17 package org.apache.commons.math.analysis.solvers; 18 19 import org.apache.commons.math.ConvergenceException; 20 import org.apache.commons.math.FunctionEvaluationException; 21 import org.apache.commons.math.MaxIterationsExceededException; 22 import org.apache.commons.math.analysis.UnivariateRealFunction; 23 import org.apache.commons.math.util.FastMath; 24 import org.apache.commons.math.util.MathUtils; 25 26 /** 27 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html"> 28 * Ridders' Method</a> for root finding of real univariate functions. For 29 * reference, see C. Ridders, <i>A new algorithm for computing a single root 30 * of a real continuous function </i>, IEEE Transactions on Circuits and 31 * Systems, 26 (1979), 979 - 980. 32 * <p> 33 * The function should be continuous but not necessarily smooth.</p> 34 * 35 * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 fvr. 2011) $ 36 * @since 1.2 37 */ 38 public class RiddersSolver extends UnivariateRealSolverImpl { 39 40 /** 41 * Construct a solver for the given function. 42 * 43 * @param f function to solve 44 * @deprecated as of 2.0 the function to solve is passed as an argument 45 * to the {@link #solve(UnivariateRealFunction, double, double)} or 46 * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)} 47 * method. 48 */ 49 @Deprecated 50 public RiddersSolver(UnivariateRealFunction f) { 51 super(f, 100, 1E-6); 52 } 53 54 /** 55 * Construct a solver. 56 * @deprecated in 2.2 57 */ 58 @Deprecated 59 public RiddersSolver() { 60 super(100, 1E-6); 61 } 62 63 /** {@inheritDoc} */ 64 @Deprecated 65 public double solve(final double min, final double max) 66 throws ConvergenceException, FunctionEvaluationException { 67 return solve(f, min, max); 68 } 69 70 /** {@inheritDoc} */ 71 @Deprecated 72 public double solve(final double min, final double max, final double initial) 73 throws ConvergenceException, FunctionEvaluationException { 74 return solve(f, min, max, initial); 75 } 76 77 /** 78 * Find a root in the given interval with initial value. 79 * <p> 80 * Requires bracketing condition.</p> 81 * 82 * @param f the function to solve 83 * @param min the lower bound for the interval 84 * @param max the upper bound for the interval 85 * @param initial the start value to use 86 * @param maxEval Maximum number of evaluations. 87 * @return the point at which the function value is zero 88 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 89 * @throws FunctionEvaluationException if an error occurs evaluating the function 90 * @throws IllegalArgumentException if any parameters are invalid 91 */ 92 @Override 93 public double solve(int maxEval, final UnivariateRealFunction f, 94 final double min, final double max, final double initial) 95 throws MaxIterationsExceededException, FunctionEvaluationException { 96 setMaximalIterationCount(maxEval); 97 return solve(f, min, max, initial); 98 } 99 100 /** 101 * Find a root in the given interval with initial value. 102 * <p> 103 * Requires bracketing condition.</p> 104 * 105 * @param f the function to solve 106 * @param min the lower bound for the interval 107 * @param max the upper bound for the interval 108 * @param initial the start value to use 109 * @return the point at which the function value is zero 110 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 111 * @throws FunctionEvaluationException if an error occurs evaluating the function 112 * @throws IllegalArgumentException if any parameters are invalid 113 * @deprecated in 2.2 (to be removed in 3.0). 114 */ 115 @Deprecated 116 public double solve(final UnivariateRealFunction f, 117 final double min, final double max, final double initial) 118 throws MaxIterationsExceededException, FunctionEvaluationException { 119 120 // check for zeros before verifying bracketing 121 if (f.value(min) == 0.0) { return min; } 122 if (f.value(max) == 0.0) { return max; } 123 if (f.value(initial) == 0.0) { return initial; } 124 125 verifyBracketing(min, max, f); 126 verifySequence(min, initial, max); 127 if (isBracketing(min, initial, f)) { 128 return solve(f, min, initial); 129 } else { 130 return solve(f, initial, max); 131 } 132 } 133 134 /** 135 * Find a root in the given interval. 136 * <p> 137 * Requires bracketing condition.</p> 138 * 139 * @param f the function to solve 140 * @param min the lower bound for the interval 141 * @param max the upper bound for the interval 142 * @param maxEval Maximum number of evaluations. 143 * @return the point at which the function value is zero 144 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 145 * @throws FunctionEvaluationException if an error occurs evaluating the function 146 * @throws IllegalArgumentException if any parameters are invalid 147 */ 148 @Override 149 public double solve(int maxEval, final UnivariateRealFunction f, 150 final double min, final double max) 151 throws MaxIterationsExceededException, FunctionEvaluationException { 152 setMaximalIterationCount(maxEval); 153 return solve(f, min, max); 154 } 155 156 /** 157 * Find a root in the given interval. 158 * <p> 159 * Requires bracketing condition.</p> 160 * 161 * @param f the function to solve 162 * @param min the lower bound for the interval 163 * @param max the upper bound for the interval 164 * @return the point at which the function value is zero 165 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 166 * @throws FunctionEvaluationException if an error occurs evaluating the function 167 * @throws IllegalArgumentException if any parameters are invalid 168 * @deprecated in 2.2 (to be removed in 3.0). 169 */ 170 @Deprecated 171 public double solve(final UnivariateRealFunction f, 172 final double min, final double max) 173 throws MaxIterationsExceededException, FunctionEvaluationException { 174 175 // [x1, x2] is the bracketing interval in each iteration 176 // x3 is the midpoint of [x1, x2] 177 // x is the new root approximation and an endpoint of the new interval 178 double x1 = min; 179 double y1 = f.value(x1); 180 double x2 = max; 181 double y2 = f.value(x2); 182 183 // check for zeros before verifying bracketing 184 if (y1 == 0.0) { 185 return min; 186 } 187 if (y2 == 0.0) { 188 return max; 189 } 190 verifyBracketing(min, max, f); 191 192 int i = 1; 193 double oldx = Double.POSITIVE_INFINITY; 194 while (i <= maximalIterationCount) { 195 // calculate the new root approximation 196 final double x3 = 0.5 * (x1 + x2); 197 final double y3 = f.value(x3); 198 if (FastMath.abs(y3) <= functionValueAccuracy) { 199 setResult(x3, i); 200 return result; 201 } 202 final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing 203 final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) * 204 (x3 - x1) / FastMath.sqrt(delta); 205 final double x = x3 - correction; // correction != 0 206 final double y = f.value(x); 207 208 // check for convergence 209 final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy); 210 if (FastMath.abs(x - oldx) <= tolerance) { 211 setResult(x, i); 212 return result; 213 } 214 if (FastMath.abs(y) <= functionValueAccuracy) { 215 setResult(x, i); 216 return result; 217 } 218 219 // prepare the new interval for next iteration 220 // Ridders' method guarantees x1 < x < x2 221 if (correction > 0.0) { // x1 < x < x3 222 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) { 223 x2 = x; 224 y2 = y; 225 } else { 226 x1 = x; 227 x2 = x3; 228 y1 = y; 229 y2 = y3; 230 } 231 } else { // x3 < x < x2 232 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) { 233 x1 = x; 234 y1 = y; 235 } else { 236 x1 = x3; 237 x2 = x; 238 y1 = y3; 239 y2 = y; 240 } 241 } 242 oldx = x; 243 i++; 244 } 245 throw new MaxIterationsExceededException(maximalIterationCount); 246 } 247 } 248
