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; 18 19 import org.apache.commons.math.FunctionEvaluationException; 20 import org.apache.commons.math.MaxIterationsExceededException; 21 import org.apache.commons.math.util.MathUtils; 22 23 /** 24 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html"> 25 * Ridders' Method</a> for root finding of real univariate functions. For 26 * reference, see C. Ridders, <i>A new algorithm for computing a single root 27 * of a real continuous function </i>, IEEE Transactions on Circuits and 28 * Systems, 26 (1979), 979 - 980. 29 * <p> 30 * The function should be continuous but not necessarily smooth.</p> 31 * 32 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ 33 * @since 1.2 34 */ 35 public class RiddersSolver extends UnivariateRealSolverImpl { 36 37 /** serializable version identifier */ 38 private static final long serialVersionUID = -4703139035737911735L; 39 40 /** 41 * Construct a solver for the given function. 42 * 43 * @param f function to solve 44 */ 45 public RiddersSolver(UnivariateRealFunction f) { 46 super(f, 100, 1E-6); 47 } 48 49 /** 50 * Find a root in the given interval with initial value. 51 * <p> 52 * Requires bracketing condition.</p> 53 * 54 * @param min the lower bound for the interval 55 * @param max the upper bound for the interval 56 * @param initial the start value to use 57 * @return the point at which the function value is zero 58 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 59 * @throws FunctionEvaluationException if an error occurs evaluating the 60 * function 61 * @throws IllegalArgumentException if any parameters are invalid 62 */ 63 public double solve(double min, double max, double initial) throws 64 MaxIterationsExceededException, FunctionEvaluationException { 65 66 // check for zeros before verifying bracketing 67 if (f.value(min) == 0.0) { return min; } 68 if (f.value(max) == 0.0) { return max; } 69 if (f.value(initial) == 0.0) { return initial; } 70 71 verifyBracketing(min, max, f); 72 verifySequence(min, initial, max); 73 if (isBracketing(min, initial, f)) { 74 return solve(min, initial); 75 } else { 76 return solve(initial, max); 77 } 78 } 79 80 /** 81 * Find a root in the given interval. 82 * <p> 83 * Requires bracketing condition.</p> 84 * 85 * @param min the lower bound for the interval 86 * @param max the upper bound for the interval 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 90 * function 91 * @throws IllegalArgumentException if any parameters are invalid 92 */ 93 public double solve(double min, double max) throws MaxIterationsExceededException, 94 FunctionEvaluationException { 95 96 // [x1, x2] is the bracketing interval in each iteration 97 // x3 is the midpoint of [x1, x2] 98 // x is the new root approximation and an endpoint of the new interval 99 double x1, x2, x3, x, oldx, y1, y2, y3, y, delta, correction, tolerance; 100 101 x1 = min; y1 = f.value(x1); 102 x2 = max; y2 = f.value(x2); 103 104 // check for zeros before verifying bracketing 105 if (y1 == 0.0) { return min; } 106 if (y2 == 0.0) { return max; } 107 verifyBracketing(min, max, f); 108 109 int i = 1; 110 oldx = Double.POSITIVE_INFINITY; 111 while (i <= maximalIterationCount) { 112 // calculate the new root approximation 113 x3 = 0.5 * (x1 + x2); 114 y3 = f.value(x3); 115 if (Math.abs(y3) <= functionValueAccuracy) { 116 setResult(x3, i); 117 return result; 118 } 119 delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing 120 correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) * 121 (x3 - x1) / Math.sqrt(delta); 122 x = x3 - correction; // correction != 0 123 y = f.value(x); 124 125 // check for convergence 126 tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy); 127 if (Math.abs(x - oldx) <= tolerance) { 128 setResult(x, i); 129 return result; 130 } 131 if (Math.abs(y) <= functionValueAccuracy) { 132 setResult(x, i); 133 return result; 134 } 135 136 // prepare the new interval for next iteration 137 // Ridders' method guarantees x1 < x < x2 138 if (correction > 0.0) { // x1 < x < x3 139 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) { 140 x2 = x; y2 = y; 141 } else { 142 x1 = x; x2 = x3; 143 y1 = y; y2 = y3; 144 } 145 } else { // x3 < x < x2 146 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) { 147 x1 = x; y1 = y; 148 } else { 149 x1 = x3; x2 = x; 150 y1 = y3; y2 = y; 151 } 152 } 153 oldx = x; 154 i++; 155 } 156 throw new MaxIterationsExceededException(maximalIterationCount); 157 } 158 }