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.math3.analysis.solvers; 018 019 import org.apache.commons.math3.util.FastMath; 020 import org.apache.commons.math3.exception.NoBracketingException; 021 import org.apache.commons.math3.exception.TooManyEvaluationsException; 022 023 /** 024 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html"> 025 * Ridders' Method</a> for root finding of real univariate functions. For 026 * reference, see C. Ridders, <i>A new algorithm for computing a single root 027 * of a real continuous function </i>, IEEE Transactions on Circuits and 028 * Systems, 26 (1979), 979 - 980. 029 * <p> 030 * The function should be continuous but not necessarily smooth.</p> 031 * 032 * @version $Id: RiddersSolver.java 1379560 2012-08-31 19:40:30Z erans $ 033 * @since 1.2 034 */ 035 public class RiddersSolver extends AbstractUnivariateSolver { 036 /** Default absolute accuracy. */ 037 private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6; 038 039 /** 040 * Construct a solver with default accuracy (1e-6). 041 */ 042 public RiddersSolver() { 043 this(DEFAULT_ABSOLUTE_ACCURACY); 044 } 045 /** 046 * Construct a solver. 047 * 048 * @param absoluteAccuracy Absolute accuracy. 049 */ 050 public RiddersSolver(double absoluteAccuracy) { 051 super(absoluteAccuracy); 052 } 053 /** 054 * Construct a solver. 055 * 056 * @param relativeAccuracy Relative accuracy. 057 * @param absoluteAccuracy Absolute accuracy. 058 */ 059 public RiddersSolver(double relativeAccuracy, 060 double absoluteAccuracy) { 061 super(relativeAccuracy, absoluteAccuracy); 062 } 063 064 /** 065 * {@inheritDoc} 066 */ 067 @Override 068 protected double doSolve() 069 throws TooManyEvaluationsException, 070 NoBracketingException { 071 double min = getMin(); 072 double max = getMax(); 073 // [x1, x2] is the bracketing interval in each iteration 074 // x3 is the midpoint of [x1, x2] 075 // x is the new root approximation and an endpoint of the new interval 076 double x1 = min; 077 double y1 = computeObjectiveValue(x1); 078 double x2 = max; 079 double y2 = computeObjectiveValue(x2); 080 081 // check for zeros before verifying bracketing 082 if (y1 == 0) { 083 return min; 084 } 085 if (y2 == 0) { 086 return max; 087 } 088 verifyBracketing(min, max); 089 090 final double absoluteAccuracy = getAbsoluteAccuracy(); 091 final double functionValueAccuracy = getFunctionValueAccuracy(); 092 final double relativeAccuracy = getRelativeAccuracy(); 093 094 double oldx = Double.POSITIVE_INFINITY; 095 while (true) { 096 // calculate the new root approximation 097 final double x3 = 0.5 * (x1 + x2); 098 final double y3 = computeObjectiveValue(x3); 099 if (FastMath.abs(y3) <= functionValueAccuracy) { 100 return x3; 101 } 102 final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing 103 final double correction = (FastMath.signum(y2) * FastMath.signum(y3)) * 104 (x3 - x1) / FastMath.sqrt(delta); 105 final double x = x3 - correction; // correction != 0 106 final double y = computeObjectiveValue(x); 107 108 // check for convergence 109 final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy); 110 if (FastMath.abs(x - oldx) <= tolerance) { 111 return x; 112 } 113 if (FastMath.abs(y) <= functionValueAccuracy) { 114 return x; 115 } 116 117 // prepare the new interval for next iteration 118 // Ridders' method guarantees x1 < x < x2 119 if (correction > 0.0) { // x1 < x < x3 120 if (FastMath.signum(y1) + FastMath.signum(y) == 0.0) { 121 x2 = x; 122 y2 = y; 123 } else { 124 x1 = x; 125 x2 = x3; 126 y1 = y; 127 y2 = y3; 128 } 129 } else { // x3 < x < x2 130 if (FastMath.signum(y2) + FastMath.signum(y) == 0.0) { 131 x1 = x; 132 y1 = y; 133 } else { 134 x1 = x3; 135 x2 = x; 136 y1 = y3; 137 y2 = y; 138 } 139 } 140 oldx = x; 141 } 142 } 143 }