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.MaxIterationsExceededException; 023 import org.apache.commons.math.analysis.UnivariateRealFunction; 024 025 026 /** 027 * Implements a modified version of the 028 * <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a> 029 * for approximating a zero of a real univariate function. 030 * <p> 031 * The algorithm is modified to maintain bracketing of a root by successive 032 * approximations. Because of forced bracketing, convergence may be slower than 033 * the unrestricted secant algorithm. However, this implementation should in 034 * general outperform the 035 * <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html"> 036 * regula falsi method.</a></p> 037 * <p> 038 * The function is assumed to be continuous but not necessarily smooth.</p> 039 * 040 * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $ 041 */ 042 public class SecantSolver extends UnivariateRealSolverImpl { 043 044 /** 045 * Construct a solver for the given function. 046 * @param f function to solve. 047 * @deprecated as of 2.0 the function to solve is passed as an argument 048 * to the {@link #solve(UnivariateRealFunction, double, double)} or 049 * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)} 050 * method. 051 */ 052 @Deprecated 053 public SecantSolver(UnivariateRealFunction f) { 054 super(f, 100, 1E-6); 055 } 056 057 /** 058 * Construct a solver. 059 */ 060 public SecantSolver() { 061 super(100, 1E-6); 062 } 063 064 /** {@inheritDoc} */ 065 @Deprecated 066 public double solve(final double min, final double max) 067 throws ConvergenceException, FunctionEvaluationException { 068 return solve(f, min, max); 069 } 070 071 /** {@inheritDoc} */ 072 @Deprecated 073 public double solve(final double min, final double max, final double initial) 074 throws ConvergenceException, FunctionEvaluationException { 075 return solve(f, min, max, initial); 076 } 077 078 /** 079 * Find a zero in the given interval. 080 * 081 * @param f the function to solve 082 * @param min the lower bound for the interval 083 * @param max the upper bound for the interval 084 * @param initial the start value to use (ignored) 085 * @return the value where the function is zero 086 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 087 * @throws FunctionEvaluationException if an error occurs evaluating the 088 * function 089 * @throws IllegalArgumentException if min is not less than max or the 090 * signs of the values of the function at the endpoints are not opposites 091 */ 092 public double solve(final UnivariateRealFunction f, 093 final double min, final double max, final double initial) 094 throws MaxIterationsExceededException, FunctionEvaluationException { 095 return solve(f, min, max); 096 } 097 098 /** 099 * Find a zero in the given interval. 100 * @param f the function to solve 101 * @param min the lower bound for the interval. 102 * @param max the upper bound for the interval. 103 * @return the value where the function is zero 104 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded 105 * @throws FunctionEvaluationException if an error occurs evaluating the 106 * function 107 * @throws IllegalArgumentException if min is not less than max or the 108 * signs of the values of the function at the endpoints are not opposites 109 */ 110 public double solve(final UnivariateRealFunction f, 111 final double min, final double max) 112 throws MaxIterationsExceededException, FunctionEvaluationException { 113 114 clearResult(); 115 verifyInterval(min, max); 116 117 // Index 0 is the old approximation for the root. 118 // Index 1 is the last calculated approximation for the root. 119 // Index 2 is a bracket for the root with respect to x0. 120 // OldDelta is the length of the bracketing interval of the last 121 // iteration. 122 double x0 = min; 123 double x1 = max; 124 double y0 = f.value(x0); 125 double y1 = f.value(x1); 126 127 // Verify bracketing 128 if (y0 * y1 >= 0) { 129 throw MathRuntimeException.createIllegalArgumentException( 130 "function values at endpoints do not have different signs, " + 131 "endpoints: [{0}, {1}], values: [{2}, {3}]", 132 min, max, y0, y1); 133 } 134 135 double x2 = x0; 136 double y2 = y0; 137 double oldDelta = x2 - x1; 138 int i = 0; 139 while (i < maximalIterationCount) { 140 if (Math.abs(y2) < Math.abs(y1)) { 141 x0 = x1; 142 x1 = x2; 143 x2 = x0; 144 y0 = y1; 145 y1 = y2; 146 y2 = y0; 147 } 148 if (Math.abs(y1) <= functionValueAccuracy) { 149 setResult(x1, i); 150 return result; 151 } 152 if (Math.abs(oldDelta) < 153 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy)) { 154 setResult(x1, i); 155 return result; 156 } 157 double delta; 158 if (Math.abs(y1) > Math.abs(y0)) { 159 // Function value increased in last iteration. Force bisection. 160 delta = 0.5 * oldDelta; 161 } else { 162 delta = (x0 - x1) / (1 - y0 / y1); 163 if (delta / oldDelta > 1) { 164 // New approximation falls outside bracket. 165 // Fall back to bisection. 166 delta = 0.5 * oldDelta; 167 } 168 } 169 x0 = x1; 170 y0 = y1; 171 x1 = x1 + delta; 172 y1 = f.value(x1); 173 if ((y1 > 0) == (y2 > 0)) { 174 // New bracket is (x0,x1). 175 x2 = x0; 176 y2 = y0; 177 } 178 oldDelta = x2 - x1; 179 i++; 180 } 181 throw new MaxIterationsExceededException(maximalIterationCount); 182 } 183 184 }