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 }