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.MaxIterationsExceededException;
022 import org.apache.commons.math.analysis.UnivariateRealFunction;
023 import org.apache.commons.math.util.MathUtils;
024
025 /**
026 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
027 * Ridders' Method</a> for root finding of real univariate functions. For
028 * reference, see C. Ridders, <i>A new algorithm for computing a single root
029 * of a real continuous function </i>, IEEE Transactions on Circuits and
030 * Systems, 26 (1979), 979 - 980.
031 * <p>
032 * The function should be continuous but not necessarily smooth.</p>
033 *
034 * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $
035 * @since 1.2
036 */
037 public class RiddersSolver extends UnivariateRealSolverImpl {
038
039 /**
040 * Construct a solver for the given function.
041 *
042 * @param f function to solve
043 * @deprecated as of 2.0 the function to solve is passed as an argument
044 * to the {@link #solve(UnivariateRealFunction, double, double)} or
045 * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}
046 * method.
047 */
048 @Deprecated
049 public RiddersSolver(UnivariateRealFunction f) {
050 super(f, 100, 1E-6);
051 }
052
053 /**
054 * Construct a solver.
055 */
056 public RiddersSolver() {
057 super(100, 1E-6);
058 }
059
060 /** {@inheritDoc} */
061 @Deprecated
062 public double solve(final double min, final double max)
063 throws ConvergenceException, FunctionEvaluationException {
064 return solve(f, min, max);
065 }
066
067 /** {@inheritDoc} */
068 @Deprecated
069 public double solve(final double min, final double max, final double initial)
070 throws ConvergenceException, FunctionEvaluationException {
071 return solve(f, min, max, initial);
072 }
073
074 /**
075 * Find a root in the given interval with initial value.
076 * <p>
077 * Requires bracketing condition.</p>
078 *
079 * @param f the function to solve
080 * @param min the lower bound for the interval
081 * @param max the upper bound for the interval
082 * @param initial the start value to use
083 * @return the point at which the function value is zero
084 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
085 * @throws FunctionEvaluationException if an error occurs evaluating the
086 * function
087 * @throws IllegalArgumentException if any parameters are invalid
088 */
089 public double solve(final UnivariateRealFunction f,
090 final double min, final double max, final double initial)
091 throws MaxIterationsExceededException, FunctionEvaluationException {
092
093 // check for zeros before verifying bracketing
094 if (f.value(min) == 0.0) { return min; }
095 if (f.value(max) == 0.0) { return max; }
096 if (f.value(initial) == 0.0) { return initial; }
097
098 verifyBracketing(min, max, f);
099 verifySequence(min, initial, max);
100 if (isBracketing(min, initial, f)) {
101 return solve(f, min, initial);
102 } else {
103 return solve(f, initial, max);
104 }
105 }
106
107 /**
108 * Find a root in the given interval.
109 * <p>
110 * Requires bracketing condition.</p>
111 *
112 * @param f the function to solve
113 * @param min the lower bound for the interval
114 * @param max the upper bound for the interval
115 * @return the point at which the function value is zero
116 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
117 * @throws FunctionEvaluationException if an error occurs evaluating the
118 * function
119 * @throws IllegalArgumentException if any parameters are invalid
120 */
121 public double solve(final UnivariateRealFunction f,
122 final double min, final double max)
123 throws MaxIterationsExceededException, FunctionEvaluationException {
124
125 // [x1, x2] is the bracketing interval in each iteration
126 // x3 is the midpoint of [x1, x2]
127 // x is the new root approximation and an endpoint of the new interval
128 double x1 = min;
129 double y1 = f.value(x1);
130 double x2 = max;
131 double y2 = f.value(x2);
132
133 // check for zeros before verifying bracketing
134 if (y1 == 0.0) {
135 return min;
136 }
137 if (y2 == 0.0) {
138 return max;
139 }
140 verifyBracketing(min, max, f);
141
142 int i = 1;
143 double oldx = Double.POSITIVE_INFINITY;
144 while (i <= maximalIterationCount) {
145 // calculate the new root approximation
146 final double x3 = 0.5 * (x1 + x2);
147 final double y3 = f.value(x3);
148 if (Math.abs(y3) <= functionValueAccuracy) {
149 setResult(x3, i);
150 return result;
151 }
152 final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing
153 final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *
154 (x3 - x1) / Math.sqrt(delta);
155 final double x = x3 - correction; // correction != 0
156 final double y = f.value(x);
157
158 // check for convergence
159 final double tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy);
160 if (Math.abs(x - oldx) <= tolerance) {
161 setResult(x, i);
162 return result;
163 }
164 if (Math.abs(y) <= functionValueAccuracy) {
165 setResult(x, i);
166 return result;
167 }
168
169 // prepare the new interval for next iteration
170 // Ridders' method guarantees x1 < x < x2
171 if (correction > 0.0) { // x1 < x < x3
172 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {
173 x2 = x;
174 y2 = y;
175 } else {
176 x1 = x;
177 x2 = x3;
178 y1 = y;
179 y2 = y3;
180 }
181 } else { // x3 < x < x2
182 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {
183 x1 = x;
184 y1 = y;
185 } else {
186 x1 = x3;
187 x2 = x;
188 y1 = y3;
189 y2 = y;
190 }
191 }
192 oldx = x;
193 i++;
194 }
195 throw new MaxIterationsExceededException(maximalIterationCount);
196 }
197 }