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.FastMath;
024 import org.apache.commons.math.util.MathUtils;
025
026 /**
027 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
028 * Ridders' Method</a> for root finding of real univariate functions. For
029 * reference, see C. Ridders, <i>A new algorithm for computing a single root
030 * of a real continuous function </i>, IEEE Transactions on Circuits and
031 * Systems, 26 (1979), 979 - 980.
032 * <p>
033 * The function should be continuous but not necessarily smooth.</p>
034 *
035 * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 f??vr. 2011) $
036 * @since 1.2
037 */
038 public class RiddersSolver extends UnivariateRealSolverImpl {
039
040 /**
041 * Construct a solver for the given function.
042 *
043 * @param f function to solve
044 * @deprecated as of 2.0 the function to solve is passed as an argument
045 * to the {@link #solve(UnivariateRealFunction, double, double)} or
046 * {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}
047 * method.
048 */
049 @Deprecated
050 public RiddersSolver(UnivariateRealFunction f) {
051 super(f, 100, 1E-6);
052 }
053
054 /**
055 * Construct a solver.
056 * @deprecated in 2.2
057 */
058 @Deprecated
059 public RiddersSolver() {
060 super(100, 1E-6);
061 }
062
063 /** {@inheritDoc} */
064 @Deprecated
065 public double solve(final double min, final double max)
066 throws ConvergenceException, FunctionEvaluationException {
067 return solve(f, min, max);
068 }
069
070 /** {@inheritDoc} */
071 @Deprecated
072 public double solve(final double min, final double max, final double initial)
073 throws ConvergenceException, FunctionEvaluationException {
074 return solve(f, min, max, initial);
075 }
076
077 /**
078 * Find a root in the given interval with initial value.
079 * <p>
080 * Requires bracketing condition.</p>
081 *
082 * @param f the function to solve
083 * @param min the lower bound for the interval
084 * @param max the upper bound for the interval
085 * @param initial the start value to use
086 * @param maxEval Maximum number of evaluations.
087 * @return the point at which the function value is zero
088 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
089 * @throws FunctionEvaluationException if an error occurs evaluating the function
090 * @throws IllegalArgumentException if any parameters are invalid
091 */
092 @Override
093 public double solve(int maxEval, final UnivariateRealFunction f,
094 final double min, final double max, final double initial)
095 throws MaxIterationsExceededException, FunctionEvaluationException {
096 setMaximalIterationCount(maxEval);
097 return solve(f, min, max, initial);
098 }
099
100 /**
101 * Find a root in the given interval with initial value.
102 * <p>
103 * Requires bracketing condition.</p>
104 *
105 * @param f the function to solve
106 * @param min the lower bound for the interval
107 * @param max the upper bound for the interval
108 * @param initial the start value to use
109 * @return the point at which the function value is zero
110 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
111 * @throws FunctionEvaluationException if an error occurs evaluating the function
112 * @throws IllegalArgumentException if any parameters are invalid
113 * @deprecated in 2.2 (to be removed in 3.0).
114 */
115 @Deprecated
116 public double solve(final UnivariateRealFunction f,
117 final double min, final double max, final double initial)
118 throws MaxIterationsExceededException, FunctionEvaluationException {
119
120 // check for zeros before verifying bracketing
121 if (f.value(min) == 0.0) { return min; }
122 if (f.value(max) == 0.0) { return max; }
123 if (f.value(initial) == 0.0) { return initial; }
124
125 verifyBracketing(min, max, f);
126 verifySequence(min, initial, max);
127 if (isBracketing(min, initial, f)) {
128 return solve(f, min, initial);
129 } else {
130 return solve(f, initial, max);
131 }
132 }
133
134 /**
135 * Find a root in the given interval.
136 * <p>
137 * Requires bracketing condition.</p>
138 *
139 * @param f the function to solve
140 * @param min the lower bound for the interval
141 * @param max the upper bound for the interval
142 * @param maxEval Maximum number of evaluations.
143 * @return the point at which the function value is zero
144 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
145 * @throws FunctionEvaluationException if an error occurs evaluating the function
146 * @throws IllegalArgumentException if any parameters are invalid
147 */
148 @Override
149 public double solve(int maxEval, final UnivariateRealFunction f,
150 final double min, final double max)
151 throws MaxIterationsExceededException, FunctionEvaluationException {
152 setMaximalIterationCount(maxEval);
153 return solve(f, min, max);
154 }
155
156 /**
157 * Find a root in the given interval.
158 * <p>
159 * Requires bracketing condition.</p>
160 *
161 * @param f the function to solve
162 * @param min the lower bound for the interval
163 * @param max the upper bound for the interval
164 * @return the point at which the function value is zero
165 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
166 * @throws FunctionEvaluationException if an error occurs evaluating the function
167 * @throws IllegalArgumentException if any parameters are invalid
168 * @deprecated in 2.2 (to be removed in 3.0).
169 */
170 @Deprecated
171 public double solve(final UnivariateRealFunction f,
172 final double min, final double max)
173 throws MaxIterationsExceededException, FunctionEvaluationException {
174
175 // [x1, x2] is the bracketing interval in each iteration
176 // x3 is the midpoint of [x1, x2]
177 // x is the new root approximation and an endpoint of the new interval
178 double x1 = min;
179 double y1 = f.value(x1);
180 double x2 = max;
181 double y2 = f.value(x2);
182
183 // check for zeros before verifying bracketing
184 if (y1 == 0.0) {
185 return min;
186 }
187 if (y2 == 0.0) {
188 return max;
189 }
190 verifyBracketing(min, max, f);
191
192 int i = 1;
193 double oldx = Double.POSITIVE_INFINITY;
194 while (i <= maximalIterationCount) {
195 // calculate the new root approximation
196 final double x3 = 0.5 * (x1 + x2);
197 final double y3 = f.value(x3);
198 if (FastMath.abs(y3) <= functionValueAccuracy) {
199 setResult(x3, i);
200 return result;
201 }
202 final double delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing
203 final double correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *
204 (x3 - x1) / FastMath.sqrt(delta);
205 final double x = x3 - correction; // correction != 0
206 final double y = f.value(x);
207
208 // check for convergence
209 final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy);
210 if (FastMath.abs(x - oldx) <= tolerance) {
211 setResult(x, i);
212 return result;
213 }
214 if (FastMath.abs(y) <= functionValueAccuracy) {
215 setResult(x, i);
216 return result;
217 }
218
219 // prepare the new interval for next iteration
220 // Ridders' method guarantees x1 < x < x2
221 if (correction > 0.0) { // x1 < x < x3
222 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {
223 x2 = x;
224 y2 = y;
225 } else {
226 x1 = x;
227 x2 = x3;
228 y1 = y;
229 y2 = y3;
230 }
231 } else { // x3 < x < x2
232 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {
233 x1 = x;
234 y1 = y;
235 } else {
236 x1 = x3;
237 x2 = x;
238 y1 = y3;
239 y2 = y;
240 }
241 }
242 oldx = x;
243 i++;
244 }
245 throw new MaxIterationsExceededException(maximalIterationCount);
246 }
247 }