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: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 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, x2, x3, x, oldx, y1, y2, y3, y, delta, correction, tolerance;
129
130 x1 = min; y1 = f.value(x1);
131 x2 = max; y2 = f.value(x2);
132
133 // check for zeros before verifying bracketing
134 if (y1 == 0.0) { return min; }
135 if (y2 == 0.0) { return max; }
136 verifyBracketing(min, max, f);
137
138 int i = 1;
139 oldx = Double.POSITIVE_INFINITY;
140 while (i <= maximalIterationCount) {
141 // calculate the new root approximation
142 x3 = 0.5 * (x1 + x2);
143 y3 = f.value(x3);
144 if (Math.abs(y3) <= functionValueAccuracy) {
145 setResult(x3, i);
146 return result;
147 }
148 delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing
149 correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *
150 (x3 - x1) / Math.sqrt(delta);
151 x = x3 - correction; // correction != 0
152 y = f.value(x);
153
154 // check for convergence
155 tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy);
156 if (Math.abs(x - oldx) <= tolerance) {
157 setResult(x, i);
158 return result;
159 }
160 if (Math.abs(y) <= functionValueAccuracy) {
161 setResult(x, i);
162 return result;
163 }
164
165 // prepare the new interval for next iteration
166 // Ridders' method guarantees x1 < x < x2
167 if (correction > 0.0) { // x1 < x < x3
168 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {
169 x2 = x; y2 = y;
170 } else {
171 x1 = x; x2 = x3;
172 y1 = y; y2 = y3;
173 }
174 } else { // x3 < x < x2
175 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {
176 x1 = x; y1 = y;
177 } else {
178 x1 = x3; x2 = x;
179 y1 = y3; y2 = y;
180 }
181 }
182 oldx = x;
183 i++;
184 }
185 throw new MaxIterationsExceededException(maximalIterationCount);
186 }
187 }