1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.math.analysis;
18
19 import org.apache.commons.math.FunctionEvaluationException;
20 import org.apache.commons.math.MaxIterationsExceededException;
21 import org.apache.commons.math.util.MathUtils;
22
23 /**
24 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
25 * Ridders' Method</a> for root finding of real univariate functions. For
26 * reference, see C. Ridders, <i>A new algorithm for computing a single root
27 * of a real continuous function </i>, IEEE Transactions on Circuits and
28 * Systems, 26 (1979), 979 - 980.
29 * <p>
30 * The function should be continuous but not necessarily smooth.</p>
31 *
32 * @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $
33 * @since 1.2
34 */
35 public class RiddersSolver extends UnivariateRealSolverImpl {
36
37 /** serializable version identifier */
38 private static final long serialVersionUID = -4703139035737911735L;
39
40 /**
41 * Construct a solver for the given function.
42 *
43 * @param f function to solve
44 */
45 public RiddersSolver(UnivariateRealFunction f) {
46 super(f, 100, 1E-6);
47 }
48
49 /**
50 * Find a root in the given interval with initial value.
51 * <p>
52 * Requires bracketing condition.</p>
53 *
54 * @param min the lower bound for the interval
55 * @param max the upper bound for the interval
56 * @param initial the start value to use
57 * @return the point at which the function value is zero
58 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
59 * @throws FunctionEvaluationException if an error occurs evaluating the
60 * function
61 * @throws IllegalArgumentException if any parameters are invalid
62 */
63 public double solve(double min, double max, double initial) throws
64 MaxIterationsExceededException, FunctionEvaluationException {
65
66 // check for zeros before verifying bracketing
67 if (f.value(min) == 0.0) { return min; }
68 if (f.value(max) == 0.0) { return max; }
69 if (f.value(initial) == 0.0) { return initial; }
70
71 verifyBracketing(min, max, f);
72 verifySequence(min, initial, max);
73 if (isBracketing(min, initial, f)) {
74 return solve(min, initial);
75 } else {
76 return solve(initial, max);
77 }
78 }
79
80 /**
81 * Find a root in the given interval.
82 * <p>
83 * Requires bracketing condition.</p>
84 *
85 * @param min the lower bound for the interval
86 * @param max the upper bound for the interval
87 * @return the point at which the function value is zero
88 * @throws MaxIterationsExceededException if the maximum iteration count is exceeded
89 * @throws FunctionEvaluationException if an error occurs evaluating the
90 * function
91 * @throws IllegalArgumentException if any parameters are invalid
92 */
93 public double solve(double min, double max) throws MaxIterationsExceededException,
94 FunctionEvaluationException {
95
96 // [x1, x2] is the bracketing interval in each iteration
97 // x3 is the midpoint of [x1, x2]
98 // x is the new root approximation and an endpoint of the new interval
99 double x1, x2, x3, x, oldx, y1, y2, y3, y, delta, correction, tolerance;
100
101 x1 = min; y1 = f.value(x1);
102 x2 = max; y2 = f.value(x2);
103
104 // check for zeros before verifying bracketing
105 if (y1 == 0.0) { return min; }
106 if (y2 == 0.0) { return max; }
107 verifyBracketing(min, max, f);
108
109 int i = 1;
110 oldx = Double.POSITIVE_INFINITY;
111 while (i <= maximalIterationCount) {
112 // calculate the new root approximation
113 x3 = 0.5 * (x1 + x2);
114 y3 = f.value(x3);
115 if (Math.abs(y3) <= functionValueAccuracy) {
116 setResult(x3, i);
117 return result;
118 }
119 delta = 1 - (y1 * y2) / (y3 * y3); // delta > 1 due to bracketing
120 correction = (MathUtils.sign(y2) * MathUtils.sign(y3)) *
121 (x3 - x1) / Math.sqrt(delta);
122 x = x3 - correction; // correction != 0
123 y = f.value(x);
124
125 // check for convergence
126 tolerance = Math.max(relativeAccuracy * Math.abs(x), absoluteAccuracy);
127 if (Math.abs(x - oldx) <= tolerance) {
128 setResult(x, i);
129 return result;
130 }
131 if (Math.abs(y) <= functionValueAccuracy) {
132 setResult(x, i);
133 return result;
134 }
135
136 // prepare the new interval for next iteration
137 // Ridders' method guarantees x1 < x < x2
138 if (correction > 0.0) { // x1 < x < x3
139 if (MathUtils.sign(y1) + MathUtils.sign(y) == 0.0) {
140 x2 = x; y2 = y;
141 } else {
142 x1 = x; x2 = x3;
143 y1 = y; y2 = y3;
144 }
145 } else { // x3 < x < x2
146 if (MathUtils.sign(y2) + MathUtils.sign(y) == 0.0) {
147 x1 = x; y1 = y;
148 } else {
149 x1 = x3; x2 = x;
150 y1 = y3; y2 = y;
151 }
152 }
153 oldx = x;
154 i++;
155 }
156 throw new MaxIterationsExceededException(maximalIterationCount);
157 }
158 }