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.ConvergenceException;
21
22 /**
23 * Utility routines for {@link UnivariateRealSolver} objects.
24 *
25 * @version $Revision: 615734 $ $Date: 2008-01-27 23:10:03 -0700 (Sun, 27 Jan 2008) $
26 */
27 public class UnivariateRealSolverUtils {
28 /**
29 * Default constructor.
30 */
31 private UnivariateRealSolverUtils() {
32 super();
33 }
34
35 /** Cached solver factory */
36 private static UnivariateRealSolverFactory factory = null;
37
38 /**
39 * Convenience method to find a zero of a univariate real function. A default
40 * solver is used.
41 *
42 * @param f the function.
43 * @param x0 the lower bound for the interval.
44 * @param x1 the upper bound for the interval.
45 * @return a value where the function is zero.
46 * @throws ConvergenceException if the iteration count was exceeded
47 * @throws FunctionEvaluationException if an error occurs evaluating
48 * the function
49 * @throws IllegalArgumentException if f is null or the endpoints do not
50 * specify a valid interval
51 */
52 public static double solve(UnivariateRealFunction f, double x0, double x1)
53 throws ConvergenceException, FunctionEvaluationException {
54 setup(f);
55 return factory.newDefaultSolver(f).solve(x0, x1);
56 }
57
58 /**
59 * Convenience method to find a zero of a univariate real function. A default
60 * solver is used.
61 *
62 * @param f the function
63 * @param x0 the lower bound for the interval
64 * @param x1 the upper bound for the interval
65 * @param absoluteAccuracy the accuracy to be used by the solver
66 * @return a value where the function is zero
67 * @throws ConvergenceException if the iteration count is exceeded
68 * @throws FunctionEvaluationException if an error occurs evaluating the
69 * function
70 * @throws IllegalArgumentException if f is null, the endpoints do not
71 * specify a valid interval, or the absoluteAccuracy is not valid for the
72 * default solver
73 */
74 public static double solve(UnivariateRealFunction f, double x0, double x1,
75 double absoluteAccuracy) throws ConvergenceException,
76 FunctionEvaluationException {
77
78 setup(f);
79 UnivariateRealSolver solver = factory.newDefaultSolver(f);
80 solver.setAbsoluteAccuracy(absoluteAccuracy);
81 return solver.solve(x0, x1);
82 }
83
84 /**
85 * This method attempts to find two values a and b satisfying <ul>
86 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
87 * <li> <code> f(a) * f(b) < 0 </code></li>
88 * </ul>
89 * If f is continuous on <code>[a,b],</code> this means that <code>a</code>
90 * and <code>b</code> bracket a root of f.
91 * <p>
92 * The algorithm starts by setting
93 * <code>a := initial -1; b := initial +1,</code> examines the value of the
94 * function at <code>a</code> and <code>b</code> and keeps moving
95 * the endpoints out by one unit each time through a loop that terminates
96 * when one of the following happens: <ul>
97 * <li> <code> f(a) * f(b) < 0 </code> -- success!</li>
98 * <li> <code> a = lower </code> and <code> b = upper</code>
99 * -- ConvergenceException </li>
100 * <li> <code> Integer.MAX_VALUE</code> iterations elapse
101 * -- ConvergenceException </li>
102 * </ul></p>
103 * <p>
104 * <strong>Note: </strong> this method can take
105 * <code>Integer.MAX_VALUE</code> iterations to throw a
106 * <code>ConvergenceException.</code> Unless you are confident that there
107 * is a root between <code>lowerBound</code> and <code>upperBound</code>
108 * near <code>initial,</code> it is better to use
109 * {@link #bracket(UnivariateRealFunction, double, double, double, int)},
110 * explicitly specifying the maximum number of iterations.</p>
111 *
112 * @param function the function
113 * @param initial initial midpoint of interval being expanded to
114 * bracket a root
115 * @param lowerBound lower bound (a is never lower than this value)
116 * @param upperBound upper bound (b never is greater than this
117 * value)
118 * @return a two element array holding {a, b}
119 * @throws ConvergenceException if a root can not be bracketted
120 * @throws FunctionEvaluationException if an error occurs evaluating the
121 * function
122 * @throws IllegalArgumentException if function is null, maximumIterations
123 * is not positive, or initial is not between lowerBound and upperBound
124 */
125 public static double[] bracket(UnivariateRealFunction function,
126 double initial, double lowerBound, double upperBound)
127 throws ConvergenceException, FunctionEvaluationException {
128 return bracket( function, initial, lowerBound, upperBound,
129 Integer.MAX_VALUE ) ;
130 }
131
132 /**
133 * This method attempts to find two values a and b satisfying <ul>
134 * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li>
135 * <li> <code> f(a) * f(b) < 0 </code> </li>
136 * </ul>
137 * If f is continuous on <code>[a,b],</code> this means that <code>a</code>
138 * and <code>b</code> bracket a root of f.
139 * <p>
140 * The algorithm starts by setting
141 * <code>a := initial -1; b := initial +1,</code> examines the value of the
142 * function at <code>a</code> and <code>b</code> and keeps moving
143 * the endpoints out by one unit each time through a loop that terminates
144 * when one of the following happens: <ul>
145 * <li> <code> f(a) * f(b) < 0 </code> -- success!</li>
146 * <li> <code> a = lower </code> and <code> b = upper</code>
147 * -- ConvergenceException </li>
148 * <li> <code> maximumIterations</code> iterations elapse
149 * -- ConvergenceException </li></ul></p>
150 *
151 * @param function the function
152 * @param initial initial midpoint of interval being expanded to
153 * bracket a root
154 * @param lowerBound lower bound (a is never lower than this value)
155 * @param upperBound upper bound (b never is greater than this
156 * value)
157 * @param maximumIterations maximum number of iterations to perform
158 * @return a two element array holding {a, b}.
159 * @throws ConvergenceException if the algorithm fails to find a and b
160 * satisfying the desired conditions
161 * @throws FunctionEvaluationException if an error occurs evaluating the
162 * function
163 * @throws IllegalArgumentException if function is null, maximumIterations
164 * is not positive, or initial is not between lowerBound and upperBound
165 */
166 public static double[] bracket(UnivariateRealFunction function,
167 double initial, double lowerBound, double upperBound,
168 int maximumIterations) throws ConvergenceException,
169 FunctionEvaluationException {
170
171 if (function == null) {
172 throw new IllegalArgumentException ("function is null.");
173 }
174 if (maximumIterations <= 0) {
175 throw new IllegalArgumentException
176 ("bad value for maximumIterations: " + maximumIterations);
177 }
178 if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) {
179 throw new IllegalArgumentException
180 ("Invalid endpoint parameters: lowerBound=" + lowerBound +
181 " initial=" + initial + " upperBound=" + upperBound);
182 }
183 double a = initial;
184 double b = initial;
185 double fa;
186 double fb;
187 int numIterations = 0 ;
188
189 do {
190 a = Math.max(a - 1.0, lowerBound);
191 b = Math.min(b + 1.0, upperBound);
192 fa = function.value(a);
193
194 fb = function.value(b);
195 numIterations++ ;
196 } while ((fa * fb > 0.0) && (numIterations < maximumIterations) &&
197 ((a > lowerBound) || (b < upperBound)));
198
199 if (fa * fb >= 0.0 ) {
200 throw new ConvergenceException
201 ("Number of iterations={0}, maximum iterations={1}, initial={2}, lower bound={3}, upper bound={4}, final a value={5}, final b value={6}, f(a)={7}, f(b)={8}",
202 new Object[] { new Integer(numIterations), new Integer(maximumIterations),
203 new Double(initial), new Double(lowerBound), new Double(upperBound),
204 new Double(a), new Double(b), new Double(fa), new Double(fb) });
205 }
206
207 return new double[]{a, b};
208 }
209
210 /**
211 * Compute the midpoint of two values.
212 *
213 * @param a first value.
214 * @param b second value.
215 * @return the midpoint.
216 */
217 public static double midpoint(double a, double b) {
218 return (a + b) * .5;
219 }
220
221 /**
222 * Checks to see if f is null, throwing IllegalArgumentException if so.
223 * Also initializes factory if factory is null.
224 *
225 * @param f input function
226 * @throws IllegalArgumentException if f is null
227 */
228 private static void setup(UnivariateRealFunction f) {
229
230 if (f == null) {
231 throw new IllegalArgumentException("function can not be null.");
232 }
233
234 if (factory == null) {
235 factory = UnivariateRealSolverFactory.newInstance();
236 }
237 }
238 }