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.MathException;
20  import junit.framework.TestCase;
21  
22  /**
23   * Testcase for Muller solver.
24   * <p>
25   * Muller's method converges almost quadratically near roots, but it can
26   * be very slow in regions far away from zeros. Test runs show that for
27   * reasonably good initial values, for a default absolute accuracy of 1E-6,
28   * it generally takes 5 to 10 iterations for the solver to converge.
29   * <p>
30   * Tests for the exponential function illustrate the situations where
31   * Muller solver performs poorly.
32   * 
33   * @version $Revision$ $Date$ 
34   */
35  public final class MullerSolverTest extends TestCase {
36  
37      /**
38       * Test of solver for the sine function.
39       */
40      public void testSinFunction() throws MathException {
41          UnivariateRealFunction f = new SinFunction();
42          UnivariateRealSolver solver = new MullerSolver(f);
43          double min, max, expected, result, tolerance;
44  
45          min = 3.0; max = 4.0; expected = Math.PI;
46          tolerance = Math.max(solver.getAbsoluteAccuracy(),
47                      Math.abs(expected * solver.getRelativeAccuracy()));
48          result = solver.solve(min, max);
49          assertEquals(expected, result, tolerance);
50  
51          min = -1.0; max = 1.5; expected = 0.0;
52          tolerance = Math.max(solver.getAbsoluteAccuracy(),
53                      Math.abs(expected * solver.getRelativeAccuracy()));
54          result = solver.solve(min, max);
55          assertEquals(expected, result, tolerance);
56      }
57  
58      /**
59       * Test of solver for the sine function using solve2().
60       */
61      public void testSinFunction2() throws MathException {
62          UnivariateRealFunction f = new SinFunction();
63          MullerSolver solver = new MullerSolver(f);
64          double min, max, expected, result, tolerance;
65  
66          min = 3.0; max = 4.0; expected = Math.PI;
67          tolerance = Math.max(solver.getAbsoluteAccuracy(),
68                      Math.abs(expected * solver.getRelativeAccuracy()));
69          result = solver.solve2(min, max);
70          assertEquals(expected, result, tolerance);
71  
72          min = -1.0; max = 1.5; expected = 0.0;
73          tolerance = Math.max(solver.getAbsoluteAccuracy(),
74                      Math.abs(expected * solver.getRelativeAccuracy()));
75          result = solver.solve2(min, max);
76          assertEquals(expected, result, tolerance);
77      }
78  
79      /**
80       * Test of solver for the quintic function.
81       */
82      public void testQuinticFunction() throws MathException {
83          UnivariateRealFunction f = new QuinticFunction();
84          UnivariateRealSolver solver = new MullerSolver(f);
85          double min, max, expected, result, tolerance;
86  
87          min = -0.4; max = 0.2; expected = 0.0;
88          tolerance = Math.max(solver.getAbsoluteAccuracy(),
89                      Math.abs(expected * solver.getRelativeAccuracy()));
90          result = solver.solve(min, max);
91          assertEquals(expected, result, tolerance);
92  
93          min = 0.75; max = 1.5; expected = 1.0;
94          tolerance = Math.max(solver.getAbsoluteAccuracy(),
95                      Math.abs(expected * solver.getRelativeAccuracy()));
96          result = solver.solve(min, max);
97          assertEquals(expected, result, tolerance);
98  
99          min = -0.9; max = -0.2; expected = -0.5;
100         tolerance = Math.max(solver.getAbsoluteAccuracy(),
101                     Math.abs(expected * solver.getRelativeAccuracy()));
102         result = solver.solve(min, max);
103         assertEquals(expected, result, tolerance);
104     }
105 
106     /**
107      * Test of solver for the quintic function using solve2().
108      */
109     public void testQuinticFunction2() throws MathException {
110         UnivariateRealFunction f = new QuinticFunction();
111         MullerSolver solver = new MullerSolver(f);
112         double min, max, expected, result, tolerance;
113 
114         min = -0.4; max = 0.2; expected = 0.0;
115         tolerance = Math.max(solver.getAbsoluteAccuracy(),
116                     Math.abs(expected * solver.getRelativeAccuracy()));
117         result = solver.solve2(min, max);
118         assertEquals(expected, result, tolerance);
119 
120         min = 0.75; max = 1.5; expected = 1.0;
121         tolerance = Math.max(solver.getAbsoluteAccuracy(),
122                     Math.abs(expected * solver.getRelativeAccuracy()));
123         result = solver.solve2(min, max);
124         assertEquals(expected, result, tolerance);
125 
126         min = -0.9; max = -0.2; expected = -0.5;
127         tolerance = Math.max(solver.getAbsoluteAccuracy(),
128                     Math.abs(expected * solver.getRelativeAccuracy()));
129         result = solver.solve2(min, max);
130         assertEquals(expected, result, tolerance);
131     }
132 
133     /**
134      * Test of solver for the exponential function.
135      * <p>
136      * It takes 10 to 15 iterations for the last two tests to converge.
137      * In fact, if not for the bisection alternative, the solver would
138      * exceed the default maximal iteration of 100.
139      */
140     public void testExpm1Function() throws MathException {
141         UnivariateRealFunction f = new Expm1Function();
142         UnivariateRealSolver solver = new MullerSolver(f);
143         double min, max, expected, result, tolerance;
144 
145         min = -1.0; max = 2.0; expected = 0.0;
146         tolerance = Math.max(solver.getAbsoluteAccuracy(),
147                     Math.abs(expected * solver.getRelativeAccuracy()));
148         result = solver.solve(min, max);
149         assertEquals(expected, result, tolerance);
150 
151         min = -20.0; max = 10.0; expected = 0.0;
152         tolerance = Math.max(solver.getAbsoluteAccuracy(),
153                     Math.abs(expected * solver.getRelativeAccuracy()));
154         result = solver.solve(min, max);
155         assertEquals(expected, result, tolerance);
156 
157         min = -50.0; max = 100.0; expected = 0.0;
158         tolerance = Math.max(solver.getAbsoluteAccuracy(),
159                     Math.abs(expected * solver.getRelativeAccuracy()));
160         result = solver.solve(min, max);
161         assertEquals(expected, result, tolerance);
162     }
163 
164     /**
165      * Test of solver for the exponential function using solve2().
166      * <p>
167      * It takes 25 to 50 iterations for the last two tests to converge.
168      */
169     public void testExpm1Function2() throws MathException {
170         UnivariateRealFunction f = new Expm1Function();
171         MullerSolver solver = new MullerSolver(f);
172         double min, max, expected, result, tolerance;
173 
174         min = -1.0; max = 2.0; expected = 0.0;
175         tolerance = Math.max(solver.getAbsoluteAccuracy(),
176                     Math.abs(expected * solver.getRelativeAccuracy()));
177         result = solver.solve2(min, max);
178         assertEquals(expected, result, tolerance);
179 
180         min = -20.0; max = 10.0; expected = 0.0;
181         tolerance = Math.max(solver.getAbsoluteAccuracy(),
182                     Math.abs(expected * solver.getRelativeAccuracy()));
183         result = solver.solve2(min, max);
184         assertEquals(expected, result, tolerance);
185 
186         min = -50.0; max = 100.0; expected = 0.0;
187         tolerance = Math.max(solver.getAbsoluteAccuracy(),
188                     Math.abs(expected * solver.getRelativeAccuracy()));
189         result = solver.solve2(min, max);
190         assertEquals(expected, result, tolerance);
191     }
192 
193     /**
194      * Test of parameters for the solver.
195      */
196     public void testParameters() throws Exception {
197         UnivariateRealFunction f = new SinFunction();
198         UnivariateRealSolver solver = new MullerSolver(f);
199 
200         try {
201             // bad interval
202             solver.solve(1, -1);
203             fail("Expecting IllegalArgumentException - bad interval");
204         } catch (IllegalArgumentException ex) {
205             // expected
206         }
207         try {
208             // no bracketing
209             solver.solve(2, 3);
210             fail("Expecting IllegalArgumentException - no bracketing");
211         } catch (IllegalArgumentException ex) {
212             // expected
213         }
214     }
215 }