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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
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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  
18  package org.apache.commons.math.ode;
19  
20  import junit.framework.*;
21  
22  import org.apache.commons.math.ode.DerivativeException;
23  import org.apache.commons.math.ode.FirstOrderIntegrator;
24  import org.apache.commons.math.ode.GillIntegrator;
25  import org.apache.commons.math.ode.IntegratorException;
26  import org.apache.commons.math.ode.StepHandler;
27  import org.apache.commons.math.ode.StepInterpolator;
28  import org.apache.commons.math.ode.SwitchingFunction;
29  
30  public class GillIntegratorTest
31    extends TestCase {
32  
33    public GillIntegratorTest(String name) {
34      super(name);
35    }
36  
37    public void testDimensionCheck() {
38      try  {
39        TestProblem1 pb = new TestProblem1();
40        new GillIntegrator(0.01).integrate(pb,
41                                           0.0, new double[pb.getDimension()+10],
42                                           1.0, new double[pb.getDimension()+10]);
43          fail("an exception should have been thrown");
44      } catch(DerivativeException de) {
45        fail("wrong exception caught");
46      } catch(IntegratorException ie) {
47      }
48    }
49    
50    public void testDecreasingSteps()
51      throws DerivativeException, IntegratorException  {
52        
53      TestProblemAbstract[] problems = TestProblemFactory.getProblems();
54      for (int k = 0; k < problems.length; ++k) {
55  
56        double previousError = Double.NaN;
57        for (int i = 5; i < 10; ++i) {
58  
59          TestProblemAbstract pb = (TestProblemAbstract) problems[k].clone();
60          double step = (pb.getFinalTime() - pb.getInitialTime())
61            * Math.pow(2.0, -i);
62  
63          FirstOrderIntegrator integ = new GillIntegrator(step);
64          TestProblemHandler handler = new TestProblemHandler(pb, integ);
65          integ.setStepHandler(handler);
66          SwitchingFunction[] functions = pb.getSwitchingFunctions();
67          for (int l = 0; l < functions.length; ++l) {
68            integ.addSwitchingFunction(functions[l],
69                                       Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
70          }
71          integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
72                          pb.getFinalTime(), new double[pb.getDimension()]);
73  
74          double error = handler.getMaximalValueError();
75          if (i > 5) {
76            assertTrue(error < Math.abs(previousError));
77          }
78          previousError = error;
79          assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
80  
81        }
82  
83      }
84  
85    }
86  
87    public void testSmallStep()
88      throws DerivativeException, IntegratorException {
89  
90      TestProblem1 pb = new TestProblem1();
91      double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
92  
93      FirstOrderIntegrator integ = new GillIntegrator(step);
94      TestProblemHandler handler = new TestProblemHandler(pb, integ);
95      integ.setStepHandler(handler);
96      integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
97                      pb.getFinalTime(), new double[pb.getDimension()]);
98  
99      assertTrue(handler.getLastError() < 2.0e-13);
100     assertTrue(handler.getMaximalValueError() < 4.0e-12);
101     assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
102     assertEquals("Gill", integ.getName());
103 
104   }
105 
106   public void testBigStep()
107     throws DerivativeException, IntegratorException {
108 
109     TestProblem1 pb = new TestProblem1();
110     double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;
111 
112     FirstOrderIntegrator integ = new GillIntegrator(step);
113     TestProblemHandler handler = new TestProblemHandler(pb, integ);
114     integ.setStepHandler(handler);
115     integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
116                     pb.getFinalTime(), new double[pb.getDimension()]);
117 
118     assertTrue(handler.getLastError() > 0.0004);
119     assertTrue(handler.getMaximalValueError() > 0.005);
120     assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
121 
122   }
123 
124   public void testKepler()
125     throws DerivativeException, IntegratorException {
126 
127     final TestProblem3 pb  = new TestProblem3(0.9);
128     double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
129 
130     FirstOrderIntegrator integ = new GillIntegrator(step);
131     integ.setStepHandler(new KeplerStepHandler(pb));
132     integ.integrate(pb,
133                     pb.getInitialTime(), pb.getInitialState(),
134                     pb.getFinalTime(), new double[pb.getDimension()]);
135   }
136 
137   public void testUnstableDerivative()
138   throws DerivativeException, IntegratorException {
139     final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
140     FirstOrderIntegrator integ = new GillIntegrator(0.3);
141     integ.addSwitchingFunction(stepProblem, 1.0, 1.0e-12, 1000);
142     double[] y = { Double.NaN };
143     integ.integrate(stepProblem, 0.0, new double[] { 0.0 }, 10.0, y);
144     assertEquals(8.0, y[0], 1.0e-12);
145   }
146 
147   private static class KeplerStepHandler implements StepHandler {
148     public KeplerStepHandler(TestProblem3 pb) {
149       this.pb = pb;
150       reset();
151     }
152     public boolean requiresDenseOutput() {
153       return false;
154     }
155     public void reset() {
156       maxError = 0;
157     }
158     public void handleStep(StepInterpolator interpolator,
159                            boolean isLast) {
160 
161       double[] interpolatedY = interpolator.getInterpolatedState ();
162       double[] theoreticalY  = pb.computeTheoreticalState(interpolator.getCurrentTime());
163       double dx = interpolatedY[0] - theoreticalY[0];
164       double dy = interpolatedY[1] - theoreticalY[1];
165       double error = dx * dx + dy * dy;
166       if (error > maxError) {
167         maxError = error;
168       }
169       if (isLast) {
170         // even with more than 1000 evaluations per period,
171         // RK4 is not able to integrate such an eccentric
172         // orbit with a good accuracy
173         assertTrue(maxError > 0.001);
174       }
175     }
176     private double maxError;
177     private TestProblem3 pb;
178   }
179 
180   public static Test suite() {
181     return new TestSuite(GillIntegratorTest.class);
182   }
183 
184 }