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17  
18  package org.apache.commons.math.ode;
19  
20  import org.apache.commons.math.ode.DerivativeException;
21  import org.apache.commons.math.ode.FirstOrderIntegrator;
22  import org.apache.commons.math.ode.GraggBulirschStoerIntegrator;
23  import org.apache.commons.math.ode.IntegratorException;
24  import org.apache.commons.math.ode.StepHandler;
25  import org.apache.commons.math.ode.StepInterpolator;
26  import org.apache.commons.math.ode.SwitchingFunction;
27  
28  import junit.framework.*;
29  
30  public class GraggBulirschStoerIntegratorTest
31    extends TestCase {
32  
33    public GraggBulirschStoerIntegratorTest(String name) {
34      super(name);
35    }
36  
37    public void testDimensionCheck() {
38      try  {
39        TestProblem1 pb = new TestProblem1();
40        AdaptiveStepsizeIntegrator integrator =
41          new GraggBulirschStoerIntegrator(0.0, 1.0, 1.0e-10, 1.0e-10);
42        integrator.integrate(pb,
43                             0.0, new double[pb.getDimension()+10],
44                             1.0, new double[pb.getDimension()+10]);
45        fail("an exception should have been thrown");
46      } catch(DerivativeException de) {
47        fail("wrong exception caught");
48      } catch(IntegratorException ie) {
49      }
50    }
51  
52    public void testNullIntervalCheck() {
53      try  {
54        TestProblem1 pb = new TestProblem1();
55        GraggBulirschStoerIntegrator integrator =
56          new GraggBulirschStoerIntegrator(0.0, 1.0, 1.0e-10, 1.0e-10);
57        integrator.integrate(pb,
58                             0.0, new double[pb.getDimension()],
59                             0.0, new double[pb.getDimension()]);
60        fail("an exception should have been thrown");
61      } catch(DerivativeException de) {
62        fail("wrong exception caught");
63      } catch(IntegratorException ie) {
64      }
65    }
66  
67    public void testMinStep()
68      throws DerivativeException, IntegratorException {
69  
70      try {
71        TestProblem5 pb  = new TestProblem5();
72        double minStep   = 0.1 * Math.abs(pb.getFinalTime() - pb.getInitialTime());
73        double maxStep   = Math.abs(pb.getFinalTime() - pb.getInitialTime());
74        double[] vecAbsoluteTolerance = { 1.0e-20, 1.0e-21 };
75        double[] vecRelativeTolerance = { 1.0e-20, 1.0e-21 };
76  
77        FirstOrderIntegrator integ =
78          new GraggBulirschStoerIntegrator(minStep, maxStep,
79                                           vecAbsoluteTolerance, vecRelativeTolerance);
80        TestProblemHandler handler = new TestProblemHandler(pb, integ);
81        integ.setStepHandler(handler);
82        integ.integrate(pb,
83                        pb.getInitialTime(), pb.getInitialState(),
84                        pb.getFinalTime(), new double[pb.getDimension()]);
85        fail("an exception should have been thrown");
86      } catch(DerivativeException de) {
87        fail("wrong exception caught");
88      } catch(IntegratorException ie) {
89      }
90  
91    }
92  
93    public void testIncreasingTolerance()
94      throws DerivativeException, IntegratorException {
95  
96      int previousCalls = Integer.MAX_VALUE;
97      for (int i = -12; i < -4; ++i) {
98        TestProblem1 pb     = new TestProblem1();
99        double minStep      = 0;
100       double maxStep      = pb.getFinalTime() - pb.getInitialTime();
101       double absTolerance = Math.pow(10.0, i);
102       double relTolerance = absTolerance;
103 
104       FirstOrderIntegrator integ =
105         new GraggBulirschStoerIntegrator(minStep, maxStep,
106                                          absTolerance, relTolerance);
107       TestProblemHandler handler = new TestProblemHandler(pb, integ);
108       integ.setStepHandler(handler);
109       integ.integrate(pb,
110                       pb.getInitialTime(), pb.getInitialState(),
111                       pb.getFinalTime(), new double[pb.getDimension()]);
112 
113       // the coefficients are only valid for this test
114       // and have been obtained from trial and error
115       // there is no general relation between local and global errors
116       double ratio =  handler.getMaximalValueError() / absTolerance;
117       assertTrue(ratio < 2.4);
118       assertTrue(ratio > 0.02);
119       assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
120 
121       int calls = pb.getCalls();
122       assertTrue(calls <= previousCalls);
123       previousCalls = calls;
124 
125     }
126 
127   }
128 
129   public void testIntegratorControls()
130   throws DerivativeException, IntegratorException {
131 
132     TestProblem3 pb = new TestProblem3(0.999);
133     GraggBulirschStoerIntegrator integ =
134         new GraggBulirschStoerIntegrator(0, pb.getFinalTime() - pb.getInitialTime(),
135                 1.0e-8, 1.0e-10);
136 
137     double errorWithDefaultSettings = getMaxError(integ, pb);
138 
139     // stability control
140     integ.setStabilityCheck(true, 2, 1, 0.99);
141     assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
142     integ.setStabilityCheck(true, -1, -1, -1);
143 
144     integ.setStepsizeControl(0.5, 0.99, 0.1, 2.5);
145     assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
146     integ.setStepsizeControl(-1, -1, -1, -1);
147 
148     integ.setOrderControl(10, 0.7, 0.95);
149     assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
150     integ.setOrderControl(-1, -1, -1);
151 
152     integ.setInterpolationControl(true, 3);
153     assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
154     integ.setInterpolationControl(true, -1);
155 
156   }
157 
158   private double getMaxError(FirstOrderIntegrator integrator, TestProblemAbstract pb)
159     throws DerivativeException, IntegratorException {
160       TestProblemHandler handler = new TestProblemHandler(pb, integrator);
161       integrator.setStepHandler(handler);
162       integrator.integrate(pb,
163                            pb.getInitialTime(), pb.getInitialState(),
164                            pb.getFinalTime(), new double[pb.getDimension()]);
165       return handler.getMaximalValueError();
166   }
167 
168   public void testSwitchingFunctions()
169     throws DerivativeException, IntegratorException {
170 
171     TestProblem4 pb = new TestProblem4();
172     double minStep = 0;
173     double maxStep = pb.getFinalTime() - pb.getInitialTime();
174     double scalAbsoluteTolerance = 1.0e-10;
175     double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
176 
177     FirstOrderIntegrator integ = new GraggBulirschStoerIntegrator(minStep, maxStep,
178                                                                   scalAbsoluteTolerance,
179                                                                   scalRelativeTolerance);
180     TestProblemHandler handler = new TestProblemHandler(pb, integ);
181     integ.setStepHandler(handler);
182     SwitchingFunction[] functions = pb.getSwitchingFunctions();
183     for (int l = 0; l < functions.length; ++l) {
184       integ.addSwitchingFunction(functions[l],
185                                  Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 1000);
186     }
187     integ.integrate(pb,
188                     pb.getInitialTime(), pb.getInitialState(),
189                     pb.getFinalTime(), new double[pb.getDimension()]);
190 
191     assertTrue(handler.getMaximalValueError() < 5.0e-8);
192     assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
193     assertEquals(12.0, handler.getLastTime(), 1.0e-8 * maxStep);
194 
195   }
196 
197   public void testKepler()
198     throws DerivativeException, IntegratorException {
199 
200     final TestProblem3 pb = new TestProblem3(0.9);
201     double minStep        = 0;
202     double maxStep        = pb.getFinalTime() - pb.getInitialTime();
203     double absTolerance   = 1.0e-6;
204     double relTolerance   = 1.0e-6;
205 
206     FirstOrderIntegrator integ =
207       new GraggBulirschStoerIntegrator(minStep, maxStep,
208                                        absTolerance, relTolerance);
209     integ.setStepHandler(new KeplerStepHandler(pb));
210     integ.integrate(pb,
211                     pb.getInitialTime(), pb.getInitialState(),
212                     pb.getFinalTime(), new double[pb.getDimension()]);
213 
214     assertTrue(pb.getCalls() < 2150);
215 
216   }
217 
218   public void testVariableSteps()
219     throws DerivativeException, IntegratorException {
220 
221     final TestProblem3 pb = new TestProblem3(0.9);
222     double minStep        = 0;
223     double maxStep        = pb.getFinalTime() - pb.getInitialTime();
224     double absTolerance   = 1.0e-8;
225     double relTolerance   = 1.0e-8;
226     FirstOrderIntegrator integ =
227       new GraggBulirschStoerIntegrator(minStep, maxStep,
228                                        absTolerance, relTolerance);
229     integ.setStepHandler(new VariableStepHandler());
230     integ.integrate(pb,
231                     pb.getInitialTime(), pb.getInitialState(),
232                     pb.getFinalTime(), new double[pb.getDimension()]);
233     assertEquals("Gragg-Bulirsch-Stoer", integ.getName());
234   }
235 
236   public void testUnstableDerivative()
237     throws DerivativeException, IntegratorException {
238     final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
239     FirstOrderIntegrator integ =
240       new GraggBulirschStoerIntegrator(0.1, 10, 1.0e-12, 0.0);
241     integ.addSwitchingFunction(stepProblem, 1.0, 1.0e-12, 1000);
242     double[] y = { Double.NaN };
243     integ.integrate(stepProblem, 0.0, new double[] { 0.0 }, 10.0, y);
244     assertEquals(8.0, y[0], 1.0e-12);
245   }
246 
247   private static class KeplerStepHandler implements StepHandler {
248     public KeplerStepHandler(TestProblem3 pb) {
249       this.pb = pb;
250       reset();
251     }
252     public boolean requiresDenseOutput() {
253       return true;
254     }
255     public void reset() {
256       nbSteps = 0;
257       maxError = 0;
258     }
259     public void handleStep(StepInterpolator interpolator,
260                            boolean isLast)
261     throws DerivativeException {
262 
263       ++nbSteps;
264       for (int a = 1; a < 100; ++a) {
265 
266         double prev   = interpolator.getPreviousTime();
267         double curr   = interpolator.getCurrentTime();
268         double interp = ((100 - a) * prev + a * curr) / 100;
269         interpolator.setInterpolatedTime(interp);
270 
271         double[] interpolatedY = interpolator.getInterpolatedState ();
272         double[] theoreticalY  = pb.computeTheoreticalState(interpolator.getInterpolatedTime());
273         double dx = interpolatedY[0] - theoreticalY[0];
274         double dy = interpolatedY[1] - theoreticalY[1];
275         double error = dx * dx + dy * dy;
276         if (error > maxError) {
277           maxError = error;
278         }
279       }
280       if (isLast) {
281         assertTrue(maxError < 2.7e-6);
282         assertTrue(nbSteps < 80);
283       }
284     }
285     private int nbSteps;
286     private double maxError;
287     private TestProblem3 pb;
288   }
289 
290   public static class VariableStepHandler implements StepHandler {
291     public VariableStepHandler() {
292       reset();
293     }
294     public boolean requiresDenseOutput() {
295       return false;
296     }
297     public void reset() {
298       firstTime = true;
299       minStep = 0;
300       maxStep = 0;
301     }
302     public void handleStep(StepInterpolator interpolator,
303                            boolean isLast) {
304 
305       double step = Math.abs(interpolator.getCurrentTime()
306                              - interpolator.getPreviousTime());
307       if (firstTime) {
308         minStep   = Math.abs(step);
309         maxStep   = minStep;
310         firstTime = false;
311       } else {
312         if (step < minStep) {
313           minStep = step;
314         }
315         if (step > maxStep) {
316           maxStep = step;
317         }
318       }
319 
320       if (isLast) {
321         assertTrue(minStep < 8.2e-3);
322         assertTrue(maxStep > 1.7);
323       }
324     }
325     private boolean firstTime;
326     private double  minStep;
327     private double  maxStep;
328   }
329   public static Test suite() {
330     return new TestSuite(GraggBulirschStoerIntegratorTest.class);
331   }
332 
333 }