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18 package org.apache.commons.math.ode.nonstiff;
19
20 import junit.framework.*;
21
22 import org.apache.commons.math.ode.DerivativeException;
23 import org.apache.commons.math.ode.FirstOrderDifferentialEquations;
24 import org.apache.commons.math.ode.FirstOrderIntegrator;
25 import org.apache.commons.math.ode.IntegratorException;
26 import org.apache.commons.math.ode.TestProblem1;
27 import org.apache.commons.math.ode.TestProblem3;
28 import org.apache.commons.math.ode.TestProblem5;
29 import org.apache.commons.math.ode.TestProblemAbstract;
30 import org.apache.commons.math.ode.TestProblemFactory;
31 import org.apache.commons.math.ode.TestProblemHandler;
32 import org.apache.commons.math.ode.events.EventHandler;
33 import org.apache.commons.math.ode.nonstiff.ThreeEighthesIntegrator;
34 import org.apache.commons.math.ode.sampling.StepHandler;
35 import org.apache.commons.math.ode.sampling.StepInterpolator;
36
37 public class ThreeEighthesIntegratorTest
38 extends TestCase {
39
40 public ThreeEighthesIntegratorTest(String name) {
41 super(name);
42 }
43
44 public void testDimensionCheck() {
45 try {
46 TestProblem1 pb = new TestProblem1();
47 new ThreeEighthesIntegrator(0.01).integrate(pb,
48 0.0, new double[pb.getDimension()+10],
49 1.0, new double[pb.getDimension()+10]);
50 fail("an exception should have been thrown");
51 } catch(DerivativeException de) {
52 fail("wrong exception caught");
53 } catch(IntegratorException ie) {
54 }
55 }
56
57 public void testDecreasingSteps()
58 throws DerivativeException, IntegratorException {
59
60 TestProblemAbstract[] problems = TestProblemFactory.getProblems();
61 for (int k = 0; k < problems.length; ++k) {
62
63 double previousError = Double.NaN;
64 for (int i = 4; i < 10; ++i) {
65
66 TestProblemAbstract pb = problems[k].copy();
67 double step = (pb.getFinalTime() - pb.getInitialTime())
68 * Math.pow(2.0, -i);
69
70 FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
71 TestProblemHandler handler = new TestProblemHandler(pb, integ);
72 integ.addStepHandler(handler);
73 EventHandler[] functions = pb.getEventsHandlers();
74 for (int l = 0; l < functions.length; ++l) {
75 integ.addEventHandler(functions[l],
76 Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
77 }
78 double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
79 pb.getFinalTime(), new double[pb.getDimension()]);
80 if (functions.length == 0) {
81 assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
82 }
83
84 double error = handler.getMaximalValueError();
85 if (i > 4) {
86 assertTrue(error < Math.abs(previousError));
87 }
88 previousError = error;
89 assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
90
91 }
92
93 }
94
95 }
96
97 public void testSmallStep()
98 throws DerivativeException, IntegratorException {
99
100 TestProblem1 pb = new TestProblem1();
101 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
102
103 FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
104 TestProblemHandler handler = new TestProblemHandler(pb, integ);
105 integ.addStepHandler(handler);
106 integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
107 pb.getFinalTime(), new double[pb.getDimension()]);
108
109 assertTrue(handler.getLastError() < 2.0e-13);
110 assertTrue(handler.getMaximalValueError() < 4.0e-12);
111 assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
112 assertEquals("3/8", integ.getName());
113
114 }
115
116 public void testBigStep()
117 throws DerivativeException, IntegratorException {
118
119 TestProblem1 pb = new TestProblem1();
120 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;
121
122 FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
123 TestProblemHandler handler = new TestProblemHandler(pb, integ);
124 integ.addStepHandler(handler);
125 integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
126 pb.getFinalTime(), new double[pb.getDimension()]);
127
128 assertTrue(handler.getLastError() > 0.0004);
129 assertTrue(handler.getMaximalValueError() > 0.005);
130 assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
131
132 }
133
134 public void testBackward()
135 throws DerivativeException, IntegratorException {
136
137 TestProblem5 pb = new TestProblem5();
138 double step = Math.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;
139
140 FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
141 TestProblemHandler handler = new TestProblemHandler(pb, integ);
142 integ.addStepHandler(handler);
143 integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
144 pb.getFinalTime(), new double[pb.getDimension()]);
145
146 assertTrue(handler.getLastError() < 5.0e-10);
147 assertTrue(handler.getMaximalValueError() < 7.0e-10);
148 assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
149 assertEquals("3/8", integ.getName());
150 }
151
152 public void testKepler()
153 throws DerivativeException, IntegratorException {
154
155 final TestProblem3 pb = new TestProblem3(0.9);
156 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
157
158 FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
159 integ.addStepHandler(new KeplerHandler(pb));
160 integ.integrate(pb,
161 pb.getInitialTime(), pb.getInitialState(),
162 pb.getFinalTime(), new double[pb.getDimension()]);
163 }
164
165 private static class KeplerHandler implements StepHandler {
166
167 public KeplerHandler(TestProblem3 pb) {
168 this.pb = pb;
169 maxError = 0;
170 }
171
172 public boolean requiresDenseOutput() {
173 return false;
174 }
175
176 public void reset() {
177 maxError = 0;
178 }
179
180 public void handleStep(StepInterpolator interpolator,
181 boolean isLast) throws DerivativeException {
182
183 double[] interpolatedY = interpolator.getInterpolatedState();
184 double[] theoreticalY = pb.computeTheoreticalState(interpolator.getCurrentTime());
185 double dx = interpolatedY[0] - theoreticalY[0];
186 double dy = interpolatedY[1] - theoreticalY[1];
187 double error = dx * dx + dy * dy;
188 if (error > maxError) {
189 maxError = error;
190 }
191 if (isLast) {
192
193
194
195 assertTrue(maxError > 0.005);
196 }
197 }
198
199 private TestProblem3 pb;
200 private double maxError = 0;
201
202 }
203
204 public void testStepSize()
205 throws DerivativeException, IntegratorException {
206 final double step = 1.23456;
207 FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
208 integ.addStepHandler(new StepHandler() {
209 public void handleStep(StepInterpolator interpolator, boolean isLast) {
210 if (! isLast) {
211 assertEquals(step,
212 interpolator.getCurrentTime() - interpolator.getPreviousTime(),
213 1.0e-12);
214 }
215 }
216 public boolean requiresDenseOutput() {
217 return false;
218 }
219 public void reset() {
220 }
221 });
222 integ.integrate(new FirstOrderDifferentialEquations() {
223 public void computeDerivatives(double t, double[] y, double[] dot) {
224 dot[0] = 1.0;
225 }
226 public int getDimension() {
227 return 1;
228 }
229 }, 0.0, new double[] { 0.0 }, 5.0, new double[1]);
230 }
231
232 public static Test suite() {
233 return new TestSuite(ThreeEighthesIntegratorTest.class);
234 }
235
236 }