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18 package org.apache.commons.math4.legacy.ode.nonstiff;
19
20
21 import java.io.ByteArrayInputStream;
22 import java.io.ByteArrayOutputStream;
23 import java.io.IOException;
24 import java.io.ObjectInputStream;
25 import java.io.ObjectOutputStream;
26 import java.util.Random;
27
28 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
29 import org.apache.commons.math4.legacy.exception.MaxCountExceededException;
30 import org.apache.commons.math4.legacy.exception.NoBracketingException;
31 import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
32 import org.apache.commons.math4.legacy.ode.ContinuousOutputModel;
33 import org.apache.commons.math4.legacy.ode.EquationsMapper;
34 import org.apache.commons.math4.legacy.ode.TestProblem1;
35 import org.apache.commons.math4.legacy.ode.TestProblem3;
36 import org.apache.commons.math4.legacy.ode.sampling.StepHandler;
37 import org.apache.commons.math4.legacy.ode.sampling.StepInterpolatorTestUtils;
38 import org.apache.commons.math4.core.jdkmath.JdkMath;
39 import org.junit.Assert;
40 import org.junit.Test;
41
42 public class EulerStepInterpolatorTest {
43
44 @Test
45 public void noReset() throws MaxCountExceededException {
46
47 double[] y = { 0.0, 1.0, -2.0 };
48 double[][] yDot = { { 1.0, 2.0, -2.0 } };
49 EulerStepInterpolator interpolator = new EulerStepInterpolator();
50 interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true,
51 new EquationsMapper(0, y.length),
52 new EquationsMapper[0]);
53 interpolator.storeTime(0);
54 interpolator.shift();
55 interpolator.storeTime(1);
56
57 double[] result = interpolator.getInterpolatedState();
58 for (int i = 0; i < result.length; ++i) {
59 Assert.assertTrue(JdkMath.abs(result[i] - y[i]) < 1.0e-10);
60 }
61 }
62
63 @Test
64 public void interpolationAtBounds() throws MaxCountExceededException {
65
66 double t0 = 0;
67 double[] y0 = {0.0, 1.0, -2.0};
68
69 double[] y = y0.clone();
70 double[][] yDot = { new double[y0.length] };
71 EulerStepInterpolator interpolator = new EulerStepInterpolator();
72 interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true,
73 new EquationsMapper(0, y.length),
74 new EquationsMapper[0]);
75 interpolator.storeTime(t0);
76
77 double dt = 1.0;
78 interpolator.shift();
79 y[0] = 1.0;
80 y[1] = 3.0;
81 y[2] = -4.0;
82 yDot[0][0] = (y[0] - y0[0]) / dt;
83 yDot[0][1] = (y[1] - y0[1]) / dt;
84 yDot[0][2] = (y[2] - y0[2]) / dt;
85 interpolator.storeTime(t0 + dt);
86
87 interpolator.setInterpolatedTime(interpolator.getPreviousTime());
88 double[] result = interpolator.getInterpolatedState();
89 for (int i = 0; i < result.length; ++i) {
90 Assert.assertTrue(JdkMath.abs(result[i] - y0[i]) < 1.0e-10);
91 }
92
93 interpolator.setInterpolatedTime(interpolator.getCurrentTime());
94 result = interpolator.getInterpolatedState();
95 for (int i = 0; i < result.length; ++i) {
96 Assert.assertTrue(JdkMath.abs(result[i] - y[i]) < 1.0e-10);
97 }
98 }
99
100 @Test
101 public void interpolationInside() throws MaxCountExceededException {
102
103 double[] y = { 0.0, 1.0, -2.0 };
104 double[][] yDot = { { 1.0, 2.0, -2.0 } };
105 EulerStepInterpolator interpolator = new EulerStepInterpolator();
106 interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true,
107 new EquationsMapper(0, y.length),
108 new EquationsMapper[0]);
109 interpolator.storeTime(0);
110 interpolator.shift();
111 y[0] = 1.0;
112 y[1] = 3.0;
113 y[2] = -4.0;
114 interpolator.storeTime(1);
115
116 interpolator.setInterpolatedTime(0.1);
117 double[] result = interpolator.getInterpolatedState();
118 Assert.assertTrue(JdkMath.abs(result[0] - 0.1) < 1.0e-10);
119 Assert.assertTrue(JdkMath.abs(result[1] - 1.2) < 1.0e-10);
120 Assert.assertTrue(JdkMath.abs(result[2] + 2.2) < 1.0e-10);
121
122 interpolator.setInterpolatedTime(0.5);
123 result = interpolator.getInterpolatedState();
124 Assert.assertTrue(JdkMath.abs(result[0] - 0.5) < 1.0e-10);
125 Assert.assertTrue(JdkMath.abs(result[1] - 2.0) < 1.0e-10);
126 Assert.assertTrue(JdkMath.abs(result[2] + 3.0) < 1.0e-10);
127 }
128
129 @Test
130 public void derivativesConsistency()
131 throws DimensionMismatchException, NumberIsTooSmallException,
132 MaxCountExceededException, NoBracketingException {
133 TestProblem3 pb = new TestProblem3();
134 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
135 EulerIntegrator integ = new EulerIntegrator(step);
136 StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 0.01, 5.1e-12);
137 }
138
139 @Test
140 public void serialization()
141 throws IOException, ClassNotFoundException,
142 DimensionMismatchException, NumberIsTooSmallException,
143 MaxCountExceededException, NoBracketingException {
144
145 TestProblem1 pb = new TestProblem1();
146 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
147 EulerIntegrator integ = new EulerIntegrator(step);
148 integ.addStepHandler(new ContinuousOutputModel());
149 integ.integrate(pb,
150 pb.getInitialTime(), pb.getInitialState(),
151 pb.getFinalTime(), new double[pb.getDimension()]);
152
153 ByteArrayOutputStream bos = new ByteArrayOutputStream();
154 ObjectOutputStream oos = new ObjectOutputStream(bos);
155 for (StepHandler handler : integ.getStepHandlers()) {
156 oos.writeObject(handler);
157 }
158
159 ByteArrayInputStream bis = new ByteArrayInputStream(bos.toByteArray());
160 ObjectInputStream ois = new ObjectInputStream(bis);
161 ContinuousOutputModel cm = (ContinuousOutputModel) ois.readObject();
162
163 Random random = new Random(347588535632L);
164 double maxError = 0.0;
165 for (int i = 0; i < 1000; ++i) {
166 double r = random.nextDouble();
167 double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
168 cm.setInterpolatedTime(time);
169 double[] interpolatedY = cm.getInterpolatedState ();
170 double[] theoreticalY = pb.computeTheoreticalState(time);
171 double dx = interpolatedY[0] - theoreticalY[0];
172 double dy = interpolatedY[1] - theoreticalY[1];
173 double error = dx * dx + dy * dy;
174 if (error > maxError) {
175 maxError = error;
176 }
177 }
178 Assert.assertTrue(maxError < 0.001);
179 }
180
181 private static final class DummyIntegrator extends RungeKuttaIntegrator {
182
183
184 protected DummyIntegrator(RungeKuttaStepInterpolator prototype) {
185 super("dummy", new double[0], new double[0][0], new double[0], prototype, Double.NaN);
186 }
187 }
188 }