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18 package org.apache.commons.math4.legacy.ode.nonstiff;
19
20
21 import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
22 import org.apache.commons.math4.legacy.exception.MaxCountExceededException;
23 import org.apache.commons.math4.legacy.exception.NoBracketingException;
24 import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
25 import org.apache.commons.math4.legacy.ode.FirstOrderDifferentialEquations;
26 import org.apache.commons.math4.legacy.ode.FirstOrderIntegrator;
27 import org.apache.commons.math4.legacy.ode.TestProblem1;
28 import org.apache.commons.math4.legacy.ode.TestProblem2;
29 import org.apache.commons.math4.legacy.ode.TestProblem3;
30 import org.apache.commons.math4.legacy.ode.TestProblem4;
31 import org.apache.commons.math4.legacy.ode.TestProblem5;
32 import org.apache.commons.math4.legacy.ode.TestProblem6;
33 import org.apache.commons.math4.legacy.ode.TestProblemAbstract;
34 import org.apache.commons.math4.legacy.ode.TestProblemHandler;
35 import org.apache.commons.math4.legacy.ode.events.EventHandler;
36 import org.apache.commons.math4.legacy.ode.sampling.StepHandler;
37 import org.apache.commons.math4.legacy.ode.sampling.StepInterpolator;
38 import org.apache.commons.math4.core.jdkmath.JdkMath;
39 import org.junit.Assert;
40 import org.junit.Test;
41
42 public class EulerIntegratorTest {
43
44 @Test(expected=DimensionMismatchException.class)
45 public void testDimensionCheck()
46 throws DimensionMismatchException, NumberIsTooSmallException,
47 MaxCountExceededException, NoBracketingException {
48 TestProblem1 pb = new TestProblem1();
49 new EulerIntegrator(0.01).integrate(pb,
50 0.0, new double[pb.getDimension()+10],
51 1.0, new double[pb.getDimension()+10]);
52 Assert.fail("an exception should have been thrown");
53 }
54
55 @Test
56 public void testDecreasingSteps()
57 throws DimensionMismatchException, NumberIsTooSmallException,
58 MaxCountExceededException, NoBracketingException {
59
60 for (TestProblemAbstract pb : new TestProblemAbstract[] {
61 new TestProblem1(), new TestProblem2(), new TestProblem3(),
62 new TestProblem4(), new TestProblem5(), new TestProblem6()
63 }) {
64
65 double previousValueError = Double.NaN;
66 double previousTimeError = Double.NaN;
67 for (int i = 4; i < 8; ++i) {
68
69 double step = (pb.getFinalTime() - pb.getInitialTime()) * JdkMath.pow(2.0, -i);
70
71 FirstOrderIntegrator integ = new EulerIntegrator(step);
72 TestProblemHandler handler = new TestProblemHandler(pb, integ);
73 integ.addStepHandler(handler);
74 EventHandler[] functions = pb.getEventsHandlers();
75 for (int l = 0; l < functions.length; ++l) {
76 integ.addEventHandler(functions[l],
77 Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
78 }
79 double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
80 pb.getFinalTime(), new double[pb.getDimension()]);
81 if (functions.length == 0) {
82 Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
83 }
84
85 double valueError = handler.getMaximalValueError();
86 if (i > 4) {
87 Assert.assertTrue(valueError < JdkMath.abs(previousValueError));
88 }
89 previousValueError = valueError;
90
91 double timeError = handler.getMaximalTimeError();
92 if (i > 4) {
93 Assert.assertTrue(timeError <= JdkMath.abs(previousTimeError));
94 }
95 previousTimeError = timeError;
96 }
97 }
98 }
99
100 @Test
101 public void testSmallStep()
102 throws DimensionMismatchException, NumberIsTooSmallException,
103 MaxCountExceededException, NoBracketingException {
104
105 TestProblem1 pb = new TestProblem1();
106 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
107
108 FirstOrderIntegrator integ = new EulerIntegrator(step);
109 TestProblemHandler handler = new TestProblemHandler(pb, integ);
110 integ.addStepHandler(handler);
111 integ.integrate(pb,
112 pb.getInitialTime(), pb.getInitialState(),
113 pb.getFinalTime(), new double[pb.getDimension()]);
114
115 Assert.assertTrue(handler.getLastError() < 2.0e-4);
116 Assert.assertTrue(handler.getMaximalValueError() < 1.0e-3);
117 Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
118 Assert.assertEquals("Euler", integ.getName());
119 }
120
121 @Test
122 public void testBigStep()
123 throws DimensionMismatchException, NumberIsTooSmallException,
124 MaxCountExceededException, NoBracketingException {
125
126 TestProblem1 pb = new TestProblem1();
127 double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;
128
129 FirstOrderIntegrator integ = new EulerIntegrator(step);
130 TestProblemHandler handler = new TestProblemHandler(pb, integ);
131 integ.addStepHandler(handler);
132 integ.integrate(pb,
133 pb.getInitialTime(), pb.getInitialState(),
134 pb.getFinalTime(), new double[pb.getDimension()]);
135
136 Assert.assertTrue(handler.getLastError() > 0.01);
137 Assert.assertTrue(handler.getMaximalValueError() > 0.2);
138 Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
139 }
140
141 @Test
142 public void testBackward()
143 throws DimensionMismatchException, NumberIsTooSmallException,
144 MaxCountExceededException, NoBracketingException {
145
146 TestProblem5 pb = new TestProblem5();
147 double step = JdkMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;
148
149 FirstOrderIntegrator integ = new EulerIntegrator(step);
150 TestProblemHandler handler = new TestProblemHandler(pb, integ);
151 integ.addStepHandler(handler);
152 integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
153 pb.getFinalTime(), new double[pb.getDimension()]);
154
155 Assert.assertTrue(handler.getLastError() < 0.45);
156 Assert.assertTrue(handler.getMaximalValueError() < 0.45);
157 Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
158 Assert.assertEquals("Euler", integ.getName());
159 }
160
161 @Test
162 public void testStepSize()
163 throws DimensionMismatchException, NumberIsTooSmallException,
164 MaxCountExceededException, NoBracketingException {
165 final double step = 1.23456;
166 FirstOrderIntegrator integ = new EulerIntegrator(step);
167 integ.addStepHandler(new StepHandler() {
168 @Override
169 public void handleStep(StepInterpolator interpolator, boolean isLast) {
170 if (! isLast) {
171 Assert.assertEquals(step,
172 interpolator.getCurrentTime() - interpolator.getPreviousTime(),
173 1.0e-12);
174 }
175 }
176 @Override
177 public void init(double t0, double[] y0, double t) {
178 }
179 });
180 integ.integrate(new FirstOrderDifferentialEquations() {
181 @Override
182 public void computeDerivatives(double t, double[] y, double[] dot) {
183 dot[0] = 1.0;
184 }
185 @Override
186 public int getDimension() {
187 return 1;
188 }
189 }, 0.0, new double[] { 0.0 }, 5.0, new double[1]);
190 }
191 }