1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
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
6    * (the "License"); you may not use this file except in compliance with
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.nonstiff;
19  
20  import static org.junit.Assert.assertTrue;
21  
22  import java.io.ByteArrayInputStream;
23  import java.io.ByteArrayOutputStream;
24  import java.io.IOException;
25  import java.io.ObjectInputStream;
26  import java.io.ObjectOutputStream;
27  import java.util.Random;
28  
29  import org.apache.commons.math.ode.ContinuousOutputModel;
30  import org.apache.commons.math.ode.DerivativeException;
31  import org.apache.commons.math.ode.IntegratorException;
32  import org.apache.commons.math.ode.TestProblem1;
33  import org.apache.commons.math.ode.TestProblem3;
34  import org.apache.commons.math.ode.sampling.StepHandler;
35  import org.apache.commons.math.ode.sampling.StepInterpolatorTestUtils;
36  import org.junit.Test;
37  
38  public class EulerStepInterpolatorTest {
39  
40    @Test
41    public void noReset() throws DerivativeException {
42  
43      double[]   y    =   { 0.0, 1.0, -2.0 };
44      double[][] yDot = { { 1.0, 2.0, -2.0 } };
45      EulerStepInterpolator interpolator = new EulerStepInterpolator();
46      interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true);
47      interpolator.storeTime(0);
48      interpolator.shift();
49      interpolator.storeTime(1);
50  
51      double[] result = interpolator.getInterpolatedState();
52      for (int i = 0; i < result.length; ++i) {
53        assertTrue(Math.abs(result[i] - y[i]) < 1.0e-10);
54      }
55  
56    }
57  
58    @Test
59    public void interpolationAtBounds()
60      throws DerivativeException {
61  
62      double   t0 = 0;
63      double[] y0 = {0.0, 1.0, -2.0};
64  
65      double[] y = y0.clone();
66      double[][] yDot = { new double[y0.length] };
67      EulerStepInterpolator interpolator = new EulerStepInterpolator();
68      interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true);
69      interpolator.storeTime(t0);
70  
71      double dt = 1.0;
72      y[0] =  1.0;
73      y[1] =  3.0;
74      y[2] = -4.0;
75      yDot[0][0] = (y[0] - y0[0]) / dt;
76      yDot[0][1] = (y[1] - y0[1]) / dt;
77      yDot[0][2] = (y[2] - y0[2]) / dt;
78      interpolator.shift();
79      interpolator.storeTime(t0 + dt);
80  
81      interpolator.setInterpolatedTime(interpolator.getPreviousTime());
82      double[] result = interpolator.getInterpolatedState();
83      for (int i = 0; i < result.length; ++i) {
84        assertTrue(Math.abs(result[i] - y0[i]) < 1.0e-10);
85      }
86  
87      interpolator.setInterpolatedTime(interpolator.getCurrentTime());
88      result = interpolator.getInterpolatedState();
89      for (int i = 0; i < result.length; ++i) {
90        assertTrue(Math.abs(result[i] - y[i]) < 1.0e-10);
91      }
92  
93    }
94  
95    @Test
96    public void interpolationInside()
97    throws DerivativeException {
98  
99      double[]   y    =   { 1.0, 3.0, -4.0 };
100     double[][] yDot = { { 1.0, 2.0, -2.0 } };
101     EulerStepInterpolator interpolator = new EulerStepInterpolator();
102     interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true);
103     interpolator.storeTime(0);
104     interpolator.shift();
105     interpolator.storeTime(1);
106 
107     interpolator.setInterpolatedTime(0.1);
108     double[] result = interpolator.getInterpolatedState();
109     assertTrue(Math.abs(result[0] - 0.1) < 1.0e-10);
110     assertTrue(Math.abs(result[1] - 1.2) < 1.0e-10);
111     assertTrue(Math.abs(result[2] + 2.2) < 1.0e-10);
112 
113     interpolator.setInterpolatedTime(0.5);
114     result = interpolator.getInterpolatedState();
115     assertTrue(Math.abs(result[0] - 0.5) < 1.0e-10);
116     assertTrue(Math.abs(result[1] - 2.0) < 1.0e-10);
117     assertTrue(Math.abs(result[2] + 3.0) < 1.0e-10);
118 
119   }
120 
121   @Test
122   public void derivativesConsistency()
123   throws DerivativeException, IntegratorException {
124     TestProblem3 pb = new TestProblem3();
125     double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
126     EulerIntegrator integ = new EulerIntegrator(step);
127     StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 1.0e-10);
128   }
129 
130   @Test
131   public void serialization()
132     throws DerivativeException, IntegratorException,
133            IOException, ClassNotFoundException {
134 
135     TestProblem1 pb = new TestProblem1();
136     double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
137     EulerIntegrator integ = new EulerIntegrator(step);
138     integ.addStepHandler(new ContinuousOutputModel());
139     integ.integrate(pb,
140                     pb.getInitialTime(), pb.getInitialState(),
141                     pb.getFinalTime(), new double[pb.getDimension()]);
142 
143     ByteArrayOutputStream bos = new ByteArrayOutputStream();
144     ObjectOutputStream    oos = new ObjectOutputStream(bos);
145     for (StepHandler handler : integ.getStepHandlers()) {
146         oos.writeObject(handler);
147     }
148     
149     ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
150     ObjectInputStream     ois = new ObjectInputStream(bis);
151     ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();
152 
153     Random random = new Random(347588535632l);
154     double maxError = 0.0;
155     for (int i = 0; i < 1000; ++i) {
156       double r = random.nextDouble();
157       double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
158       cm.setInterpolatedTime(time);
159       double[] interpolatedY = cm.getInterpolatedState ();
160       double[] theoreticalY  = pb.computeTheoreticalState(time);
161       double dx = interpolatedY[0] - theoreticalY[0];
162       double dy = interpolatedY[1] - theoreticalY[1];
163       double error = dx * dx + dy * dy;
164       if (error > maxError) {
165         maxError = error;
166       }
167     }
168     assertTrue(maxError < 0.001);
169 
170   }
171 
172   private static class DummyIntegrator extends RungeKuttaIntegrator {
173 
174       
175       protected DummyIntegrator(RungeKuttaStepInterpolator prototype) {
176           super("dummy", new double[0], new double[0][0], new double[0], prototype, Double.NaN);
177       }
178 
179   }
180 
181 }