src/test/java/org/apache/commons/math3/ode/nonstiff/EulerStepInterpolatorTest.java

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 * The ASF licenses this file to You under the Apache License, Version 2.0
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package org.apache.commons.math3.ode.nonstiff;


import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.util.Random;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.ContinuousOutputModel;
import org.apache.commons.math3.ode.EquationsMapper;
import org.apache.commons.math3.ode.TestProblem1;
import org.apache.commons.math3.ode.TestProblem3;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.ode.sampling.StepInterpolatorTestUtils;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class EulerStepInterpolatorTest {

  @Test
  public void noReset() throws MaxCountExceededException {

    double[]   y    =   { 0.0, 1.0, -2.0 };
    double[][] yDot = { { 1.0, 2.0, -2.0 } };
    EulerStepInterpolator interpolator = new EulerStepInterpolator();
    interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true,
                              new EquationsMapper(0, y.length),
                              new EquationsMapper[0]);
    interpolator.storeTime(0);
    interpolator.shift();
    interpolator.storeTime(1);

    double[] result = interpolator.getInterpolatedState();
    for (int i = 0; i < result.length; ++i) {
      Assert.assertTrue(FastMath.abs(result[i] - y[i]) < 1.0e-10);
    }

  }

  @Test
  public void interpolationAtBounds() throws MaxCountExceededException {

    double   t0 = 0;
    double[] y0 = {0.0, 1.0, -2.0};

    double[] y = y0.clone();
    double[][] yDot = { new double[y0.length] };
    EulerStepInterpolator interpolator = new EulerStepInterpolator();
    interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true,
                              new EquationsMapper(0, y.length),
                              new EquationsMapper[0]);
    interpolator.storeTime(t0);

    double dt = 1.0;
    interpolator.shift();
    y[0] =  1.0;
    y[1] =  3.0;
    y[2] = -4.0;
    yDot[0][0] = (y[0] - y0[0]) / dt;
    yDot[0][1] = (y[1] - y0[1]) / dt;
    yDot[0][2] = (y[2] - y0[2]) / dt;
    interpolator.storeTime(t0 + dt);

    interpolator.setInterpolatedTime(interpolator.getPreviousTime());
    double[] result = interpolator.getInterpolatedState();
    for (int i = 0; i < result.length; ++i) {
        Assert.assertTrue(FastMath.abs(result[i] - y0[i]) < 1.0e-10);
    }

    interpolator.setInterpolatedTime(interpolator.getCurrentTime());
    result = interpolator.getInterpolatedState();
    for (int i = 0; i < result.length; ++i) {
      Assert.assertTrue(FastMath.abs(result[i] - y[i]) < 1.0e-10);
    }

  }

  @Test
  public void interpolationInside() throws MaxCountExceededException {

    double[]   y    =   { 0.0, 1.0, -2.0 };
    double[][] yDot = { { 1.0, 2.0, -2.0 } };
    EulerStepInterpolator interpolator = new EulerStepInterpolator();
    interpolator.reinitialize(new DummyIntegrator(interpolator), y, yDot, true,
                              new EquationsMapper(0, y.length),
                              new EquationsMapper[0]);
    interpolator.storeTime(0);
    interpolator.shift();
    y[0] =  1.0;
    y[1] =  3.0;
    y[2] = -4.0;
    interpolator.storeTime(1);

    interpolator.setInterpolatedTime(0.1);
    double[] result = interpolator.getInterpolatedState();
    Assert.assertTrue(FastMath.abs(result[0] - 0.1) < 1.0e-10);
    Assert.assertTrue(FastMath.abs(result[1] - 1.2) < 1.0e-10);
    Assert.assertTrue(FastMath.abs(result[2] + 2.2) < 1.0e-10);

    interpolator.setInterpolatedTime(0.5);
    result = interpolator.getInterpolatedState();
    Assert.assertTrue(FastMath.abs(result[0] - 0.5) < 1.0e-10);
    Assert.assertTrue(FastMath.abs(result[1] - 2.0) < 1.0e-10);
    Assert.assertTrue(FastMath.abs(result[2] + 3.0) < 1.0e-10);

  }

  @Test
  public void derivativesConsistency()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    TestProblem3 pb = new TestProblem3();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    EulerIntegrator integ = new EulerIntegrator(step);
    StepInterpolatorTestUtils.checkDerivativesConsistency(integ, pb, 0.01, 5.1e-12);
  }

  @Test
  public void serialization()
    throws IOException, ClassNotFoundException,
           DimensionMismatchException, NumberIsTooSmallException,
           MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    EulerIntegrator integ = new EulerIntegrator(step);
    integ.addStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    for (StepHandler handler : integ.getStepHandlers()) {
        oos.writeObject(handler);
    }

    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());
    ObjectInputStream     ois = new ObjectInputStream(bis);
    ContinuousOutputModel cm  = (ContinuousOutputModel) ois.readObject();

    Random random = new Random(347588535632l);
    double maxError = 0.0;
    for (int i = 0; i < 1000; ++i) {
      double r = random.nextDouble();
      double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
      cm.setInterpolatedTime(time);
      double[] interpolatedY = cm.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(time);
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {
        maxError = error;
      }
    }
    Assert.assertTrue(maxError < 0.001);

  }

  private static class DummyIntegrator extends RungeKuttaIntegrator {


      protected DummyIntegrator(RungeKuttaStepInterpolator prototype) {
          super("dummy", new double[0], new double[0][0], new double[0], prototype, Double.NaN);
      }

  }

}