text: /*
   * Licensed to the Apache Software Foundation (ASF) under one or more
   * contributor license agreements.  See the NOTICE file distributed with
   * this work for additional information regarding copyright ownership.
   * The ASF licenses this file to You under the Apache License, Version 2.0
   * (the "License"); you may not use this file except in compliance with
   * the License.  You may obtain a copy of the License at
   *
   *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  
  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, 1.0e-10);
    }
  
    @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);
        }
  
    }
  
  }
  