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Java example source code file (ClassicalRungeKuttaIntegratorTest.java)

This example Java source code file (ClassicalRungeKuttaIntegratorTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

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Java - Java tags/keywords

classicalrungekuttaintegrator, dimensionmismatchexception, firstorderdifferentialequations, firstorderintegrator, keplerhandler, maxcountexceededexception, nobracketingexception, numberistoosmallexception, stephandler, test, testproblem1, testproblem3, testproblem5, testproblemhandler

The ClassicalRungeKuttaIntegratorTest.java Java example source code

/*
 * 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 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.FirstOrderDifferentialEquations;
import org.apache.commons.math3.ode.FirstOrderIntegrator;
import org.apache.commons.math3.ode.TestProblem1;
import org.apache.commons.math3.ode.TestProblem2;
import org.apache.commons.math3.ode.TestProblem3;
import org.apache.commons.math3.ode.TestProblem4;
import org.apache.commons.math3.ode.TestProblem5;
import org.apache.commons.math3.ode.TestProblem6;
import org.apache.commons.math3.ode.TestProblemAbstract;
import org.apache.commons.math3.ode.TestProblemHandler;
import org.apache.commons.math3.ode.events.EventHandler;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class ClassicalRungeKuttaIntegratorTest {

  @Test
  public void testMissedEndEvent()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      final double   t0     = 1878250320.0000029;
      final double   tEvent = 1878250379.9999986;
      final double[] k      = { 1.0e-4, 1.0e-5, 1.0e-6 };
      FirstOrderDifferentialEquations ode = new FirstOrderDifferentialEquations() {

          public int getDimension() {
              return k.length;
          }

          public void computeDerivatives(double t, double[] y, double[] yDot) {
              for (int i = 0; i < y.length; ++i) {
                  yDot[i] = k[i] * y[i];
              }
          }
      };

      ClassicalRungeKuttaIntegrator integrator = new ClassicalRungeKuttaIntegrator(60.0);

      double[] y0   = new double[k.length];
      for (int i = 0; i < y0.length; ++i) {
          y0[i] = i + 1;
      }
      double[] y    = new double[k.length];

      double finalT = integrator.integrate(ode, t0, y0, tEvent, y);
      Assert.assertEquals(tEvent, finalT, 5.0e-6);
      for (int i = 0; i < y.length; ++i) {
          Assert.assertEquals(y0[i] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
      }

      integrator.addEventHandler(new EventHandler() {

          public void init(double t0, double[] y0, double t) {
          }

          public void resetState(double t, double[] y) {
          }

          public double g(double t, double[] y) {
              return t - tEvent;
          }

          public Action eventOccurred(double t, double[] y, boolean increasing) {
              Assert.assertEquals(tEvent, t, 5.0e-6);
              return Action.CONTINUE;
          }
      }, Double.POSITIVE_INFINITY, 1.0e-20, 100);
      finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y);
      Assert.assertEquals(tEvent + 120, finalT, 5.0e-6);
      for (int i = 0; i < y.length; ++i) {
          Assert.assertEquals(y0[i] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
      }

  }

  @Test
  public void testSanityChecks()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                        0.0, new double[pb.getDimension()+10],
                                                        1.0, new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
    } catch(DimensionMismatchException ie) {
    }
    try  {
        TestProblem1 pb = new TestProblem1();
        new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                          0.0, new double[pb.getDimension()],
                                                          1.0, new double[pb.getDimension()+10]);
          Assert.fail("an exception should have been thrown");
      } catch(DimensionMismatchException ie) {
      }
    try  {
      TestProblem1 pb = new TestProblem1();
      new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
                                                        0.0, new double[pb.getDimension()],
                                                        0.0, new double[pb.getDimension()]);
        Assert.fail("an exception should have been thrown");
    } catch(NumberIsTooSmallException ie) {
    }
  }

  @Test
  public void testDecreasingSteps()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    for (TestProblemAbstract pb : new TestProblemAbstract[] {
        new TestProblem1(), new TestProblem2(), new TestProblem3(),
        new TestProblem4(), new TestProblem5(), new TestProblem6()
    }) {

      double previousValueError = Double.NaN;
      double previousTimeError = Double.NaN;
      for (int i = 4; i < 10; ++i) {

        double step = (pb.getFinalTime() - pb.getInitialTime()) * FastMath.pow(2.0, -i);

        FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        EventHandler[] functions = pb.getEventsHandlers();
        for (int l = 0; l < functions.length; ++l) {
          integ.addEventHandler(functions[l],
                                     Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
        }
        Assert.assertEquals(functions.length, integ.getEventHandlers().size());
        double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                                          pb.getFinalTime(), new double[pb.getDimension()]);
        if (functions.length == 0) {
            Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
        }

        double error = handler.getMaximalValueError();
        if (i > 4) {
          Assert.assertTrue(error < 1.01 * FastMath.abs(previousValueError));
        }
        previousValueError = error;

        double timeError = handler.getMaximalTimeError();
        if (i > 4) {
          Assert.assertTrue(timeError <= FastMath.abs(previousTimeError));
        }
        previousTimeError = timeError;

        integ.clearEventHandlers();
        Assert.assertEquals(0, integ.getEventHandlers().size());
      }

    }

  }

  @Test
  public void testSmallStep()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getLastError() < 2.0e-13);
    Assert.assertTrue(handler.getMaximalValueError() < 4.0e-12);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    Assert.assertEquals("classical Runge-Kutta", integ.getName());
  }

  @Test
  public void testBigStep()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getLastError() > 0.0004);
    Assert.assertTrue(handler.getMaximalValueError() > 0.005);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);

  }

  @Test
  public void testBackward()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    TestProblem5 pb = new TestProblem5();
    double step = FastMath.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.addStepHandler(handler);
    integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);

    Assert.assertTrue(handler.getLastError() < 5.0e-10);
    Assert.assertTrue(handler.getMaximalValueError() < 7.0e-10);
    Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
    Assert.assertEquals("classical Runge-Kutta", integ.getName());
  }

  @Test
  public void testKepler()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {

    final TestProblem3 pb  = new TestProblem3(0.9);
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;

    FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
    integ.addStepHandler(new KeplerHandler(pb));
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);
  }

  private static class KeplerHandler implements StepHandler {
    public KeplerHandler(TestProblem3 pb) {
      this.pb = pb;
      maxError = 0;
    }
    public void init(double t0, double[] y0, double t) {
      maxError = 0;
    }
    public void handleStep(StepInterpolator interpolator, boolean isLast)
        throws MaxCountExceededException {

      double[] interpolatedY = interpolator.getInterpolatedState ();
      double[] theoreticalY  = pb.computeTheoreticalState(interpolator.getCurrentTime());
      double dx = interpolatedY[0] - theoreticalY[0];
      double dy = interpolatedY[1] - theoreticalY[1];
      double error = dx * dx + dy * dy;
      if (error > maxError) {
        maxError = error;
      }
      if (isLast) {
        // even with more than 1000 evaluations per period,
        // RK4 is not able to integrate such an eccentric
        // orbit with a good accuracy
        Assert.assertTrue(maxError > 0.005);
      }
    }
    private double maxError = 0;
    private TestProblem3 pb;
  }

  @Test
  public void testStepSize()
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException {
      final double step = 1.23456;
      FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(step);
      integ.addStepHandler(new StepHandler() {
          public void handleStep(StepInterpolator interpolator, boolean isLast) {
              if (! isLast) {
                  Assert.assertEquals(step,
                               interpolator.getCurrentTime() - interpolator.getPreviousTime(),
                               1.0e-12);
              }
          }
          public void init(double t0, double[] y0, double t) {
          }
      });
      integ.integrate(new FirstOrderDifferentialEquations() {
          public void computeDerivatives(double t, double[] y, double[] dot) {
              dot[0] = 1.0;
          }
          public int getDimension() {
              return 1;
          }
      }, 0.0, new double[] { 0.0 }, 5.0, new double[1]);
  }

  @Test
  public void testTooLargeFirstStep() {

      RungeKuttaIntegrator integ = new ClassicalRungeKuttaIntegrator(0.5);
      final double start = 0.0;
      final double end   = 0.001;
      FirstOrderDifferentialEquations equations = new FirstOrderDifferentialEquations() {

          public int getDimension() {
              return 1;
          }

          public void computeDerivatives(double t, double[] y, double[] yDot) {
              Assert.assertTrue(t >= FastMath.nextAfter(start, Double.NEGATIVE_INFINITY));
              Assert.assertTrue(t <= FastMath.nextAfter(end,   Double.POSITIVE_INFINITY));
              yDot[0] = -100.0 * y[0];
          }

      };

      integ.integrate(equations, start, new double[] { 1.0 }, end, new double[1]);

  }

}

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