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* 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
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* http://www.apache.org/licenses/LICENSE-2.0
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* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math4.ode.nonstiff;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.MaxCountExceededException;
import org.apache.commons.math4.exception.NoBracketingException;
import org.apache.commons.math4.exception.NumberIsTooSmallException;
import org.apache.commons.math4.ode.FirstOrderIntegrator;
import org.apache.commons.math4.ode.TestProblem1;
import org.apache.commons.math4.ode.TestProblem3;
import org.apache.commons.math4.ode.TestProblem4;
import org.apache.commons.math4.ode.TestProblem5;
import org.apache.commons.math4.ode.TestProblemAbstract;
import org.apache.commons.math4.ode.TestProblemHandler;
import org.apache.commons.math4.ode.events.EventHandler;
import org.apache.commons.math4.ode.nonstiff.AdaptiveStepsizeIntegrator;
import org.apache.commons.math4.ode.nonstiff.DormandPrince54Integrator;
import org.apache.commons.math4.ode.nonstiff.EmbeddedRungeKuttaIntegrator;
import org.apache.commons.math4.ode.sampling.StepHandler;
import org.apache.commons.math4.ode.sampling.StepInterpolator;
import org.apache.commons.math4.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class DormandPrince54IntegratorTest {
@Test(expected=DimensionMismatchException.class)
public void testDimensionCheck()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
DormandPrince54Integrator integrator = new DormandPrince54Integrator(0.0, 1.0,
1.0e-10, 1.0e-10);
integrator.integrate(pb,
0.0, new double[pb.getDimension()+10],
1.0, new double[pb.getDimension()+10]);
}
@Test(expected=NumberIsTooSmallException.class)
public void testMinStep()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
double minStep = 0.1 * (pb.getFinalTime() - pb.getInitialTime());
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };
FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
vecAbsoluteTolerance,
vecRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.fail("an exception should have been thrown");
}
@Test
public void testSmallLastStep()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblemAbstract pb = new TestProblem5();
double minStep = 1.25;
double maxStep = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
double scalAbsoluteTolerance = 6.0e-4;
double scalRelativeTolerance = 6.0e-4;
AdaptiveStepsizeIntegrator integ =
new DormandPrince54Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
DP54SmallLastHandler handler = new DP54SmallLastHandler(minStep);
integ.addStepHandler(handler);
integ.setInitialStepSize(1.7);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertTrue(handler.wasLastSeen());
Assert.assertEquals("Dormand-Prince 5(4)", integ.getName());
}
@Test
public void testBackward()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem5 pb = new TestProblem5();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
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-7);
Assert.assertTrue(handler.getMaximalValueError() < 2.0e-7);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
Assert.assertEquals("Dormand-Prince 5(4)", integ.getName());
}
private static class DP54SmallLastHandler implements StepHandler {
public DP54SmallLastHandler(double minStep) {
lastSeen = false;
this.minStep = minStep;
}
@Override
public void init(double t0, double[] y0, double t) {
}
@Override
public void handleStep(StepInterpolator interpolator, boolean isLast) {
if (isLast) {
lastSeen = true;
double h = interpolator.getCurrentTime() - interpolator.getPreviousTime();
Assert.assertTrue(FastMath.abs(h) < minStep);
}
}
public boolean wasLastSeen() {
return lastSeen;
}
private boolean lastSeen;
private double minStep;
}
@Test
public void testIncreasingTolerance()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
int previousCalls = Integer.MAX_VALUE;
for (int i = -12; i < -2; ++i) {
TestProblem1 pb = new TestProblem1();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = FastMath.pow(10.0, i);
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
EmbeddedRungeKuttaIntegrator integ =
new DormandPrince54Integrator(minStep, maxStep,
scalAbsoluteTolerance, scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.setSafety(0.8);
integ.setMaxGrowth(5.0);
integ.setMinReduction(0.3);
integ.addStepHandler(handler);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(0.8, integ.getSafety(), 1.0e-12);
Assert.assertEquals(5.0, integ.getMaxGrowth(), 1.0e-12);
Assert.assertEquals(0.3, integ.getMinReduction(), 1.0e-12);
// the 0.7 factor is only valid for this test
// and has been obtained from trial and error
// there is no general relation between local and global errors
Assert.assertTrue(handler.getMaximalValueError() < (0.7 * scalAbsoluteTolerance));
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
int calls = pb.getCalls();
Assert.assertEquals(integ.getEvaluations(), calls);
Assert.assertTrue(calls <= previousCalls);
previousCalls = calls;
}
}
@Test
public void testEvents()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem4 pb = new TestProblem4();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
EventHandler[] functions = pb.getEventsHandlers();
double convergence = 1.0e-8 * maxStep;
for (int l = 0; l < functions.length; ++l) {
integ.addEventHandler(functions[l],
Double.POSITIVE_INFINITY, convergence, 1000);
}
Assert.assertEquals(functions.length, integ.getEventHandlers().size());
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertTrue(handler.getMaximalValueError() < 5.0e-6);
Assert.assertEquals(0, handler.getMaximalTimeError(), convergence);
Assert.assertEquals(12.0, handler.getLastTime(), convergence);
integ.clearEventHandlers();
Assert.assertEquals(0, integ.getEventHandlers().size());
}
@Test
public void testKepler()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
integ.addStepHandler(new KeplerHandler(pb));
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(integ.getEvaluations(), pb.getCalls());
Assert.assertTrue(pb.getCalls() < 2800);
}
@Test
public void testVariableSteps()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince54Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
integ.addStepHandler(new VariableHandler());
double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
}
private static class KeplerHandler implements StepHandler {
public KeplerHandler(TestProblem3 pb) {
this.pb = pb;
}
@Override
public void init(double t0, double[] y0, double t) {
nbSteps = 0;
maxError = 0;
}
@Override
public void handleStep(StepInterpolator interpolator, boolean isLast)
throws MaxCountExceededException {
++nbSteps;
for (int a = 1; a < 10; ++a) {
double prev = interpolator.getPreviousTime();
double curr = interpolator.getCurrentTime();
double interp = ((10 - a) * prev + a * curr) / 10;
interpolator.setInterpolatedTime(interp);
double[] interpolatedY = interpolator.getInterpolatedState ();
double[] theoreticalY = pb.computeTheoreticalState(interpolator.getInterpolatedTime());
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) {
Assert.assertTrue(maxError < 7.0e-10);
Assert.assertTrue(nbSteps < 400);
}
}
private int nbSteps;
private double maxError;
private TestProblem3 pb;
}
private static class VariableHandler implements StepHandler {
public VariableHandler() {
firstTime = true;
minStep = 0;
maxStep = 0;
}
@Override
public void init(double t0, double[] y0, double t) {
firstTime = true;
minStep = 0;
maxStep = 0;
}
@Override
public void handleStep(StepInterpolator interpolator,
boolean isLast) {
double step = FastMath.abs(interpolator.getCurrentTime()
- interpolator.getPreviousTime());
if (firstTime) {
minStep = FastMath.abs(step);
maxStep = minStep;
firstTime = false;
} else {
if (step < minStep) {
minStep = step;
}
if (step > maxStep) {
maxStep = step;
}
}
if (isLast) {
Assert.assertTrue(minStep < (1.0 / 450.0));
Assert.assertTrue(maxStep > (1.0 / 4.2));
}
}
private boolean firstTime;
private double minStep;
private double maxStep;
}
}