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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
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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.math.ode.nonstiff;
import junit.framework.*;
import org.apache.commons.math.ode.DerivativeException;
import org.apache.commons.math.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math.ode.FirstOrderIntegrator;
import org.apache.commons.math.ode.IntegratorException;
import org.apache.commons.math.ode.TestProblem1;
import org.apache.commons.math.ode.TestProblem3;
import org.apache.commons.math.ode.TestProblem5;
import org.apache.commons.math.ode.TestProblemAbstract;
import org.apache.commons.math.ode.TestProblemFactory;
import org.apache.commons.math.ode.TestProblemHandler;
import org.apache.commons.math.ode.events.EventHandler;
import org.apache.commons.math.ode.nonstiff.GillIntegrator;
import org.apache.commons.math.ode.sampling.StepHandler;
import org.apache.commons.math.ode.sampling.StepInterpolator;
public class GillIntegratorTest
extends TestCase {
public GillIntegratorTest(String name) {
super(name);
}
public void testDimensionCheck() {
try {
TestProblem1 pb = new TestProblem1();
new GillIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()+10],
1.0, new double[pb.getDimension()+10]);
fail("an exception should have been thrown");
} catch(DerivativeException de) {
fail("wrong exception caught");
} catch(IntegratorException ie) {
}
}
public void testDecreasingSteps()
throws DerivativeException, IntegratorException {
TestProblemAbstract[] problems = TestProblemFactory.getProblems();
for (int k = 0; k < problems.length; ++k) {
double previousError = Double.NaN;
for (int i = 5; i < 10; ++i) {
TestProblemAbstract pb = problems[k].copy();
double step = (pb.getFinalTime() - pb.getInitialTime())
* Math.pow(2.0, -i);
FirstOrderIntegrator integ = new GillIntegrator(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);
}
double stopTime = integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
if (functions.length == 0) {
assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
}
double error = handler.getMaximalValueError();
if (i > 5) {
assertTrue(error < Math.abs(previousError));
}
previousError = error;
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
}
}
}
public void testSmallStep()
throws DerivativeException, IntegratorException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
FirstOrderIntegrator integ = new GillIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
assertTrue(handler.getLastError() < 2.0e-13);
assertTrue(handler.getMaximalValueError() < 4.0e-12);
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
assertEquals("Gill", integ.getName());
}
public void testBigStep()
throws DerivativeException, IntegratorException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;
FirstOrderIntegrator integ = new GillIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
assertTrue(handler.getLastError() > 0.0004);
assertTrue(handler.getMaximalValueError() > 0.005);
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
}
public void testBackward()
throws DerivativeException, IntegratorException {
TestProblem5 pb = new TestProblem5();
double step = Math.abs(pb.getFinalTime() - pb.getInitialTime()) * 0.001;
FirstOrderIntegrator integ = new GillIntegrator(step);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
assertTrue(handler.getLastError() < 5.0e-10);
assertTrue(handler.getMaximalValueError() < 7.0e-10);
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
assertEquals("Gill", integ.getName());
}
public void testKepler()
throws DerivativeException, IntegratorException {
final TestProblem3 pb = new TestProblem3(0.9);
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.0003;
FirstOrderIntegrator integ = new GillIntegrator(step);
integ.addStepHandler(new KeplerStepHandler(pb));
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
}
public void testUnstableDerivative()
throws DerivativeException, IntegratorException {
final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
FirstOrderIntegrator integ = new GillIntegrator(0.3);
integ.addEventHandler(stepProblem, 1.0, 1.0e-12, 1000);
double[] y = { Double.NaN };
integ.integrate(stepProblem, 0.0, new double[] { 0.0 }, 10.0, y);
assertEquals(8.0, y[0], 1.0e-12);
}
private static class KeplerStepHandler implements StepHandler {
public KeplerStepHandler(TestProblem3 pb) {
this.pb = pb;
reset();
}
public boolean requiresDenseOutput() {
return false;
}
public void reset() {
maxError = 0;
}
public void handleStep(StepInterpolator interpolator,
boolean isLast) throws DerivativeException {
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
assertTrue(maxError > 0.001);
}
}
private double maxError;
private TestProblem3 pb;
}
public void testStepSize()
throws DerivativeException, IntegratorException {
final double step = 1.23456;
FirstOrderIntegrator integ = new GillIntegrator(step);
integ.addStepHandler(new StepHandler() {
public void handleStep(StepInterpolator interpolator, boolean isLast) {
if (! isLast) {
assertEquals(step,
interpolator.getCurrentTime() - interpolator.getPreviousTime(),
1.0e-12);
}
}
public boolean requiresDenseOutput() {
return false;
}
public void reset() {
}
});
integ.integrate(new FirstOrderDifferentialEquations() {
private static final long serialVersionUID = 0L;
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]);
}
}