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* 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.
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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.FirstOrderDifferentialEquations;
import org.apache.commons.math4.ode.FirstOrderIntegrator;
import org.apache.commons.math4.ode.TestProblem1;
import org.apache.commons.math4.ode.TestProblem2;
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.TestProblem6;
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.ThreeEighthesIntegrator;
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 ThreeEighthesIntegratorTest {
@Test(expected=DimensionMismatchException.class)
public void testDimensionCheck()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
new ThreeEighthesIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()+10],
1.0, new double[pb.getDimension()+10]);
Assert.fail("an exception should have been thrown");
}
@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 ThreeEighthesIntegrator(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) {
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;
}
}
}
@Test
public void testSmallStep()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
FirstOrderIntegrator integ = new ThreeEighthesIntegrator(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("3/8", 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 ThreeEighthesIntegrator(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 ThreeEighthesIntegrator(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("3/8", 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 ThreeEighthesIntegrator(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;
}
@Override
public void init(double t0, double[] y0, double t) {
maxError = 0;
}
@Override
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 TestProblem3 pb;
private double maxError = 0;
}
@Test
public void testStepSize()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final double step = 1.23456;
FirstOrderIntegrator integ = new ThreeEighthesIntegrator(step);
integ.addStepHandler(new StepHandler() {
@Override
public void handleStep(StepInterpolator interpolator, boolean isLast) {
if (! isLast) {
Assert.assertEquals(step,
interpolator.getCurrentTime() - interpolator.getPreviousTime(),
1.0e-12);
}
}
@Override
public void init(double t0, double[] y0, double t) {
}
});
integ.integrate(new FirstOrderDifferentialEquations() {
@Override
public void computeDerivatives(double t, double[] y, double[] dot) {
dot[0] = 1.0;
}
@Override
public int getDimension() {
return 1;
}
}, 0.0, new double[] { 0.0 }, 5.0, new double[1]);
}
}