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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
*
* 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,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
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package org.apache.commons.math4.ode.nonstiff;
import java.io.ObjectInput;
import java.io.ObjectOutput;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.MathIllegalStateException;
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.AbstractIntegrator;
import org.apache.commons.math4.ode.ExpandableStatefulODE;
import org.apache.commons.math4.ode.FirstOrderIntegrator;
import org.apache.commons.math4.ode.MultistepIntegrator;
import org.apache.commons.math4.ode.TestProblem1;
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.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 AdamsBashforthIntegratorTest {
@Test(expected=DimensionMismatchException.class)
public void dimensionCheck() throws NumberIsTooSmallException, DimensionMismatchException, MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
FirstOrderIntegrator integ =
new AdamsBashforthIntegrator(2, 0.0, 1.0, 1.0e-10, 1.0e-10);
integ.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 AdamsBashforthIntegrator(4, 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()]);
}
@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;
FirstOrderIntegrator integ = new AdamsBashforthIntegrator(4, 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()]);
// the 2.6 and 122 factors are only valid for this test
// and has been obtained from trial and error
// there are no general relationship between local and global errors
Assert.assertTrue(handler.getMaximalValueError() > (2.6 * scalAbsoluteTolerance));
Assert.assertTrue(handler.getMaximalValueError() < (122 * scalAbsoluteTolerance));
int calls = pb.getCalls();
Assert.assertEquals(integ.getEvaluations(), calls);
Assert.assertTrue(calls <= previousCalls);
previousCalls = calls;
}
}
@Test(expected = MaxCountExceededException.class)
public void exceedMaxEvaluations() throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
double range = pb.getFinalTime() - pb.getInitialTime();
AdamsBashforthIntegrator integ = new AdamsBashforthIntegrator(2, 0, range, 1.0e-12, 1.0e-12);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.setMaxEvaluations(650);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
}
@Test
public void backward() throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException {
TestProblem5 pb = new TestProblem5();
double range = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
AdamsBashforthIntegrator integ = new AdamsBashforthIntegrator(4, 0, range, 1.0e-12, 1.0e-12);
integ.setStarterIntegrator(new PerfectStarter(pb, (integ.getNSteps() + 5) / 2));
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(0.0, handler.getLastError(), 4.3e-8);
Assert.assertEquals(0.0, handler.getMaximalValueError(), 4.3e-8);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-16);
Assert.assertEquals("Adams-Bashforth", integ.getName());
}
@Test
public void polynomial() throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException {
TestProblem6 pb = new TestProblem6();
double range = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
for (int nSteps = 2; nSteps < 8; ++nSteps) {
AdamsBashforthIntegrator integ =
new AdamsBashforthIntegrator(nSteps, 1.0e-6 * range, 0.1 * range, 1.0e-4, 1.0e-4);
integ.setStarterIntegrator(new PerfectStarter(pb, nSteps));
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
if (nSteps < 5) {
Assert.assertTrue(handler.getMaximalValueError() > 0.005);
} else {
Assert.assertTrue(handler.getMaximalValueError() < 5.0e-10);
}
}
}
@Test(expected=MathIllegalStateException.class)
public void testStartFailure() {
TestProblem1 pb = new TestProblem1();
double minStep = 0.0001 * (pb.getFinalTime() - pb.getInitialTime());
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-6;
double scalRelativeTolerance = 1.0e-7;
MultistepIntegrator integ =
new AdamsBashforthIntegrator(6, minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
integ.setStarterIntegrator(new DormandPrince853Integrator(0.5 * (pb.getFinalTime() - pb.getInitialTime()),
pb.getFinalTime() - pb.getInitialTime(),
0.1, 0.1));
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
}
private static class PerfectStarter extends AbstractIntegrator {
private final PerfectInterpolator interpolator;
private final int nbSteps;
public PerfectStarter(final TestProblemAbstract problem, final int nbSteps) {
this.interpolator = new PerfectInterpolator(problem);
this.nbSteps = nbSteps;
}
@Override
public void integrate(ExpandableStatefulODE equations, double t) {
double tStart = equations.getTime() + 0.01 * (t - equations.getTime());
getCounter().increment(nbSteps);
for (int i = 0; i < nbSteps; ++i) {
double tK = ((nbSteps - 1 - (i + 1)) * equations.getTime() + (i + 1) * tStart) / (nbSteps - 1);
interpolator.setPreviousTime(interpolator.getCurrentTime());
interpolator.setCurrentTime(tK);
interpolator.setInterpolatedTime(tK);
for (StepHandler handler : getStepHandlers()) {
handler.handleStep(interpolator, i == nbSteps - 1);
}
}
}
}
private static class PerfectInterpolator implements StepInterpolator {
private final TestProblemAbstract problem;
private double previousTime;
private double currentTime;
private double interpolatedTime;
public PerfectInterpolator(final TestProblemAbstract problem) {
this.problem = problem;
this.previousTime = problem.getInitialTime();
this.currentTime = problem.getInitialTime();
this.interpolatedTime = problem.getInitialTime();
}
@Override
public void readExternal(ObjectInput arg0) {
}
@Override
public void writeExternal(ObjectOutput arg0) {
}
@Override
public double getPreviousTime() {
return previousTime;
}
public void setPreviousTime(double time) {
previousTime = time;
}
@Override
public double getCurrentTime() {
return currentTime;
}
public void setCurrentTime(double time) {
currentTime = time;
}
@Override
public double getInterpolatedTime() {
return interpolatedTime;
}
@Override
public void setInterpolatedTime(double time) {
interpolatedTime = time;
}
@Override
public double[] getInterpolatedState() {
return problem.computeTheoreticalState(interpolatedTime);
}
@Override
public double[] getInterpolatedDerivatives() {
double[] y = problem.computeTheoreticalState(interpolatedTime);
double[] yDot = new double[y.length];
problem.computeDerivatives(interpolatedTime, y, yDot);
return yDot;
}
@Override
public double[] getInterpolatedSecondaryState(int index) {
return null;
}
@Override
public double[] getInterpolatedSecondaryDerivatives(int index) {
return null;
}
@Override
public boolean isForward() {
return problem.getFinalTime() > problem.getInitialTime();
}
@Override
public StepInterpolator copy() {
return this;
}
}
}