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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.TestCase;
import org.apache.commons.math.ConvergenceException;
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.TestProblem4;
import org.apache.commons.math.ode.TestProblem5;
import org.apache.commons.math.ode.TestProblemHandler;
import org.apache.commons.math.ode.events.EventException;
import org.apache.commons.math.ode.events.EventHandler;
import org.apache.commons.math.ode.sampling.StepHandler;
import org.apache.commons.math.ode.sampling.StepInterpolator;
public class HighamHall54IntegratorTest
extends TestCase {
public HighamHall54IntegratorTest(String name) {
super(name);
}
public void testWrongDerivative() {
try {
HighamHall54Integrator integrator =
new HighamHall54Integrator(0.0, 1.0, 1.0e-10, 1.0e-10);
FirstOrderDifferentialEquations equations =
new FirstOrderDifferentialEquations() {
private static final long serialVersionUID = -1157081786301178032L;
public void computeDerivatives(double t, double[] y, double[] dot)
throws DerivativeException {
if (t < -0.5) {
throw new DerivativeException("{0}", "oops");
} else {
throw new DerivativeException(new RuntimeException("oops"));
}
}
public int getDimension() {
return 1;
}
};
try {
integrator.integrate(equations, -1.0, new double[1], 0.0, new double[1]);
fail("an exception should have been thrown");
} catch(DerivativeException de) {
// expected behavior
}
try {
integrator.integrate(equations, 0.0, new double[1], 1.0, new double[1]);
fail("an exception should have been thrown");
} catch(DerivativeException de) {
// expected behavior
}
} catch (Exception e) {
fail("wrong exception caught: " + e.getMessage());
}
}
public void testMinStep() {
try {
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 HighamHall54Integrator(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()]);
fail("an exception should have been thrown");
} catch(DerivativeException de) {
fail("wrong exception caught");
} catch(IntegratorException ie) {
}
}
public void testIncreasingTolerance()
throws DerivativeException, IntegratorException {
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 = Math.pow(10.0, i);
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ = new HighamHall54Integrator(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 1.3 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
assertTrue(handler.getMaximalValueError() < (1.3 * scalAbsoluteTolerance));
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
int calls = pb.getCalls();
assertEquals(integ.getEvaluations(), calls);
assertTrue(calls <= previousCalls);
previousCalls = calls;
}
}
public void testBackward()
throws DerivativeException, IntegratorException {
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 HighamHall54Integrator(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()]);
assertTrue(handler.getLastError() < 5.0e-7);
assertTrue(handler.getMaximalValueError() < 5.0e-7);
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
assertEquals("Higham-Hall 5(4)", integ.getName());
}
public void testEvents()
throws DerivativeException, IntegratorException {
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 HighamHall54Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
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-8 * maxStep, 1000);
}
assertEquals(functions.length, integ.getEventHandlers().size());
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
assertTrue(handler.getMaximalValueError() < 1.0e-7);
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
assertEquals(12.0, handler.getLastTime(), 1.0e-8 * maxStep);
integ.clearEventHandlers();
assertEquals(0, integ.getEventHandlers().size());
}
public void testEventsErrors() {
final TestProblem1 pb = new TestProblem1();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep,
scalAbsoluteTolerance, scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.addEventHandler(new EventHandler() {
public int eventOccurred(double t, double[] y, boolean increasing) {
return EventHandler.CONTINUE;
}
public double g(double t, double[] y) throws EventException {
double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2;
double offset = t - middle;
if (offset > 0) {
throw new EventException("Evaluation failed for argument = {0}", t);
}
return offset;
}
public void resetState(double t, double[] y) {
}
private static final long serialVersionUID = 935652725339916361L;
}, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 1000);
try {
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
} catch (Exception e) {
fail("wrong exception type caught");
}
}
public void testEventsNoConvergence() {
final TestProblem1 pb = new TestProblem1();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep,
scalAbsoluteTolerance, scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.addEventHandler(new EventHandler() {
public int eventOccurred(double t, double[] y, boolean increasing) {
return EventHandler.CONTINUE;
}
public double g(double t, double[] y) {
double middle = (pb.getInitialTime() + pb.getFinalTime()) / 2;
double offset = t - middle;
return (offset > 0) ? (offset + 0.5) : (offset - 0.5);
}
public void resetState(double t, double[] y) {
}
private static final long serialVersionUID = 935652725339916361L;
}, Double.POSITIVE_INFINITY, 1.0e-8 * maxStep, 3);
try {
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
assertTrue(ie.getCause() != null);
assertTrue(ie.getCause() instanceof ConvergenceException);
} catch (Exception e) {
fail("wrong exception type caught");
}
}
public void testSanityChecks() {
try {
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
try {
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]);
integ.integrate(pb, pb.getInitialTime(), new double[6],
pb.getFinalTime(), new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
}
try {
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[6]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
}
try {
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep, new double[2], new double[4]);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
}
try {
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep, new double[4], new double[2]);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
}
try {
FirstOrderIntegrator integ =
new HighamHall54Integrator(minStep, maxStep, new double[4], new double[4]);
integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
pb.getInitialTime(), new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch (IntegratorException ie) {
// expected behavior
}
} catch (Exception e) {
fail("wrong exception caught: " + e.getMessage());
}
}
public void testKepler()
throws DerivativeException, IntegratorException {
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double[] vecAbsoluteTolerance = { 1.0e-8, 1.0e-8, 1.0e-10, 1.0e-10 };
double[] vecRelativeTolerance = { 1.0e-10, 1.0e-10, 1.0e-8, 1.0e-8 };
FirstOrderIntegrator integ = new HighamHall54Integrator(minStep, maxStep,
vecAbsoluteTolerance,
vecRelativeTolerance);
integ.addStepHandler(new KeplerHandler(pb));
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
assertEquals("Higham-Hall 5(4)", integ.getName());
}
private static class KeplerHandler implements StepHandler {
public KeplerHandler(TestProblem3 pb) {
this.pb = pb;
nbSteps = 0;
maxError = 0;
}
public boolean requiresDenseOutput() {
return false;
}
public void reset() {
nbSteps = 0;
maxError = 0;
}
public void handleStep(StepInterpolator interpolator,
boolean isLast) throws DerivativeException {
++nbSteps;
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) {
assertTrue(maxError < 4.2e-11);
assertTrue(nbSteps < 670);
}
}
private TestProblem3 pb;
private int nbSteps;
private double maxError;
}
}