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* http://www.apache.org/licenses/LICENSE-2.0
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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.ClassicalRungeKuttaIntegrator;
import org.apache.commons.math.ode.sampling.StepHandler;
import org.apache.commons.math.ode.sampling.StepInterpolator;
public class ClassicalRungeKuttaIntegratorTest
extends TestCase {
public ClassicalRungeKuttaIntegratorTest(String name) {
super(name);
}
public void testMissedEndEvent() throws IntegratorException, DerivativeException {
final double t0 = 1878250320.0000029;
final double tEvent = 1878250379.9999986;
final double[] k = { 1.0e-4, 1.0e-5, 1.0e-6 };
FirstOrderDifferentialEquations ode = new FirstOrderDifferentialEquations() {
public int getDimension() {
return k.length;
}
public void computeDerivatives(double t, double[] y, double[] yDot) {
for (int i = 0; i < y.length; ++i) {
yDot[i] = k[i] * y[i];
}
}
};
ClassicalRungeKuttaIntegrator integrator = new ClassicalRungeKuttaIntegrator(60.0);
double[] y0 = new double[k.length];
for (int i = 0; i < y0.length; ++i) {
y0[i] = i + 1;
}
double[] y = new double[k.length];
double finalT = integrator.integrate(ode, t0, y0, tEvent, y);
Assert.assertEquals(tEvent, finalT, 5.0e-6);
for (int i = 0; i < y.length; ++i) {
Assert.assertEquals(y0[i] * Math.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
}
integrator.addEventHandler(new EventHandler() {
public void resetState(double t, double[] y) {
}
public double g(double t, double[] y) {
return t - tEvent;
}
public int eventOccurred(double t, double[] y, boolean increasing) {
Assert.assertEquals(tEvent, t, 5.0e-6);
return CONTINUE;
}
}, Double.POSITIVE_INFINITY, 1.0e-20, 100);
finalT = integrator.integrate(ode, t0, y0, tEvent + 120, y);
Assert.assertEquals(tEvent + 120, finalT, 5.0e-6);
for (int i = 0; i < y.length; ++i) {
Assert.assertEquals(y0[i] * Math.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
}
}
public void testSanityChecks() {
try {
TestProblem1 pb = new TestProblem1();
new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()+10],
1.0, new double[pb.getDimension()]);
fail("an exception should have been thrown");
} catch(DerivativeException de) {
fail("wrong exception caught");
} catch(IntegratorException ie) {
}
try {
TestProblem1 pb = new TestProblem1();
new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()],
1.0, new double[pb.getDimension()+10]);
fail("an exception should have been thrown");
} catch(DerivativeException de) {
fail("wrong exception caught");
} catch(IntegratorException ie) {
}
try {
TestProblem1 pb = new TestProblem1();
new ClassicalRungeKuttaIntegrator(0.01).integrate(pb,
0.0, new double[pb.getDimension()],
0.0, new double[pb.getDimension()]);
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 = 4; i < 10; ++i) {
TestProblemAbstract pb = problems[k].copy();
double step = (pb.getFinalTime() - pb.getInitialTime()) * Math.pow(2.0, -i);
FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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);
}
assertEquals(functions.length, integ.getEventHandlers().size());
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 > 4) {
assertTrue(error < Math.abs(previousError));
}
previousError = error;
assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
integ.clearEventHandlers();
assertEquals(0, integ.getEventHandlers().size());
}
}
}
public void testSmallStep()
throws DerivativeException, IntegratorException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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("classical Runge-Kutta", integ.getName());
}
public void testBigStep()
throws DerivativeException, IntegratorException {
TestProblem1 pb = new TestProblem1();
double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;
FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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 ClassicalRungeKuttaIntegrator(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("classical Runge-Kutta", 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 ClassicalRungeKuttaIntegrator(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;
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 > 0.005);
}
}
private double maxError = 0;
private TestProblem3 pb;
}
public void testStepSize()
throws DerivativeException, IntegratorException {
final double step = 1.23456;
FirstOrderIntegrator integ = new ClassicalRungeKuttaIntegrator(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]);
}
}