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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.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.TestProblem3;
import org.apache.commons.math4.ode.TestProblem4;
import org.apache.commons.math4.ode.TestProblem5;
import org.apache.commons.math4.ode.TestProblemHandler;
import org.apache.commons.math4.ode.events.EventHandler;
import org.apache.commons.math4.ode.nonstiff.AdaptiveStepsizeIntegrator;
import org.apache.commons.math4.ode.nonstiff.DormandPrince853Integrator;
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 DormandPrince853IntegratorTest {
@Test
public void testMissedEndEvent()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
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() {
@Override
public int getDimension() {
return k.length;
}
@Override
public void computeDerivatives(double t, double[] y, double[] yDot) {
for (int i = 0; i < y.length; ++i) {
yDot[i] = k[i] * y[i];
}
}
};
DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 100.0,
1.0e-10, 1.0e-10);
double[] y0 = new double[k.length];
for (int i = 0; i < y0.length; ++i) {
y0[i] = i + 1;
}
double[] y = new double[k.length];
integrator.setInitialStepSize(60.0);
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] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
}
integrator.setInitialStepSize(60.0);
integrator.addEventHandler(new EventHandler() {
@Override
public void init(double t0, double[] y0, double t) {
}
@Override
public void resetState(double t, double[] y) {
}
@Override
public double g(double t, double[] y) {
return t - tEvent;
}
@Override
public Action eventOccurred(double t, double[] y, boolean increasing) {
Assert.assertEquals(tEvent, t, 5.0e-6);
return Action.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] * FastMath.exp(k[i] * (finalT - t0)), y[i], 1.0e-9);
}
}
@Test(expected=DimensionMismatchException.class)
public void testDimensionCheck()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 1.0,
1.0e-10, 1.0e-10);
integrator.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(expected=NumberIsTooSmallException.class)
public void testNullIntervalCheck()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem1 pb = new TestProblem1();
DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.0, 1.0,
1.0e-10, 1.0e-10);
integrator.integrate(pb,
0.0, new double[pb.getDimension()],
0.0, new double[pb.getDimension()]);
Assert.fail("an exception should have been thrown");
}
@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 DormandPrince853Integrator(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()]);
Assert.fail("an exception should have been thrown");
}
@Test
public void testIncreasingTolerance()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
int previousCalls = Integer.MAX_VALUE;
AdaptiveStepsizeIntegrator integ =
new DormandPrince853Integrator(0, Double.POSITIVE_INFINITY,
Double.NaN, Double.NaN);
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;
integ.setStepSizeControl(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
Assert.assertTrue(handler.getMaximalValueError() < (1.3 * scalAbsoluteTolerance));
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
int calls = pb.getCalls();
Assert.assertEquals(integ.getEvaluations(), calls);
Assert.assertTrue(calls <= previousCalls);
previousCalls = calls;
}
}
@Test
public void testTooLargeFirstStep()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
AdaptiveStepsizeIntegrator integ =
new DormandPrince853Integrator(0, Double.POSITIVE_INFINITY, Double.NaN, Double.NaN);
final double start = 0.0;
final double end = 0.001;
FirstOrderDifferentialEquations equations = new FirstOrderDifferentialEquations() {
@Override
public int getDimension() {
return 1;
}
@Override
public void computeDerivatives(double t, double[] y, double[] yDot) {
Assert.assertTrue(t >= FastMath.nextAfter(start, Double.NEGATIVE_INFINITY));
Assert.assertTrue(t <= FastMath.nextAfter(end, Double.POSITIVE_INFINITY));
yDot[0] = -100.0 * y[0];
}
};
integ.setStepSizeControl(0, 1.0, 1.0e-6, 1.0e-8);
integ.integrate(equations, start, new double[] { 1.0 }, end, new double[1]);
}
@Test
public void testBackward()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
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 DormandPrince853Integrator(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()]);
Assert.assertTrue(handler.getLastError() < 1.1e-7);
Assert.assertTrue(handler.getMaximalValueError() < 1.1e-7);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
Assert.assertEquals("Dormand-Prince 8 (5, 3)", integ.getName());
}
@Test
public void testEvents()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
TestProblem4 pb = new TestProblem4();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-9;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince853Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
EventHandler[] functions = pb.getEventsHandlers();
double convergence = 1.0e-8 * maxStep;
for (int l = 0; l < functions.length; ++l) {
integ.addEventHandler(functions[l], Double.POSITIVE_INFINITY, convergence, 1000);
}
Assert.assertEquals(functions.length, integ.getEventHandlers().size());
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(0, handler.getMaximalValueError(), 2.1e-7);
Assert.assertEquals(0, handler.getMaximalTimeError(), convergence);
Assert.assertEquals(12.0, handler.getLastTime(), convergence);
integ.clearEventHandlers();
Assert.assertEquals(0, integ.getEventHandlers().size());
}
@Test
public void testKepler()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince853Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
integ.addStepHandler(new KeplerHandler(pb));
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(integ.getEvaluations(), pb.getCalls());
Assert.assertTrue(pb.getCalls() < 3300);
}
@Test
public void testVariableSteps()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-8;
double scalRelativeTolerance = scalAbsoluteTolerance;
FirstOrderIntegrator integ = new DormandPrince853Integrator(minStep, maxStep,
scalAbsoluteTolerance,
scalRelativeTolerance);
integ.addStepHandler(new VariableHandler());
double stopTime = integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(pb.getFinalTime(), stopTime, 1.0e-10);
Assert.assertEquals("Dormand-Prince 8 (5, 3)", integ.getName());
}
@Test
public void testUnstableDerivative()
throws DimensionMismatchException, NumberIsTooSmallException,
MaxCountExceededException, NoBracketingException {
final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
FirstOrderIntegrator integ =
new DormandPrince853Integrator(0.1, 10, 1.0e-12, 0.0);
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);
Assert.assertEquals(8.0, y[0], 1.0e-12);
}
@Test
public void testEventsScheduling() {
FirstOrderDifferentialEquations sincos = new FirstOrderDifferentialEquations() {
@Override
public int getDimension() {
return 2;
}
@Override
public void computeDerivatives(double t, double[] y, double[] yDot) {
yDot[0] = y[1];
yDot[1] = -y[0];
}
};
SchedulingChecker sinChecker = new SchedulingChecker(0); // events at 0, PI, 2PI ...
SchedulingChecker cosChecker = new SchedulingChecker(1); // events at PI/2, 3PI/2, 5PI/2 ...
FirstOrderIntegrator integ =
new DormandPrince853Integrator(0.001, 1.0, 1.0e-12, 0.0);
integ.addEventHandler(sinChecker, 0.01, 1.0e-7, 100);
integ.addStepHandler(sinChecker);
integ.addEventHandler(cosChecker, 0.01, 1.0e-7, 100);
integ.addStepHandler(cosChecker);
double t0 = 0.5;
double[] y0 = new double[] { FastMath.sin(t0), FastMath.cos(t0) };
double t = 10.0;
double[] y = new double[2];
integ.integrate(sincos, t0, y0, t, y);
}
private static class SchedulingChecker implements StepHandler, EventHandler {
int index;
double tMin;
public SchedulingChecker(int index) {
this.index = index;
}
@Override
public void init(double t0, double[] y0, double t) {
tMin = t0;
}
@Override
public void handleStep(StepInterpolator interpolator, boolean isLast) {
tMin = interpolator.getCurrentTime();
}
@Override
public double g(double t, double[] y) {
// once a step has been handled by handleStep,
// events checking should only refer to dates after the step
Assert.assertTrue(t >= tMin);
return y[index];
}
@Override
public Action eventOccurred(double t, double[] y, boolean increasing) {
return Action.RESET_STATE;
}
@Override
public void resetState(double t, double[] y) {
// in fact, we don't need to reset anything for the test
}
}
private static class KeplerHandler implements StepHandler {
public KeplerHandler(TestProblem3 pb) {
this.pb = pb;
}
@Override
public void init(double t0, double[] y0, double t) {
nbSteps = 0;
maxError = 0;
}
@Override
public void handleStep(StepInterpolator interpolator, boolean isLast)
throws MaxCountExceededException {
++nbSteps;
for (int a = 1; a < 10; ++a) {
double prev = interpolator.getPreviousTime();
double curr = interpolator.getCurrentTime();
double interp = ((10 - a) * prev + a * curr) / 10;
interpolator.setInterpolatedTime(interp);
double[] interpolatedY = interpolator.getInterpolatedState ();
double[] theoreticalY = pb.computeTheoreticalState(interpolator.getInterpolatedTime());
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) {
Assert.assertTrue(maxError < 2.4e-10);
Assert.assertTrue(nbSteps < 150);
}
}
private int nbSteps;
private double maxError;
private TestProblem3 pb;
}
private static class VariableHandler implements StepHandler {
public VariableHandler() {
firstTime = true;
minStep = 0;
maxStep = 0;
}
@Override
public void init(double t0, double[] y0, double t) {
firstTime = true;
minStep = 0;
maxStep = 0;
}
@Override
public void handleStep(StepInterpolator interpolator,
boolean isLast) {
double step = FastMath.abs(interpolator.getCurrentTime()
- interpolator.getPreviousTime());
if (firstTime) {
minStep = FastMath.abs(step);
maxStep = minStep;
firstTime = false;
} else {
if (step < minStep) {
minStep = step;
}
if (step > maxStep) {
maxStep = step;
}
}
if (isLast) {
Assert.assertTrue(minStep < (1.0 / 100.0));
Assert.assertTrue(maxStep > (1.0 / 2.0));
}
}
private boolean firstTime = true;
private double minStep = 0;
private double maxStep = 0;
}
}