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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.math3.ode.nonstiff;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math3.ode.FirstOrderIntegrator;
import org.apache.commons.math3.ode.TestProblem1;
import org.apache.commons.math3.ode.TestProblem3;
import org.apache.commons.math3.ode.TestProblem4;
import org.apache.commons.math3.ode.TestProblem5;
import org.apache.commons.math3.ode.TestProblemAbstract;
import org.apache.commons.math3.ode.TestProblemHandler;
import org.apache.commons.math3.ode.events.EventHandler;
import org.apache.commons.math3.ode.sampling.StepHandler;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;
public class GraggBulirschStoerIntegratorTest {
@Test(expected=DimensionMismatchException.class)
public void testDimensionCheck() {
TestProblem1 pb = new TestProblem1();
AdaptiveStepsizeIntegrator integrator =
new GraggBulirschStoerIntegrator(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]);
}
@Test(expected=NumberIsTooSmallException.class)
public void testNullIntervalCheck() {
TestProblem1 pb = new TestProblem1();
GraggBulirschStoerIntegrator integrator =
new GraggBulirschStoerIntegrator(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()]);
}
@Test(expected=NumberIsTooSmallException.class)
public void testMinStep() {
TestProblem5 pb = new TestProblem5();
double minStep = 0.1 * FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
double maxStep = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());
double[] vecAbsoluteTolerance = { 1.0e-20, 1.0e-21 };
double[] vecRelativeTolerance = { 1.0e-20, 1.0e-21 };
FirstOrderIntegrator integ =
new GraggBulirschStoerIntegrator(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 testBackward()
{
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 GraggBulirschStoerIntegrator(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() < 7.5e-9);
Assert.assertTrue(handler.getMaximalValueError() < 8.1e-9);
Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
Assert.assertEquals("Gragg-Bulirsch-Stoer", integ.getName());
}
@Test
public void testIncreasingTolerance()
{
int previousCalls = Integer.MAX_VALUE;
for (int i = -12; i < -4; ++i) {
TestProblem1 pb = new TestProblem1();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double absTolerance = FastMath.pow(10.0, i);
double relTolerance = absTolerance;
FirstOrderIntegrator integ =
new GraggBulirschStoerIntegrator(minStep, maxStep,
absTolerance, relTolerance);
TestProblemHandler handler = new TestProblemHandler(pb, integ);
integ.addStepHandler(handler);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
// the coefficients are only valid for this test
// and have been obtained from trial and error
// there is no general relation between local and global errors
double ratio = handler.getMaximalValueError() / absTolerance;
Assert.assertTrue(ratio < 2.4);
Assert.assertTrue(ratio > 0.02);
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 testIntegratorControls()
{
TestProblem3 pb = new TestProblem3(0.999);
GraggBulirschStoerIntegrator integ =
new GraggBulirschStoerIntegrator(0, pb.getFinalTime() - pb.getInitialTime(),
1.0e-8, 1.0e-10);
double errorWithDefaultSettings = getMaxError(integ, pb);
// stability control
integ.setStabilityCheck(true, 2, 1, 0.99);
Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
integ.setStabilityCheck(true, -1, -1, -1);
integ.setControlFactors(0.5, 0.99, 0.1, 2.5);
Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
integ.setControlFactors(-1, -1, -1, -1);
integ.setOrderControl(10, 0.7, 0.95);
Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
integ.setOrderControl(-1, -1, -1);
integ.setInterpolationControl(true, 3);
Assert.assertTrue(errorWithDefaultSettings < getMaxError(integ, pb));
integ.setInterpolationControl(true, -1);
}
private double getMaxError(FirstOrderIntegrator integrator, TestProblemAbstract pb)
{
TestProblemHandler handler = new TestProblemHandler(pb, integrator);
integrator.addStepHandler(handler);
integrator.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
return handler.getMaximalValueError();
}
@Test
public void testEvents()
{
TestProblem4 pb = new TestProblem4();
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double scalAbsoluteTolerance = 1.0e-10;
double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;
FirstOrderIntegrator integ = new GraggBulirschStoerIntegrator(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.assertTrue(handler.getMaximalValueError() < 4.0e-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()
{
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double absTolerance = 1.0e-6;
double relTolerance = 1.0e-6;
FirstOrderIntegrator integ =
new GraggBulirschStoerIntegrator(minStep, maxStep,
absTolerance, relTolerance);
integ.addStepHandler(new KeplerStepHandler(pb));
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Assert.assertEquals(integ.getEvaluations(), pb.getCalls());
Assert.assertTrue(pb.getCalls() < 2150);
}
@Test
public void testVariableSteps()
{
final TestProblem3 pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
double absTolerance = 1.0e-8;
double relTolerance = 1.0e-8;
FirstOrderIntegrator integ =
new GraggBulirschStoerIntegrator(minStep, maxStep,
absTolerance, relTolerance);
integ.addStepHandler(new VariableStepHandler());
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("Gragg-Bulirsch-Stoer", integ.getName());
}
@Test
public void testTooLargeFirstStep() {
AdaptiveStepsizeIntegrator integ =
new GraggBulirschStoerIntegrator(0, Double.POSITIVE_INFINITY, Double.NaN, Double.NaN);
final double start = 0.0;
final double end = 0.001;
FirstOrderDifferentialEquations equations = new FirstOrderDifferentialEquations() {
public int getDimension() {
return 1;
}
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 testUnstableDerivative() {
final StepProblem stepProblem = new StepProblem(0.0, 1.0, 2.0);
FirstOrderIntegrator integ =
new GraggBulirschStoerIntegrator(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 testIssue596() {
FirstOrderIntegrator integ = new GraggBulirschStoerIntegrator(1e-10, 100.0, 1e-7, 1e-7);
integ.addStepHandler(new StepHandler() {
public void init(double t0, double[] y0, double t) {
}
public void handleStep(StepInterpolator interpolator, boolean isLast) {
double t = interpolator.getCurrentTime();
interpolator.setInterpolatedTime(t);
double[] y = interpolator.getInterpolatedState();
double[] yDot = interpolator.getInterpolatedDerivatives();
Assert.assertEquals(3.0 * t - 5.0, y[0], 1.0e-14);
Assert.assertEquals(3.0, yDot[0], 1.0e-14);
}
});
double[] y = {4.0};
double t0 = 3.0;
double tend = 10.0;
integ.integrate(new FirstOrderDifferentialEquations() {
public int getDimension() {
return 1;
}
public void computeDerivatives(double t, double[] y, double[] yDot) {
yDot[0] = 3.0;
}
}, t0, y, tend, y);
}
private static class KeplerStepHandler implements StepHandler {
public KeplerStepHandler(TestProblem3 pb) {
this.pb = pb;
}
public void init(double t0, double[] y0, double t) {
nbSteps = 0;
maxError = 0;
}
public void handleStep(StepInterpolator interpolator, boolean isLast) {
++nbSteps;
for (int a = 1; a < 100; ++a) {
double prev = interpolator.getPreviousTime();
double curr = interpolator.getCurrentTime();
double interp = ((100 - a) * prev + a * curr) / 100;
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 < 2.7e-6);
Assert.assertTrue(nbSteps < 80);
}
}
private int nbSteps;
private double maxError;
private TestProblem3 pb;
}
public static class VariableStepHandler implements StepHandler {
public VariableStepHandler() {
firstTime = true;
minStep = 0;
maxStep = 0;
}
public void init(double t0, double[] y0, double t) {
firstTime = true;
minStep = 0;
maxStep = 0;
}
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 < 8.2e-3);
Assert.assertTrue(maxStep > 1.5);
}
}
private boolean firstTime;
private double minStep;
private double maxStep;
}
}