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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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
*
* 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
* limitations under the License.
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package org.apache.commons.math4.ode;
import java.util.Random;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.MathIllegalArgumentException;
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.ContinuousOutputModel;
import org.apache.commons.math4.ode.FirstOrderDifferentialEquations;
import org.apache.commons.math4.ode.FirstOrderIntegrator;
import org.apache.commons.math4.ode.nonstiff.DormandPrince54Integrator;
import org.apache.commons.math4.ode.nonstiff.DormandPrince853Integrator;
import org.apache.commons.math4.ode.sampling.DummyStepInterpolator;
import org.apache.commons.math4.ode.sampling.StepInterpolator;
import org.apache.commons.math4.util.FastMath;
import org.junit.After;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;
public class ContinuousOutputModelTest {
public ContinuousOutputModelTest() {
pb = null;
integ = null;
}
@Test
public void testBoundaries() throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException {
integ.addStepHandler(new ContinuousOutputModel());
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
ContinuousOutputModel cm = (ContinuousOutputModel) integ.getStepHandlers().iterator().next();
cm.setInterpolatedTime(2.0 * pb.getInitialTime() - pb.getFinalTime());
cm.setInterpolatedTime(2.0 * pb.getFinalTime() - pb.getInitialTime());
cm.setInterpolatedTime(0.5 * (pb.getFinalTime() + pb.getInitialTime()));
}
@Test
public void testRandomAccess() throws DimensionMismatchException, NumberIsTooSmallException, MaxCountExceededException, NoBracketingException {
ContinuousOutputModel cm = new ContinuousOutputModel();
integ.addStepHandler(cm);
integ.integrate(pb,
pb.getInitialTime(), pb.getInitialState(),
pb.getFinalTime(), new double[pb.getDimension()]);
Random random = new Random(347588535632l);
double maxError = 0.0;
double maxErrorDot = 0.0;
for (int i = 0; i < 1000; ++i) {
double r = random.nextDouble();
double time = r * pb.getInitialTime() + (1.0 - r) * pb.getFinalTime();
cm.setInterpolatedTime(time);
double[] interpolatedY = cm.getInterpolatedState();
double[] interpolatedYDot = cm.getInterpolatedDerivatives();
double[] theoreticalY = pb.computeTheoreticalState(time);
double[] theoreticalYDot = new double[pb.getDimension()];
pb.doComputeDerivatives(time, theoreticalY, theoreticalYDot);
double dx = interpolatedY[0] - theoreticalY[0];
double dy = interpolatedY[1] - theoreticalY[1];
double error = dx * dx + dy * dy;
maxError = FastMath.max(maxError, error);
double dxDot = interpolatedYDot[0] - theoreticalYDot[0];
double dyDot = interpolatedYDot[1] - theoreticalYDot[1];
double errorDot = dxDot * dxDot + dyDot * dyDot;
maxErrorDot = FastMath.max(maxErrorDot, errorDot);
}
Assert.assertEquals(0.0, maxError, 1.0e-9);
Assert.assertEquals(0.0, maxErrorDot, 4.0e-7);
}
@Test
public void testModelsMerging() throws MaxCountExceededException, MathIllegalArgumentException {
// theoretical solution: y[0] = cos(t), y[1] = sin(t)
FirstOrderDifferentialEquations problem =
new FirstOrderDifferentialEquations() {
@Override
public void computeDerivatives(double t, double[] y, double[] dot) {
dot[0] = -y[1];
dot[1] = y[0];
}
@Override
public int getDimension() {
return 2;
}
};
// integrate backward from π to 0;
ContinuousOutputModel cm1 = new ContinuousOutputModel();
FirstOrderIntegrator integ1 =
new DormandPrince853Integrator(0, 1.0, 1.0e-8, 1.0e-8);
integ1.addStepHandler(cm1);
integ1.integrate(problem, FastMath.PI, new double[] { -1.0, 0.0 },
0, new double[2]);
// integrate backward from 2π to π
ContinuousOutputModel cm2 = new ContinuousOutputModel();
FirstOrderIntegrator integ2 =
new DormandPrince853Integrator(0, 0.1, 1.0e-12, 1.0e-12);
integ2.addStepHandler(cm2);
integ2.integrate(problem, 2.0 * FastMath.PI, new double[] { 1.0, 0.0 },
FastMath.PI, new double[2]);
// merge the two half circles
ContinuousOutputModel cm = new ContinuousOutputModel();
cm.append(cm2);
cm.append(new ContinuousOutputModel());
cm.append(cm1);
// check circle
Assert.assertEquals(2.0 * FastMath.PI, cm.getInitialTime(), 1.0e-12);
Assert.assertEquals(0, cm.getFinalTime(), 1.0e-12);
Assert.assertEquals(cm.getFinalTime(), cm.getInterpolatedTime(), 1.0e-12);
for (double t = 0; t < 2.0 * FastMath.PI; t += 0.1) {
cm.setInterpolatedTime(t);
double[] y = cm.getInterpolatedState();
Assert.assertEquals(FastMath.cos(t), y[0], 1.0e-7);
Assert.assertEquals(FastMath.sin(t), y[1], 1.0e-7);
}
}
@Test
public void testErrorConditions() throws MaxCountExceededException, MathIllegalArgumentException {
ContinuousOutputModel cm = new ContinuousOutputModel();
cm.handleStep(buildInterpolator(0, new double[] { 0.0, 1.0, -2.0 }, 1), true);
// dimension mismatch
Assert.assertTrue(checkAppendError(cm, 1.0, new double[] { 0.0, 1.0 }, 2.0));
// hole between time ranges
Assert.assertTrue(checkAppendError(cm, 10.0, new double[] { 0.0, 1.0, -2.0 }, 20.0));
// propagation direction mismatch
Assert.assertTrue(checkAppendError(cm, 1.0, new double[] { 0.0, 1.0, -2.0 }, 0.0));
// no errors
Assert.assertFalse(checkAppendError(cm, 1.0, new double[] { 0.0, 1.0, -2.0 }, 2.0));
}
private boolean checkAppendError(ContinuousOutputModel cm,
double t0, double[] y0, double t1)
throws MaxCountExceededException, MathIllegalArgumentException {
try {
ContinuousOutputModel otherCm = new ContinuousOutputModel();
otherCm.handleStep(buildInterpolator(t0, y0, t1), true);
cm.append(otherCm);
} catch(MathIllegalArgumentException iae) {
return true; // there was an allowable error
}
return false; // no allowable error
}
private StepInterpolator buildInterpolator(double t0, double[] y0, double t1) {
DummyStepInterpolator interpolator = new DummyStepInterpolator(y0, new double[y0.length], t1 >= t0);
interpolator.storeTime(t0);
interpolator.shift();
interpolator.storeTime(t1);
return interpolator;
}
public void checkValue(double value, double reference) {
Assert.assertTrue(FastMath.abs(value - reference) < 1.0e-10);
}
@Before
public void setUp() {
pb = new TestProblem3(0.9);
double minStep = 0;
double maxStep = pb.getFinalTime() - pb.getInitialTime();
integ = new DormandPrince54Integrator(minStep, maxStep, 1.0e-8, 1.0e-8);
}
@After
public void tearDown() {
pb = null;
integ = null;
}
TestProblem3 pb;
FirstOrderIntegrator integ;
}