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Java example source code file (AdamsMoultonIntegratorTest.java)

This example Java source code file (AdamsMoultonIntegratorTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

adamsmoultonintegrator, dimensionmismatchexception, firstorderintegrator, maxcountexceededexception, nobracketingexception, numberistoosmallexception, perfectinterpolator, perfectstarter, stepinterpolator, testproblem1, testproblem5, testproblem6, testproblemabstract, testproblemhandler

The AdamsMoultonIntegratorTest.java Java example source code

/*
 * 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.
 */

package org.apache.commons.math3.ode.nonstiff;


import java.io.ObjectInput;
import java.io.ObjectOutput;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.AbstractIntegrator;
import org.apache.commons.math3.ode.ExpandableStatefulODE;
import org.apache.commons.math3.ode.FirstOrderIntegrator;
import org.apache.commons.math3.ode.TestProblem1;
import org.apache.commons.math3.ode.TestProblem5;
import org.apache.commons.math3.ode.TestProblem6;
import org.apache.commons.math3.ode.TestProblemAbstract;
import org.apache.commons.math3.ode.TestProblemHandler;
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 AdamsMoultonIntegratorTest {

    @Test(expected=DimensionMismatchException.class)
    public void dimensionCheck()
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        TestProblem1 pb = new TestProblem1();
        FirstOrderIntegrator integ =
            new AdamsMoultonIntegrator(2, 0.0, 1.0, 1.0e-10, 1.0e-10);
        integ.integrate(pb,
                        0.0, new double[pb.getDimension()+10],
                        1.0, new double[pb.getDimension()+10]);
    }

    @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 AdamsMoultonIntegrator(4, 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 testIncreasingTolerance()
            throws DimensionMismatchException, NumberIsTooSmallException,
            MaxCountExceededException, NoBracketingException {

        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 = FastMath.pow(10.0, i);
            double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

            FirstOrderIntegrator integ = new AdamsMoultonIntegrator(4, 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 0.45 and 8.69 factors are 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() > (0.45 * scalAbsoluteTolerance));
            Assert.assertTrue(handler.getMaximalValueError() < (8.69 * scalAbsoluteTolerance));
            Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-16);

            int calls = pb.getCalls();
            Assert.assertEquals(integ.getEvaluations(), calls);
            Assert.assertTrue(calls <= previousCalls);
            previousCalls = calls;

        }

    }

    @Test(expected = MaxCountExceededException.class)
    public void exceedMaxEvaluations()
            throws DimensionMismatchException, NumberIsTooSmallException,
            MaxCountExceededException, NoBracketingException {

        TestProblem1 pb  = new TestProblem1();
        double range = pb.getFinalTime() - pb.getInitialTime();

        AdamsMoultonIntegrator integ = new AdamsMoultonIntegrator(2, 0, range, 1.0e-12, 1.0e-12);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.setMaxEvaluations(650);
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);

    }

    @Test
    public void backward()
            throws DimensionMismatchException, NumberIsTooSmallException,
            MaxCountExceededException, NoBracketingException {

        TestProblem5 pb = new TestProblem5();
        double range = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());

        FirstOrderIntegrator integ = new AdamsMoultonIntegrator(4, 0, range, 1.0e-12, 1.0e-12);
        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() < 3.0e-9);
        Assert.assertTrue(handler.getMaximalValueError() < 3.0e-9);
        Assert.assertEquals(0, handler.getMaximalTimeError(), 1.0e-16);
        Assert.assertEquals("Adams-Moulton", integ.getName());
    }

    @Test
    public void polynomial()
            throws DimensionMismatchException, NumberIsTooSmallException,
            MaxCountExceededException, NoBracketingException {
        TestProblem6 pb = new TestProblem6();
        double range = FastMath.abs(pb.getFinalTime() - pb.getInitialTime());

        for (int nSteps = 2; nSteps < 8; ++nSteps) {
            AdamsMoultonIntegrator integ =
                new AdamsMoultonIntegrator(nSteps, 1.0e-6 * range, 0.1 * range, 1.0e-5, 1.0e-5);
            integ.setStarterIntegrator(new PerfectStarter(pb, nSteps));
            TestProblemHandler handler = new TestProblemHandler(pb, integ);
            integ.addStepHandler(handler);
            integ.integrate(pb, pb.getInitialTime(), pb.getInitialState(),
                            pb.getFinalTime(), new double[pb.getDimension()]);
            if (nSteps < 5) {
                Assert.assertTrue(handler.getMaximalValueError() > 2.2e-05);
            } else {
                Assert.assertTrue(handler.getMaximalValueError() < 1.1e-11);
            }
        }

    }

    private static class PerfectStarter extends AbstractIntegrator {

        private final PerfectInterpolator interpolator;
        private final int nbSteps;

        public PerfectStarter(final TestProblemAbstract problem, final int nbSteps) {
            this.interpolator = new PerfectInterpolator(problem);
            this.nbSteps      = nbSteps;
        }

        public void integrate(ExpandableStatefulODE equations, double t) {
            double tStart = equations.getTime() + 0.01 * (t - equations.getTime());
            getCounter().increment(nbSteps);
            for (int i = 0; i < nbSteps; ++i) {
                double tK = ((nbSteps - 1 - (i + 1)) * equations.getTime() + (i + 1) * tStart) / (nbSteps - 1);
                interpolator.setPreviousTime(interpolator.getCurrentTime());
                interpolator.setCurrentTime(tK);
                interpolator.setInterpolatedTime(tK);
                for (StepHandler handler : getStepHandlers()) {
                    handler.handleStep(interpolator, i == nbSteps - 1);
                }
            }
        }

    }

    private static class PerfectInterpolator implements StepInterpolator {
        private final TestProblemAbstract problem;
        private double previousTime;
        private double currentTime;
        private double interpolatedTime;

        public PerfectInterpolator(final TestProblemAbstract problem) {
            this.problem          = problem;
            this.previousTime     = problem.getInitialTime();
            this.currentTime      = problem.getInitialTime();
            this.interpolatedTime = problem.getInitialTime();
        }

        public void readExternal(ObjectInput arg0) {
        }

        public void writeExternal(ObjectOutput arg0) {
        }

        public double getPreviousTime() {
            return previousTime;
        }

        public void setPreviousTime(double time) {
            previousTime = time;
        }

        public double getCurrentTime() {
            return currentTime;
        }

        public void setCurrentTime(double time) {
            currentTime = time;
        }

        public double getInterpolatedTime() {
            return interpolatedTime;
        }

        public void setInterpolatedTime(double time) {
            interpolatedTime = time;
        }

        public double[] getInterpolatedState() {
            return problem.computeTheoreticalState(interpolatedTime);
        }

        public double[] getInterpolatedDerivatives() {
            double[] y = problem.computeTheoreticalState(interpolatedTime);
            double[] yDot = new double[y.length];
            problem.computeDerivatives(interpolatedTime, y, yDot);
            return yDot;
        }

        public double[] getInterpolatedSecondaryState(int index) {
            return null;
        }

        public double[] getInterpolatedSecondaryDerivatives(int index) {
            return null;
        }

        public boolean isForward() {
            return problem.getFinalTime() > problem.getInitialTime();
        }

        public StepInterpolator copy() {
            return this;
        }

    }

}

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