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Java example source code file (AdamsFieldIntegratorAbstractTest.java)

This example Java source code file (AdamsFieldIntegratorAbstractTest.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.

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Java - Java tags/keywords

adamsfieldintegrator, dormandprince853fieldintegrator, fieldexpandableode, fieldodestateandderivative, firstorderfieldintegrator, perfectinterpolator, perfectstarter, realfieldelement, testfieldproblem1, testfieldproblem5, testfieldproblem6, testfieldproblemabstract, testfieldproblemhandler

The AdamsFieldIntegratorAbstractTest.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 org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.ode.AbstractFieldIntegrator;
import org.apache.commons.math3.ode.FieldExpandableODE;
import org.apache.commons.math3.ode.FieldODEState;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.ode.FirstOrderFieldIntegrator;
import org.apache.commons.math3.ode.MultistepFieldIntegrator;
import org.apache.commons.math3.ode.TestFieldProblem1;
import org.apache.commons.math3.ode.TestFieldProblem5;
import org.apache.commons.math3.ode.TestFieldProblem6;
import org.apache.commons.math3.ode.TestFieldProblemAbstract;
import org.apache.commons.math3.ode.TestFieldProblemHandler;
import org.apache.commons.math3.ode.sampling.FieldStepHandler;
import org.apache.commons.math3.ode.sampling.FieldStepInterpolator;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public abstract class AdamsFieldIntegratorAbstractTest {

    protected abstract <T extends RealFieldElement AdamsFieldIntegrator
    createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,
                     final double scalAbsoluteTolerance, final double scalRelativeTolerance);

    protected abstract <T extends RealFieldElement AdamsFieldIntegrator
    createIntegrator(Field<T> field, final int nSteps, final double minStep, final double maxStep,
                     final double[] vecAbsoluteTolerance, final double[] vecRelativeTolerance);

    @Test(expected=NumberIsTooSmallException.class)
    public abstract void testMinStep();

    protected <T extends RealFieldElement void doDimensionCheck(final Field field) {
        TestFieldProblem1<T> pb = new TestFieldProblem1(field);

        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.1).getReal();
        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
        double[] vecAbsoluteTolerance = { 1.0e-15, 1.0e-16 };
        double[] vecRelativeTolerance = { 1.0e-15, 1.0e-16 };

        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 4, minStep, maxStep,
                                                              vecAbsoluteTolerance,
                                                              vecRelativeTolerance);
        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());

    }

    @Test
    public abstract void testIncreasingTolerance();

    protected <T extends RealFieldElement void doTestIncreasingTolerance(final Field field,
                                                                             double ratioMin, double ratioMax) {

        int previousCalls = Integer.MAX_VALUE;
        for (int i = -12; i < -2; ++i) {
            TestFieldProblem1<T> pb = new TestFieldProblem1(field);
            double minStep = 0;
            double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
            double scalAbsoluteTolerance = FastMath.pow(10.0, i);
            double scalRelativeTolerance = 0.01 * scalAbsoluteTolerance;

            FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 4, minStep, maxStep,
                                                                  scalAbsoluteTolerance,
                                                                  scalRelativeTolerance);
            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler(pb, integ);
            integ.addStepHandler(handler);
            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());

            Assert.assertTrue(handler.getMaximalValueError().getReal() > ratioMin * scalAbsoluteTolerance);
            Assert.assertTrue(handler.getMaximalValueError().getReal() < ratioMax * scalAbsoluteTolerance);

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

        }

    }

    @Test(expected = MaxCountExceededException.class)
    public abstract void exceedMaxEvaluations();

    protected <T extends RealFieldElement void doExceedMaxEvaluations(final Field field, final int max) {

        TestFieldProblem1<T> pb  = new TestFieldProblem1(field);
        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();

        FirstOrderFieldIntegrator<T> integ = createIntegrator(field, 2, 0, range, 1.0e-12, 1.0e-12);
        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.setMaxEvaluations(max);
        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());

    }

    @Test
    public abstract void backward();

    protected <T extends RealFieldElement void doBackward(final Field field,
                                                              final double epsilonLast,
                                                              final double epsilonMaxValue,
                                                              final double epsilonMaxTime,
                                                              final String name) {

        TestFieldProblem5<T> pb = new TestFieldProblem5(field);
        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();

        AdamsFieldIntegrator<T> integ = createIntegrator(field, 4, 0, range, 1.0e-12, 1.0e-12);
        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());

        Assert.assertEquals(0.0, handler.getLastError().getReal(), epsilonLast);
        Assert.assertEquals(0.0, handler.getMaximalValueError().getReal(), epsilonMaxValue);
        Assert.assertEquals(0, handler.getMaximalTimeError().getReal(), epsilonMaxTime);
        Assert.assertEquals(name, integ.getName());
    }

    @Test
    public abstract void polynomial();

    protected <T extends RealFieldElement void doPolynomial(final Field field,
                                                                final int nLimit,
                                                                final double epsilonBad,
                                                                final double epsilonGood) {
        TestFieldProblem6<T> pb = new TestFieldProblem6(field);
        double range = pb.getFinalTime().subtract(pb.getInitialState().getTime()).abs().getReal();

        for (int nSteps = 2; nSteps < 8; ++nSteps) {
            AdamsFieldIntegrator<T> integ = createIntegrator(field, nSteps, 1.0e-6 * range, 0.1 * range, 1.0e-4, 1.0e-4);
            integ.setStarterIntegrator(new PerfectStarter<T>(pb, nSteps));
            TestFieldProblemHandler<T> handler = new TestFieldProblemHandler(pb, integ);
            integ.addStepHandler(handler);
            integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
            if (nSteps < nLimit) {
                Assert.assertTrue(handler.getMaximalValueError().getReal() > epsilonBad);
            } else {
                Assert.assertTrue(handler.getMaximalValueError().getReal() < epsilonGood);
            }
        }

    }

    @Test(expected=MathIllegalStateException.class)
    public abstract void testStartFailure();

    protected <T extends RealFieldElement void doTestStartFailure(final Field field) {
        TestFieldProblem1<T> pb = new TestFieldProblem1(field);
        double minStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).multiply(0.0001).getReal();
        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
        double scalAbsoluteTolerance = 1.0e-6;
        double scalRelativeTolerance = 1.0e-7;

        MultistepFieldIntegrator<T> integ = createIntegrator(field, 6, minStep, maxStep,
                                                             scalAbsoluteTolerance,
                                                             scalRelativeTolerance);
        integ.setStarterIntegrator(new DormandPrince853FieldIntegrator<T>(field, maxStep * 0.5, maxStep, 0.1, 0.1));
        TestFieldProblemHandler<T> handler = new TestFieldProblemHandler(pb, integ);
        integ.addStepHandler(handler);
        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());

    }

    private static class PerfectStarter<T extends RealFieldElement extends AbstractFieldIntegrator {

        private final PerfectInterpolator<T> interpolator;
        private final int nbSteps;

        public PerfectStarter(final TestFieldProblemAbstract<T> problem, final int nbSteps) {
            super(problem.getField(), "perfect-starter");
            this.interpolator = new PerfectInterpolator<T>(problem);
            this.nbSteps      = nbSteps;
        }

        public FieldODEStateAndDerivative<T> integrate(FieldExpandableODE equations,
                                                       FieldODEState<T> initialState, T finalTime) {
            T tStart = initialState.getTime().add(finalTime.subtract(initialState.getTime()).multiply(0.01));
            getEvaluationsCounter().increment(nbSteps);
            interpolator.setCurrentTime(initialState.getTime());
            for (int i = 0; i < nbSteps; ++i) {
                T tK = initialState.getTime().multiply(nbSteps - 1 - (i + 1)).add(tStart.multiply(i + 1)).divide(nbSteps - 1);
                interpolator.setPreviousTime(interpolator.getCurrentTime());
                interpolator.setCurrentTime(tK);
                for (FieldStepHandler<T> handler : getStepHandlers()) {
                    handler.handleStep(interpolator, i == nbSteps - 1);
                }
            }
            return interpolator.getInterpolatedState(tStart);
        }

    }

    private static class PerfectInterpolator<T extends RealFieldElement implements FieldStepInterpolator {
        private final TestFieldProblemAbstract<T> problem;
        private T previousTime;
        private T currentTime;

        public PerfectInterpolator(final TestFieldProblemAbstract<T> problem) {
            this.problem = problem;
        }

        public void setPreviousTime(T previousTime) {
            this.previousTime = previousTime;
        }

        public void setCurrentTime(T currentTime) {
            this.currentTime = currentTime;
        }

        public T getCurrentTime() {
            return currentTime;
        }

        public boolean isForward() {
            return problem.getFinalTime().subtract(problem.getInitialState().getTime()).getReal() >= 0;
        }

        public FieldODEStateAndDerivative<T> getPreviousState() {
            return getInterpolatedState(previousTime);
        }

        public FieldODEStateAndDerivative<T> getCurrentState() {
            return getInterpolatedState(currentTime);
        }

        public FieldODEStateAndDerivative<T> getInterpolatedState(T time) {
            T[] y    = problem.computeTheoreticalState(time);
            T[] yDot = problem.computeDerivatives(time, y);
            return new FieldODEStateAndDerivative<T>(time, y, yDot);
        }

    }

}

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