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Java example source code file (ContinuousOutputFieldModelTest.java)

This example Java source code file (ContinuousOutputFieldModelTest.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

continuousoutputfieldmodel, dormandprince54fieldintegrator, dormandprince853fieldintegrator, dummyfieldstepinterpolator, fieldequationsmapper, fieldexpandableode, fieldodestateandderivative, fieldstepinterpolator, firstorderfielddifferentialequations, firstorderfieldintegrator, random, realfieldelement, testfieldproblem3, util

The ContinuousOutputFieldModelTest.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;

import java.util.Random;

import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.nonstiff.DormandPrince54FieldIntegrator;
import org.apache.commons.math3.ode.nonstiff.DormandPrince853FieldIntegrator;
import org.apache.commons.math3.ode.sampling.DummyFieldStepInterpolator;
import org.apache.commons.math3.ode.sampling.FieldStepInterpolator;
import org.apache.commons.math3.util.Decimal64Field;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;
import org.junit.Assert;
import org.junit.Test;

public class ContinuousOutputFieldModelTest {

    @Test
    public void testBoundaries() {
        doTestBoundaries(Decimal64Field.getInstance());
    }

    private <T extends RealFieldElement void doTestBoundaries(final Field field) {
        TestFieldProblem3<T> pb = new TestFieldProblem3(field, field.getZero().add(0.9));
        double minStep = 0;
        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
        FirstOrderFieldIntegrator<T> integ = new DormandPrince54FieldIntegrator(field, minStep, maxStep, 1.0e-8, 1.0e-8);
        integ.addStepHandler(new ContinuousOutputFieldModel<T>());
        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());
        ContinuousOutputFieldModel<T> cm = (ContinuousOutputFieldModel) integ.getStepHandlers().iterator().next();
        cm.getInterpolatedState(pb.getInitialState().getTime().multiply(2).subtract(pb.getFinalTime()));
        cm.getInterpolatedState(pb.getFinalTime().multiply(2).subtract(pb.getInitialState().getTime()));
        cm.getInterpolatedState(pb.getInitialState().getTime().add(pb.getFinalTime()).multiply(0.5));
    }

    @Test
    public void testRandomAccess() {
        doTestRandomAccess(Decimal64Field.getInstance());
    }

    private <T extends RealFieldElement void doTestRandomAccess(final Field field)  {

        TestFieldProblem3<T> pb = new TestFieldProblem3(field, field.getZero().add(0.9));
        double minStep = 0;
        double maxStep = pb.getFinalTime().subtract(pb.getInitialState().getTime()).getReal();
        FirstOrderFieldIntegrator<T> integ = new DormandPrince54FieldIntegrator(field, minStep, maxStep, 1.0e-8, 1.0e-8);
        ContinuousOutputFieldModel<T> cm = new ContinuousOutputFieldModel();
        integ.addStepHandler(cm);
        integ.integrate(new FieldExpandableODE<T>(pb), pb.getInitialState(), pb.getFinalTime());

        Random random = new Random(347588535632l);
        T maxError    = field.getZero();
        T maxErrorDot = field.getZero();
        for (int i = 0; i < 1000; ++i) {
            double r = random.nextDouble();
            T time = pb.getInitialState().getTime().multiply(r).add(pb.getFinalTime().multiply(1.0 - r));
            FieldODEStateAndDerivative<T> interpolated = cm.getInterpolatedState(time);
            T[] theoreticalY = pb.computeTheoreticalState(time);
            T[] theoreticalYDot  = pb.doComputeDerivatives(time, theoreticalY);
            T dx = interpolated.getState()[0].subtract(theoreticalY[0]);
            T dy = interpolated.getState()[1].subtract(theoreticalY[1]);
            T error = dx.multiply(dx).add(dy.multiply(dy));
            maxError = MathUtils.max(maxError, error);
            T dxDot = interpolated.getDerivative()[0].subtract(theoreticalYDot[0]);
            T dyDot = interpolated.getDerivative()[1].subtract(theoreticalYDot[1]);
            T errorDot = dxDot.multiply(dxDot).add(dyDot.multiply(dyDot));
            maxErrorDot = MathUtils.max(maxErrorDot, errorDot);
        }

        Assert.assertEquals(0.0, maxError.getReal(),    1.0e-9);
        Assert.assertEquals(0.0, maxErrorDot.getReal(), 4.0e-7);

    }

    @Test
    public void testModelsMerging() {
        doTestModelsMerging(Decimal64Field.getInstance());
    }

    private <T extends RealFieldElement void doTestModelsMerging(final Field field) {

        // theoretical solution: y[0] = cos(t), y[1] = sin(t)
        FirstOrderFieldDifferentialEquations<T> problem =
                        new FirstOrderFieldDifferentialEquations<T>() {
            public T[] computeDerivatives(T t, T[] y) {
                T[] yDot = MathArrays.buildArray(field, 2);
                yDot[0] = y[1].negate();
                yDot[1] = y[0];
                return yDot;
            }
            public int getDimension() {
                return 2;
            }
            public void init(T t0, T[] y0, T finalTime) {
            }
        };

        // integrate backward from π to 0;
        ContinuousOutputFieldModel<T> cm1 = new ContinuousOutputFieldModel();
        FirstOrderFieldIntegrator<T> integ1 =
                        new DormandPrince853FieldIntegrator<T>(field, 0, 1.0, 1.0e-8, 1.0e-8);
        integ1.addStepHandler(cm1);
        T t0 = field.getZero().add(FastMath.PI);
        T[] y0 = MathArrays.buildArray(field, 2);
        y0[0] = field.getOne().negate();
        y0[1] = field.getZero();
        integ1.integrate(new FieldExpandableODE<T>(problem),
                         new FieldODEState<T>(t0, y0),
                         field.getZero());

        // integrate backward from 2π to π
        ContinuousOutputFieldModel<T> cm2 = new ContinuousOutputFieldModel();
        FirstOrderFieldIntegrator<T> integ2 =
                        new DormandPrince853FieldIntegrator<T>(field, 0, 0.1, 1.0e-12, 1.0e-12);
        integ2.addStepHandler(cm2);
        t0 = field.getZero().add(2.0 * FastMath.PI);
        y0[0] = field.getOne();
        y0[1] = field.getZero();
        integ2.integrate(new FieldExpandableODE<T>(problem),
                         new FieldODEState<T>(t0, y0),
                         field.getZero().add(FastMath.PI));

        // merge the two half circles
        ContinuousOutputFieldModel<T> cm = new ContinuousOutputFieldModel();
        cm.append(cm2);
        cm.append(new ContinuousOutputFieldModel<T>());
        cm.append(cm1);

        // check circle
        Assert.assertEquals(2.0 * FastMath.PI, cm.getInitialTime().getReal(), 1.0e-12);
        Assert.assertEquals(0, cm.getFinalTime().getReal(), 1.0e-12);
        for (double t = 0; t < 2.0 * FastMath.PI; t += 0.1) {
            FieldODEStateAndDerivative<T> interpolated = cm.getInterpolatedState(field.getZero().add(t));
            Assert.assertEquals(FastMath.cos(t), interpolated.getState()[0].getReal(), 1.0e-7);
            Assert.assertEquals(FastMath.sin(t), interpolated.getState()[1].getReal(), 1.0e-7);
        }

    }

    @Test
    public void testErrorConditions() {
        doTestErrorConditions(Decimal64Field.getInstance());
    }

    private <T extends RealFieldElement void doTestErrorConditions(final Field field) {
        ContinuousOutputFieldModel<T> cm = new ContinuousOutputFieldModel();
        cm.handleStep(buildInterpolator(field, 0, 1, new double[] { 0.0, 1.0, -2.0 }), true);

        // dimension mismatch
        Assert.assertTrue(checkAppendError(field, cm, 1.0, 2.0, new double[] { 0.0, 1.0 }));

        // hole between time ranges
        Assert.assertTrue(checkAppendError(field, cm, 10.0, 20.0, new double[] { 0.0, 1.0, -2.0 }));

        // propagation direction mismatch
        Assert.assertTrue(checkAppendError(field, cm, 1.0, 0.0, new double[] { 0.0, 1.0, -2.0 }));

        // no errors
        Assert.assertFalse(checkAppendError(field, cm, 1.0, 2.0, new double[] { 0.0, 1.0, -2.0 }));

    }

    private <T extends RealFieldElement boolean checkAppendError(Field field, ContinuousOutputFieldModel cm,
                                                                     double t0, double t1, double[] y) {
        try {
            ContinuousOutputFieldModel<T> otherCm = new ContinuousOutputFieldModel();
            otherCm.handleStep(buildInterpolator(field, t0, t1, y), true);
            cm.append(otherCm);
        } catch(IllegalArgumentException iae) {
            return true; // there was an allowable error
        }
        return false; // no allowable error
    }

    private <T extends RealFieldElement FieldStepInterpolator buildInterpolator(Field field,
                                                                                       double t0, double t1, double[] y) {
        T[] fieldY = MathArrays.buildArray(field, y.length);
        for (int i = 0; i < y.length; ++i) {
            fieldY[i] = field.getZero().add(y[i]);
        }
        final FieldODEStateAndDerivative<T> s0 = new FieldODEStateAndDerivative(field.getZero().add(t0), fieldY, fieldY);
        final FieldODEStateAndDerivative<T> s1 = new FieldODEStateAndDerivative(field.getZero().add(t1), fieldY, fieldY);
        final FieldEquationsMapper<T> mapper   = new FieldExpandableODE(new FirstOrderFieldDifferentialEquations() {
            public int getDimension() {
                return s0.getStateDimension();
            }
            public void init(T t0, T[] y0, T finalTime) {
            }
            public T[] computeDerivatives(T t, T[] y) {
                return y;
            }
        }).getMapper();
        return new DummyFieldStepInterpolator<T>(t1 >= t0, s0, s1, s0, s1, mapper);
    }

    public void checkValue(double value, double reference) {
        Assert.assertTrue(FastMath.abs(value - reference) < 1.0e-10);
    }

}

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