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Java example source code file (TestFieldProblem3.java)

This example Java source code file (TestFieldProblem3.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

override, realfieldelement, testfieldproblem3, testfieldproblemabstract

The TestFieldProblem3.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 org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.util.MathArrays;

/**
 * This class is used in the junit tests for the ODE integrators.

 * <p>This specific problem is the following differential equation :
 * <pre>
 *    y1'' = -y1/r^3  y1 (0) = 1-e  y1' (0) = 0
 *    y2'' = -y2/r^3  y2 (0) = 0    y2' (0) =sqrt((1+e)/(1-e))
 *    r = sqrt (y1^2 + y2^2), e = 0.9
 * </pre>
 * This is a two-body problem in the plane which can be solved by
 * Kepler's equation
 * <pre>
 *   y1 (t) = ...
 * </pre>
 * </p>

 * @param <T> the type of the field elements
 */
public class TestFieldProblem3<T extends RealFieldElement
extends TestFieldProblemAbstract<T> {

    /** Eccentricity */
    T e;

    /**
     * Simple constructor.
     * @param field field to which elements belong
     * @param e eccentricity
     */
    public TestFieldProblem3(Field<T> field, T e) {
        super(field);
        this.e = e;
        T[] y0 = MathArrays.buildArray(field, 4);
        y0[0] = e.subtract(1).negate();
        y0[1] = field.getZero();
        y0[2] = field.getZero();
        y0[3] = e.add(1).divide(y0[0]).sqrt();
        setInitialConditions(convert(0.0), y0);
        setFinalConditions(convert(20.0));
        setErrorScale(convert(1.0, 1.0, 1.0, 1.0));
    }

    /**
     * Simple constructor.
     * @param field field to which elements belong
     */
    public TestFieldProblem3(Field<T> field) {
        this(field, field.getZero().add(0.1));
    }

    @Override
    public T[] doComputeDerivatives(T t, T[] y) {

        final T[] yDot = MathArrays.buildArray(getField(), getDimension());

        // current radius
        T r2 = y[0].multiply(y[0]).add(y[1].multiply(y[1]));
        T invR3 = r2.multiply(r2.sqrt()).reciprocal();

        // compute the derivatives
        yDot[0] = y[2];
        yDot[1] = y[3];
        yDot[2] = invR3.negate().multiply(y[0]);
        yDot[3] = invR3.negate().multiply(y[1]);

        return yDot;

    }

    @Override
    public T[] computeTheoreticalState(T t) {

        final T[] y = MathArrays.buildArray(getField(), getDimension());

        // solve Kepler's equation
        T E = t;
        T d = convert(0);
        T corr = convert(999.0);
        for (int i = 0; (i < 50) && (corr.abs().getReal() > 1.0e-12); ++i) {
            T f2  = e.multiply(E.sin());
            T f0  = d.subtract(f2);
            T f1  = e.multiply(E.cos()).subtract(1).negate();
            T f12 = f1.add(f1);
            corr  = f0.multiply(f12).divide(f1.multiply(f12).subtract(f0.multiply(f2)));
            d = d.subtract(corr);
            E = t.add(d);
        }

        T cosE = E.cos();
        T sinE = E.sin();

        y[0] = cosE.subtract(e);
        y[1] = e.multiply(e).subtract(1).negate().sqrt().multiply(sinE);
        y[2] = sinE.divide(e.multiply(cosE).subtract(1));
        y[3] = e.multiply(e).subtract(1).negate().sqrt().multiply(cosE).divide(e.multiply(cosE).subtract(1).negate());

        return y;

    }

}

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