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Java example source code file (RungeKuttaFieldStepInterpolatorAbstractTest.java)

This example Java source code file (RungeKuttaFieldStepInterpolatorAbstractTest.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

class, equationsmapper, field, fieldequationsmapper, fieldodestateandderivative, firstorderfielddifferentialequations, override, realfieldelement, rungekuttafieldstepinterpolator, rungekuttastepinterpolator, sincos, suppresswarnings, test

The RungeKuttaFieldStepInterpolatorAbstractTest.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
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 */

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


import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.AbstractIntegrator;
import org.apache.commons.math3.ode.EquationsMapper;
import org.apache.commons.math3.ode.ExpandableStatefulODE;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldExpandableODE;
import org.apache.commons.math3.ode.FirstOrderFieldDifferentialEquations;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.junit.Assert;
import org.junit.Test;

public abstract class RungeKuttaFieldStepInterpolatorAbstractTest {

    protected abstract <T extends RealFieldElement RungeKuttaFieldStepInterpolator
        createInterpolator(Field<T> field, boolean forward, T[][] yDotK,
                           FieldODEStateAndDerivative<T> globalPreviousState,
                           FieldODEStateAndDerivative<T> globalCurrentState,
                           FieldODEStateAndDerivative<T> softPreviousState,
                           FieldODEStateAndDerivative<T> softCurrentState,
                           FieldEquationsMapper<T> mapper);

    protected abstract <T extends RealFieldElement FieldButcherArrayProvider
        createButcherArrayProvider(final Field<T> field);

    @Test
    public abstract void interpolationAtBounds();

    protected <T extends RealFieldElement void doInterpolationAtBounds(final Field field, double epsilon) {

        RungeKuttaFieldStepInterpolator<T> interpolator = setUpInterpolator(field,
                                                                            new SinCos<T>(field),
                                                                            0.0, new double[] { 0.0, 1.0 }, 0.125);

        Assert.assertEquals(0.0, interpolator.getPreviousState().getTime().getReal(), 1.0e-15);
        for (int i = 0; i < 2; ++i) {
            Assert.assertEquals(interpolator.getPreviousState().getState()[i].getReal(),
                                interpolator.getInterpolatedState(interpolator.getPreviousState().getTime()).getState()[i].getReal(),
                                epsilon);
        }
        Assert.assertEquals(0.125, interpolator.getCurrentState().getTime().getReal(), 1.0e-15);
        for (int i = 0; i < 2; ++i) {
            Assert.assertEquals(interpolator.getCurrentState().getState()[i].getReal(),
                                interpolator.getInterpolatedState(interpolator.getCurrentState().getTime()).getState()[i].getReal(),
                                epsilon);
        }

    }

    @Test
    public abstract void interpolationInside();

    protected <T extends RealFieldElement void doInterpolationInside(final Field field,
                                                                         double epsilonSin, double epsilonCos) {

        RungeKuttaFieldStepInterpolator<T> interpolator = setUpInterpolator(field,
                                                                            new SinCos<T>(field),
                                                                            0.0, new double[] { 0.0, 1.0 }, 0.0125);

        int n = 100;
        double maxErrorSin = 0;
        double maxErrorCos = 0;
        for (int i = 0; i <= n; ++i) {
            T t =     interpolator.getPreviousState().getTime().multiply(n - i).
                  add(interpolator.getCurrentState().getTime().multiply(i)).
                  divide(n);
            FieldODEStateAndDerivative<T> state = interpolator.getInterpolatedState(t);
            maxErrorSin = FastMath.max(maxErrorSin, state.getState()[0].subtract(t.sin()).abs().getReal());
            maxErrorCos = FastMath.max(maxErrorCos, state.getState()[1].subtract(t.cos()).abs().getReal());
        }
        Assert.assertEquals(0.0, maxErrorSin, epsilonSin);
        Assert.assertEquals(0.0, maxErrorCos, epsilonCos);

    }

    @Test
    public abstract void nonFieldInterpolatorConsistency();

    protected <T extends RealFieldElement void doNonFieldInterpolatorConsistency(final Field field,
                                                                                     double epsilonSin, double epsilonCos,
                                                                                     double epsilonSinDot, double epsilonCosDot) {

        FirstOrderFieldDifferentialEquations<T> eqn = new SinCos(field);
        RungeKuttaFieldStepInterpolator<T> fieldInterpolator =
                        setUpInterpolator(field, eqn, 0.0, new double[] { 0.0, 1.0 }, 0.125);
        RungeKuttaStepInterpolator regularInterpolator = convertInterpolator(fieldInterpolator, eqn);

        int n = 100;
        double maxErrorSin    = 0;
        double maxErrorCos    = 0;
        double maxErrorSinDot = 0;
        double maxErrorCosDot = 0;
        for (int i = 0; i <= n; ++i) {

            T t =     fieldInterpolator.getPreviousState().getTime().multiply(n - i).
                  add(fieldInterpolator.getCurrentState().getTime().multiply(i)).
                  divide(n);

            FieldODEStateAndDerivative<T> state = fieldInterpolator.getInterpolatedState(t);
            T[] fieldY    = state.getState();
            T[] fieldYDot = state.getDerivative();

            regularInterpolator.setInterpolatedTime(t.getReal());
            double[] regularY     = regularInterpolator.getInterpolatedState();
            double[] regularYDot  = regularInterpolator.getInterpolatedDerivatives();

            maxErrorSin    = FastMath.max(maxErrorSin,    fieldY[0].subtract(regularY[0]).abs().getReal());
            maxErrorCos    = FastMath.max(maxErrorCos,    fieldY[1].subtract(regularY[1]).abs().getReal());
            maxErrorSinDot = FastMath.max(maxErrorSinDot, fieldYDot[0].subtract(regularYDot[0]).abs().getReal());
            maxErrorCosDot = FastMath.max(maxErrorCosDot, fieldYDot[1].subtract(regularYDot[1]).abs().getReal());

        }
        Assert.assertEquals(0.0, maxErrorSin,    epsilonSin);
        Assert.assertEquals(0.0, maxErrorCos,    epsilonCos);
        Assert.assertEquals(0.0, maxErrorSinDot, epsilonSinDot);
        Assert.assertEquals(0.0, maxErrorCosDot, epsilonCosDot);

    }

    private <T extends RealFieldElement
    RungeKuttaFieldStepInterpolator<T> setUpInterpolator(final Field field,
                                                         final FirstOrderFieldDifferentialEquations<T> eqn,
                                                         final double t0, final double[] y0,
                                                         final double t1) {

        // get the Butcher arrays from the field integrator
        FieldButcherArrayProvider<T> provider = createButcherArrayProvider(field);
        T[][] a = provider.getA();
        T[]   b = provider.getB();
        T[]   c = provider.getC();

        // store initial state
        T     t          = field.getZero().add(t0);
        T[]   fieldY     = MathArrays.buildArray(field, eqn.getDimension());
        T[][] fieldYDotK = MathArrays.buildArray(field, b.length, -1);
        for (int i = 0; i < y0.length; ++i) {
            fieldY[i] = field.getZero().add(y0[i]);
        }
        fieldYDotK[0] = eqn.computeDerivatives(t, fieldY);
        FieldODEStateAndDerivative<T> s0 = new FieldODEStateAndDerivative(t, fieldY, fieldYDotK[0]);

        // perform one integration step, in order to get consistent derivatives
        T h = field.getZero().add(t1 - t0);
        for (int k = 0; k < a.length; ++k) {
            for (int i = 0; i < y0.length; ++i) {
                fieldY[i] = field.getZero().add(y0[i]);
                for (int s = 0; s <= k; ++s) {
                    fieldY[i] = fieldY[i].add(h.multiply(a[k][s].multiply(fieldYDotK[s][i])));
                }
            }
            fieldYDotK[k + 1] = eqn.computeDerivatives(h.multiply(c[k]).add(t0), fieldY);
        }

        // store state at step end
        t = field.getZero().add(t1);
        for (int i = 0; i < y0.length; ++i) {
            fieldY[i] = field.getZero().add(y0[i]);
            for (int s = 0; s < b.length; ++s) {
                fieldY[i] = fieldY[i].add(h.multiply(b[s].multiply(fieldYDotK[s][i])));
            }
        }
        FieldODEStateAndDerivative<T> s1 = new FieldODEStateAndDerivative(t, fieldY,
                                                                             eqn.computeDerivatives(t, fieldY));

        return createInterpolator(field, t1 > t0, fieldYDotK, s0, s1, s0, s1,
                                  new FieldExpandableODE<T>(eqn).getMapper());

    }

    private <T extends RealFieldElement
    RungeKuttaStepInterpolator convertInterpolator(final RungeKuttaFieldStepInterpolator<T> fieldInterpolator,
                                                   final FirstOrderFieldDifferentialEquations<T> eqn) {

        RungeKuttaStepInterpolator regularInterpolator = null;
        try {

            String interpolatorName = fieldInterpolator.getClass().getName();
            String integratorName = interpolatorName.replaceAll("Field", "");
            @SuppressWarnings("unchecked")
            Class<RungeKuttaStepInterpolator> clz = (Class) Class.forName(integratorName);
            regularInterpolator = clz.newInstance();

            double[][] yDotArray = null;
            java.lang.reflect.Field fYD = RungeKuttaFieldStepInterpolator.class.getDeclaredField("yDotK");
            fYD.setAccessible(true);
            @SuppressWarnings("unchecked")
            T[][] fieldYDotk = (T[][]) fYD.get(fieldInterpolator);
            yDotArray = new double[fieldYDotk.length][];
            for (int i = 0; i < yDotArray.length; ++i) {
                yDotArray[i] = new double[fieldYDotk[i].length];
                for (int j = 0; j < yDotArray[i].length; ++j) {
                    yDotArray[i][j] = fieldYDotk[i][j].getReal();
                }
            }
            double[] y = new double[yDotArray[0].length];

            EquationsMapper primaryMapper = null;
            EquationsMapper[] secondaryMappers = null;
            java.lang.reflect.Field fMapper = AbstractFieldStepInterpolator.class.getDeclaredField("mapper");
            fMapper.setAccessible(true);
            @SuppressWarnings("unchecked")
            FieldEquationsMapper<T> mapper = (FieldEquationsMapper) fMapper.get(fieldInterpolator);
            java.lang.reflect.Field fStart = FieldEquationsMapper.class.getDeclaredField("start");
            fStart.setAccessible(true);
            int[] start = (int[]) fStart.get(mapper);
            primaryMapper = new EquationsMapper(start[0], start[1]);
            secondaryMappers = new EquationsMapper[mapper.getNumberOfEquations() - 1];
            for (int i = 0; i < secondaryMappers.length; ++i) {
                secondaryMappers[i] = new EquationsMapper(start[i + 1], start[i + 2]);
            }

            AbstractIntegrator dummyIntegrator = new AbstractIntegrator("dummy") {
                @Override
                public void integrate(ExpandableStatefulODE equations, double t) {
                    Assert.fail("this method should not be called");
                }
                @Override
                public void computeDerivatives(final double t, final double[] y, final double[] yDot) {
                    T fieldT = fieldInterpolator.getCurrentState().getTime().getField().getZero().add(t);
                    T[] fieldY = MathArrays.buildArray(fieldInterpolator.getCurrentState().getTime().getField(), y.length);
                    for (int i = 0; i < y.length; ++i) {
                        fieldY[i] = fieldInterpolator.getCurrentState().getTime().getField().getZero().add(y[i]);
                    }
                    T[] fieldYDot = eqn.computeDerivatives(fieldT, fieldY);
                    for (int i = 0; i < yDot.length; ++i) {
                        yDot[i] = fieldYDot[i].getReal();
                    }
                }
            };
            regularInterpolator.reinitialize(dummyIntegrator, y, yDotArray,
                                             fieldInterpolator.isForward(),
                                             primaryMapper, secondaryMappers);

            T[] fieldPreviousY = fieldInterpolator.getPreviousState().getState();
            for (int i = 0; i < y.length; ++i) {
                y[i] = fieldPreviousY[i].getReal();
            }
            regularInterpolator.storeTime(fieldInterpolator.getPreviousState().getTime().getReal());

            regularInterpolator.shift();

            T[] fieldCurrentY = fieldInterpolator.getCurrentState().getState();
            for (int i = 0; i < y.length; ++i) {
                y[i] = fieldCurrentY[i].getReal();
            }
            regularInterpolator.storeTime(fieldInterpolator.getCurrentState().getTime().getReal());

        } catch (ClassNotFoundException cnfe) {
            Assert.fail(cnfe.getLocalizedMessage());
        } catch (InstantiationException ie) {
            Assert.fail(ie.getLocalizedMessage());
        } catch (IllegalAccessException iae) {
            Assert.fail(iae.getLocalizedMessage());
        } catch (NoSuchFieldException nsfe) {
            Assert.fail(nsfe.getLocalizedMessage());
        } catch (IllegalArgumentException iae) {
            Assert.fail(iae.getLocalizedMessage());
        }

        return regularInterpolator;

    }

    private static class SinCos<T extends RealFieldElement implements FirstOrderFieldDifferentialEquations {
        private final Field<T> field;
        protected SinCos(final Field<T> field) {
            this.field = field;
        }
        public int getDimension() {
            return 2;
        }
        public void init(final T t0, final T[] y0, final T finalTime) {
        }
        public T[] computeDerivatives(final T t, final T[] y) {
            T[] yDot = MathArrays.buildArray(field, 2);
            yDot[0] = y[1];
            yDot[1] = y[0].negate();
            return yDot;
        }
    }

}

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