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Java example source code file (HighamHall54FieldIntegrator.java)

This example Java source code file (HighamHall54FieldIntegrator.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

embeddedrungekuttafieldintegrator, fieldequationsmapper, fieldodestateandderivative, higham-hall, highamhall54fieldintegrator, highamhall54fieldstepinterpolator, method_name, override, realfieldelement, string

The HighamHall54FieldIntegrator.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.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;


/**
 * This class implements the 5(4) Higham and Hall integrator for
 * Ordinary Differential Equations.
 *
 * <p>This integrator is an embedded Runge-Kutta integrator
 * of order 5(4) used in local extrapolation mode (i.e. the solution
 * is computed using the high order formula) with stepsize control
 * (and automatic step initialization) and continuous output. This
 * method uses 7 functions evaluations per step.</p>
 *
 * @param <T> the type of the field elements
 * @since 3.6
 */

public class HighamHall54FieldIntegrator<T extends RealFieldElement
    extends EmbeddedRungeKuttaFieldIntegrator<T> {

    /** Integrator method name. */
    private static final String METHOD_NAME = "Higham-Hall 5(4)";

    /** Error weights Butcher array. */
    private final T[] e ;

    /** Simple constructor.
     * Build a fifth order Higham and Hall integrator with the given step bounds
     * @param field field to which the time and state vector elements belong
     * @param minStep minimal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param maxStep maximal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param scalAbsoluteTolerance allowed absolute error
     * @param scalRelativeTolerance allowed relative error
     */
    public HighamHall54FieldIntegrator(final Field<T> field,
                                       final double minStep, final double maxStep,
                                       final double scalAbsoluteTolerance,
                                       final double scalRelativeTolerance) {
        super(field, METHOD_NAME, -1,
              minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
        e = MathArrays.buildArray(field, 7);
        e[0] = fraction(-1,  20);
        e[1] = field.getZero();
        e[2] = fraction(81, 160);
        e[3] = fraction(-6,   5);
        e[4] = fraction(25,  32);
        e[5] = fraction( 1,  16);
        e[6] = fraction(-1,  10);
    }

    /** Simple constructor.
     * Build a fifth order Higham and Hall integrator with the given step bounds
     * @param field field to which the time and state vector elements belong
     * @param minStep minimal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param maxStep maximal step (sign is irrelevant, regardless of
     * integration direction, forward or backward), the last step can
     * be smaller than this
     * @param vecAbsoluteTolerance allowed absolute error
     * @param vecRelativeTolerance allowed relative error
     */
    public HighamHall54FieldIntegrator(final Field<T> field,
                                       final double minStep, final double maxStep,
                                       final double[] vecAbsoluteTolerance,
                                       final double[] vecRelativeTolerance) {
        super(field, METHOD_NAME, -1,
              minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
        e = MathArrays.buildArray(field, 7);
        e[0] = fraction(-1,  20);
        e[1] = field.getZero();
        e[2] = fraction(81, 160);
        e[3] = fraction(-6,   5);
        e[4] = fraction(25,  32);
        e[5] = fraction( 1,  16);
        e[6] = fraction(-1,  10);
    }

    /** {@inheritDoc} */
    public T[] getC() {
        final T[] c = MathArrays.buildArray(getField(), 6);
        c[0] = fraction(2, 9);
        c[1] = fraction(1, 3);
        c[2] = fraction(1, 2);
        c[3] = fraction(3, 5);
        c[4] = getField().getOne();
        c[5] = getField().getOne();
        return c;
    }

    /** {@inheritDoc} */
    public T[][] getA() {
        final T[][] a = MathArrays.buildArray(getField(), 6, -1);
        for (int i = 0; i < a.length; ++i) {
            a[i] = MathArrays.buildArray(getField(), i + 1);
        }
        a[0][0] = fraction(     2,     9);
        a[1][0] = fraction(     1,    12);
        a[1][1] = fraction(     1,     4);
        a[2][0] = fraction(     1,     8);
        a[2][1] = getField().getZero();
        a[2][2] = fraction(     3,     8);
        a[3][0] = fraction(    91,   500);
        a[3][1] = fraction(   -27,   100);
        a[3][2] = fraction(    78,   125);
        a[3][3] = fraction(     8,   125);
        a[4][0] = fraction(   -11,    20);
        a[4][1] = fraction(    27,    20);
        a[4][2] = fraction(    12,     5);
        a[4][3] = fraction(   -36,     5);
        a[4][4] = fraction(     5,     1);
        a[5][0] = fraction(     1,    12);
        a[5][1] = getField().getZero();
        a[5][2] = fraction(    27,    32);
        a[5][3] = fraction(    -4,     3);
        a[5][4] = fraction(   125,    96);
        a[5][5] = fraction(     5,    48);
        return a;
    }

    /** {@inheritDoc} */
    public T[] getB() {
        final T[] b = MathArrays.buildArray(getField(), 7);
        b[0] = fraction(  1, 12);
        b[1] = getField().getZero();
        b[2] = fraction( 27, 32);
        b[3] = fraction( -4,  3);
        b[4] = fraction(125, 96);
        b[5] = fraction(  5, 48);
        b[6] = getField().getZero();
        return b;
    }

    /** {@inheritDoc} */
    @Override
    protected HighamHall54FieldStepInterpolator<T>
        createInterpolator(final boolean forward, T[][] yDotK,
                           final FieldODEStateAndDerivative<T> globalPreviousState,
                           final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper mapper) {
        return new HighamHall54FieldStepInterpolator<T>(getField(), forward, yDotK,
                                                        globalPreviousState, globalCurrentState,
                                                        globalPreviousState, globalCurrentState,
                                                        mapper);
    }

    /** {@inheritDoc} */
    @Override
    public int getOrder() {
        return 5;
    }

    /** {@inheritDoc} */
    @Override
    protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {

        T error = getField().getZero();

        for (int j = 0; j < mainSetDimension; ++j) {
            T errSum = yDotK[0][j].multiply(e[0]);
            for (int l = 1; l < e.length; ++l) {
                errSum = errSum.add(yDotK[l][j].multiply(e[l]));
            }

            final T yScale = MathUtils.max(y0[j].abs(), y1[j].abs());
            final T tol    = (vecAbsoluteTolerance == null) ?
                             yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) :
                             yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]);
            final T ratio  = h.multiply(errSum).divide(tol);
            error = error.add(ratio.multiply(ratio));

        }

        return error.divide(mainSetDimension).sqrt();

    }

}

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