DormandPrince54Integrator.java

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 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The Hipparchus project 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
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 * 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.hipparchus.ode.nonstiff;

import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.util.FastMath;


/**
 * This class implements the 5(4) Dormand-Prince 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. However, since this
 * is an <i>fsal</i>, the last evaluation of one step is the same as
 * the first evaluation of the next step and hence can be avoided. So
 * the cost is really 6 functions evaluations per step.</p>
 *
 * <p>This method has been published (whithout the continuous output
 * that was added by Shampine in 1986) in the following article :
 * <pre>
 *  A family of embedded Runge-Kutta formulae
 *  J. R. Dormand and P. J. Prince
 *  Journal of Computational and Applied Mathematics
 *  volume 6, no 1, 1980, pp. 19-26
 * </pre></p>
 *
 */

public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {

    /** Integrator method name. */
    static final String METHOD_NAME = "Dormand-Prince 5(4)";

    /** Error array, element 1. */
    static final double E1 =     71.0 / 57600.0;

    // element 2 is zero, so it is neither stored nor used

    /** Error array, element 3. */
    static final double E3 =    -71.0 / 16695.0;

    /** Error array, element 4. */
    static final double E4 =     71.0 / 1920.0;

    /** Error array, element 5. */
    static final double E5 = -17253.0 / 339200.0;

    /** Error array, element 6. */
    static final double E6 =     22.0 / 525.0;

    /** Error array, element 7. */
    static final double E7 =     -1.0 / 40.0;

    /** Simple constructor.
     * Build a fifth order Dormand-Prince integrator with the given step bounds
     * @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 DormandPrince54Integrator(final double minStep, final double maxStep,
                                     final double scalAbsoluteTolerance,
                                     final double scalRelativeTolerance) {
        super(METHOD_NAME, 6,
              minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
    }

    /** Simple constructor.
     * Build a fifth order Dormand-Prince integrator with the given step bounds
     * @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 DormandPrince54Integrator(final double minStep, final double maxStep,
                                     final double[] vecAbsoluteTolerance,
                                     final double[] vecRelativeTolerance) {
        super(METHOD_NAME, 6,
              minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
    }

    /** {@inheritDoc} */
    @Override
    public double[] getC() {
        return new double[] {
            1.0 / 5.0, 3.0 / 10.0, 4.0 / 5.0, 8.0 / 9.0, 1.0, 1.0
        };
    }

    /** {@inheritDoc} */
    @Override
    public double[][] getA() {
        return new double[][] {
            { 1.0 / 5.0 },
            { 3.0 / 40.0, 9.0 / 40.0 },
            { 44.0 / 45.0, -56.0 / 15.0, 32.0 / 9.0 },
            { 19372.0 / 6561.0, -25360.0 / 2187.0, 64448.0 / 6561.0,  -212.0 / 729.0 },
            { 9017.0 / 3168.0, -355.0 / 33.0, 46732.0 / 5247.0, 49.0 / 176.0, -5103.0 / 18656.0 },
            { 35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0, 11.0 / 84.0 }
        };
    }

    /** {@inheritDoc} */
    @Override
    public double[] getB() {
        return new double[] {
            35.0 / 384.0, 0.0, 500.0 / 1113.0, 125.0 / 192.0, -2187.0 / 6784.0, 11.0 / 84.0, 0.0
        };
    }

    /** {@inheritDoc} */
    @Override
    protected DormandPrince54StateInterpolator
    createInterpolator(final boolean forward, double[][] yDotK,
                       final ODEStateAndDerivative globalPreviousState,
                       final ODEStateAndDerivative globalCurrentState,
                       final EquationsMapper mapper) {
        return new DormandPrince54StateInterpolator(forward, yDotK,
                                                   globalPreviousState, globalCurrentState,
                                                   globalPreviousState, globalCurrentState,
                                                   mapper);
    }

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

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

        final StepsizeHelper helper = getStepSizeHelper();
        double error = 0;

        for (int j = 0; j < helper.getMainSetDimension(); ++j) {
            final double errSum = E1 * yDotK[0][j] +  E3 * yDotK[2][j] +
                                  E4 * yDotK[3][j] +  E5 * yDotK[4][j] +
                                  E6 * yDotK[5][j] +  E7 * yDotK[6][j];

            final double tol = helper.getTolerance(j, FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j])));
            final double ratio  = h * errSum / tol;
            error += ratio * ratio;

        }

        return FastMath.sqrt(error / helper.getMainSetDimension());

    }

}