GillStateInterpolator.java

/*
 * Licensed to the Hipparchus project under one or more
 * 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
 *
 *      https://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.hipparchus.ode.nonstiff.interpolators;

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

/**
 * This class implements a step interpolator for the Gill fourth
 * order Runge-Kutta integrator.
 *
 * <p>This interpolator allows to compute dense output inside the last
 * step computed. The interpolation equation is consistent with the
 * integration scheme :</p>
 * <ul>
 *   <li>Using reference point at step start:<br>
 *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub>)
 *                    + &theta; (h/6) [ (6 - 9 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
 *                                    + (    6 &theta; - 4 &theta;<sup>2</sup>) ((1-1/&radic;2) y'<sub>2</sub> + (1+1/&radic;2)) y'<sub>3</sub>)
 *                                    + (  - 3 &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
 *                                    ]
 *   </li>
 *   <li>Using reference point at step start:<br>
 *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub> + h)
 *                    - (1 - &theta;) (h/6) [ (1 - 5 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
 *                                          + (2 + 2 &theta; - 4 &theta;<sup>2</sup>) ((1-1/&radic;2) y'<sub>2</sub> + (1+1/&radic;2)) y'<sub>3</sub>)
 *                                          + (1 +   &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
 *                                          ]
 *   </li>
 * </ul>
 * <p>where &theta; belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
 * are the four evaluations of the derivatives already computed during
 * the step.</p>
 *
 * @see GillIntegrator
 */

public class GillStateInterpolator extends RungeKuttaStateInterpolator {

    /** First Gill coefficient. */
    private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5);

    /** Second Gill coefficient. */
    private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5);

    /** Serializable version identifier. */
    private static final long serialVersionUID = 20160328L;

    /** Simple constructor.
     * @param forward integration direction indicator
     * @param yDotK slopes at the intermediate points
     * @param globalPreviousState start of the global step
     * @param globalCurrentState end of the global step
     * @param softPreviousState start of the restricted step
     * @param softCurrentState end of the restricted step
     * @param mapper equations mapper for the all equations
     */
    public GillStateInterpolator(final boolean forward,
                                 final double[][] yDotK,
                                 final ODEStateAndDerivative globalPreviousState,
                                 final ODEStateAndDerivative globalCurrentState,
                                 final ODEStateAndDerivative softPreviousState,
                                 final ODEStateAndDerivative softCurrentState,
                                 final EquationsMapper mapper) {
        super(forward, yDotK, globalPreviousState, globalCurrentState, softPreviousState, softCurrentState, mapper);
    }

    /** {@inheritDoc} */
    @Override
    protected GillStateInterpolator create(final boolean newForward, final double[][] newYDotK,
                                           final ODEStateAndDerivative newGlobalPreviousState,
                                           final ODEStateAndDerivative newGlobalCurrentState,
                                           final ODEStateAndDerivative newSoftPreviousState,
                                           final ODEStateAndDerivative newSoftCurrentState,
                                           final EquationsMapper newMapper) {
        return new GillStateInterpolator(newForward, newYDotK,
                                         newGlobalPreviousState, newGlobalCurrentState,
                                         newSoftPreviousState, newSoftCurrentState,
                                         newMapper);
    }

    /** {@inheritDoc} */
    @Override
    protected ODEStateAndDerivative computeInterpolatedStateAndDerivatives(final EquationsMapper mapper,
                                                                           final double time, final double theta,
                                                                           final double thetaH, final double oneMinusThetaH) {

        final double twoTheta   = 2 * theta;
        final double fourTheta2 = twoTheta * twoTheta;
        final double coeffDot1  = theta * (twoTheta - 3) + 1;
        final double cDot23     = twoTheta * (1 - theta);
        final double coeffDot2  = cDot23  * ONE_MINUS_INV_SQRT_2;
        final double coeffDot3  = cDot23  * ONE_PLUS_INV_SQRT_2;
        final double coeffDot4  = theta * (twoTheta - 1);

        final double[] interpolatedState;
        final double[] interpolatedDerivatives;
        if (getGlobalPreviousState() != null && theta <= 0.5) {
            final double s         = thetaH / 6.0;
            final double c23       = s * (6 * theta - fourTheta2);
            final double coeff1    = s * (6 - 9 * theta + fourTheta2);
            final double coeff2    = c23  * ONE_MINUS_INV_SQRT_2;
            final double coeff3    = c23  * ONE_PLUS_INV_SQRT_2;
            final double coeff4    = s * (-3 * theta + fourTheta2);
            interpolatedState       = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3 , coeffDot4);
        } else {
            final double s      = oneMinusThetaH / -6.0;
            final double c23    = s * (2 + twoTheta - fourTheta2);
            final double coeff1 = s * (1 - 5 * theta + fourTheta2);
            final double coeff2 = c23  * ONE_MINUS_INV_SQRT_2;
            final double coeff3 = c23  * ONE_PLUS_INV_SQRT_2;
            final double coeff4 = s * (1 + theta + fourTheta2);
            interpolatedState       = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3 , coeffDot4);
        }

        return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);

    }

}