ClassicalRungeKuttaStateInterpolator.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
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 *      https://www.apache.org/licenses/LICENSE-2.0
 *
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 * 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.interpolators;

import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.ode.nonstiff.ClassicalRungeKuttaIntegrator;

/**
 * This class implements a step interpolator for the classical 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>) (y'<sub>2</sub> + y'<sub>3</sub>)
 *                                     + (   -3 &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
 *                                    ]
 *   </li>
 *   <li>Using reference point at step end:<br>
 *   y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub> + h)
 *                    + (1 - &theta;) (h/6) [ (-4 &theta;^2 + 5 &theta; - 1) y'<sub>1</sub>
 *                                          +(4 &theta;^2 - 2 &theta; - 2) (y'<sub>2</sub> + y'<sub>3</sub>)
 *                                          -(4 &theta;^2 +   &theta; + 1) 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 ClassicalRungeKuttaIntegrator
 */

public class ClassicalRungeKuttaStateInterpolator extends RungeKuttaStateInterpolator {

    /** 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 ClassicalRungeKuttaStateInterpolator(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 ClassicalRungeKuttaStateInterpolator create(final boolean newForward, final double[][] newYDotK,
                                                          final ODEStateAndDerivative newGlobalPreviousState,
                                                          final ODEStateAndDerivative newGlobalCurrentState,
                                                          final ODEStateAndDerivative newSoftPreviousState,
                                                          final ODEStateAndDerivative newSoftCurrentState,
                                                          final EquationsMapper newMapper) {
        return new ClassicalRungeKuttaStateInterpolator(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 oneMinusTheta             = 1.0 - theta;
        final double oneMinus2Theta            = 1.0 - theta * 2.0;
        final double coeffDot1                 = oneMinusTheta * oneMinus2Theta;
        final double coeffDot23                =  theta * oneMinusTheta * 2;
        final double coeffDot4                 = -theta * oneMinus2Theta;
        final double[] interpolatedState;
        final double[] interpolatedDerivatives;

        if (getGlobalPreviousState() != null && theta <= 0.5) {
            final double fourTheta2      = theta * theta * 4;
            final double s               = thetaH / 6.0;
            final double coeff1          = s * (fourTheta2 - theta * 9 + 6);
            final double coeff23         = s * (theta * 6 - fourTheta2);
            final double coeff4          = s * (fourTheta2 - theta * 3);
            interpolatedState       = previousStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
        } else {
            final double fourTheta       = theta * 4;
            final double s               = oneMinusThetaH / 6.0;
            final double coeff1          = s * (theta * (-fourTheta + 5) - 1);
            final double coeff23         = s * (theta * ( fourTheta - 2) - 2);
            final double coeff4          = s * (theta * (-fourTheta - 1) - 1);
            interpolatedState       = currentStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
        }

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

    }

}