MidpointStateInterpolator.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
 *
 *      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.hipparchus.ode.nonstiff;

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

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

class MidpointStateInterpolator
    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
     */
    MidpointStateInterpolator(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 MidpointStateInterpolator create(final boolean newForward, final double[][] newYDotK,
                                               final ODEStateAndDerivative newGlobalPreviousState,
                                               final ODEStateAndDerivative newGlobalCurrentState,
                                               final ODEStateAndDerivative newSoftPreviousState,
                                               final ODEStateAndDerivative newSoftCurrentState,
                                               final EquationsMapper newMapper) {
        return new MidpointStateInterpolator(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 coeffDot2 = 2 * theta;
        final double coeffDot1 = 1 - coeffDot2;

        final double[] interpolatedState;
        final double[] interpolatedDerivatives;
        if (getGlobalPreviousState() != null && theta <= 0.5) {

            final double coeff1     = theta * oneMinusThetaH;
            final double coeff2     = theta * thetaH;
            interpolatedState       = previousStateLinearCombination(coeff1, coeff2);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
        } else {
            final double coeff1     =  oneMinusThetaH * theta;
            final double coeff2     = -oneMinusThetaH * (1.0 + theta);
            interpolatedState       = currentStateLinearCombination(coeff1, coeff2);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
        }

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

    }

}