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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
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/*
 * 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;

/**
 * This class implements a step interpolator for second order
 * Runge-Kutta integrator.
 *
 * This interpolator computes dense output inside the last
 * step computed. The interpolation equation is consistent with the
 * integration scheme :
 * 

 *   Using reference point at step start:

 *   y(t_n + θ h) = y (t_n) + θ h [(1 - θ) y'₁ + θ y'₂]
 *   
 *   Using reference point at step end:

 *   y(t_n + θ h) = y (t_n + h) + (1-θ) h [θ y'₁ - (1+θ) y'₂]
 *   
 * 
 * 
 *
 * where θ belongs to [0 ; 1] and where y'₁ and y'₂ are the two
 * evaluations of the derivatives already computed during the
 * step.
 *
 * @see MidpointFieldIntegrator
 * @param  the type of the field elements
 * @since 3.6
 */

class MidpointFieldStepInterpolator>
    extends RungeKuttaFieldStepInterpolator {

    /** Simple constructor.
     * @param field field to which the time and state vector elements belong
     * @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
     */
    MidpointFieldStepInterpolator(final Field field, final boolean forward,
                                             final T[][] yDotK,
                                             final FieldODEStateAndDerivative globalPreviousState,
                                             final FieldODEStateAndDerivative globalCurrentState,
                                             final FieldODEStateAndDerivative softPreviousState,
                                             final FieldODEStateAndDerivative softCurrentState,
                                             final FieldEquationsMapper mapper) {
        super(field, forward, yDotK,
              globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
              mapper);
    }

    /** {@inheritDoc} */
    @Override
    protected MidpointFieldStepInterpolator create(final Field newField, final boolean newForward, final T[][] newYDotK,
                                                      final FieldODEStateAndDerivative newGlobalPreviousState,
                                                      final FieldODEStateAndDerivative newGlobalCurrentState,
                                                      final FieldODEStateAndDerivative newSoftPreviousState,
                                                      final FieldODEStateAndDerivative newSoftCurrentState,
                                                      final FieldEquationsMapper newMapper) {
        return new MidpointFieldStepInterpolator(newField, newForward, newYDotK,
                                                    newGlobalPreviousState, newGlobalCurrentState,
                                                    newSoftPreviousState, newSoftCurrentState,
                                                    newMapper);
    }

    /** {@inheritDoc} */
    @SuppressWarnings("unchecked")
    @Override
    protected FieldODEStateAndDerivative computeInterpolatedStateAndDerivatives(final FieldEquationsMapper mapper,
                                                                                   final T time, final T theta,
                                                                                   final T thetaH, final T oneMinusThetaH) {

        final T coeffDot2 = theta.multiply(2);
        final T coeffDot1 = time.getField().getOne().subtract(coeffDot2);
        final T[] interpolatedState;
        final T[] interpolatedDerivatives;

        if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
            final T coeff1 = theta.multiply(oneMinusThetaH);
            final T coeff2 = theta.multiply(thetaH);
            interpolatedState       = previousStateLinearCombination(coeff1, coeff2);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
        } else {
            final T coeff1 = oneMinusThetaH.multiply(theta);
            final T coeff2 = oneMinusThetaH.multiply(theta.add(1)).negate();
            interpolatedState       = currentStateLinearCombination(coeff1, coeff2);
            interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2);
        }

        return new FieldODEStateAndDerivative(time, interpolatedState, interpolatedDerivatives);

    }

}