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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 the 3/8 fourth
 * order Runge-Kutta integrator.
 *
 * 

This interpolator allows to compute dense output inside the last * step computed. The interpolation equation is consistent with the * integration scheme : *

    *
  • Using reference point at step start:
    * y(tn + θ h) = y (tn) * + θ (h/8) [ (8 - 15 θ + 8 θ2) y'1 * + 3 * (15 θ - 12 θ2) y'2 * + 3 θ y'3 * + (-3 θ + 4 θ2) y'4 * ] *
  • *
  • Using reference point at step end:
    * y(tn + θ h) = y (tn + h) * - (1 - θ) (h/8) [(1 - 7 θ + 8 θ2) y'1 * + 3 (1 + θ - 4 θ2) y'2 * + 3 (1 + θ) y'3 * + (1 + θ + 4 θ2) y'4 * ] *
  • *
*

* * where θ belongs to [0 ; 1] and where y'1 to y'4 are the four * evaluations of the derivatives already computed during the * step.

* * @see ThreeEighthesFieldIntegrator * @param the type of the field elements * @since 3.6 */ class ThreeEighthesFieldStepInterpolator> 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 */ ThreeEighthesFieldStepInterpolator(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 ThreeEighthesFieldStepInterpolator 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 ThreeEighthesFieldStepInterpolator(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 coeffDot3 = theta.multiply(0.75); final T coeffDot1 = coeffDot3.multiply(theta.multiply(4).subtract(5)).add(1); final T coeffDot2 = coeffDot3.multiply(theta.multiply(-6).add(5)); final T coeffDot4 = coeffDot3.multiply(theta.multiply(2).subtract(1)); final T[] interpolatedState; final T[] interpolatedDerivatives; if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) { final T s = thetaH.divide(8); final T fourTheta2 = theta.multiply(theta).multiply(4); final T coeff1 = s.multiply(fourTheta2.multiply(2).subtract(theta.multiply(15)).add(8)); final T coeff2 = s.multiply(theta.multiply(5).subtract(fourTheta2)).multiply(3); final T coeff3 = s.multiply(theta).multiply(3); final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3))); interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4); interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4); } else { final T s = oneMinusThetaH.divide(-8); final T fourTheta2 = theta.multiply(theta).multiply(4); final T thetaPlus1 = theta.add(1); final T coeff1 = s.multiply(fourTheta2.multiply(2).subtract(theta.multiply(7)).add(1)); final T coeff2 = s.multiply(thetaPlus1.subtract(fourTheta2)).multiply(3); final T coeff3 = s.multiply(thetaPlus1).multiply(3); final T coeff4 = s.multiply(thetaPlus1.add(fourTheta2)); interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4); interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4); } return new FieldODEStateAndDerivative(time, interpolatedState, interpolatedDerivatives); } }




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