/* * 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 : *

*

* * 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); } }