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With inspiration from other libraries
/*
* 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 classical 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/6) [ (6 - 9 θ + 4 θ2) y'1
* + ( 6 θ - 4 θ2) (y'2 + y'3)
* + ( -3 θ + 4 θ2) y'4
* ]
*
* - Using reference point at step end:
* y(tn + θ h) = y (tn + h)
* + (1 - θ) (h/6) [ (-4 θ^2 + 5 θ - 1) y'1
* +(4 θ^2 - 2 θ - 2) (y'2 + y'3)
* -(4 θ^2 + θ + 1) 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 ClassicalRungeKuttaFieldIntegrator
* @param the type of the field elements
* @since 3.6
*/
class ClassicalRungeKuttaFieldStepInterpolator>
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
*/
ClassicalRungeKuttaFieldStepInterpolator(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 ClassicalRungeKuttaFieldStepInterpolator 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 ClassicalRungeKuttaFieldStepInterpolator(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 one = time.getField().getOne();
final T oneMinusTheta = one.subtract(theta);
final T oneMinus2Theta = one.subtract(theta.multiply(2));
final T coeffDot1 = oneMinusTheta.multiply(oneMinus2Theta);
final T coeffDot23 = theta.multiply(oneMinusTheta).multiply(2);
final T coeffDot4 = theta.multiply(oneMinus2Theta).negate();
final T[] interpolatedState;
final T[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
final T fourTheta2 = theta.multiply(theta).multiply(4);
final T s = thetaH.divide(6.0);
final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(9)).add(6));
final T coeff23 = s.multiply(theta.multiply(6).subtract(fourTheta2));
final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
interpolatedState = previousStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
} else {
final T fourTheta = theta.multiply(4);
final T s = oneMinusThetaH.divide(6);
final T coeff1 = s.multiply(theta.multiply(fourTheta.negate().add(5)).subtract(1));
final T coeff23 = s.multiply(theta.multiply(fourTheta.subtract(2)).subtract(2));
final T coeff4 = s.multiply(theta.multiply(fourTheta.negate().subtract(1)).subtract(1));
interpolatedState = currentStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
}
return new FieldODEStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
}
}