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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.ode.sampling.StepInterpolator;
/**
* This class implements a step interpolator for the classical fourth
* order Runge-Kutta integrator.
*
* <p>This interpolator allows to compute 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> + θ h) = y (t<sub>n</sub>)
* + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
* + ( 6 θ - 4 θ<sup>2</sup>) (y'<sub>2</sub> + y'<sub>3</sub>)
* + ( -3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
* ]
* </li>
* <li>Using reference point at step end:<br>
* y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
* + (1 - θ) (h/6) [ (-4 θ^2 + 5 θ - 1) y'<sub>1</sub>
* +(4 θ^2 - 2 θ - 2) (y'<sub>2</sub> + y'<sub>3</sub>)
* -(4 θ^2 + θ + 1) y'<sub>4</sub>
* ]
* </li>
* </ul>
* </p>
*
* where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub> are the four
* evaluations of the derivatives already computed during the
* step.</p>
*
* @see ClassicalRungeKuttaIntegrator
* @since 1.2
*/
class ClassicalRungeKuttaStepInterpolator
extends RungeKuttaStepInterpolator {
/** Serializable version identifier. */
private static final long serialVersionUID = 20111120L;
/** Simple constructor.
* This constructor builds an instance that is not usable yet, the
* {@link RungeKuttaStepInterpolator#reinitialize} method should be
* called before using the instance in order to initialize the
* internal arrays. This constructor is used only in order to delay
* the initialization in some cases. The {@link RungeKuttaIntegrator}
* class uses the prototyping design pattern to create the step
* interpolators by cloning an uninitialized model and latter initializing
* the copy.
*/
// CHECKSTYLE: stop RedundantModifier
// the public modifier here is needed for serialization
public ClassicalRungeKuttaStepInterpolator() {
}
// CHECKSTYLE: resume RedundantModifier
/** Copy constructor.
* @param interpolator interpolator to copy from. The copy is a deep
* copy: its arrays are separated from the original arrays of the
* instance
*/
ClassicalRungeKuttaStepInterpolator(final ClassicalRungeKuttaStepInterpolator interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new ClassicalRungeKuttaStepInterpolator(this);
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH) {
final double oneMinusTheta = 1 - theta;
final double oneMinus2Theta = 1 - 2 * theta;
final double coeffDot1 = oneMinusTheta * oneMinus2Theta;
final double coeffDot23 = 2 * theta * oneMinusTheta;
final double coeffDot4 = -theta * oneMinus2Theta;
if ((previousState != null) && (theta <= 0.5)) {
final double fourTheta2 = 4 * theta * theta;
final double s = theta * h / 6.0;
final double coeff1 = s * ( 6 - 9 * theta + fourTheta2);
final double coeff23 = s * ( 6 * theta - fourTheta2);
final double coeff4 = s * (-3 * theta + fourTheta2);
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot23 = yDotK[1][i] + yDotK[2][i];
final double yDot4 = yDotK[3][i];
interpolatedState[i] =
previousState[i] + coeff1 * yDot1 + coeff23 * yDot23 + coeff4 * yDot4;
interpolatedDerivatives[i] =
coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4;
}
} else {
final double fourTheta = 4 * theta;
final double s = oneMinusThetaH / 6.0;
final double coeff1 = s * ((-fourTheta + 5) * theta - 1);
final double coeff23 = s * (( fourTheta - 2) * theta - 2);
final double coeff4 = s * ((-fourTheta - 1) * theta - 1);
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot23 = yDotK[1][i] + yDotK[2][i];
final double yDot4 = yDotK[3][i];
interpolatedState[i] =
currentState[i] + coeff1 * yDot1 + coeff23 * yDot23 + coeff4 * yDot4;
interpolatedDerivatives[i] =
coeffDot1 * yDot1 + coeffDot23 * yDot23 + coeffDot4 * yDot4;
}
}
}
}
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