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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.ode.sampling.StepInterpolator;
/**
* 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 ThreeEighthesIntegrator
* @since 1.2
*/
class ThreeEighthesStepInterpolator
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
* org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#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 later initializing the copy.
*/
// CHECKSTYLE: stop RedundantModifier
// the public modifier here is needed for serialization
public ThreeEighthesStepInterpolator() {
}
// 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
*/
ThreeEighthesStepInterpolator(final ThreeEighthesStepInterpolator interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new ThreeEighthesStepInterpolator(this);
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH) {
final double coeffDot3 = 0.75 * theta;
final double coeffDot1 = coeffDot3 * (4 * theta - 5) + 1;
final double coeffDot2 = coeffDot3 * (5 - 6 * theta);
final double coeffDot4 = coeffDot3 * (2 * theta - 1);
if ((previousState != null) && (theta <= 0.5)) {
final double s = theta * h / 8.0;
final double fourTheta2 = 4 * theta * theta;
final double coeff1 = s * (8 - 15 * theta + 2 * fourTheta2);
final double coeff2 = 3 * s * (5 * theta - fourTheta2);
final double coeff3 = 3 * s * theta;
final double coeff4 = s * (-3 * theta + fourTheta2);
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
final double yDot3 = yDotK[2][i];
final double yDot4 = yDotK[3][i];
interpolatedState[i] =
previousState[i] + coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 + coeff4 * yDot4;
interpolatedDerivatives[i] =
coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
}
} else {
final double s = oneMinusThetaH / 8.0;
final double fourTheta2 = 4 * theta * theta;
final double coeff1 = s * (1 - 7 * theta + 2 * fourTheta2);
final double coeff2 = 3 * s * (1 + theta - fourTheta2);
final double coeff3 = 3 * s * (1 + theta);
final double coeff4 = s * (1 + theta + fourTheta2);
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
final double yDot3 = yDotK[2][i];
final double yDot4 = yDotK[3][i];
interpolatedState[i] =
currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
interpolatedDerivatives[i] =
coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
}
}
}
}